Rat Locomotion Analysis Based on Straight Line Detection in Hough Space

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the authors propose the locomotion analysis of rats through the analysis of images. The method consists of detecting lines in the Hough transform space where these lines are marked on the rat’s limb. Based on the found lines, the angles formed by the joints are calculated, along with the distance between them. With these calculations, it is possible to estimate the biomechanical model of the gait. The proposed method is very basic; however, it might be effective.
I have the following remarks that have to be addressed:
1) The paper addresses kinematic analysis of rat motion. This subject is very thoroughly researched, and there are hundreds of publications on this topic. Authors noticed some fraction of them in the introduction section; however, they do not justify why the new method is needed.
2) Why, instead of a line that is drawn over the test rat, put markers over its body joints similarly to how it is done in motion capture approaches? You will also get angles that can be calculated between vectors defined by tracked joints. The joint-based approach seems to me more intuitive and easy to deploy.
3) Please compare your method with existing ones and show the pros and cons of your approach.
4) Is your method robust to rotation of the observed target? Please estimate the potential error caused by the fact that the observed target might not be exactly positioned perpendicular to the camera.
5) Equation (3) - please make the assumption that sin theta must not be equal to zero.
6) Page 8: Figure 3 should not be split between separate pages; please correct it.
7) Table 2: Please be consistent and use the same floating-point precision (3 digits) in all values.

Author Response

                                              June 24, 2025

 

Dear Editor in Chief:

Mathematics

I am pleased to resubmit for publication the revised version of our manuscript entitled: “Rat locomotion analysis based on straight line detection in Hough space”. The manuscript was identified as mathematics-3710285. I am very thankful to the Editor and reviewers for their thorough review. We have revised our research article in the light of their useful suggestions and comments, and hope our revision has improved the manuscript to a level of their satisfaction. In the manuscript, the changes for improvement were marked in blue and red for what was eliminated. Considering the reviewer´s comments, the manuscript was reviewed by a native speaking.  

 

Reviewers´ comments:

 

Reviewer 1

 

1) The paper addresses kinematic analysis of rat motion. This subject is very thoroughly researched, and there are hundreds of publications on this topic. Authors noticed some fraction of them in the introduction section; however, they do not justify why the new method is needed.

Response:

We appreciate the reviewer’s observation. While we acknowledge that kinematic analysis of rat locomotion is a well-explored field, our study is aimed at proposing a low-cost and accessible method that can be implemented in laboratories with limited resources, without requiring specialized motion capture systems or advanced equipment. Most of the existing approaches rely on commercial software or marker-based systems that are often expensive or require specific hardware (e.g., high-speed cameras, infrared systems).

Our method offers an alternative by using image processing through the Hough transform to extract geometric information (angles and distances between limbs), which can be analyzed to infer gait patterns. Although basic, this method is advantageous in terms of accessibility and cost-effectiveness.

 

2) Why, instead of a line that is drawn over the test rat, put markers over its body joints similarly to how it is done in motion capture approaches? You will also get angles that can be calculated between vectors defined by tracked joints. The joint-based approach seems to me more intuitive and easy to deploy.

Response:

We appreciate this valuable suggestion. In fact, during our experimental design, we opted not to use physical reflective markers or external objects attached to the animal's joints. Instead, we shaved the fur of the hind limbs and manually drew the anatomical lines corresponding to the bones and joint axes using permanent ink. This approach ensured consistent visual references for the subsequent line detection in image processing, while avoiding additional weight or discomfort to the animal, as well as the risk of marker detachment or occlusion during locomotion.

We acknowledge that joint-based tracking using physical markers is widely adopted in commercial motion capture systems; however, these systems often require specialized hardware and software, increasing both the cost and the complexity of the experimental setup. Our method seeks to offer a low-cost, accessible, and non-intrusive alternative, especially suitable for laboratories with limited resources.

Moreover, the use of line detection through the Hough Transform allows the extraction of geometric features (angles, segment lengths, and intersection points) in a consistent and automated way, based on the ink-drawn reference lines. While joint-based vector analysis can be highly effective, our proposed method shows comparable accuracy (angular error < 0.14°) and provides a reliable estimation of locomotor geometry, as validated against a professional design software.

 

3) Please compare your method with existing ones and show the pros and cons of your approach.

Response:

We thank the reviewer for this important observation. In the revised manuscript, we have included a comparative analysis of our method (MMHTS) with other commonly used approaches for locomotion analysis in rats. This comparison is now presented in Table 4 (Discussion section, paragraph 2, lines 351-353 and Table 4; the text is marked in blue) and is briefly summarized below:

Commercial systems such as CatWalk XT® or DigiGait® offer high-resolution dynamic analysis and advanced automation, but they require expensive hardware and infrastructure, which limits their accessibility in many research environments.

Deep learning-based tools like DeepLabCut provide markerless tracking with high precision and flexibility across species and setups, but demand significant computational resources and expertise in neural network training and programming.

Manual video analysis software (e.g., Kinovea) represents a free and educationally useful tool, though it requires extensive manual input, offers limited precision, and is not scalable for larger datasets.

Our method, MMHTS, presents a low-cost and easy-to-implement alternative that does not depend on commercial software or high-end equipment. Although limited to 2D analysis and reliant on anatomical marking on the animal’s skin, Department has demonstrated excellent accuracy (angular error < 0.14°) when validated against professional design software, and can be semi-automated for efficient image processing.

 

Considering your comment, the text was added

“Next, in Table 4, the MMHTS technique is qualitatively compared to other software, where its advantages and disadvantages are shown.

 

and Table 4 was also added 

 

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

The added text is marked in blue.

 

4) Is your method robust to rotation of the observed target? Please estimate the potential error caused by the fact that the observed target might not be exactly positioned perpendicular to the camera.

Response:

We appreciate the reviewer’s comment, as perspective distortion can indeed affect the accuracy of 2D motion analysis when the subject is not perfectly aligned perpendicularly to the camera’s plane. In preliminary trials, we observed that untrained rats often display natural exploratory behavior, including partial body rotations at the beginning of the tunnel walk, which could introduce angular measurement errors.

To minimize this variability and ensure consistent alignment during image acquisition, we implemented a behavioral training protocol. Each experimental rat was trained to walk through a transparent acrylic tunnel (100 cm long × 10 cm high × 10 cm wide) for 10 minutes per day over a period of 10 consecutive days. During this habituation, we recorded the time taken to walk back and forth through the tunnel and continued the training until all animals achieved a steady and uninterrupted locomotion pattern, with a time variability of less than 5% among subjects.

Additionally, after each training session, the tunnel was cleaned with a diluted cane vinegar solution to eliminate olfactory trails left by previous animals. This prevented additional exploratory behavior and helped promote direct forward movement.

Only videos from these standardized walking trials—where animals moved continuously and without lateral turning—were included in the analysis. While perfect perpendicularity cannot be guaranteed, this protocol allowed us to greatly reduce variability in orientation.

 

5) Equation (3) - please make the assumption that sin theta must not be equal to zero

Dear reviewer, thanks for your comment to improve the quality of our work.

 Response:

Taking into consideration your comment, in section 2: Locomotion Analysis in Hough Space, Subsection; 2.1. Straight Line Detection; Page 3, paragraph 1, lines 128 to 132 were added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

The added text is marked in blue.

 

6) Page 8: Figure 3 should not be split between separate pages; please correct it.
Response:

Dear reviewer, Figure 3 was corrected according to your suggestion.

 

7) Table 2: Please be consistent and use the same floating-point precision (3 digits) in all values

Response:

Review estimator, the correction was made on Table 2. The changes are marked in blue.

 

 

Reviewer 2

 

• The presented in good English

Response:

Dear reviewer, we appreciate your comment.

 

2) Add the abalation studies. Also rewrite the contribution more clearly to reflect the experimental work. 

Response

Taking your comment into consideration, in section 3.3., Measurements, paragraph 3, lines 305 to 310 the text was added,

“In other words, the MMHTS method is efficient since measurement errors are small. This follows since the error is defined based on the difference between the measurements made with our MMHTS proposal and the measurements made with the AutoCAD® professional software. In addition, the MMHTS technique is easy to implement, it has under economic cost, its accuracy depends on the experience of the test expert, its implementation does not require additional hardware and the software is easy to handle”

The added text is marked in blue.

 

3) Give angle limits for the stability of proposed system. 

Dear reviewer, we appreciate your comment to improve our work

Response:

Physically there are limits in the pattern of the march due to the anatomy of the rat since there are limits in its joints. However, in the mathematical model there are no limits and therefore it is possible to analyze the entire range of joints in both physiological and pathological conditions.

 

Taking your comment into consideration, in Section 2, Subsection 2.1, page 3, paragraph 1 was added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

4) Quantitative aspects of normal locomotion in rats. Life sciences, 25(2), 171-179.

Response:

We thank the reviewer for suggesting this fundamental reference. The study by Hruska et al. (1979) presents a detailed quantitative analysis of spontaneous locomotion in rats, using footprint tracking to measure spatial parameters (such as stride length, width, and foot placement symmetry), and video recordings to analyze temporal aspects of the gait cycle.

Our methodological approach differs from theirs in two important ways:

1. Our analysis was conducted under controlled and trained locomotion, not spontaneous movement. All animals were behaviorally conditioned to walk continuously in a narrow acrylic tunnel, reducing variability due to exploratory behavior.
2. Locomotion parameters were derived by drawing anatomical lines directly on the shaved skin of the hindlimbs, corresponding to underlying bone segments. These lines allowed us to identify angular points (vertices) representing joints, from which we calculated angles and distances between segments.

Although we have not yet completed a direct quantitative comparison between the values obtained using the MMHTS method and those reported by Hruska et al. or other sources, we acknowledge the value of such a comparison and plan to carry it out in a subsequent stage. We are currently finalizing the implementation of the software system that will allow us to extract these parameters from video recordings in a semi-automated manner. This perspective has been included in the revised manuscript (Section 1, lines 61–68), and the work of Hruska et al. has been cited as a key reference for future validation efforts.

 

Considering your comment, next text was added Section 1, lines 61–68,

One of the most frequently cited references in the study of rat locomotion is the work of Hruska et al., who conducted a quantitative analysis of gait by recording plantar footprints under conditions of spontaneous locomotion [18]. Although their study provides valuable normative data, it does not enable a direct assessment of the structural geometry of the limbs during movement. In the present study, we introduce an alternative methodology based on the analysis of joint angles derived from anatomically guided skin markings, which may offer complementary insights to those obtained through footprint-based approaches.

 

The added text is marked in blue.

 

5)  Three-dimensional analysis of locomotion patterns after hindlimb suspension and subsequent long-term reloading in growing rats. Journal of Biomechanics, 176, 112389.

Response:

We thank the reviewer for recommending this highly relevant study. Nishida et al. (2024) provide an insightful three-dimensional kinematic analysis of gait alterations in rats following a well-established model of hindlimb suspension (HS) and long-term reloading. In this model, the rats’ hindlimbs are suspended via a tail harness, preventing ground contact for several weeks during development. This method induces musculoskeletal disuse and simulates conditions such as microgravity or immobilization. After reloading, 3D motion capture is used to detect persistent locomotor changes, such as reduced hip adduction and increased toe-out angle, even months after recovery.

Although our proposed method (MMHTS) is limited to two-dimensional structural analysis and does not involve unloading paradigms, it offers a complementary perspective. Whereas the 3D model used by Nishida et al. focuses on functional recovery after structural disruption, MMHTS provides a geometric approach to analyzing joint angles and limb segment coordination under controlled, repeatable locomotion conditions.

In particular, MMHTS can be valuable in early-stage or lower-resource studies where behavioral training ensures reproducible gait without requiring specialized motion capture equipment. Moreover, our method could be adapted for use in reloading models such as HS, particularly during the screening or monitoring phases of functional recovery.

We have included this comparison in the revised manuscript (Section 3.3, lines 374–382) to highlight the complementary nature of both approaches.

 

Considering your comment, next text was added (Section 3.3, lines 374–382),

In more complex models involving structural alterations due to disuse, our method could serve as a tool for angular structural evaluation during the recovery phases. For example, a recent study employed three-dimensional kinematic analysis to examine locomotion patterns in developing rats following prolonged hindlimb suspension and subsequent long-term reloading [33]. The MMHTS method proposed in this work does not capture three-dimensional data; however, it offers a reproducible two-dimensional structural analysis alternative, based on anatomical references marked on the skin. This approach is useful for functional follow-up studies in preclinical models, particularly those requiring a simple and accessible implementation for locomotion assessment.

 

The added text is marked in blue.

 

How the authors find this article useful to add in their research

6) Yang, W.W., et al., Dissecting Genetic Mechanisms of Differential Locomotion, Depression, and Allodynia after Spinal Cord Injury 370 in Three Mouse Strains. Cells, 2024. 13(9).

