An Image Segmentation Method Using an Active Contour Model Based on Improved SPF and LIF
Round 1
Reviewer 1 Report
An image segmentation algorithm is proposed, which based on improved SPF and LIF functions in an Active Contour Method for quick and accurate image segmentation. It is difficult to follow the descriptions and mathematic models in 2.1. The reader has to read the references to understand the model. Several symbol definitions are missing. More specifically: g, phi are not formally defined in 2.1. Is phi defined in line 168? epsilon is not defined in 2.2 Plenty of acronyms are not defined like ESF, SBGFRLS An improved SPF function is presented in 3.1 The new ACM method that can be applied to non homogeneous images and is independent of the initial position is described in 3.2 The mathematic models could be more comprehensive if their description was assisted graphically (displaying the inner/outer regions, where each function is applied etc) The complexity of the proposed algorithm is given in lines 238-241 but the fact that it is simpler than other approaches is not justified enough. Generally it is not made clear why the proposed method has more advantages than other approaches. Give a table with the complexity of other approaches to compare. The proposed model is compared in MATLAB with the other described models using their matlab code available at mathworks. Fig. 4 is unreadable. Use a bold line to indicate the segmentation and the border edges The most useful comparison is the test of the proposed segmentation method on real applications instead of artificial test images as is the case in Fig. 6,Table 1. Minor errors must be corrected like in: Line 109: “functional”
Author Response
Dear,
We are very grateful to you for your valuable comments and suggestions. We have carefully revised the paper in accordance with these comments and suggestions. The added and modified parts are shown in red in the revised manuscript (and changes are marked). The main revisions are as follows.
Comment 1: It is difficult to follow the descriptions and mathematic models in 2.1. The reader has to read the references to understand the model. Several symbol definitions are missing. More specifically: g, phi are not formally defined in 2.1. Is phi defined in line 168?
Response: Thank you very much for your valuable suggestion.
We have corrected these problems as follows:
On Page 3: The g is a strictly decreasing function and the ϕ represents the level set function.
Comment 2: Epsilon is not defined in 2.2
Response: Thank you very much for your valuable suggestion.
On Page 4: In practice, the Heaviside function H(ϕ) and the Dirac delta function δ(ϕ) have to be approximated by two smooth functions Hε(ϕ) and δε(ϕ) when ε 0, and they are given typically as, respectively.
Comment 3: Plenty of acronyms are not defined like ESF, SBGFRLS.
Response: Thank you very much for your valuable suggestion.
We have corrected the acronyms in this revised manuscript.
Comment 4: An improved SPF function is presented in 3.1. The new ACM method that can be applied to non homogeneous images and is independent of the initial position is described in 3.2. The mathematic models could be more comprehensive if their description was assisted graphically (displaying the inner/outer regions, where each function is applied etc).
Response: Thank you very much for your valuable suggestion.
First, if the mathematic models can be comprehensive to their description assisted graphically, it is an interesting thing. Following the described mathematic models about the C-V [11], the SBGFRLS [23], the LBF [24], the LSACM [28], the LIF [31], etc, I have not found the same description.
Second, on Page 7: It is noted that the selection of the weight parameter λ is important to control the influence of the local and the global terms. Li et al. [44] declared that the local term is rigorous to the initialization to some extent and the global one is incorporated into the local framework thereby forming a hybrid ACM. Then, with the mutual assistance of the local and the global forces, the robustness to the initialization can be improved, and the global force is dominant if the evolution curve is away from the object. When the contour is placed and is near to the object boundaries, the LIF model plays a dominant role, and the fine details can be detected accurately. In contrast, the new SPF model plays a key role when the contour is located far away from the object boundaries, and owing to the assistance of the SPF, a flexible initialization is allowed. It follows that the automatic adjustment between the LIF and SPF models in our ACM is very obvious. Furthermore, the objective of the dynamic adjustment is to find out an optimal scheme for image segmentation.
In summary, to the best of our knowledge, the mathematic models for Subsections 3.1 and 3.2 assisted graphically is difficult. Furthermore, the additional tasks will be carried out in our future work.
Comment 5: The complexity of the proposed algorithm is given in lines 238-241 but the fact that it is simpler than other approaches is not justified enough. Generally it is not made clear why the proposed method has more advantages than other approaches. Give a table with the complexity of other approaches to compare. The proposed model is compared in MATLAB with the other described models using their matlab code available at mathworks.
Response: Thank you very much for your valuable question.
The reason for selecting these particular image segmentation approaches is as follows:
On Page 8: It is well known that the convolution operations are the most time consuming when it comes to the time complexity of an algorithm. Then, it is necessary to explain complexity of the convolution operations. When an algorithm requires a convolution operation, the time cost is approximately O(n2 × N) [45], where the size of an image is N and the Gaussian kernel is n, and N is larger than n2.