Response:

We thank the reviewer for highlighting this relevant study. The work by Yang et al. (2024) presents an analysis of locomotor, affective, and pain-related alterations following spinal cord injury in different mouse strains, using the CatWalk XT system and transcriptomic profiling. Although the present manuscript does not include experimental data derived from an injury model, it is important to note that the MMHTS method was originally developed and applied in the context of a study involving penetrating cortical injury to the primary motor cortex in rats, specifically targeting the region responsible for hindlimb motor control. In that study, video recordings were obtained both before the lesion (baseline) and at several time points afterward, including vehicle-treated and tamoxifen-treated groups. However, the results from that experimental work have not yet been submitted for review, as they will be part of a future publication currently in preparation.

In this article, we focus exclusively on presenting and validating the MMHTS method as a structural locomotion analysis tool. We believe that this method may prove especially useful in injury models similar to that of Yang et al., particularly in settings where advanced commercial platforms or 3D motion capture systems are not available. MMHTS offers reproducible angular measurements based on anatomical references, which may help correlate structural gait characteristics with molecular or genetic responses.

This study has been cited in the revised manuscript (Section 3.3, lines 382–388) to contextualize the potential applications of MMHTS in neurotrauma research.

 

Considering your comment, the following text was added (Section 3.3, lines 382–488),

The MMHTS method may also serve as a practical tool in models involving central nervous system injury. While more sophisticated 3D gait systems provide high-resolution analysis, MMHTS offers a low-cost alternative for structural gait evaluation. This could be especially valuable in contexts like the cortical injury model in which MMHTS was initially applied, or in studies similar to that of Yang et al., which combined behavioral phenotyping and transcriptomics after spinal cord injury [34].

 

The added text is marked in blue.

 

Reviewer 3

1. In the introduction section: The authors could more explicitly state the specific drawbacks or limitations of the existing methods (e.g., cost, complexity, specific inaccuracies) that their proposed method aims to overcome

 

Response:

Dear reviewer, we appreciate your comment. Taking your comment into consideration, in seation 1, introduction, paragraph 4, Lines 106 to 108, the following text was added.

Some advantages of our proposal are easy implementation, low computational cost, does not require additional hardware or software and accuracy can be very good since the measurements are almost similar to professional design software.

 

The added text is marked in blue.

 

2. In the methodology section: In step (c), the paper mentions applying a threshold to create a binary image. The authors should specify the thresholding method used (e.g., manual, Otsu's method, adaptive thresholding), as this choice significantly impacts the resulting binary image and the accuracy of the Hough transform.

Response:

Dear reviewer, as mentioned, binarization is important in image processing since the binary image obtained depends on the binarization methodology. In our proposal, a global threshold method was applied where the selected value is the average value between the minimum pixel value and the maximum pixel value. 

 

Taking your comment into consideration, in section 3.2, Line Identification in the Hough Transform Space, paragraph 2, lines 242 to 244 the text was added,

 

In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments, it was 48.

Also in section 3.4. (discussion), point 10 was added

• The accuracy of the MMHTS method can improve whether image binarization is done using an adaptive technique.

 

The added text is marked in blue.

 

And in step (e), the paper states that lines are identified in Hough space, and later specifies that "higher points in the space" were found. The process for identifying these peaks should be detailed. Is it an automated maximum-finding algorithm?

Response:

Dear reviewer, in our numerical work the Matlab 2024B scientific software was used and this software already has functions to find the maximum value in numerical data. Then, answering your question, in our work we do not develop the algorithm to find the maximum value in the data of the Houghh transform, but if we apply the function of the Matlab software, which is enough to obtain good results.

 

What is the search radius or sensitivity for peak detection? This is critical for reproducibility.

Response

Dear reviewer, we appreciate your observation to improve the quality of our work.

Based on the geometric of the problem shown in Figure 1 and on the fundamental concept of the Hough transform, which was developed to detect lines in images, in our work, it is considered that the lines marked in the limb of the rat are the most significant in the image under study, and therefore, these lines correspond to the maximum points in the space of the Hough transform. Taking this into consideration, the MMHTS method is repeatable in the measurement of the angles and lengths of the lines marked in the limb of the rat. However, the user's experience (human expert in animal movement tests) must be mentioned, and plays a very important role to obtaining good results in the movement analysis.

 

Moreover, the method for input and marking which relies on lines drawn with permanent ink on the rat's limbs and user-selected start and end points (p0​ and p4​). This manual marking and selection can be leaded to significant error.

Response:

As mentioned, the user's experience plays an important role, since based on his knowledge, he can properly select the P0 and P4 points, significantly reducing errors in the measurement.

 

Taking your comment into consideration, in section 3.4 discussion was added point 11,

 

11. The error due to the selection of P_0 and P_4 points can be significantly reduced if the MMHTS method is combined with an automatic points location method.

 

The authors should discuss how the initial lines were drawn to ensure they accurately represented the underlying bone structure and acknowledge the potential for user-introduced variability and bias.

Response:

We thank the reviewer for this valuable suggestion. In the revised discussion section, we now explicitly summarize the main advantages of MMHTS, including its computational simplicity, interpretability, and the fact that it does not rely on frequency domain transformations. We also acknowledge its limitations, such as dependence on line quality and the need for manual marking in its current version. These points are now discussed in direct contrast to PCA-, FFT-, and neural network-based methods, and are highlighted in blue in the revised manuscript.

 

Considering your comment, the following text was included in section 3.4, lines 356-373

Based on our experience in preclinical studies involving motor function analysis, the MMHTS method was developed as a practical and accessible alternative to more complex and costly gait analysis systems. Its implementation in MATLAB using built-in functions allows for efficient processing without the need for frequency domain transformations, as required in FFT-based analyses. Furthermore, the outputs segment angles, distances, and intersection points are easily interpretable and directly applicable to movement analysis in experimental models.

This approach is particularly suitable for research groups that require flexible and low-cost tools without sacrificing analytical precision. However, we recognize that the current version of MMHTS relies on manual marking of anatomical reference lines, which may introduce inter-user variability depending on consistency in line placement. While more advanced tools such as PCA-based systems or deep learning models like DeepLabCut offer automated solutions, they also entail steeper technical requirements.

We consider this first version of MMHTS a foundational step towards a more automated and robust methodology. As outlined in the “Future Work” section, our next steps include the integration of semi-automated landmark detection and broader validation across subjects and experimental conditions to improve reproducibility and reduce user dependency.

 

4.---- In the discussion section: The authors should give more highlights about the specific advantages of MMHTS (e.g., computational efficiency, no need for frequency domain transformation) and disadvantages (e.g., sensitivity to line quality, requirement for manual marking) in relation to these other techniques

Response:

Dear reviewer, we appreciate your observation.

 

Considering your comment, in section 3.4. Discussion, Paragraph 2, Table 4 was added

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

 

 

 

Reviewer 4

 

1. The human is heavily involved in manually marking lines on the rat’s limbs, which introduces human bias and reduces scalability.

Response:

We appreciate the reviewer’s comment. While manual marking was chosen for its simplicity and low cost, we acknowledge that it may introduce user bias and limit scalability. Based on our experience, we have identified consistent anatomical landmarks—such as the hip, heel, tarsal-metatarsal joint, nose tip, eye, and base of the tail, that are suitable for automated detection.

In the revised manuscript, we now include a future work proposal to implement semi-automatic detection of these landmarks using classical computer vision or deep learning tools (e.g., DeepLabCut), to reduce human intervention and improve reproducibility. This addition is marked in blue in the “Future Work” section.

 

Next text was added (Section 3.4, lines 394-403):

In future versions of the MMHTS method, we aim to incorporate a semi-automated strategy for the detection of anatomical landmarks, building on empirical experience from tracking visible structures during rodent locomotion. Key points such as the hip, heel, tarsal-metatarsal joint, tip of the nose, eye, and the base of the tail have proven to be consistent and easily identifiable throughout the gait cycle. Additionally, tracing a longitudinal line along the tail may provide valuable insights into tail dynamics associated with balance and directional movement. The integration of classical computer vision techniques (e.g., edge detection, contour extraction, Hough transform) or deep learning-based tools (e.g., DeepLabCut) may help reduce observer bias, improve reproducibility, and enhance the scalability of the system for large-scale motion analysis.

 

2. Validation on a larger animal sample and multiple trials is essential for robust conclusions.

Response:

We agree with the reviewer that validation on a larger sample and across multiple trials is essential to strengthen the robustness and generalizability of the MMHTS method. In the present study, our main objective was to describe and validate the mathematical and procedural foundations of the technique, using a single trained subject as a proof of concept.

As noted in the revised manuscript, we consider this initial implementation a starting point for broader experimental application. In future work, we plan to extend validation to a larger cohort of animals, including intra- and inter-subject variability, and to evaluate reproducibility across different users. This will allow us to better assess the accuracy, consistency, and practical applicability of the MMHTS method in preclinical research settings. A note reflecting this future direction has been added to the manuscript and is marked in blue.

 

Next text was added (Section 3.4, lines: 404-408):

As this study represents a proof of concept based on a single trained subject, future work will include validation of the MMHTS method using a larger sample of animals and repeated trials. This will allow us to assess the method’s reproducibility, ac-curacy, and robustness across subjects and users, and further support its application in preclinical gait analysis studies.

 

3. The authors are suggested to discuss the biological significance and potential impact on gait analysis of error values.

Response:

We thank the reviewer for this suggestion. In the revised manuscript, we now briefly discuss the biological implications of the observed error values. Although the angular and length measurement errors are low (<0.15° and ~0.13 pixels, respectively), they may still influence gait classification or detection of subtle motor deficits. We note this as a consideration for interpreting results, especially in studies involving small differences between experimental groups.

 

Next text was added (Section 3.3, lines: 311-318):

Although the angular and length measurement errors obtained with the MMHTS method are relatively low (less than 0.15° for angles and approximately 0.13 pixels for segment lengths), it is important to consider their potential biological impact. In particular, such deviations, although minimal, could influence the detection of subtle gait abnormalities or lead to misclassification of locomotor patterns in studies involving small inter-group differences. Therefore, these error margins should be taken into account when interpreting experimental results, especially in preclinical models assessing motor recovery or drug effects.

 

4. The step-by-step process of image acquisition, preprocessing, and line detection lacks clarity. Exact thresholds, parameter tuning, and Hough space resolution settings should be explicitly stated to allow reproducibility.

Response:

We thank the reviewer for this important comment. In the revised manuscript, we have expanded the methodological description in Section 3.2 to clarify the image processing pipeline. We now specify the exact thresholding method (global threshold = 48), the resolution of the Hough space (180 angles × 640 distances), and the use of built-in MATLAB functions for peak detection. These additions are intended to improve transparency and reproducibility, and are marked in blue in the revised version.

 

Next text was added in Section 3.2, lines: 242-244

After performing the procedure in Section 2.1, the RGB image (Figure 3a) was first converted to grayscale  and a global threshold was applied to the resulting image, obtaining the binary image . In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments was 48.

 

5. The manuscript contains grammatical errors and awkward phrasing that reduce clarity. Professional language editing is recommended.

Response:

We respectfully acknowledge the reviewer’s concern. However, other reviewers noted that the manuscript is written in good English, and we have carefully reviewed the text to ensure clarity and correct grammar. Nevertheless, considering your comment, a native speaking English reviewed the manuscript

 

6. A quantitative comparison with state-of-the-art methods such as neural network-based or PCA-based motion analysis systems is lacking and should be provided to justify the advantages of MMHTS.

Response:

We thank the reviewer for this valuable suggestion. In the revised manuscript, we include a qualitative comparison (Table 4) between MMHTS and state-of-the-art methods such as DeepLabCut (neural networks) and PCA-based approaches. While a full quantitative comparison was beyond the scope of this proof-of-concept study, we acknowledge its importance and plan to address it in future work. This intention is now stated explicitly in the revised discussion.

 

Next text was added in Section 3.4, lines 408-413:

While the current study provides a qualitative comparison between MMHTS and other motion analysis methods (Table 4), we recognize the importance of conducting a direct quantitative comparison with state-of-the-art techniques such as neural network-based models (e.g., DeepLabCut) and PCA-based systems. This type of analysis will be included in future work to further validate the strengths and limitations of MMHTS across different experimental settings and datasets.

 

Thank you very much for your kind attention. We hope you find our manuscript suitable for publication and look forward to hearing from you soon.

 

Sincerely:

Dr. José Trinidad Guillen Bonilla

Departamento de Electro-fotónica, CUCEI.

Universidad de Guadalajara,

Blvd- M. García Barragan 1421, Guadalajara, Jalisco,

1. P. 44410, México.

e-mail: trinidad.guillen@academicos.udg.mx

Tel.: +52 (33) 1378 5900 (ext. 27655)

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article: Rat locomotion analysis based on straight line detection in  Hough space"

1) The presented in good English. 

2) Add the abalation studies. Also rewrite the contribution more clearly to reflect the experimental work. 

3) Give angle limits for the stability of proposed system. 

Apart from the research gap mentioned in literature, following comparision can improve the research 

4) Quantitative aspects of normal locomotion in rats. Life sciences, 25(2), 171-179.

5)  Three-dimensional analysis of locomotion patterns after hindlimb suspension and subsequent long-term reloading in growing rats. Journal of Biomechanics, 176, 112389.

How the authors find this article useful to add in their research

6) Yang, W.W., et al., Dissecting Genetic Mechanisms of Differential Locomotion, Depression, and Allodynia after Spinal Cord Injury 370 in Three Mouse Strains. Cells, 2024. 13(9).

Author Response

June 24, 2025

 

Dear Editor in Chief:

Mathematics

I am pleased to resubmit for publication the revised version of our manuscript entitled: “Rat locomotion analysis based on straight line detection in Hough space”. The manuscript was identified as mathematics-3710285. I am very thankful to the Editor and reviewers for their thorough review. We have revised our research article in the light of their useful suggestions and comments, and hope our revision has improved the manuscript to a level of their satisfaction. In the manuscript, the changes for improvement were marked in blue and red for what was eliminated. Considering the reviewer´s comments, the manuscript was reviewed by a native speaking.  

 

Reviewers´ comments:

 

Reviewer 1

 

1) The paper addresses kinematic analysis of rat motion. This subject is very thoroughly researched, and there are hundreds of publications on this topic. Authors noticed some fraction of them in the introduction section; however, they do not justify why the new method is needed.

Response:

We appreciate the reviewer’s observation. While we acknowledge that kinematic analysis of rat locomotion is a well-explored field, our study is aimed at proposing a low-cost and accessible method that can be implemented in laboratories with limited resources, without requiring specialized motion capture systems or advanced equipment. Most of the existing approaches rely on commercial software or marker-based systems that are often expensive or require specific hardware (e.g., high-speed cameras, infrared systems).

Our method offers an alternative by using image processing through the Hough transform to extract geometric information (angles and distances between limbs), which can be analyzed to infer gait patterns. Although basic, this method is advantageous in terms of accessibility and cost-effectiveness.

 

2) Why, instead of a line that is drawn over the test rat, put markers over its body joints similarly to how it is done in motion capture approaches? You will also get angles that can be calculated between vectors defined by tracked joints. The joint-based approach seems to me more intuitive and easy to deploy.

Response:

We appreciate this valuable suggestion. In fact, during our experimental design, we opted not to use physical reflective markers or external objects attached to the animal's joints. Instead, we shaved the fur of the hind limbs and manually drew the anatomical lines corresponding to the bones and joint axes using permanent ink. This approach ensured consistent visual references for the subsequent line detection in image processing, while avoiding additional weight or discomfort to the animal, as well as the risk of marker detachment or occlusion during locomotion.

We acknowledge that joint-based tracking using physical markers is widely adopted in commercial motion capture systems; however, these systems often require specialized hardware and software, increasing both the cost and the complexity of the experimental setup. Our method seeks to offer a low-cost, accessible, and non-intrusive alternative, especially suitable for laboratories with limited resources.

Moreover, the use of line detection through the Hough Transform allows the extraction of geometric features (angles, segment lengths, and intersection points) in a consistent and automated way, based on the ink-drawn reference lines. While joint-based vector analysis can be highly effective, our proposed method shows comparable accuracy (angular error < 0.14°) and provides a reliable estimation of locomotor geometry, as validated against a professional design software.

 

3) Please compare your method with existing ones and show the pros and cons of your approach.

Response:

We thank the reviewer for this important observation. In the revised manuscript, we have included a comparative analysis of our method (MMHTS) with other commonly used approaches for locomotion analysis in rats. This comparison is now presented in Table 4 (Discussion section, paragraph 2, lines 351-353 and Table 4; the text is marked in blue) and is briefly summarized below:

Commercial systems such as CatWalk XT® or DigiGait® offer high-resolution dynamic analysis and advanced automation, but they require expensive hardware and infrastructure, which limits their accessibility in many research environments.

Deep learning-based tools like DeepLabCut provide markerless tracking with high precision and flexibility across species and setups, but demand significant computational resources and expertise in neural network training and programming.

Manual video analysis software (e.g., Kinovea) represents a free and educationally useful tool, though it requires extensive manual input, offers limited precision, and is not scalable for larger datasets.

Our method, MMHTS, presents a low-cost and easy-to-implement alternative that does not depend on commercial software or high-end equipment. Although limited to 2D analysis and reliant on anatomical marking on the animal’s skin, Department has demonstrated excellent accuracy (angular error < 0.14°) when validated against professional design software, and can be semi-automated for efficient image processing.

 

Considering your comment, the text was added

“Next, in Table 4, the MMHTS technique is qualitatively compared to other software, where its advantages and disadvantages are shown.

 

and Table 4 was also added 

 

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

The added text is marked in blue.

 

4) Is your method robust to rotation of the observed target? Please estimate the potential error caused by the fact that the observed target might not be exactly positioned perpendicular to the camera.

Response:

We appreciate the reviewer’s comment, as perspective distortion can indeed affect the accuracy of 2D motion analysis when the subject is not perfectly aligned perpendicularly to the camera’s plane. In preliminary trials, we observed that untrained rats often display natural exploratory behavior, including partial body rotations at the beginning of the tunnel walk, which could introduce angular measurement errors.

To minimize this variability and ensure consistent alignment during image acquisition, we implemented a behavioral training protocol. Each experimental rat was trained to walk through a transparent acrylic tunnel (100 cm long × 10 cm high × 10 cm wide) for 10 minutes per day over a period of 10 consecutive days. During this habituation, we recorded the time taken to walk back and forth through the tunnel and continued the training until all animals achieved a steady and uninterrupted locomotion pattern, with a time variability of less than 5% among subjects.

Additionally, after each training session, the tunnel was cleaned with a diluted cane vinegar solution to eliminate olfactory trails left by previous animals. This prevented additional exploratory behavior and helped promote direct forward movement.

Only videos from these standardized walking trials—where animals moved continuously and without lateral turning—were included in the analysis. While perfect perpendicularity cannot be guaranteed, this protocol allowed us to greatly reduce variability in orientation.

 

5) Equation (3) - please make the assumption that sin theta must not be equal to zero

Dear reviewer, thanks for your comment to improve the quality of our work.

 Response:

Taking into consideration your comment, in section 2: Locomotion Analysis in Hough Space, Subsection; 2.1. Straight Line Detection; Page 3, paragraph 1, lines 128 to 132 were added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

The added text is marked in blue.

 

6) Page 8: Figure 3 should not be split between separate pages; please correct it.
Response:

Dear reviewer, Figure 3 was corrected according to your suggestion.

 

7) Table 2: Please be consistent and use the same floating-point precision (3 digits) in all values

Response:

Review estimator, the correction was made on Table 2. The changes are marked in blue.

 

 

Reviewer 2

 

• The presented in good English

Response:

Dear reviewer, we appreciate your comment.

 

2) Add the abalation studies. Also rewrite the contribution more clearly to reflect the experimental work. 

Response

Taking your comment into consideration, in section 3.3., Measurements, paragraph 3, lines 305 to 310 the text was added,

“In other words, the MMHTS method is efficient since measurement errors are small. This follows since the error is defined based on the difference between the measurements made with our MMHTS proposal and the measurements made with the AutoCAD® professional software. In addition, the MMHTS technique is easy to implement, it has under economic cost, its accuracy depends on the experience of the test expert, its implementation does not require additional hardware and the software is easy to handle”

The added text is marked in blue.

 

3) Give angle limits for the stability of proposed system. 

Dear reviewer, we appreciate your comment to improve our work

Response:

Physically there are limits in the pattern of the march due to the anatomy of the rat since there are limits in its joints. However, in the mathematical model there are no limits and therefore it is possible to analyze the entire range of joints in both physiological and pathological conditions.

 

Taking your comment into consideration, in Section 2, Subsection 2.1, page 3, paragraph 1 was added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

4) Quantitative aspects of normal locomotion in rats. Life sciences, 25(2), 171-179.

Response:

We thank the reviewer for suggesting this fundamental reference. The study by Hruska et al. (1979) presents a detailed quantitative analysis of spontaneous locomotion in rats, using footprint tracking to measure spatial parameters (such as stride length, width, and foot placement symmetry), and video recordings to analyze temporal aspects of the gait cycle.

Our methodological approach differs from theirs in two important ways:

1. Our analysis was conducted under controlled and trained locomotion, not spontaneous movement. All animals were behaviorally conditioned to walk continuously in a narrow acrylic tunnel, reducing variability due to exploratory behavior.
2. Locomotion parameters were derived by drawing anatomical lines directly on the shaved skin of the hindlimbs, corresponding to underlying bone segments. These lines allowed us to identify angular points (vertices) representing joints, from which we calculated angles and distances between segments.

Although we have not yet completed a direct quantitative comparison between the values obtained using the MMHTS method and those reported by Hruska et al. or other sources, we acknowledge the value of such a comparison and plan to carry it out in a subsequent stage. We are currently finalizing the implementation of the software system that will allow us to extract these parameters from video recordings in a semi-automated manner. This perspective has been included in the revised manuscript (Section 1, lines 61–68), and the work of Hruska et al. has been cited as a key reference for future validation efforts.

 

Considering your comment, next text was added Section 1, lines 61–68,

One of the most frequently cited references in the study of rat locomotion is the work of Hruska et al., who conducted a quantitative analysis of gait by recording plantar footprints under conditions of spontaneous locomotion [18]. Although their study provides valuable normative data, it does not enable a direct assessment of the structural geometry of the limbs during movement. In the present study, we introduce an alternative methodology based on the analysis of joint angles derived from anatomically guided skin markings, which may offer complementary insights to those obtained through footprint-based approaches.

 

The added text is marked in blue.

 

5)  Three-dimensional analysis of locomotion patterns after hindlimb suspension and subsequent long-term reloading in growing rats. Journal of Biomechanics, 176, 112389.

Response:

We thank the reviewer for recommending this highly relevant study. Nishida et al. (2024) provide an insightful three-dimensional kinematic analysis of gait alterations in rats following a well-established model of hindlimb suspension (HS) and long-term reloading. In this model, the rats’ hindlimbs are suspended via a tail harness, preventing ground contact for several weeks during development. This method induces musculoskeletal disuse and simulates conditions such as microgravity or immobilization. After reloading, 3D motion capture is used to detect persistent locomotor changes, such as reduced hip adduction and increased toe-out angle, even months after recovery.

Although our proposed method (MMHTS) is limited to two-dimensional structural analysis and does not involve unloading paradigms, it offers a complementary perspective. Whereas the 3D model used by Nishida et al. focuses on functional recovery after structural disruption, MMHTS provides a geometric approach to analyzing joint angles and limb segment coordination under controlled, repeatable locomotion conditions.

In particular, MMHTS can be valuable in early-stage or lower-resource studies where behavioral training ensures reproducible gait without requiring specialized motion capture equipment. Moreover, our method could be adapted for use in reloading models such as HS, particularly during the screening or monitoring phases of functional recovery.

We have included this comparison in the revised manuscript (Section 3.3, lines 374–382) to highlight the complementary nature of both approaches.

 

Considering your comment, next text was added (Section 3.3, lines 374–382),

In more complex models involving structural alterations due to disuse, our method could serve as a tool for angular structural evaluation during the recovery phases. For example, a recent study employed three-dimensional kinematic analysis to examine locomotion patterns in developing rats following prolonged hindlimb suspension and subsequent long-term reloading [33]. The MMHTS method proposed in this work does not capture three-dimensional data; however, it offers a reproducible two-dimensional structural analysis alternative, based on anatomical references marked on the skin. This approach is useful for functional follow-up studies in preclinical models, particularly those requiring a simple and accessible implementation for locomotion assessment.

 

The added text is marked in blue.

 

How the authors find this article useful to add in their research

6) Yang, W.W., et al., Dissecting Genetic Mechanisms of Differential Locomotion, Depression, and Allodynia after Spinal Cord Injury 370 in Three Mouse Strains. Cells, 2024. 13(9).

Response:

We thank the reviewer for highlighting this relevant study. The work by Yang et al. (2024) presents an analysis of locomotor, affective, and pain-related alterations following spinal cord injury in different mouse strains, using the CatWalk XT system and transcriptomic profiling. Although the present manuscript does not include experimental data derived from an injury model, it is important to note that the MMHTS method was originally developed and applied in the context of a study involving penetrating cortical injury to the primary motor cortex in rats, specifically targeting the region responsible for hindlimb motor control. In that study, video recordings were obtained both before the lesion (baseline) and at several time points afterward, including vehicle-treated and tamoxifen-treated groups. However, the results from that experimental work have not yet been submitted for review, as they will be part of a future publication currently in preparation.

In this article, we focus exclusively on presenting and validating the MMHTS method as a structural locomotion analysis tool. We believe that this method may prove especially useful in injury models similar to that of Yang et al., particularly in settings where advanced commercial platforms or 3D motion capture systems are not available. MMHTS offers reproducible angular measurements based on anatomical references, which may help correlate structural gait characteristics with molecular or genetic responses.