The C-V model [46] needs to be reinitialized in every iteration, so its time cost is very high and then the computational complexity is O(N2) [31]. The LBF model [24] usually needs to perform four convolution operations in each iteration, which greatly increases the computational time complexity. This situation generates that the time complexity is O(itr × 4 × n2 × N), where the parameter itr is the number of iterations. Meanwhile, the SBGFRLS model [23] has three convolution operations, two of them come from gradient calculation (horizontal and vertical) and the other is from mask image and filter mask. Thus, the total computational complexity of the SBGFRLS model is O(itr × 3 × n2 × N). The LIF model [31] includes two convolution operations in each iteration. Then, the total computational time required for the LIF model is O(itr × 2 × n2 × N). For our SPFLIF-IS algorithm, the computational complexity mainly focuses on Step 6. In Algorithm 1, Step 6 is the most time-consuming to calculate the LIF model. The computational complexity of our proposed method is O(itr × 2 × n2 × N), where n is the size of Gaussian kernel function, and N is the image size. Since in most cases, N >> n2, the complexity of SPFLIF-IS is O(N) approximately, which is close to that of LIF model in [31]. It follows that our proposed method is much more efficient computationally than the C-V model [31], the LBF model [24], and the SBGFRLS model [23]. Since the SPFLIF-IS decreases some Gaussian convolution operations, its time costs and iteration operations are drastically reduced. Therefore, the computational complexity of our SPFLIF-IS method is lower than that of the other related ACMs [6, 8, 11, 12, 15, 17, 20, 23, 24, 31, 42, 46].
Comment 6: Fig. 4 is unreadable. Use a bold line to indicate the segmentation and the border edges. The most useful comparison is the test of the proposed segmentation method on real applications instead of artificial test images as is the case in Fig. 6, Table 1.
Response: Thank you very much for your valuable suggestion.
Some quantitative studies on varying the levels of artificial noise submitted to the images are added as follows:
On Page 11: Figure 4 illustrates the original images with different intensity noise and the comparison results of the six state-of-the-art segmentation methods, where the original images without noise in Figure 4(a) are coming from [45]. For Figure 4, the Row 1 shows the original images and the segmentation results. From the Row 2 to the Row 5, we added Gaussian noise with zero means and different variances (σ = 0.01, 0.02, 0.03, and 0.05). Figure 4(c) and 4(f) show that the LBF model and the LSACM model cannot analyze the five images. Although the C-V model and the SBGFRLS model can segment the first and the second image, both models don't perform well when the intensity of noise increases and the results are shown in Figure 4(b) and 4(d). It can be observed from Figure 4(e) that the LIF model could analyze the images without Gaussian noisy well. When it comes to segment the Gaussian noisy images, the LIF model has a poor performance. As shown in Figure 4(g), the object boundaries are accurately extracted by our proposed SPFLIF-IS model.
Comment 7: Minor errors must be corrected like in: Line 109: “functional”.
Response: Thank you very much for your valuable suggestion.
On Page 2: Wang et al. [27] defined an energy functional, which combined the merits of the C-V model and the LBF model [21].
Zhao et al. [30] adopted the local region statistical information and gradient information to construct the energy functional and face same problem.
Zhang et al. [31] introduced a local image fitting (LIF) energy functional to extract the local image information, and proposed a Gaussian filtering method for variational level set to regularize the level set function, which can be interpreted as a constraint on the differences between the original image and the fitting image [12, 24].
On Pages 3 and 4: The C-V model is proposed based on the assumption that the original image intensity is homogeneous. The energy functional of the C-V model [46] is expressed as (6)
Thus, energy functional is special in the ACM.
Thank you once again for your constructive and valuable comments.
Best wishes,
Prof. Jiucheng Xu, Ph.D.,
On behalf of all authors
College of Computer and Information Engineering, Henan Normal University
Email: [email protected]
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors propose a active contour model to image segmentation. The presentation and methodology are fine and the results provided are better to other 4 state-of-art methods, almost in the hardest examples. The comparison is done visually and statistically. I suggest that the author should test the method over a wide set of images, and some texture images, in order to test the robustness of your method.
In line 162, there is not defined the term LFI or, maybe, it should be LIF.
Author Response
Dear,
We are very grateful to you for your valuable comments and suggestions. We have carefully revised the paper in accordance with these comments and suggestions. The added and modified parts are shown in red in the revised manuscript (and changes are marked). The main revisions are as follows.
Comment 1: The authors propose an active contour model to image segmentation. The presentation and methodology are fine and the results provided are better to other 4 state-of-art methods, almost in the hardest examples. The comparison is done visually and statistically. I suggest that the author should test the method over a wide set of images, and some texture images, in order to test the robustness of your method.
Response: Thank you very much for your valuable suggestion.
We have tested the method over a wide set of images and some texture images, and the results are shown as follows.
On Page 9: The five representative ACM algorithms are the state-of-the-art level set methods published recently for image segmentation. They show improvements over the classical ACM and are specially selected based on the level set method for comparison experiments. The chosen parameters for these models can be found in [23, 24, 28, 31, 46]. Then, the segmentation results of the images with intensity inhomogeneity of the six models are illustrated in Figure 2, where the original images shown in Figure 2(a) can be found in [2].
On Page 9: It can be seen from Figure 2(b), 2(d) and 2(f) that the C-V model, the SBGFRLS and the LSACM model fails to analyze the first image with intensity inhomogeneity. As shown in Figure 2(d) and 2(f), the SBGFRLS model and the LSACM model cannot get the ideal segmentation results of the second image. The object boundaries of the third image are not identified by the LIF model, and the results are shown in Figure 2(e). It can be observed from Figure 2(e) and 2(f) that the true boundaries of the fourth image are not accurately extracted by the LIF model and the LSACM model. It can be obviously seen that the SPFLIF-IS model detects the true boundary, and the results are illustrated in Figure 2(g). Meanwhile, Figure 2(c) and 2(g) shows that the LBF model performs as well as the SPFLIF-IS model.