This study has been cited in the revised manuscript (Section 3.3, lines 382–388) to contextualize the potential applications of MMHTS in neurotrauma research.

 

Considering your comment, the following text was added (Section 3.3, lines 382–488),

The MMHTS method may also serve as a practical tool in models involving central nervous system injury. While more sophisticated 3D gait systems provide high-resolution analysis, MMHTS offers a low-cost alternative for structural gait evaluation. This could be especially valuable in contexts like the cortical injury model in which MMHTS was initially applied, or in studies similar to that of Yang et al., which combined behavioral phenotyping and transcriptomics after spinal cord injury [34].

 

The added text is marked in blue.

 

Reviewer 3

1. In the introduction section: The authors could more explicitly state the specific drawbacks or limitations of the existing methods (e.g., cost, complexity, specific inaccuracies) that their proposed method aims to overcome

 

Response:

Dear reviewer, we appreciate your comment. Taking your comment into consideration, in seation 1, introduction, paragraph 4, Lines 106 to 108, the following text was added.

Some advantages of our proposal are easy implementation, low computational cost, does not require additional hardware or software and accuracy can be very good since the measurements are almost similar to professional design software.

 

The added text is marked in blue.

 

2. In the methodology section: In step (c), the paper mentions applying a threshold to create a binary image. The authors should specify the thresholding method used (e.g., manual, Otsu's method, adaptive thresholding), as this choice significantly impacts the resulting binary image and the accuracy of the Hough transform.

Response:

Dear reviewer, as mentioned, binarization is important in image processing since the binary image obtained depends on the binarization methodology. In our proposal, a global threshold method was applied where the selected value is the average value between the minimum pixel value and the maximum pixel value. 

 

Taking your comment into consideration, in section 3.2, Line Identification in the Hough Transform Space, paragraph 2, lines 242 to 244 the text was added,

 

In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments, it was 48.

Also in section 3.4. (discussion), point 10 was added

• The accuracy of the MMHTS method can improve whether image binarization is done using an adaptive technique.

 

The added text is marked in blue.

 

And in step (e), the paper states that lines are identified in Hough space, and later specifies that "higher points in the space" were found. The process for identifying these peaks should be detailed. Is it an automated maximum-finding algorithm?

Response:

Dear reviewer, in our numerical work the Matlab 2024B scientific software was used and this software already has functions to find the maximum value in numerical data. Then, answering your question, in our work we do not develop the algorithm to find the maximum value in the data of the Houghh transform, but if we apply the function of the Matlab software, which is enough to obtain good results.

 

What is the search radius or sensitivity for peak detection? This is critical for reproducibility.

Response

Dear reviewer, we appreciate your observation to improve the quality of our work.

Based on the geometric of the problem shown in Figure 1 and on the fundamental concept of the Hough transform, which was developed to detect lines in images, in our work, it is considered that the lines marked in the limb of the rat are the most significant in the image under study, and therefore, these lines correspond to the maximum points in the space of the Hough transform. Taking this into consideration, the MMHTS method is repeatable in the measurement of the angles and lengths of the lines marked in the limb of the rat. However, the user's experience (human expert in animal movement tests) must be mentioned, and plays a very important role to obtaining good results in the movement analysis.

 

Moreover, the method for input and marking which relies on lines drawn with permanent ink on the rat's limbs and user-selected start and end points (p0​ and p4​). This manual marking and selection can be leaded to significant error.

Response:

As mentioned, the user's experience plays an important role, since based on his knowledge, he can properly select the P0 and P4 points, significantly reducing errors in the measurement.

 

Taking your comment into consideration, in section 3.4 discussion was added point 11,

 

11. The error due to the selection of P_0 and P_4 points can be significantly reduced if the MMHTS method is combined with an automatic points location method.

 

The authors should discuss how the initial lines were drawn to ensure they accurately represented the underlying bone structure and acknowledge the potential for user-introduced variability and bias.

Response:

We thank the reviewer for this valuable suggestion. In the revised discussion section, we now explicitly summarize the main advantages of MMHTS, including its computational simplicity, interpretability, and the fact that it does not rely on frequency domain transformations. We also acknowledge its limitations, such as dependence on line quality and the need for manual marking in its current version. These points are now discussed in direct contrast to PCA-, FFT-, and neural network-based methods, and are highlighted in blue in the revised manuscript.

 

Considering your comment, the following text was included in section 3.4, lines 356-373

Based on our experience in preclinical studies involving motor function analysis, the MMHTS method was developed as a practical and accessible alternative to more complex and costly gait analysis systems. Its implementation in MATLAB using built-in functions allows for efficient processing without the need for frequency domain transformations, as required in FFT-based analyses. Furthermore, the outputs segment angles, distances, and intersection points are easily interpretable and directly applicable to movement analysis in experimental models.

This approach is particularly suitable for research groups that require flexible and low-cost tools without sacrificing analytical precision. However, we recognize that the current version of MMHTS relies on manual marking of anatomical reference lines, which may introduce inter-user variability depending on consistency in line placement. While more advanced tools such as PCA-based systems or deep learning models like DeepLabCut offer automated solutions, they also entail steeper technical requirements.

We consider this first version of MMHTS a foundational step towards a more automated and robust methodology. As outlined in the “Future Work” section, our next steps include the integration of semi-automated landmark detection and broader validation across subjects and experimental conditions to improve reproducibility and reduce user dependency.

 

4.---- In the discussion section: The authors should give more highlights about the specific advantages of MMHTS (e.g., computational efficiency, no need for frequency domain transformation) and disadvantages (e.g., sensitivity to line quality, requirement for manual marking) in relation to these other techniques

Response:

Dear reviewer, we appreciate your observation.

 

Considering your comment, in section 3.4. Discussion, Paragraph 2, Table 4 was added

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

 

 

 

Reviewer 4

 

1. The human is heavily involved in manually marking lines on the rat’s limbs, which introduces human bias and reduces scalability.

Response:

We appreciate the reviewer’s comment. While manual marking was chosen for its simplicity and low cost, we acknowledge that it may introduce user bias and limit scalability. Based on our experience, we have identified consistent anatomical landmarks—such as the hip, heel, tarsal-metatarsal joint, nose tip, eye, and base of the tail, that are suitable for automated detection.

In the revised manuscript, we now include a future work proposal to implement semi-automatic detection of these landmarks using classical computer vision or deep learning tools (e.g., DeepLabCut), to reduce human intervention and improve reproducibility. This addition is marked in blue in the “Future Work” section.

 

Next text was added (Section 3.4, lines 394-403):

In future versions of the MMHTS method, we aim to incorporate a semi-automated strategy for the detection of anatomical landmarks, building on empirical experience from tracking visible structures during rodent locomotion. Key points such as the hip, heel, tarsal-metatarsal joint, tip of the nose, eye, and the base of the tail have proven to be consistent and easily identifiable throughout the gait cycle. Additionally, tracing a longitudinal line along the tail may provide valuable insights into tail dynamics associated with balance and directional movement. The integration of classical computer vision techniques (e.g., edge detection, contour extraction, Hough transform) or deep learning-based tools (e.g., DeepLabCut) may help reduce observer bias, improve reproducibility, and enhance the scalability of the system for large-scale motion analysis.

 

2. Validation on a larger animal sample and multiple trials is essential for robust conclusions.

Response:

We agree with the reviewer that validation on a larger sample and across multiple trials is essential to strengthen the robustness and generalizability of the MMHTS method. In the present study, our main objective was to describe and validate the mathematical and procedural foundations of the technique, using a single trained subject as a proof of concept.

As noted in the revised manuscript, we consider this initial implementation a starting point for broader experimental application. In future work, we plan to extend validation to a larger cohort of animals, including intra- and inter-subject variability, and to evaluate reproducibility across different users. This will allow us to better assess the accuracy, consistency, and practical applicability of the MMHTS method in preclinical research settings. A note reflecting this future direction has been added to the manuscript and is marked in blue.

 

Next text was added (Section 3.4, lines: 404-408):

As this study represents a proof of concept based on a single trained subject, future work will include validation of the MMHTS method using a larger sample of animals and repeated trials. This will allow us to assess the method’s reproducibility, ac-curacy, and robustness across subjects and users, and further support its application in preclinical gait analysis studies.

 

3. The authors are suggested to discuss the biological significance and potential impact on gait analysis of error values.

Response:

We thank the reviewer for this suggestion. In the revised manuscript, we now briefly discuss the biological implications of the observed error values. Although the angular and length measurement errors are low (<0.15° and ~0.13 pixels, respectively), they may still influence gait classification or detection of subtle motor deficits. We note this as a consideration for interpreting results, especially in studies involving small differences between experimental groups.

 

Next text was added (Section 3.3, lines: 311-318):

Although the angular and length measurement errors obtained with the MMHTS method are relatively low (less than 0.15° for angles and approximately 0.13 pixels for segment lengths), it is important to consider their potential biological impact. In particular, such deviations, although minimal, could influence the detection of subtle gait abnormalities or lead to misclassification of locomotor patterns in studies involving small inter-group differences. Therefore, these error margins should be taken into account when interpreting experimental results, especially in preclinical models assessing motor recovery or drug effects.

 

4. The step-by-step process of image acquisition, preprocessing, and line detection lacks clarity. Exact thresholds, parameter tuning, and Hough space resolution settings should be explicitly stated to allow reproducibility.

Response:

We thank the reviewer for this important comment. In the revised manuscript, we have expanded the methodological description in Section 3.2 to clarify the image processing pipeline. We now specify the exact thresholding method (global threshold = 48), the resolution of the Hough space (180 angles × 640 distances), and the use of built-in MATLAB functions for peak detection. These additions are intended to improve transparency and reproducibility, and are marked in blue in the revised version.

 

Next text was added in Section 3.2, lines: 242-244

After performing the procedure in Section 2.1, the RGB image (Figure 3a) was first converted to grayscale  and a global threshold was applied to the resulting image, obtaining the binary image . In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments was 48.

 

5. The manuscript contains grammatical errors and awkward phrasing that reduce clarity. Professional language editing is recommended.

Response:

We respectfully acknowledge the reviewer’s concern. However, other reviewers noted that the manuscript is written in good English, and we have carefully reviewed the text to ensure clarity and correct grammar. Nevertheless, considering your comment, a native speaking English reviewed the manuscript

 

6. A quantitative comparison with state-of-the-art methods such as neural network-based or PCA-based motion analysis systems is lacking and should be provided to justify the advantages of MMHTS.

Response:

We thank the reviewer for this valuable suggestion. In the revised manuscript, we include a qualitative comparison (Table 4) between MMHTS and state-of-the-art methods such as DeepLabCut (neural networks) and PCA-based approaches. While a full quantitative comparison was beyond the scope of this proof-of-concept study, we acknowledge its importance and plan to address it in future work. This intention is now stated explicitly in the revised discussion.

 

Next text was added in Section 3.4, lines 408-413:

While the current study provides a qualitative comparison between MMHTS and other motion analysis methods (Table 4), we recognize the importance of conducting a direct quantitative comparison with state-of-the-art techniques such as neural network-based models (e.g., DeepLabCut) and PCA-based systems. This type of analysis will be included in future work to further validate the strengths and limitations of MMHTS across different experimental settings and datasets.

 

Thank you very much for your kind attention. We hope you find our manuscript suitable for publication and look forward to hearing from you soon.

 

Sincerely:

Dr. José Trinidad Guillen Bonilla

Departamento de Electro-fotónica, CUCEI.

Universidad de Guadalajara,

Blvd- M. García Barragan 1421, Guadalajara, Jalisco,

1. P. 44410, México.

e-mail: trinidad.guillen@academicos.udg.mx

Tel.: +52 (33) 1378 5900 (ext. 27655)

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

• The authors contribute the scientific methods of the mathematical foundation of the MMHTS, RGB to binary and the application of the Hough transform. I've read throughout the paper and I really like the paper structure BTW it contains numerous grammatical errors, awkward phrasing, typos and clarity. A proofread by a professional editing service is recommended e.g., The authors frequently use incorrect prepositions, such as "Based in" instead of "Based on" and "in concordance with" instead of "in accordance with".
• All figures and tables are clear, except fig. 1(b) and (c). Enchancing fig. 1(b) and text-embedded within fig. 1(c) are needed for the reader.
• All references cited in this paper were published in or before 2024, which is appropriate.
• I will give some construtive comments for the authors to improve the paper:

1. In the introduction section: The authors could more explicitly state the specific drawbacks or limitations of the existing methods (e.g., cost, complexity, specific inaccuracies) that their proposed method aims to overcome.
2. In the methodology section: In step (c), the paper mentions applying a threshold to create a binary image. The authors should specify the thresholding method used (e.g., manual, Otsu's method, adaptive thresholding), as this choice significantly impacts the resulting binary image and the accuracy of the Hough transform. And in step (e), the paper states that lines are identified in Hough space, and later specifies that "higher points in the space" were found. The process for identifying these peaks should be detailed. Is it an automated maximum-finding algorithm? What is the search radius or sensitivity for peak detection? This is critical for reproducibility. Moreover, the method for input and marking which relies on lines drawn with permanent ink on the rat's limbs and user-selected start and end points (p0​ and p4​). This manual marking and selection can be leaded to significant error. The authors should discuss how the initial lines were drawn to ensure they accurately represented the underlying bone structure and acknowledge the potential for user-introduced variability and bias.
3. In the experimental work and results section: The results are validated against measurements from AutoCAD 2016. I've doubted that the use of AutoCAD maybe inappropriate in this case, because AutoCAD is a design software, not a metrology or scientific analysis tool. The use of this software as a ground truth is unconventional. A more standard and robust validation would involve comparison against: a manual measurements by several expert reviewers to establish inter-rater reliability or data from a commercial locomotion analysis system (like the CatWalk or DigiGait systems mentioned in the introduction).
4. In the discussion section: The authors should give more highlights about the specific advantages of MMHTS (e.g., computational efficiency, no need for frequency domain transformation) and disadvantages (e.g., sensitivity to line quality, requirement for manual marking) in relation to these other techniques.