On Page 10: Table 1 objectively describes the segmentation performance of Figure 2 in detail. It can be obviously concluded from Table 1 that the LBF performs as well as the SPFLIF-IS, the C-V exhibits a bit bad, and the LSACM achieves the worst result. Therefore, the experimental results from Figure 2 and Table 1 show that the SPFLIF-IS model can efficiently analyze the images with intensity inhomogeneity.
On Page 10: The original multi-objective images and the segmentation results of the six models are shown in Figure 3, where the original images shown in Figure 3(a) are from [41, 47]. Although our model identifies most of the boundaries of the first image, it is still a little subtle different when compared to the LBF model. As shown in Figure 3(d) and 3(f), the SBGFRLS model and the LSACM model obviously fail to segment the first, second and fourth multi-objective images. The true boundaries of the third image cannot be extracted by the C-V model, the LBF model, the SBGFRLS model and the LIF model, and the results are shown in Row 3 of Figure 3. Table 2 objectively denotes the segmentation results of Figure 3. As shown from Table 2 that the SPFLIF-IS achieves the best result, the C-V performs as well as the LBF, and the LIF exhibits the worst. It can be clearly seen from Figure3 and Table 2 that our proposed SPFLIF-IS method can segment the fourth image, but the other comparison methods cannot. The experimental results state that the SPFLIF-IS model can efficiently segment the multi-objective images.
On Page 11: Figure 4 illustrates the original images with different intensity noise and the comparison results of the six state-of-the-art segmentation methods, where the original images without noise in Figure 4(a) are coming from [45]. For Figure 4, the Row 1 shows the original images and the segmentation results. From the Row 2 to the Row 5, we added Gaussian noise with zero means and different variances (σ = 0.01, 0.02, 0.03, and 0.05). Figure 4(c) and 4(f) show that the LBF model and the LSACM model cannot analyze the five images. Although the C-V model and the SBGFRLS model can segment the first and the second image, both models don't perform well when the intensity of noise increases and the results are shown in Figure 4(b) and 4(d). It can be observed from Figure 4(e) that the LIF model could analyze the images without Gaussian noisy well. When it comes to segment the Gaussian noisy images, the LIF model has a poor performance. As shown in Figure 4(g), the object boundaries are accurately extracted by our proposed SPFLIF-IS model. Table 3 objectively states the segmentation performance of Figure 4. As we can see from Table 3, the SPFLIF-IS obtains the best results, the C-V exhibits as well as the SBGFRLS, and the LBF performs as worst as the LSACM. The experimental results demonstrate that the SPFLIF-IS model can effectively eliminate the interference of the noise and complete the segmentation of the noisy images.
On Page 12: According to Figure 5(c), 5(e) and 5(f), the object boundaries of the first image are not identified by the LBF, LIF and LSACM models, respectively. Most of the boundaries are obtained by the SBGFRLS model. However, the internal details are not recognized, and the detailed results are illustrated in Figure 5(d). It can be seen from Figure 5(e) that the LIF model fails to segment the second image. Although the C-V, LBF, SBGFRLS and LSACM models recognize the true boundaries of the second image, there is a little bit in the middle of the image, and the results are illustrated in Row 2 of the Figure 5. Table 4 objectively shows the segmentation performance of Figure 5. It is observed from Figure 5 and Table 4 that the SPFLIF-IS performs the best, the C-V exhibits the second, and the LIF shows as worst as the LSACM. Hence, the SPFLIF-IS model can eliminate the interference of the image texture and deal with the texture image well.
On Page 13: Table 5 objectively offers the segmentation performance of Figure 6. As we can see from Table 5 that the SPFLIF-IS achieves the best results, the C-V exhibits a little better than the LBF, the SBGFRLS, the LIF and the LSACM, and the LBF performs as worst as the LSACM.
On Page 14: Following the experimental techniques designed in [41, 51], the tested images were selected randomly from the BSDS500 database. Note that BSDS500 contains hundreds of natural images and their ground-truth segmentation maps generated by multiple individuals [39, 52]. To enhance the coherency of our work with the above algorithms, three comparative experiments are performed on many real-world color images, which are selected from the Berkeley segmentation data set 500 (BSDS500) composed of a set of natural images.
On Page 14: The first port of this experiment is to evaluate the value of the DICE coefficient on twenty representative real color images, which are chosen from the Berkeley segmentation data set 500 (BSDS500). These contrasted algorithms include the C-V model [46], the LBF model [24], and the LIF model [31].
On Page 14: As we can see from Table 6, the SPFLIF-IS method achieves the best values for the DICE on the twenty image data and the Mean is also the largest. The results indicate that our SPFLIF-IS model outperforms the C-V, LBF and LIF models. In summary, these results demonstrate that our SPFLIF-IS method is indeed efficient and outperforms these currently available approaches.
On Page 15: In what follows, the section of this experiment is to test the value of the JSI coefficient on the twenty representative real-world color images in Table 6. These compared algorithms are still the C-V model [46], the LBF model [24] and the LIF model [31].
On Page 15: It can be shown from Figure 7 that the SPFLIF-IS method exhibits the best values for the JSI on the twenty image data. For the image IDs: 3063, 14092, 41006, and 147091 the JSI values of the C-V model are very near to that of the SPFLIF-IS model. On the image ID: 227092, the JSI values of the C-V and LBF models are close to that of the SPFLIF-IS model. However, it is obviously observed from Figure 7 that the SPFLIF-IS method performs the great values of JSI than the C-V, LBF and LIF models.
On Pages 15 and 16: In the final part of this experiment, to fully validate the advantages of our SPFLIF-IS method in terms of DICE and JSI, the five state-of-the-art methods including (1) the C-V model [46], (2) the LBF model [24], (3) the LIF model [31], (4) the SBGFRLS model [23], and (5) the LSACM model [28] are performed on the eight real color image data selected from the Berkeley segmentation data set 500 (BSDS500). The experimental results are shown in Table 7, where the Mean describes the average values of DICE and JSI of all test image data.
On Page 16: It follows from Table 7 that the values of DICE and JSI of the SPFLIF-IS method are the highest on the eight real image data, and the Mean is also the largest. Thus, the experimental results on synthetic and real images further demonstrate the superior performance of our method. In summary, our model is able to get better results on the DICE and JSI values than those compared methods.
Comment 2: In line 162, there is not defined the term LFI or, maybe, it should be LIF.
Response: Thank you very much for your valuable suggestion.
We have modified it in this revision.
On Page 2: Zhang et al. [31] introduced a local image fitting (LIF) energy functional to extract the local image information, and proposed a Gaussian filtering method for variational level set to regularize the level set function, which can be interpreted as a constraint on the differences between the original image and the fitting image [12, 24].
On Page 5: The local fitted image (LFI) formulation [31] is defined based on the local image information, based on which the LIF model is investigated.
Thank you once again for your constructive and valuable comments.
Best wishes,
Prof. Jiucheng Xu, Ph.D.,
On behalf of all authors
College of Computer and Information Engineering, Henan Normal University
Email: [email protected]
Author Response File: Author Response.pdf
Reviewer 3 Report
Please see the attached comment sheet.
Comments for author File: Comments.pdf
Author Response
Dear,
We are very grateful to you for your valuable comments and suggestions. We have carefully revised the paper in accordance with these comments and suggestions. The added and modified parts are shown in red in the revised manuscript (and changes are marked). The main revisions are as follows.
Comment 1: Line 247 the authors stated that the Gaussian kernel size should be selected based on expert experience. What were the actual size set and who were the experts who determined the size?
Response: Thank you very much for your valuable suggestion.
The reason that the Gaussian kernel size is set is as follows:
On Pages 8 and 9: The Gaussian kernel plays an important role in practical applications, which is as a scale parameter controlling the region-scalability from small neighborhood to the whole image domain [31]. In general, the value of scale parameter should be appropriately selected from the practical images. It is well known that if its value is too small, this may cause undesirable result, and if the value is too large, this can lead to high computational complexity [31, 35]. Thus, the Gaussian kernel size supervising the regularization of the level set function should be chosen according to the practical cases [35]. Following the experimental techniques designed in [31, 35], the σ selected in our experiments is typically less than 10.
Comment 2: In Sections 4.2-4.5, the authors showed the segmentation results obtained from the five tested models and compared them to the results obtained by the SPFLIF-IS model. The authors claimed that the SPFLIF-IS model appeared to outperform all four test image sets based on their “visual evaluations”. Since visual evaluations are subjective measures, the authors should clearly label each failure with reasons to avoid ambiguity. I will illustrate my view point below.
Response: Thank you very much for your valuable suggestion.
We have added some tables to defend the arguments for all tested image sets in the revised manuscript as follow:
On Page 10: Note that since the visual evaluations in Figure 2 are partial to the subjective measures, to strengthen the objective results of our experiments, the corresponding tables have been added to defend the arguments for all the tested images in the following visual evaluations, in which each failure is clearly labelled to avoid ambiguity. In order to more clearly illustrate this state, some special symbols are adopted in tables as follows: F1: fail to detect boundaries, F2: non-ideal boundaries detected, F3: fail to detect internal boundaries, and T: true boundaries detected. Then, Table 1 objectively describes the segmentation performance of Figure 2 in detail. It can be obviously concluded from Table 1 that the LBF performs as well as the SPFLIF-IS, the C-V exhibits a bit bad, and the LSACM achieves the worst result. Therefore, the experimental results from Figure 2 and Table 1 show that the SPFLIF-IS model can efficiently analyze the images with intensity inhomogeneity.
On Page 10: Table 2 objectively denotes the segmentation performance of Figure 3. As shown from Table 2 that the SPFLIF-IS achieves the best result, the C-V performs as well as the LBF, and the LIF exhibits the worst. It can be clearly seen from Figure3 and Table 2 that our proposed SPFLIF-IS method can segment the fourth image, but the other comparison methods cannot.
On Page 11: Table 3 objectively states the segmentation performance of Figure 4. As we can see from Table 3, the SPFLIF-IS obtains the best results, the C-V exhibits as well as the SBGFRLS, and the LBF performs as worst as the LSACM.
On Page 12: Table 4 objectively shows the segmentation performance of Figure 5. It is observed from Figure 5 and Table 4 that the SPFLIF-IS performs the best, the C-V exhibits the second, and the LIF shows as worst as the LSACM.
On Page 13: Table 5 objectively offers the segmentation performance of Figure 6. As we can see from Table 5 that the SPFLIF-IS achieves the best results, the C-V exhibits a little better than the LBF, the SBGFRLS, the LIF and the LSACM, and the LBF performs as worst as the LSACM.