Author Response

June 24, 2025

 

Dear Editor in Chief:

Mathematics

I am pleased to resubmit for publication the revised version of our manuscript entitled: “Rat locomotion analysis based on straight line detection in Hough space”. The manuscript was identified as mathematics-3710285. I am very thankful to the Editor and reviewers for their thorough review. We have revised our research article in the light of their useful suggestions and comments, and hope our revision has improved the manuscript to a level of their satisfaction. In the manuscript, the changes for improvement were marked in blue and red for what was eliminated. Considering the reviewer´s comments, the manuscript was reviewed by a native speaking.  

 

Reviewers´ comments:

 

Reviewer 1

 

1) The paper addresses kinematic analysis of rat motion. This subject is very thoroughly researched, and there are hundreds of publications on this topic. Authors noticed some fraction of them in the introduction section; however, they do not justify why the new method is needed.

Response:

We appreciate the reviewer’s observation. While we acknowledge that kinematic analysis of rat locomotion is a well-explored field, our study is aimed at proposing a low-cost and accessible method that can be implemented in laboratories with limited resources, without requiring specialized motion capture systems or advanced equipment. Most of the existing approaches rely on commercial software or marker-based systems that are often expensive or require specific hardware (e.g., high-speed cameras, infrared systems).

Our method offers an alternative by using image processing through the Hough transform to extract geometric information (angles and distances between limbs), which can be analyzed to infer gait patterns. Although basic, this method is advantageous in terms of accessibility and cost-effectiveness.

 

2) Why, instead of a line that is drawn over the test rat, put markers over its body joints similarly to how it is done in motion capture approaches? You will also get angles that can be calculated between vectors defined by tracked joints. The joint-based approach seems to me more intuitive and easy to deploy.

Response:

We appreciate this valuable suggestion. In fact, during our experimental design, we opted not to use physical reflective markers or external objects attached to the animal's joints. Instead, we shaved the fur of the hind limbs and manually drew the anatomical lines corresponding to the bones and joint axes using permanent ink. This approach ensured consistent visual references for the subsequent line detection in image processing, while avoiding additional weight or discomfort to the animal, as well as the risk of marker detachment or occlusion during locomotion.

We acknowledge that joint-based tracking using physical markers is widely adopted in commercial motion capture systems; however, these systems often require specialized hardware and software, increasing both the cost and the complexity of the experimental setup. Our method seeks to offer a low-cost, accessible, and non-intrusive alternative, especially suitable for laboratories with limited resources.

Moreover, the use of line detection through the Hough Transform allows the extraction of geometric features (angles, segment lengths, and intersection points) in a consistent and automated way, based on the ink-drawn reference lines. While joint-based vector analysis can be highly effective, our proposed method shows comparable accuracy (angular error < 0.14°) and provides a reliable estimation of locomotor geometry, as validated against a professional design software.

 

3) Please compare your method with existing ones and show the pros and cons of your approach.

Response:

We thank the reviewer for this important observation. In the revised manuscript, we have included a comparative analysis of our method (MMHTS) with other commonly used approaches for locomotion analysis in rats. This comparison is now presented in Table 4 (Discussion section, paragraph 2, lines 351-353 and Table 4; the text is marked in blue) and is briefly summarized below:

Commercial systems such as CatWalk XT® or DigiGait® offer high-resolution dynamic analysis and advanced automation, but they require expensive hardware and infrastructure, which limits their accessibility in many research environments.

Deep learning-based tools like DeepLabCut provide markerless tracking with high precision and flexibility across species and setups, but demand significant computational resources and expertise in neural network training and programming.

Manual video analysis software (e.g., Kinovea) represents a free and educationally useful tool, though it requires extensive manual input, offers limited precision, and is not scalable for larger datasets.

Our method, MMHTS, presents a low-cost and easy-to-implement alternative that does not depend on commercial software or high-end equipment. Although limited to 2D analysis and reliant on anatomical marking on the animal’s skin, Department has demonstrated excellent accuracy (angular error < 0.14°) when validated against professional design software, and can be semi-automated for efficient image processing.

 

Considering your comment, the text was added

“Next, in Table 4, the MMHTS technique is qualitatively compared to other software, where its advantages and disadvantages are shown.

 

and Table 4 was also added 

 

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

The added text is marked in blue.

 

4) Is your method robust to rotation of the observed target? Please estimate the potential error caused by the fact that the observed target might not be exactly positioned perpendicular to the camera.

Response:

We appreciate the reviewer’s comment, as perspective distortion can indeed affect the accuracy of 2D motion analysis when the subject is not perfectly aligned perpendicularly to the camera’s plane. In preliminary trials, we observed that untrained rats often display natural exploratory behavior, including partial body rotations at the beginning of the tunnel walk, which could introduce angular measurement errors.

To minimize this variability and ensure consistent alignment during image acquisition, we implemented a behavioral training protocol. Each experimental rat was trained to walk through a transparent acrylic tunnel (100 cm long × 10 cm high × 10 cm wide) for 10 minutes per day over a period of 10 consecutive days. During this habituation, we recorded the time taken to walk back and forth through the tunnel and continued the training until all animals achieved a steady and uninterrupted locomotion pattern, with a time variability of less than 5% among subjects.

Additionally, after each training session, the tunnel was cleaned with a diluted cane vinegar solution to eliminate olfactory trails left by previous animals. This prevented additional exploratory behavior and helped promote direct forward movement.

Only videos from these standardized walking trials—where animals moved continuously and without lateral turning—were included in the analysis. While perfect perpendicularity cannot be guaranteed, this protocol allowed us to greatly reduce variability in orientation.

 

5) Equation (3) - please make the assumption that sin theta must not be equal to zero

Dear reviewer, thanks for your comment to improve the quality of our work.

 Response:

Taking into consideration your comment, in section 2: Locomotion Analysis in Hough Space, Subsection; 2.1. Straight Line Detection; Page 3, paragraph 1, lines 128 to 132 were added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

The added text is marked in blue.

 

6) Page 8: Figure 3 should not be split between separate pages; please correct it.
Response:

Dear reviewer, Figure 3 was corrected according to your suggestion.

 

7) Table 2: Please be consistent and use the same floating-point precision (3 digits) in all values

Response:

Review estimator, the correction was made on Table 2. The changes are marked in blue.

 

 

Reviewer 2

 

• The presented in good English

Response:

Dear reviewer, we appreciate your comment.

 

2) Add the abalation studies. Also rewrite the contribution more clearly to reflect the experimental work. 

Response

Taking your comment into consideration, in section 3.3., Measurements, paragraph 3, lines 305 to 310 the text was added,

“In other words, the MMHTS method is efficient since measurement errors are small. This follows since the error is defined based on the difference between the measurements made with our MMHTS proposal and the measurements made with the AutoCAD® professional software. In addition, the MMHTS technique is easy to implement, it has under economic cost, its accuracy depends on the experience of the test expert, its implementation does not require additional hardware and the software is easy to handle”

The added text is marked in blue.

 

3) Give angle limits for the stability of proposed system. 

Dear reviewer, we appreciate your comment to improve our work

Response:

Physically there are limits in the pattern of the march due to the anatomy of the rat since there are limits in its joints. However, in the mathematical model there are no limits and therefore it is possible to analyze the entire range of joints in both physiological and pathological conditions.

 

Taking your comment into consideration, in Section 2, Subsection 2.1, page 3, paragraph 1 was added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

4) Quantitative aspects of normal locomotion in rats. Life sciences, 25(2), 171-179.

Response:

We thank the reviewer for suggesting this fundamental reference. The study by Hruska et al. (1979) presents a detailed quantitative analysis of spontaneous locomotion in rats, using footprint tracking to measure spatial parameters (such as stride length, width, and foot placement symmetry), and video recordings to analyze temporal aspects of the gait cycle.

Our methodological approach differs from theirs in two important ways:

1. Our analysis was conducted under controlled and trained locomotion, not spontaneous movement. All animals were behaviorally conditioned to walk continuously in a narrow acrylic tunnel, reducing variability due to exploratory behavior.
2. Locomotion parameters were derived by drawing anatomical lines directly on the shaved skin of the hindlimbs, corresponding to underlying bone segments. These lines allowed us to identify angular points (vertices) representing joints, from which we calculated angles and distances between segments.

Although we have not yet completed a direct quantitative comparison between the values obtained using the MMHTS method and those reported by Hruska et al. or other sources, we acknowledge the value of such a comparison and plan to carry it out in a subsequent stage. We are currently finalizing the implementation of the software system that will allow us to extract these parameters from video recordings in a semi-automated manner. This perspective has been included in the revised manuscript (Section 1, lines 61–68), and the work of Hruska et al. has been cited as a key reference for future validation efforts.

 

Considering your comment, next text was added Section 1, lines 61–68,

One of the most frequently cited references in the study of rat locomotion is the work of Hruska et al., who conducted a quantitative analysis of gait by recording plantar footprints under conditions of spontaneous locomotion [18]. Although their study provides valuable normative data, it does not enable a direct assessment of the structural geometry of the limbs during movement. In the present study, we introduce an alternative methodology based on the analysis of joint angles derived from anatomically guided skin markings, which may offer complementary insights to those obtained through footprint-based approaches.

 

The added text is marked in blue.

 

5)  Three-dimensional analysis of locomotion patterns after hindlimb suspension and subsequent long-term reloading in growing rats. Journal of Biomechanics, 176, 112389.

Response:

We thank the reviewer for recommending this highly relevant study. Nishida et al. (2024) provide an insightful three-dimensional kinematic analysis of gait alterations in rats following a well-established model of hindlimb suspension (HS) and long-term reloading. In this model, the rats’ hindlimbs are suspended via a tail harness, preventing ground contact for several weeks during development. This method induces musculoskeletal disuse and simulates conditions such as microgravity or immobilization. After reloading, 3D motion capture is used to detect persistent locomotor changes, such as reduced hip adduction and increased toe-out angle, even months after recovery.

Although our proposed method (MMHTS) is limited to two-dimensional structural analysis and does not involve unloading paradigms, it offers a complementary perspective. Whereas the 3D model used by Nishida et al. focuses on functional recovery after structural disruption, MMHTS provides a geometric approach to analyzing joint angles and limb segment coordination under controlled, repeatable locomotion conditions.

In particular, MMHTS can be valuable in early-stage or lower-resource studies where behavioral training ensures reproducible gait without requiring specialized motion capture equipment. Moreover, our method could be adapted for use in reloading models such as HS, particularly during the screening or monitoring phases of functional recovery.

We have included this comparison in the revised manuscript (Section 3.3, lines 374–382) to highlight the complementary nature of both approaches.

 

Considering your comment, next text was added (Section 3.3, lines 374–382),

In more complex models involving structural alterations due to disuse, our method could serve as a tool for angular structural evaluation during the recovery phases. For example, a recent study employed three-dimensional kinematic analysis to examine locomotion patterns in developing rats following prolonged hindlimb suspension and subsequent long-term reloading [33]. The MMHTS method proposed in this work does not capture three-dimensional data; however, it offers a reproducible two-dimensional structural analysis alternative, based on anatomical references marked on the skin. This approach is useful for functional follow-up studies in preclinical models, particularly those requiring a simple and accessible implementation for locomotion assessment.

 

The added text is marked in blue.

 

How the authors find this article useful to add in their research

6) Yang, W.W., et al., Dissecting Genetic Mechanisms of Differential Locomotion, Depression, and Allodynia after Spinal Cord Injury 370 in Three Mouse Strains. Cells, 2024. 13(9).

Response:

We thank the reviewer for highlighting this relevant study. The work by Yang et al. (2024) presents an analysis of locomotor, affective, and pain-related alterations following spinal cord injury in different mouse strains, using the CatWalk XT system and transcriptomic profiling. Although the present manuscript does not include experimental data derived from an injury model, it is important to note that the MMHTS method was originally developed and applied in the context of a study involving penetrating cortical injury to the primary motor cortex in rats, specifically targeting the region responsible for hindlimb motor control. In that study, video recordings were obtained both before the lesion (baseline) and at several time points afterward, including vehicle-treated and tamoxifen-treated groups. However, the results from that experimental work have not yet been submitted for review, as they will be part of a future publication currently in preparation.