Comment 3: Line 269 the authors reported that the other models get the ideal segmentation results of the second image. But as I examined the second image processed by the LSACM model, the segmentation result is not ideal. As such, this result should be interpreted as a failure. Also, my visual evaluations showed that the LBF performed as well as the SPFLIF-IS method. So, the claim that the SPLIF-IS model outperformed all other model cannot be justified by this experiment.
Response: Thank you very much for your valuable suggestion.
We have modified it in the revised manuscript as follow:
On Page 9: It can be seen from Figure 2(b), 2(d) and 2(f) that the C-V model, the SBGFRLS and the LSACM model fail to analyze the first image with intensity inhomogeneity. As shown in Figure 2(d) and 2(f), the SBGFRLS model and the LSACM model cannot get the ideal segmentation results of the second image. The object boundaries of the third image are not identified by the LIF model, and the results are shown in Figure 2(e). It can be observed from Figure 2(e) and 2(f) that the true boundaries of the fourth image are not accurately extracted by the LIF model and the LSACM model. It can be obviously seen that the SPFLIF-IS model detects the true boundary, and the results are illustrated in Figure 2(g). Meanwhile, Figure 2(c) and 2(g) shows that the LBF model performs as well as the SPFLIF-IS model.
Comment 4: Line 285 the authors reported that the object boundaries of the four images are accurately extracted by our SPFLIF-IS model, and the results are demonstrated in Figure 3(g). The experimental results state that the SPFLIF-IS model can efficiently segment the multi-objective images. But my visual evaluations showed that none of the model correctly extracted the internal boundary except for the LBF model, although it is somehow vague whether or not an internal boundary does exist without seeing the clear original object picture. So, it is hard to say that the SPFLIF-IS model performed best in this case. As a reference, my evaluations are given below. I would recommend that the authors add tables like the above to defend their arguments for all four tested image sets to strengthen their claims.
Response: Thank you very much for your valuable suggestion.
We have added the evaluations and tables to strengthen our claims as follows:
On Page 10: The original multi-objective images and the segmentation results of the six models are shown in Figure 3, where the original images shown in Figure 3(a) are from [41, 47]. Although our model identifies most of the boundaries of the first image, it is still a little subtle different when compared to the LBF model. As shown in Figure 3(d) and 3(f), the SBGFRLS model and the LSACM model obviously fail to segment the first, second and fourth multi-objective images. The true boundaries of the third image cannot be extracted by the C-V model, the LBF model, the SBGFRLS model and the LIF model, and the results are shown in Row 3 of Figure 3. Table 2 objectively denotes the segmentation performance of Figure 3. As shown from Table 2 that the SPFLIF-IS achieves the best result, the C-V performs as well as the LBF, and the LIF exhibits the worst. It can be clearly seen from Figure3 and Table 2 that our proposed SPFLIF-IS method can segment the fourth image, but the other comparison methods cannot. The experimental results state that the SPFLIF-IS model can efficiently segment the multi-objective images.
Comment 5: Line 361 why only the C-V, the LBF and the LIF models were compared against the SPFLIF-IS models but not the SBGFRLS and the LSACM models? The authors should conduct additional experiments to also include these two models so as to support their claims that the SPFLIF-IS models outperformed all other five models through qualitative and quantitative tests. Otherwise, they have to make it clear that these two models were only tested through subjective visual evaluations.
Response: Thank you very much for your valuable question.
We have added the experiments as follows:
On Page 14: Following the experimental techniques designed in [41, 51], the tested images were selected randomly from the BSDS500 database. Note that BSDS500 contains hundreds of natural images and their ground-truth segmentation maps generated by multiple individuals [39, 52]. To enhance the coherency of our work with the above algorithms, three comparative experiments are performed on many real-world color images, which are selected from the Berkeley segmentation data set 500 (BSDS500) composed of a set of natural images.
On Page 14: The first port of this experiment is to evaluate the value of the DICE coefficient on twenty representative real color images, which are chosen from the Berkeley segmentation data set 500 (BSDS500). These contrasted algorithms include the C-V model [46], the LBF model [24], and the LIF model [31].
On Page 15: In what follows, the section of this experiment is to test the value of the JSI coefficient on the twenty representative real-world color images in Table 6. These compared algorithms are still the C-V model [46], the LBF model [24] and the LIF model [31].
On Pages 15 and 16: In the final part of this experiment, to fully validate the advantages of our SPFLIF-IS method in terms of DICE and JSI, the five state-of-the-art methods including (1) the C-V model [46], (2) the LBF model [24], (3) the LIF model [31], (4) the SBGFRLS model [23], and (5) the LSACM model [28] are performed on the eight real color image data selected from the Berkeley segmentation data set 500 (BSDS500). The experimental results are shown in Table 7, where the Mean describes the average values of DICE and JSI of all test image data.
It can be known from the above experimental analysis that our proposed method is designed based on an improved SPF function and the LIF model. The model combines the merits of the global image information with the local image information, which can segment the noisy images and the multi-objective images well. However, the C-V model and the SBGFRLS model are constructed with only the global image information, which is based on the assumption that the region to be segmented is homogeneous. Unfortunately, this assumption does not suit for the intensity inhomogeneous images [2, 31, 34]. The LBF model and LIF model use the local information of an image to segment the intensity inhomogeneous images and obtains the desirable segmentation results. So they are sensitive to the initial position and image noise [2, 35]. The LSACM model is proposed based on the local statistical information of an image, so this model is robust to noise while suppressing the intensity overlapping to some extent. Nevertheless, this model is assumed that the image gray is separable in a relatively small area and the offset is smooth in the whole image area. The model is easily trapped in a local minimum and has high computational complexity [55, 56]. It follows from Table 7 that the values of DICE and JSI of the SPFLIF-IS method are the highest on the eight real image data, and the Mean is also the largest. Thus, the experimental results on synthetic and real images further demonstrate the superior performance of our method. In summary, our model is able to get better results on the DICE and JSI values than those compared methods.