In this article, we focus exclusively on presenting and validating the MMHTS method as a structural locomotion analysis tool. We believe that this method may prove especially useful in injury models similar to that of Yang et al., particularly in settings where advanced commercial platforms or 3D motion capture systems are not available. MMHTS offers reproducible angular measurements based on anatomical references, which may help correlate structural gait characteristics with molecular or genetic responses.

This study has been cited in the revised manuscript (Section 3.3, lines 382–388) to contextualize the potential applications of MMHTS in neurotrauma research.

 

Considering your comment, the following text was added (Section 3.3, lines 382–488),

The MMHTS method may also serve as a practical tool in models involving central nervous system injury. While more sophisticated 3D gait systems provide high-resolution analysis, MMHTS offers a low-cost alternative for structural gait evaluation. This could be especially valuable in contexts like the cortical injury model in which MMHTS was initially applied, or in studies similar to that of Yang et al., which combined behavioral phenotyping and transcriptomics after spinal cord injury [34].

 

The added text is marked in blue.

 

Reviewer 3

1. In the introduction section: The authors could more explicitly state the specific drawbacks or limitations of the existing methods (e.g., cost, complexity, specific inaccuracies) that their proposed method aims to overcome

 

Response:

Dear reviewer, we appreciate your comment. Taking your comment into consideration, in seation 1, introduction, paragraph 4, Lines 106 to 108, the following text was added.

Some advantages of our proposal are easy implementation, low computational cost, does not require additional hardware or software and accuracy can be very good since the measurements are almost similar to professional design software.

 

The added text is marked in blue.

 

2. In the methodology section: In step (c), the paper mentions applying a threshold to create a binary image. The authors should specify the thresholding method used (e.g., manual, Otsu's method, adaptive thresholding), as this choice significantly impacts the resulting binary image and the accuracy of the Hough transform.

Response:

Dear reviewer, as mentioned, binarization is important in image processing since the binary image obtained depends on the binarization methodology. In our proposal, a global threshold method was applied where the selected value is the average value between the minimum pixel value and the maximum pixel value. 

 

Taking your comment into consideration, in section 3.2, Line Identification in the Hough Transform Space, paragraph 2, lines 242 to 244 the text was added,

 

In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments, it was 48.

Also in section 3.4. (discussion), point 10 was added

• The accuracy of the MMHTS method can improve whether image binarization is done using an adaptive technique.

 

The added text is marked in blue.

 

And in step (e), the paper states that lines are identified in Hough space, and later specifies that "higher points in the space" were found. The process for identifying these peaks should be detailed. Is it an automated maximum-finding algorithm?

Response:

Dear reviewer, in our numerical work the Matlab 2024B scientific software was used and this software already has functions to find the maximum value in numerical data. Then, answering your question, in our work we do not develop the algorithm to find the maximum value in the data of the Houghh transform, but if we apply the function of the Matlab software, which is enough to obtain good results.

 

What is the search radius or sensitivity for peak detection? This is critical for reproducibility.

Response

Dear reviewer, we appreciate your observation to improve the quality of our work.

Based on the geometric of the problem shown in Figure 1 and on the fundamental concept of the Hough transform, which was developed to detect lines in images, in our work, it is considered that the lines marked in the limb of the rat are the most significant in the image under study, and therefore, these lines correspond to the maximum points in the space of the Hough transform. Taking this into consideration, the MMHTS method is repeatable in the measurement of the angles and lengths of the lines marked in the limb of the rat. However, the user's experience (human expert in animal movement tests) must be mentioned, and plays a very important role to obtaining good results in the movement analysis.

 

Moreover, the method for input and marking which relies on lines drawn with permanent ink on the rat's limbs and user-selected start and end points (p0​ and p4​). This manual marking and selection can be leaded to significant error.

Response:

As mentioned, the user's experience plays an important role, since based on his knowledge, he can properly select the P0 and P4 points, significantly reducing errors in the measurement.

 

Taking your comment into consideration, in section 3.4 discussion was added point 11,

 

11. The error due to the selection of P_0 and P_4 points can be significantly reduced if the MMHTS method is combined with an automatic points location method.

 

The authors should discuss how the initial lines were drawn to ensure they accurately represented the underlying bone structure and acknowledge the potential for user-introduced variability and bias.

Response:

We thank the reviewer for this valuable suggestion. In the revised discussion section, we now explicitly summarize the main advantages of MMHTS, including its computational simplicity, interpretability, and the fact that it does not rely on frequency domain transformations. We also acknowledge its limitations, such as dependence on line quality and the need for manual marking in its current version. These points are now discussed in direct contrast to PCA-, FFT-, and neural network-based methods, and are highlighted in blue in the revised manuscript.

 

Considering your comment, the following text was included in section 3.4, lines 356-373

Based on our experience in preclinical studies involving motor function analysis, the MMHTS method was developed as a practical and accessible alternative to more complex and costly gait analysis systems. Its implementation in MATLAB using built-in functions allows for efficient processing without the need for frequency domain transformations, as required in FFT-based analyses. Furthermore, the outputs segment angles, distances, and intersection points are easily interpretable and directly applicable to movement analysis in experimental models.

This approach is particularly suitable for research groups that require flexible and low-cost tools without sacrificing analytical precision. However, we recognize that the current version of MMHTS relies on manual marking of anatomical reference lines, which may introduce inter-user variability depending on consistency in line placement. While more advanced tools such as PCA-based systems or deep learning models like DeepLabCut offer automated solutions, they also entail steeper technical requirements.

We consider this first version of MMHTS a foundational step towards a more automated and robust methodology. As outlined in the “Future Work” section, our next steps include the integration of semi-automated landmark detection and broader validation across subjects and experimental conditions to improve reproducibility and reduce user dependency.

 

4.---- In the discussion section: The authors should give more highlights about the specific advantages of MMHTS (e.g., computational efficiency, no need for frequency domain transformation) and disadvantages (e.g., sensitivity to line quality, requirement for manual marking) in relation to these other techniques

Response:

Dear reviewer, we appreciate your observation.

 

Considering your comment, in section 3.4. Discussion, Paragraph 2, Table 4 was added

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

 

 

 

Reviewer 4

 

1. The human is heavily involved in manually marking lines on the rat’s limbs, which introduces human bias and reduces scalability.

Response:

We appreciate the reviewer’s comment. While manual marking was chosen for its simplicity and low cost, we acknowledge that it may introduce user bias and limit scalability. Based on our experience, we have identified consistent anatomical landmarks—such as the hip, heel, tarsal-metatarsal joint, nose tip, eye, and base of the tail, that are suitable for automated detection.

In the revised manuscript, we now include a future work proposal to implement semi-automatic detection of these landmarks using classical computer vision or deep learning tools (e.g., DeepLabCut), to reduce human intervention and improve reproducibility. This addition is marked in blue in the “Future Work” section.

 

Next text was added (Section 3.4, lines 394-403):

In future versions of the MMHTS method, we aim to incorporate a semi-automated strategy for the detection of anatomical landmarks, building on empirical experience from tracking visible structures during rodent locomotion. Key points such as the hip, heel, tarsal-metatarsal joint, tip of the nose, eye, and the base of the tail have proven to be consistent and easily identifiable throughout the gait cycle. Additionally, tracing a longitudinal line along the tail may provide valuable insights into tail dynamics associated with balance and directional movement. The integration of classical computer vision techniques (e.g., edge detection, contour extraction, Hough transform) or deep learning-based tools (e.g., DeepLabCut) may help reduce observer bias, improve reproducibility, and enhance the scalability of the system for large-scale motion analysis.

 

2. Validation on a larger animal sample and multiple trials is essential for robust conclusions.

Response:

We agree with the reviewer that validation on a larger sample and across multiple trials is essential to strengthen the robustness and generalizability of the MMHTS method. In the present study, our main objective was to describe and validate the mathematical and procedural foundations of the technique, using a single trained subject as a proof of concept.

As noted in the revised manuscript, we consider this initial implementation a starting point for broader experimental application. In future work, we plan to extend validation to a larger cohort of animals, including intra- and inter-subject variability, and to evaluate reproducibility across different users. This will allow us to better assess the accuracy, consistency, and practical applicability of the MMHTS method in preclinical research settings. A note reflecting this future direction has been added to the manuscript and is marked in blue.

 

Next text was added (Section 3.4, lines: 404-408):

As this study represents a proof of concept based on a single trained subject, future work will include validation of the MMHTS method using a larger sample of animals and repeated trials. This will allow us to assess the method’s reproducibility, ac-curacy, and robustness across subjects and users, and further support its application in preclinical gait analysis studies.

 

3. The authors are suggested to discuss the biological significance and potential impact on gait analysis of error values.

Response:

We thank the reviewer for this suggestion. In the revised manuscript, we now briefly discuss the biological implications of the observed error values. Although the angular and length measurement errors are low (<0.15° and ~0.13 pixels, respectively), they may still influence gait classification or detection of subtle motor deficits. We note this as a consideration for interpreting results, especially in studies involving small differences between experimental groups.

 

Next text was added (Section 3.3, lines: 311-318):

Although the angular and length measurement errors obtained with the MMHTS method are relatively low (less than 0.15° for angles and approximately 0.13 pixels for segment lengths), it is important to consider their potential biological impact. In particular, such deviations, although minimal, could influence the detection of subtle gait abnormalities or lead to misclassification of locomotor patterns in studies involving small inter-group differences. Therefore, these error margins should be taken into account when interpreting experimental results, especially in preclinical models assessing motor recovery or drug effects.

 

4. The step-by-step process of image acquisition, preprocessing, and line detection lacks clarity. Exact thresholds, parameter tuning, and Hough space resolution settings should be explicitly stated to allow reproducibility.

Response:

We thank the reviewer for this important comment. In the revised manuscript, we have expanded the methodological description in Section 3.2 to clarify the image processing pipeline. We now specify the exact thresholding method (global threshold = 48), the resolution of the Hough space (180 angles × 640 distances), and the use of built-in MATLAB functions for peak detection. These additions are intended to improve transparency and reproducibility, and are marked in blue in the revised version.

 

Next text was added in Section 3.2, lines: 242-244

After performing the procedure in Section 2.1, the RGB image (Figure 3a) was first converted to grayscale  and a global threshold was applied to the resulting image, obtaining the binary image . In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments was 48.

 

5. The manuscript contains grammatical errors and awkward phrasing that reduce clarity. Professional language editing is recommended.

Response:

We respectfully acknowledge the reviewer’s concern. However, other reviewers noted that the manuscript is written in good English, and we have carefully reviewed the text to ensure clarity and correct grammar. Nevertheless, considering your comment, a native speaking English reviewed the manuscript

 

6. A quantitative comparison with state-of-the-art methods such as neural network-based or PCA-based motion analysis systems is lacking and should be provided to justify the advantages of MMHTS.

Response:

We thank the reviewer for this valuable suggestion. In the revised manuscript, we include a qualitative comparison (Table 4) between MMHTS and state-of-the-art methods such as DeepLabCut (neural networks) and PCA-based approaches. While a full quantitative comparison was beyond the scope of this proof-of-concept study, we acknowledge its importance and plan to address it in future work. This intention is now stated explicitly in the revised discussion.

 

Next text was added in Section 3.4, lines 408-413:

While the current study provides a qualitative comparison between MMHTS and other motion analysis methods (Table 4), we recognize the importance of conducting a direct quantitative comparison with state-of-the-art techniques such as neural network-based models (e.g., DeepLabCut) and PCA-based systems. This type of analysis will be included in future work to further validate the strengths and limitations of MMHTS across different experimental settings and datasets.

 

Thank you very much for your kind attention. We hope you find our manuscript suitable for publication and look forward to hearing from you soon.

 

Sincerely:

Dr. José Trinidad Guillen Bonilla

Departamento de Electro-fotónica, CUCEI.

Universidad de Guadalajara,

Blvd- M. García Barragan 1421, Guadalajara, Jalisco,

1. P. 44410, México.

e-mail: trinidad.guillen@academicos.udg.mx

Tel.: +52 (33) 1378 5900 (ext. 27655)

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The author of this paper proposed a method called Movement Measurement in Hough Transform Space (MMHTS) for analyzing rat locomotion using image processing. They detect the straight lines in the Hough space from the images of rat limbs marked with lines to measure angles, distances, and intersection points. Overall, the work is good; however, some changes are suggested as follows:  

• The human is heavily involved in manually marking lines on the rat’s limbs, which introduces human bias and reduces scalability.
• Validation on a larger animal sample and multiple trials is essential for robust conclusions.
• The authors are suggested to discuss the biological significance and potential impact on gait analysis of error values.
• The step-by-step process of image acquisition, preprocessing, and line detection lacks clarity. Exact thresholds, parameter tuning, and Hough space resolution settings should be explicitly stated to allow reproducibility.
• The manuscript contains grammatical errors and awkward phrasing that reduce clarity. Professional language editing is recommended.
• A quantitative comparison with state-of-the-art methods such as neural network-based or PCA-based motion analysis systems is lacking and should be provided to justify the advantages of MMHTS.