Thank you once again for your constructive and valuable comments.
Best wishes,
Prof. Jiucheng Xu, Ph.D.,
On behalf of all authors
College of Computer and Information Engineering, Henan Normal University
Email: [email protected]
Author Response File: Author Response.pdf
Reviewer 4 Report
This paper presents an approach to segment image using active contours method. They propose an improved version of SPF and LIF methods. The proposed approach semmes to be interesting and provide good results.
The related knowledge section is full of equations, they are needed of course but some visual examples can deeply improve the understanding of the existing approaches.
The proposed approach section also lacks of illustrations. Moreover, the fig. 1 illustrating the process of image segmentation is not very clear and blend data and process with same block types. The algorithm 1 is poorly written, no indentation, considering beginning and end of loop as steps obfusctae our understanding of the algorithm, please improve it.
In section 4, please indicate URLs of existing approaches source code in footnotes not int the paragraph. Moreover, you indicate where to find code of existing approach but do not propose sources for your code, please provide it. We need more reproducible research.
Please explain more deeply the different results, we can observe that your approach is performing better than others but we need to know why. Could you explain why some are perfoming bad and yours not ?
As your approach seems to be robust to noise, I suggest you to add an experiment on Berkeley database but on noisy images. moreover, considering your experiment on Berkeley you present only some images results, could you provide results on the whole database in order to prove that it is not just some well-chosen examples ? You can use mean or median JSI and DICE for comparing the approaches.
Please provide some perspectives in your conclusion.
Author Response
Dear,
We are very grateful to you for your valuable comments and suggestions. We have carefully revised the paper in accordance with these comments and suggestions. The added and modified parts are shown in red in the revised manuscript (and changes are marked). The main revisions are as follows.
Comment 1: The related knowledge section is full of equations, they are needed of course but some visual examples can deeply improve the understanding of the existing approaches.
Response: Thank you very much for your valuable suggestion.
First, if some visual examples are given to be able to deeply improve the understanding of the existing approaches, I think that it is an interesting thing. Following the described mathematic models about the GAC model in [21, 23, 44], the C-V model in [2, 21, 23, 31, 32, 34, 41], the SBGFRLS model in [21, 35], the LIF model in [31, 32, 41], etc, I have not found the description of visual examples.
Second, it is known that the process of image segmentation using the abovementioned models is dynamically adjusted. Then, to the best of our knowledge, some visual examples of the mathematic models are difficultly achieved. Furthermore, the additional tasks will be carried out in our future work.
Comment 2: The proposed approach section also lacks of illustrations.
Response: Thank you very much for your valuable suggestion.
First, if the mathematic models can be more comprehensive to their description assisted graphically, it is an interesting thing. Following the described mathematic models about the C-V [11], the SBGFRLS [23], the LBF [24], the LSACM [28], the LIF [31], etc, I have not found the same description.
Second, on Page 7: It is noted that the selection of the weight parameter λ is important to control the influence of the local and the global terms. Li et al. [44] declared that the local term is rigorous to the initialization to some extent and the global one is incorporated into the local framework thereby forming a hybrid ACM. Then, with the mutual assistance of the local and the global forces, the robustness to the initialization can be improved, and the global force is dominant if the evolution curve is away from the object. When the contour is placed and is near to the object boundaries, the LIF model plays a dominant role, and the fine details can be detected accurately. In contrast, the new SPF model plays a key role when the contour is located far away from the object boundaries, and owing to the assistance of the SPF, a flexible initialization is allowed. It follows that the automatic adjustment between the LIF and SPF models in our ACM is very obvious. Furthermore, the objective of the dynamic adjustment is to find out an optimal scheme for image segmentation.
In summary, to the best of our knowledge, the mathematic models for Subsections 3.1 and 3.2 assisted graphically is difficult. Furthermore, the additional tasks will be carried out in our future work.
Comment 3: Moreover, the fig. 1 illustrating the process of image segmentation is not very clear and blend data and process with same block types. The algorithm 1 is poorly written, no indentation, considering beginning and end of loop as steps obfusctae our understanding of the algorithm, please improve it.
Response: Thank you very much for your valuable suggestion.
We have made the suggested revision, and the results are shown in Figure 1 and Table 1.
Comment 4: In section 4, please indicate URLs of existing approaches source code in footnotes not int the paragraph. Moreover, you indicate where to find code of existing approach but do not propose sources for your code, please provide it. We need more reproducible research.
Response: Thank you very much for your valuable suggestion.
First, the URLs of existing approaches source code have been indicated in footnotes as follows:
On Page 9:
[1]The code can be available at: http://www.math.ucla.edu/~xbresson/code.html
2The code can be available at: http://www.engr.uconn.edu/~cmli/
3The code can be available at: http://www4.comp.polyu.edu.hk/~cslzhang /papers.htm
4The code can be available at: http://www4.comp.polyu.edu.hk/~cslzhang /papers.htm
On Page 13:
5The code can be available at:
https://www2.eecs.berkeley.edu/Research/ Projects/CS/vision/ bsds/.
Second, I would like to provide sources for our code at personal homepages (http://www.escience.cn/people/slin/index.html) if our manuscript is accepted.
Comment 5: Please explain more deeply the different results, we can observe that your approach is performing better than others but we need to know why. Could you explain why some are perfoming bad and yours not?
Response: Thank you very much for your valuable question.
The explanations of the different results and the disadvantages of the other models are described as follows:
On Page 16: It can be known from the above experimental analysis that our proposed method is designed based on an improved SPF function and the LIF model. The model combines the merits of the global image information with the local image information, which can segment the noisy images and the multi-objective images well. However, the C-V model and the SBGFRLS model are constructed with only the global image information, which is based on the assumption that the region to be segmented is homogeneous. Unfortunately, this assumption does not suit for the intensity inhomogeneous images [2, 31, 34]. The LBF model and LIF model use the local information of an image to segment the intensity inhomogeneous images and obtains the desirable segmentation results. So they are sensitive to the initial position and image noise [2, 35]. The LSACM model is proposed based on the local statistical information of an image, so this model is robust to noise while suppressing the intensity overlapping to some extent. Nevertheless, this model is assumed that the image gray is separable in a relatively small area and the offset is smooth in the whole image area. The model is easily trapped in a local minimum and has high computational complexity [55, 56]. It follows from Table 7 that the values of DICE and JSI of the SPFLIF-IS method are the highest on the eight real image data, and the Mean is also the largest. Thus, the experimental results on synthetic and real images further demonstrate the superior performance of our method. In summary, our model is able to get better results on the DICE and JSI values than those compared methods.
Comment 6: As your approach seems to be robust to noise, I suggest you to add an experiment on Berkeley database but on noisy images. Moreover, considering your experiment on Berkeley you present only some images results, could you provide results on the whole database in order to prove that it is not just some well-chosen examples? You can use mean or median JSI and DICE for comparing the approaches.
Response: Thank you very much for your valuable suggestion.
First, the quantitative studies on varying the levels of artificial noise submitted to the images are added as follows:
On Pages 11: Figure 4 illustrates the original images with different intensity noise and the comparison results of the six state-of-the-art segmentation methods, where the original images without noise in Figure 4(a) are coming from [45]. For Figure 4, the Row 1 shows the original images and the segmentation results. From the Row 2 to the Row 5, we added Gaussian noise with zero means and different variances (σ = 0.01, 0.02, 0.03, and 0.05). Figure 4(c) and 4(f) show that the LBF model and the LSACM model cannot analyze the five images. Although the C-V model and the SBGFRLS model can segment the first and the second image, both models don't perform well when the intensity of noise increases and the results are shown in Figure 4(b) and 4(d). It can be observed from Figure 4(e) that the LIF model could analyze the images without Gaussian noisy well. When it comes to segment the Gaussian noisy images, the LIF model has a poor performance. As shown in Figure 4(g), the object boundaries are accurately extracted by our proposed SPFLIF-IS model. Table 3 objectively states the segmentation performance of Figure 4. As we can see from Table 3, the SPFLIF-IS obtains the best results, the C-V exhibits as well as the SBGFRLS, and the LBF performs as worst as the LSACM. The experimental results demonstrate that the SPFLIF-IS model can effectively eliminate the interference of the noise and complete the segmentation of the noisy images.
Second, on Page 14: Following the experimental techniques designed in [41, 51], the tested images were selected randomly from the BSDS500 database. Note that BSDS500 contains hundreds of natural images and their ground-truth segmentation maps generated by multiple individuals [39, 52]. To enhance the coherency of our work with the above algorithms, three comparative experiments are performed on many real-world color images, which are selected from the Berkeley segmentation data set 500 (BSDS500) composed of a set of natural images.
Third, on Pages 15 and 16: In the final part of this experiment, to fully validate the advantages of our SPFLIF-IS method in terms of DICE and JSI, the five state-of-the-art methods including (1) the C-V model [46], (2) the LBF model [24], (3) the LIF model [31], (4) the SBGFRLS model [23], and (5) the LSACM model [28] are performed on the eight real color image data selected from the Berkeley segmentation data set 500 (BSDS500). The experimental results are shown in Table 7, where the Mean describes the average values of DICE and JSI of all test image data.
It can be known from the above experimental analysis that our proposed method is designed based on an improved SPF function and the LIF model. The model combines the merits of the global image information with the local image information, which can segment the noisy images and the multi-objective images well. However, the C-V model and the SBGFRLS model are constructed with only the global image information, which is based on the assumption that the region to be segmented is homogeneous. Unfortunately, this assumption does not suit for the intensity inhomogeneous images [2, 31, 34]. The LBF model and LIF model use the local information of an image to segment the intensity inhomogeneous images and obtains the desirable segmentation results. So they are sensitive to the initial position and image noise [2, 35]. The LSACM model is proposed based on the local statistical information of an image, so this model is robust to noise while suppressing the intensity overlapping to some extent. Nevertheless, this model is assumed that the image gray is separable in a relatively small area and the offset is smooth in the whole image area. The model is easily trapped in a local minimum and has high computational complexity [55, 56]. It follows from Table 7 that the values of DICE and JSI of the SPFLIF-IS method are the highest on the eight real image data, and the Mean is also the largest. Thus, the experimental results on synthetic and real images further demonstrate the superior performance of our method. In summary, our model is able to get better results on the DICE and JSI values than those compared methods.