 

Author Response

June 24, 2025

 

Dear Editor in Chief:

Mathematics

I am pleased to resubmit for publication the revised version of our manuscript entitled: “Rat locomotion analysis based on straight line detection in Hough space”. The manuscript was identified as mathematics-3710285. I am very thankful to the Editor and reviewers for their thorough review. We have revised our research article in the light of their useful suggestions and comments, and hope our revision has improved the manuscript to a level of their satisfaction. In the manuscript, the changes for improvement were marked in blue and red for what was eliminated. Considering the reviewer´s comments, the manuscript was reviewed by a native speaking.  

 

Reviewers´ comments:

 

Reviewer 1

 

1) The paper addresses kinematic analysis of rat motion. This subject is very thoroughly researched, and there are hundreds of publications on this topic. Authors noticed some fraction of them in the introduction section; however, they do not justify why the new method is needed.

Response:

We appreciate the reviewer’s observation. While we acknowledge that kinematic analysis of rat locomotion is a well-explored field, our study is aimed at proposing a low-cost and accessible method that can be implemented in laboratories with limited resources, without requiring specialized motion capture systems or advanced equipment. Most of the existing approaches rely on commercial software or marker-based systems that are often expensive or require specific hardware (e.g., high-speed cameras, infrared systems).

Our method offers an alternative by using image processing through the Hough transform to extract geometric information (angles and distances between limbs), which can be analyzed to infer gait patterns. Although basic, this method is advantageous in terms of accessibility and cost-effectiveness.

 

2) Why, instead of a line that is drawn over the test rat, put markers over its body joints similarly to how it is done in motion capture approaches? You will also get angles that can be calculated between vectors defined by tracked joints. The joint-based approach seems to me more intuitive and easy to deploy.

Response:

We appreciate this valuable suggestion. In fact, during our experimental design, we opted not to use physical reflective markers or external objects attached to the animal's joints. Instead, we shaved the fur of the hind limbs and manually drew the anatomical lines corresponding to the bones and joint axes using permanent ink. This approach ensured consistent visual references for the subsequent line detection in image processing, while avoiding additional weight or discomfort to the animal, as well as the risk of marker detachment or occlusion during locomotion.

We acknowledge that joint-based tracking using physical markers is widely adopted in commercial motion capture systems; however, these systems often require specialized hardware and software, increasing both the cost and the complexity of the experimental setup. Our method seeks to offer a low-cost, accessible, and non-intrusive alternative, especially suitable for laboratories with limited resources.

Moreover, the use of line detection through the Hough Transform allows the extraction of geometric features (angles, segment lengths, and intersection points) in a consistent and automated way, based on the ink-drawn reference lines. While joint-based vector analysis can be highly effective, our proposed method shows comparable accuracy (angular error < 0.14°) and provides a reliable estimation of locomotor geometry, as validated against a professional design software.

 

3) Please compare your method with existing ones and show the pros and cons of your approach.

Response:

We thank the reviewer for this important observation. In the revised manuscript, we have included a comparative analysis of our method (MMHTS) with other commonly used approaches for locomotion analysis in rats. This comparison is now presented in Table 4 (Discussion section, paragraph 2, lines 351-353 and Table 4; the text is marked in blue) and is briefly summarized below:

Commercial systems such as CatWalk XT® or DigiGait® offer high-resolution dynamic analysis and advanced automation, but they require expensive hardware and infrastructure, which limits their accessibility in many research environments.

Deep learning-based tools like DeepLabCut provide markerless tracking with high precision and flexibility across species and setups, but demand significant computational resources and expertise in neural network training and programming.

Manual video analysis software (e.g., Kinovea) represents a free and educationally useful tool, though it requires extensive manual input, offers limited precision, and is not scalable for larger datasets.

Our method, MMHTS, presents a low-cost and easy-to-implement alternative that does not depend on commercial software or high-end equipment. Although limited to 2D analysis and reliant on anatomical marking on the animal’s skin, Department has demonstrated excellent accuracy (angular error < 0.14°) when validated against professional design software, and can be semi-automated for efficient image processing.

 

Considering your comment, the text was added

“Next, in Table 4, the MMHTS technique is qualitatively compared to other software, where its advantages and disadvantages are shown.

 

and Table 4 was also added 

 

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

The added text is marked in blue.

 

4) Is your method robust to rotation of the observed target? Please estimate the potential error caused by the fact that the observed target might not be exactly positioned perpendicular to the camera.

Response:

We appreciate the reviewer’s comment, as perspective distortion can indeed affect the accuracy of 2D motion analysis when the subject is not perfectly aligned perpendicularly to the camera’s plane. In preliminary trials, we observed that untrained rats often display natural exploratory behavior, including partial body rotations at the beginning of the tunnel walk, which could introduce angular measurement errors.

To minimize this variability and ensure consistent alignment during image acquisition, we implemented a behavioral training protocol. Each experimental rat was trained to walk through a transparent acrylic tunnel (100 cm long × 10 cm high × 10 cm wide) for 10 minutes per day over a period of 10 consecutive days. During this habituation, we recorded the time taken to walk back and forth through the tunnel and continued the training until all animals achieved a steady and uninterrupted locomotion pattern, with a time variability of less than 5% among subjects.

Additionally, after each training session, the tunnel was cleaned with a diluted cane vinegar solution to eliminate olfactory trails left by previous animals. This prevented additional exploratory behavior and helped promote direct forward movement.

Only videos from these standardized walking trials—where animals moved continuously and without lateral turning—were included in the analysis. While perfect perpendicularity cannot be guaranteed, this protocol allowed us to greatly reduce variability in orientation.

 

5) Equation (3) - please make the assumption that sin theta must not be equal to zero

Dear reviewer, thanks for your comment to improve the quality of our work.

 Response:

Taking into consideration your comment, in section 2: Locomotion Analysis in Hough Space, Subsection; 2.1. Straight Line Detection; Page 3, paragraph 1, lines 128 to 132 were added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

The added text is marked in blue.

 

6) Page 8: Figure 3 should not be split between separate pages; please correct it.
Response:

Dear reviewer, Figure 3 was corrected according to your suggestion.

 

7) Table 2: Please be consistent and use the same floating-point precision (3 digits) in all values

Response:

Review estimator, the correction was made on Table 2. The changes are marked in blue.

 

 

Reviewer 2

 

• The presented in good English

Response:

Dear reviewer, we appreciate your comment.

 

2) Add the abalation studies. Also rewrite the contribution more clearly to reflect the experimental work. 

Response

Taking your comment into consideration, in section 3.3., Measurements, paragraph 3, lines 305 to 310 the text was added,

“In other words, the MMHTS method is efficient since measurement errors are small. This follows since the error is defined based on the difference between the measurements made with our MMHTS proposal and the measurements made with the AutoCAD® professional software. In addition, the MMHTS technique is easy to implement, it has under economic cost, its accuracy depends on the experience of the test expert, its implementation does not require additional hardware and the software is easy to handle”

The added text is marked in blue.

 

3) Give angle limits for the stability of proposed system. 

Dear reviewer, we appreciate your comment to improve our work

Response:

Physically there are limits in the pattern of the march due to the anatomy of the rat since there are limits in its joints. However, in the mathematical model there are no limits and therefore it is possible to analyze the entire range of joints in both physiological and pathological conditions.

 

Taking your comment into consideration, in Section 2, Subsection 2.1, page 3, paragraph 1 was added the text,

“If angle  is equal to zero in Equation (3), then in the Hough space, the line is undetermined and it cannot be used for the movement of the rat movement. However, analyzing figures 1b and 1c, in the movement of the extremities of the rat, the angle  It will never have a zero value since this represents that the bones of the extremities of the rat are on stalls. Therefore, considering that the condition  is satisfied and”

 

4) Quantitative aspects of normal locomotion in rats. Life sciences, 25(2), 171-179.

Response:

We thank the reviewer for suggesting this fundamental reference. The study by Hruska et al. (1979) presents a detailed quantitative analysis of spontaneous locomotion in rats, using footprint tracking to measure spatial parameters (such as stride length, width, and foot placement symmetry), and video recordings to analyze temporal aspects of the gait cycle.

Our methodological approach differs from theirs in two important ways:

1. Our analysis was conducted under controlled and trained locomotion, not spontaneous movement. All animals were behaviorally conditioned to walk continuously in a narrow acrylic tunnel, reducing variability due to exploratory behavior.
2. Locomotion parameters were derived by drawing anatomical lines directly on the shaved skin of the hindlimbs, corresponding to underlying bone segments. These lines allowed us to identify angular points (vertices) representing joints, from which we calculated angles and distances between segments.

Although we have not yet completed a direct quantitative comparison between the values obtained using the MMHTS method and those reported by Hruska et al. or other sources, we acknowledge the value of such a comparison and plan to carry it out in a subsequent stage. We are currently finalizing the implementation of the software system that will allow us to extract these parameters from video recordings in a semi-automated manner. This perspective has been included in the revised manuscript (Section 1, lines 61–68), and the work of Hruska et al. has been cited as a key reference for future validation efforts.

 

Considering your comment, next text was added Section 1, lines 61–68,

One of the most frequently cited references in the study of rat locomotion is the work of Hruska et al., who conducted a quantitative analysis of gait by recording plantar footprints under conditions of spontaneous locomotion [18]. Although their study provides valuable normative data, it does not enable a direct assessment of the structural geometry of the limbs during movement. In the present study, we introduce an alternative methodology based on the analysis of joint angles derived from anatomically guided skin markings, which may offer complementary insights to those obtained through footprint-based approaches.

 

The added text is marked in blue.

 

5)  Three-dimensional analysis of locomotion patterns after hindlimb suspension and subsequent long-term reloading in growing rats. Journal of Biomechanics, 176, 112389.

Response:

We thank the reviewer for recommending this highly relevant study. Nishida et al. (2024) provide an insightful three-dimensional kinematic analysis of gait alterations in rats following a well-established model of hindlimb suspension (HS) and long-term reloading. In this model, the rats’ hindlimbs are suspended via a tail harness, preventing ground contact for several weeks during development. This method induces musculoskeletal disuse and simulates conditions such as microgravity or immobilization. After reloading, 3D motion capture is used to detect persistent locomotor changes, such as reduced hip adduction and increased toe-out angle, even months after recovery.

Although our proposed method (MMHTS) is limited to two-dimensional structural analysis and does not involve unloading paradigms, it offers a complementary perspective. Whereas the 3D model used by Nishida et al. focuses on functional recovery after structural disruption, MMHTS provides a geometric approach to analyzing joint angles and limb segment coordination under controlled, repeatable locomotion conditions.

In particular, MMHTS can be valuable in early-stage or lower-resource studies where behavioral training ensures reproducible gait without requiring specialized motion capture equipment. Moreover, our method could be adapted for use in reloading models such as HS, particularly during the screening or monitoring phases of functional recovery.

We have included this comparison in the revised manuscript (Section 3.3, lines 374–382) to highlight the complementary nature of both approaches.

 

Considering your comment, next text was added (Section 3.3, lines 374–382),

In more complex models involving structural alterations due to disuse, our method could serve as a tool for angular structural evaluation during the recovery phases. For example, a recent study employed three-dimensional kinematic analysis to examine locomotion patterns in developing rats following prolonged hindlimb suspension and subsequent long-term reloading [33]. The MMHTS method proposed in this work does not capture three-dimensional data; however, it offers a reproducible two-dimensional structural analysis alternative, based on anatomical references marked on the skin. This approach is useful for functional follow-up studies in preclinical models, particularly those requiring a simple and accessible implementation for locomotion assessment.

 

The added text is marked in blue.

 

How the authors find this article useful to add in their research

6) Yang, W.W., et al., Dissecting Genetic Mechanisms of Differential Locomotion, Depression, and Allodynia after Spinal Cord Injury 370 in Three Mouse Strains. Cells, 2024. 13(9).

Response:

We thank the reviewer for highlighting this relevant study. The work by Yang et al. (2024) presents an analysis of locomotor, affective, and pain-related alterations following spinal cord injury in different mouse strains, using the CatWalk XT system and transcriptomic profiling. Although the present manuscript does not include experimental data derived from an injury model, it is important to note that the MMHTS method was originally developed and applied in the context of a study involving penetrating cortical injury to the primary motor cortex in rats, specifically targeting the region responsible for hindlimb motor control. In that study, video recordings were obtained both before the lesion (baseline) and at several time points afterward, including vehicle-treated and tamoxifen-treated groups. However, the results from that experimental work have not yet been submitted for review, as they will be part of a future publication currently in preparation.