Comment 7: Please provide some perspectives in your conclusion.
Response: Thank you very much for your valuable suggestion.
On Page 17: However, at present, it is difficult to find out a suitable Gaussian kernel size for all the images, and considering the uncertainty of real-world complex images, the proposed method will not be suitable for all the cases. As a future work, we plan to accommodate the Gaussian kernel size automatically, which is used to control the region-scalability from small neighborhood to the whole image domain. This is considered to be more accurate and efficient to segment real complex images and reduce the computational complexity.
Thank you once again for your constructive and valuable comments.
Best wishes,
Prof. Jiucheng Xu, Ph.D.,
On behalf of all authors
College of Computer and Information Engineering, Henan Normal University
Email: [email protected]
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have revised their paper and have addressed some of my comments.
More specifically the complexity analysis is satisfactory now.
The experimental results have been enriched by more experiments with clearer presentation of the targets achieved. Additional tables have been added towards this direction
As I mentioned in my initial comments I cannot follow the mathematical modeling and I asked if possible to be supported by some graphical representation. The authors' answer is that it is difficult to add such graphs and the referenced approaches do not describe graphically the mathematical modeling. I do not doubt about that but I still have difficutly in following the mathematical modeling so I leave to the editors to decide if it is adequate taking into consideration other reviewer comments if they are more confident about their opinion.
Some minor grammar errors still exist like in line 307: "as worst as"->"as worse as"
Author Response
Dear,
We are very grateful to you for your valuable comments and suggestions. We have carefully revised the paper in accordance with these comments and suggestions. The changes are marked in the revised manuscript. The main revisions are as follows.
Comment 1: As I mentioned in my initial comments I cannot follow the mathematical modeling and I asked if possible to be supported by some graphical representation. The authors' answer is that it is difficult to add such graphs and the referenced approaches do not describe graphically the mathematical modeling. I do not doubt about that but I still have difficutly in following the mathematical modeling so I leave to the editors to decide if it is adequate taking into consideration other reviewer comments if they are more confident about their opinion.
Response: Thank you very much for your valuable suggestion.
We have added some graphical representation of our model in Figure 1 as follows:
Comment 2: Some minor grammar errors still exist like in line 307: "as worst as"->"as worse as"
Response: Thank you very much for your valuable suggestion.
We have corrected the mistakes in this revised manuscript. In addition, American Journal Experts helped us revise the entire manuscript carefully to correct English grammar, spelling, and sentence structure so that the goals and results of the study are clear to the reader, shown in the revision with marked changes.
Thank you once again for your constructive and valuable comments.
Best wishes,
Prof. Jiucheng Xu, Ph.D.,
On behalf of all authors
College of Computer and Information Engineering, Henan Normal University
Email: [email protected]
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors have properly addressed all my concerns by adding additional examples, illustrations and experiments to show the superiority of the SPFLIF-IS method over other methods tested. These efforts are not trivial, and they should be acknowledged for their hard work. I only have two more recommendations to be made to the authors as shown below.
(1) The authors should calculate the percentage of correct detection for each method. And it should be reported in Tables 2-5 by adding a bottom row (labeled as “correctness %”) to each table.
(2) Line 393
….there is a little bit what?
The authors may just state that "nonexistent boundaries were incorrectly detected in the middle of the image
Author Response
Dear,
We are very grateful to you for your valuable comments and suggestions. We have carefully revised the paper in accordance with these comments and suggestions. The changes are marked in the revised manuscript. The main revisions are as follows.
Comment 1: The authors should calculate the percentage of correct detection for each method. And it should be reported in Tables 2-5 by adding a bottom row (labeled as “correctness %”) to each table.
Response: Thank you very much for your valuable suggestion.
First, it would be interesting if the percentage of correct detection for each method could be calculated. Following the experimental analysis of the C-V model [46], the LBF model [24], the LIF model [31], the SBGFRLS model [23], and the LSACM model [28], etc, I have not found the same description to my best knowledge after searching for several days. The reason is that the ground-truth segmentation is generally marked by experts manually. Because the ground-truth segmentation of these images has not been presented in [23, 24, 28, 31, 46], it is difficult to calculate the percentage of correct detection for each method. In Figures 3-6 and Tables 1-5, we employed these experiments to prove the validity of our proposed algorithm compared with the other related algorithms. Thus, the requested work will be taken into account in our future work.
Second, some of these tasks requested have been done in Subsection 4.7, and the segmentation results are shown in Tables 6, 7 and Figure 7, where the DICE and JSI values were selected to assess the accuracy of the target region segmentation of our model compared with other methods, and many test images are selected from the BSDS500 database that contains hundreds of natural images whose ground-truth segmentation maps have been generated by multiple individuals [39, 52].
Comment 2: Line 393….there is a little bit what? The authors may just state that "nonexistent boundaries were incorrectly detected in the middle of the image.
Response: Thank you very much for your valuable suggestion.
We have corrected the mistakes in this revised manuscript. In addition, American Journal Experts helped us revise the entire manuscript carefully to correct English grammar, spelling, and sentence structure so that the goals and results of the study are clear to the reader, shown in the revision with marked changes.
Thank you once again for your constructive and valuable comments.
Best wishes,
Prof. Jiucheng Xu, Ph.D.,
On behalf of all authors
College of Computer and Information Engineering, Henan Normal University
Email: [email protected]
Author Response File: Author Response.pdf