In this article, we focus exclusively on presenting and validating the MMHTS method as a structural locomotion analysis tool. We believe that this method may prove especially useful in injury models similar to that of Yang et al., particularly in settings where advanced commercial platforms or 3D motion capture systems are not available. MMHTS offers reproducible angular measurements based on anatomical references, which may help correlate structural gait characteristics with molecular or genetic responses.

This study has been cited in the revised manuscript (Section 3.3, lines 382–388) to contextualize the potential applications of MMHTS in neurotrauma research.

 

Considering your comment, the following text was added (Section 3.3, lines 382–488),

The MMHTS method may also serve as a practical tool in models involving central nervous system injury. While more sophisticated 3D gait systems provide high-resolution analysis, MMHTS offers a low-cost alternative for structural gait evaluation. This could be especially valuable in contexts like the cortical injury model in which MMHTS was initially applied, or in studies similar to that of Yang et al., which combined behavioral phenotyping and transcriptomics after spinal cord injury [34].

 

The added text is marked in blue.

 

Reviewer 3

1. In the introduction section: The authors could more explicitly state the specific drawbacks or limitations of the existing methods (e.g., cost, complexity, specific inaccuracies) that their proposed method aims to overcome

 

Response:

Dear reviewer, we appreciate your comment. Taking your comment into consideration, in seation 1, introduction, paragraph 4, Lines 106 to 108, the following text was added.

Some advantages of our proposal are easy implementation, low computational cost, does not require additional hardware or software and accuracy can be very good since the measurements are almost similar to professional design software.

 

The added text is marked in blue.

 

2. In the methodology section: In step (c), the paper mentions applying a threshold to create a binary image. The authors should specify the thresholding method used (e.g., manual, Otsu's method, adaptive thresholding), as this choice significantly impacts the resulting binary image and the accuracy of the Hough transform.

Response:

Dear reviewer, as mentioned, binarization is important in image processing since the binary image obtained depends on the binarization methodology. In our proposal, a global threshold method was applied where the selected value is the average value between the minimum pixel value and the maximum pixel value. 

 

Taking your comment into consideration, in section 3.2, Line Identification in the Hough Transform Space, paragraph 2, lines 242 to 244 the text was added,

 

In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments, it was 48.

Also in section 3.4. (discussion), point 10 was added

• The accuracy of the MMHTS method can improve whether image binarization is done using an adaptive technique.

 

The added text is marked in blue.

 

And in step (e), the paper states that lines are identified in Hough space, and later specifies that "higher points in the space" were found. The process for identifying these peaks should be detailed. Is it an automated maximum-finding algorithm?

Response:

Dear reviewer, in our numerical work the Matlab 2024B scientific software was used and this software already has functions to find the maximum value in numerical data. Then, answering your question, in our work we do not develop the algorithm to find the maximum value in the data of the Houghh transform, but if we apply the function of the Matlab software, which is enough to obtain good results.

 

What is the search radius or sensitivity for peak detection? This is critical for reproducibility.

Response

Dear reviewer, we appreciate your observation to improve the quality of our work.

Based on the geometric of the problem shown in Figure 1 and on the fundamental concept of the Hough transform, which was developed to detect lines in images, in our work, it is considered that the lines marked in the limb of the rat are the most significant in the image under study, and therefore, these lines correspond to the maximum points in the space of the Hough transform. Taking this into consideration, the MMHTS method is repeatable in the measurement of the angles and lengths of the lines marked in the limb of the rat. However, the user's experience (human expert in animal movement tests) must be mentioned, and plays a very important role to obtaining good results in the movement analysis.

 

Moreover, the method for input and marking which relies on lines drawn with permanent ink on the rat's limbs and user-selected start and end points (p0​ and p4​). This manual marking and selection can be leaded to significant error.

Response:

As mentioned, the user's experience plays an important role, since based on his knowledge, he can properly select the P0 and P4 points, significantly reducing errors in the measurement.

 

Taking your comment into consideration, in section 3.4 discussion was added point 11,

 

11. The error due to the selection of P_0 and P_4 points can be significantly reduced if the MMHTS method is combined with an automatic points location method.

 

The authors should discuss how the initial lines were drawn to ensure they accurately represented the underlying bone structure and acknowledge the potential for user-introduced variability and bias.

Response:

We thank the reviewer for this valuable suggestion. In the revised discussion section, we now explicitly summarize the main advantages of MMHTS, including its computational simplicity, interpretability, and the fact that it does not rely on frequency domain transformations. We also acknowledge its limitations, such as dependence on line quality and the need for manual marking in its current version. These points are now discussed in direct contrast to PCA-, FFT-, and neural network-based methods, and are highlighted in blue in the revised manuscript.

 

Considering your comment, the following text was included in section 3.4, lines 356-373

Based on our experience in preclinical studies involving motor function analysis, the MMHTS method was developed as a practical and accessible alternative to more complex and costly gait analysis systems. Its implementation in MATLAB using built-in functions allows for efficient processing without the need for frequency domain transformations, as required in FFT-based analyses. Furthermore, the outputs segment angles, distances, and intersection points are easily interpretable and directly applicable to movement analysis in experimental models.

This approach is particularly suitable for research groups that require flexible and low-cost tools without sacrificing analytical precision. However, we recognize that the current version of MMHTS relies on manual marking of anatomical reference lines, which may introduce inter-user variability depending on consistency in line placement. While more advanced tools such as PCA-based systems or deep learning models like DeepLabCut offer automated solutions, they also entail steeper technical requirements.

We consider this first version of MMHTS a foundational step towards a more automated and robust methodology. As outlined in the “Future Work” section, our next steps include the integration of semi-automated landmark detection and broader validation across subjects and experimental conditions to improve reproducibility and reduce user dependency.

 

4.---- In the discussion section: The authors should give more highlights about the specific advantages of MMHTS (e.g., computational efficiency, no need for frequency domain transformation) and disadvantages (e.g., sensitivity to line quality, requirement for manual marking) in relation to these other techniques

Response:

Dear reviewer, we appreciate your observation.

 

Considering your comment, in section 3.4. Discussion, Paragraph 2, Table 4 was added

 

Table 4. Comparison of the MMHTS method with other software: advantages and disadvantages
Method	Advantages	Disadvantages
Commercial systems (e.g., CatWalk XT®, DigiGait®)	High precision in kinematic and dynamic measurements; advanced automation; real-time multiplanar analysis	High cost; requires specialized equipment; limited accessibility in low-budget laboratories
Deep learning-based tracking (e.g., DeepLabCut)	Markerless; high accuracy; flexible across species and configurations	Requires neural network training; needs programming expertise and GPU-based computation
Manual video analysis (e.g., Kinovea)	Free; easy to use; useful for exploratory or educational purposes	High manual input; lower precision; not suitable for large datasets or automated workflows
MMHTS (this study)	Low cost; no commercial software required; simple implementation; validated low error (<0.15°); partially automatable	Limited to 2D; requires anatomical marking; sensitive to perspective and orientation if uncontrolled

 

 

 

 

Reviewer 4

 

1. The human is heavily involved in manually marking lines on the rat’s limbs, which introduces human bias and reduces scalability.

Response:

We appreciate the reviewer’s comment. While manual marking was chosen for its simplicity and low cost, we acknowledge that it may introduce user bias and limit scalability. Based on our experience, we have identified consistent anatomical landmarks—such as the hip, heel, tarsal-metatarsal joint, nose tip, eye, and base of the tail, that are suitable for automated detection.

In the revised manuscript, we now include a future work proposal to implement semi-automatic detection of these landmarks using classical computer vision or deep learning tools (e.g., DeepLabCut), to reduce human intervention and improve reproducibility. This addition is marked in blue in the “Future Work” section.

 

Next text was added (Section 3.4, lines 394-403):

In future versions of the MMHTS method, we aim to incorporate a semi-automated strategy for the detection of anatomical landmarks, building on empirical experience from tracking visible structures during rodent locomotion. Key points such as the hip, heel, tarsal-metatarsal joint, tip of the nose, eye, and the base of the tail have proven to be consistent and easily identifiable throughout the gait cycle. Additionally, tracing a longitudinal line along the tail may provide valuable insights into tail dynamics associated with balance and directional movement. The integration of classical computer vision techniques (e.g., edge detection, contour extraction, Hough transform) or deep learning-based tools (e.g., DeepLabCut) may help reduce observer bias, improve reproducibility, and enhance the scalability of the system for large-scale motion analysis.

 

2. Validation on a larger animal sample and multiple trials is essential for robust conclusions.

Response:

We agree with the reviewer that validation on a larger sample and across multiple trials is essential to strengthen the robustness and generalizability of the MMHTS method. In the present study, our main objective was to describe and validate the mathematical and procedural foundations of the technique, using a single trained subject as a proof of concept.

As noted in the revised manuscript, we consider this initial implementation a starting point for broader experimental application. In future work, we plan to extend validation to a larger cohort of animals, including intra- and inter-subject variability, and to evaluate reproducibility across different users. This will allow us to better assess the accuracy, consistency, and practical applicability of the MMHTS method in preclinical research settings. A note reflecting this future direction has been added to the manuscript and is marked in blue.

 

Next text was added (Section 3.4, lines: 404-408):

As this study represents a proof of concept based on a single trained subject, future work will include validation of the MMHTS method using a larger sample of animals and repeated trials. This will allow us to assess the method’s reproducibility, ac-curacy, and robustness across subjects and users, and further support its application in preclinical gait analysis studies.

 

3. The authors are suggested to discuss the biological significance and potential impact on gait analysis of error values.

Response:

We thank the reviewer for this suggestion. In the revised manuscript, we now briefly discuss the biological implications of the observed error values. Although the angular and length measurement errors are low (<0.15° and ~0.13 pixels, respectively), they may still influence gait classification or detection of subtle motor deficits. We note this as a consideration for interpreting results, especially in studies involving small differences between experimental groups.

 

Next text was added (Section 3.3, lines: 311-318):

Although the angular and length measurement errors obtained with the MMHTS method are relatively low (less than 0.15° for angles and approximately 0.13 pixels for segment lengths), it is important to consider their potential biological impact. In particular, such deviations, although minimal, could influence the detection of subtle gait abnormalities or lead to misclassification of locomotor patterns in studies involving small inter-group differences. Therefore, these error margins should be taken into account when interpreting experimental results, especially in preclinical models assessing motor recovery or drug effects.

 

4. The step-by-step process of image acquisition, preprocessing, and line detection lacks clarity. Exact thresholds, parameter tuning, and Hough space resolution settings should be explicitly stated to allow reproducibility.

Response:

We thank the reviewer for this important comment. In the revised manuscript, we have expanded the methodological description in Section 3.2 to clarify the image processing pipeline. We now specify the exact thresholding method (global threshold = 48), the resolution of the Hough space (180 angles × 640 distances), and the use of built-in MATLAB functions for peak detection. These additions are intended to improve transparency and reproducibility, and are marked in blue in the revised version.

 

Next text was added in Section 3.2, lines: 242-244

After performing the procedure in Section 2.1, the RGB image (Figure 3a) was first converted to grayscale  and a global threshold was applied to the resulting image, obtaining the binary image . In the binarization of the image, the selected threshold value is the average value between the minimum and maximum value of the pixels and in our experiments was 48.

 

5. The manuscript contains grammatical errors and awkward phrasing that reduce clarity. Professional language editing is recommended.

Response:

We respectfully acknowledge the reviewer’s concern. However, other reviewers noted that the manuscript is written in good English, and we have carefully reviewed the text to ensure clarity and correct grammar. Nevertheless, considering your comment, a native speaking English reviewed the manuscript

 

6. A quantitative comparison with state-of-the-art methods such as neural network-based or PCA-based motion analysis systems is lacking and should be provided to justify the advantages of MMHTS.

Response:

We thank the reviewer for this valuable suggestion. In the revised manuscript, we include a qualitative comparison (Table 4) between MMHTS and state-of-the-art methods such as DeepLabCut (neural networks) and PCA-based approaches. While a full quantitative comparison was beyond the scope of this proof-of-concept study, we acknowledge its importance and plan to address it in future work. This intention is now stated explicitly in the revised discussion.

 

Next text was added in Section 3.4, lines 408-413:

While the current study provides a qualitative comparison between MMHTS and other motion analysis methods (Table 4), we recognize the importance of conducting a direct quantitative comparison with state-of-the-art techniques such as neural network-based models (e.g., DeepLabCut) and PCA-based systems. This type of analysis will be included in future work to further validate the strengths and limitations of MMHTS across different experimental settings and datasets.

 

Thank you very much for your kind attention. We hope you find our manuscript suitable for publication and look forward to hearing from you soon.

 

Sincerely:

Dr. José Trinidad Guillen Bonilla

Departamento de Electro-fotónica, CUCEI.

Universidad de Guadalajara,

Blvd- M. García Barragan 1421, Guadalajara, Jalisco,

1. P. 44410, México.

e-mail: trinidad.guillen@academicos.udg.mx

Tel.: +52 (33) 1378 5900 (ext. 27655)

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors addressed all my remarks. In my opinion, paper can be accepted.