A Novel Image Processing Approach for Colloid Detection in Saturated Porous Media
Abstract
:1. Introduction
- To detect colloids in porous media, we apply image processing techniques to microscopic images in four different groups and compare their results, which has never been done before.
- The best methods in the field of colloid detection are introduced based on various experiments and several evaluation criteria.
- We propose an ensemble approach to perform the detection process of colloids more effectively through majority voting.
- The proposed methods can detect colloids with high accuracy, despite their simplicity and high speed.
2. Experimental Setup
2.1. Solution and Particles
2.2. Porous Media
2.3. Experimental Procedure
3. The Proposed Detection Methods
3.1. Segmentation-Based Methods
3.1.1. k-Means Clustering
- k samples are selected at random from the set X = { to be considered as the clusters’ initial centers. We take into account the cluster centers as .
- Each sample in X is placed in a cluster that is nearer to its center as follows:
- The new cluster centers are calculated using the following equation, if signify them:
- If for i = 1, 2, …, k, then the algorithm terminates; otherwise, it loops back to step 2.
3.1.2. Otsu Method
- Create the grayscale histogram H for image I by counting the number of pixels at each intensity level i as the following formula:
- Calculate the Cumulative Distribution Function (CDF) as follows:
- Calculate the mean grayscale intensity value of the image to obtain the inter-class variance as follows:
- Calculate the inter-class variance for each possible threshold value. The mathematical formulation for the threshold value T is as follows:Additionally, the mean grayscale intensity values of the background and foreground regions are specified as and . These values can be computed as follows:
- Track down the threshold value that maximizes the inter-class variance based on the following equation:
3.2. Background-Detection-Based Methods
3.2.1. Frame Differencing Plus Background Subtraction (FDBS)
- The frame difference between A and B is carried out, and the result is expressed as C.
- A background subtraction of frame A with the background model is performed, and the result is expressed as D.
- The logical AND operation between C and D is performed to obtain a result frame containing detected colloids.
3.2.2. Multi-Frame Differencing (MFD)
3.3. Filter-Based Methods
3.3.1. Laplacian Filter
3.3.2. Difference of Gaussians (DoG) Filters
3.4. Morphology-Based Methods
3.4.1. Structuring Element
- Let ; B is an open disk with a radius of r and origin-centered.
- Let ; B is a 3-by-3 square; thus, B = {(−1, −1), (−1, 0), (−1, 1), (0, −1), (0, 0), (0, 1), (1, −1), (1, 0), (1, 1)}.
- Let ; B is the “cross” indicated by B = {(−1, 0), (0, −1), (0, 0), (0, 1), (1, 0)}.
3.4.2. Basic Operations
- ❖
- Erosion
- ❖
- Dilation
- ❖
- Opening
- ❖
- Top-hat
3.5. Ensemble Approach
4. Methods and Materials
4.1. Performance Evaluation Metrics
4.1.1. Precision, Recall, and F-Measure
- True positive (TP): detecting a target correctly;
- False positive (FP): detecting a nonexistent target incorrectly, or a misplaced detection of an existing target;
- False negative (FN): a target that has not been detected.
4.1.2. Target-to-Clutter Ratio (TCR)
- Detected targets (DT) is the number of detected targets;
- Missed targets (MT) is the number of missed targets;
- False alarm (FA) denotes false alarm detections or incorrect detections.
4.2. Non-Parametric Statistical Test for Statistical Analysis
5. Results and Discussion
6. Summary and Conclusions
- The effectiveness of our ensemble approach was demonstrated, achieving the best results in terms of all evaluation metrics with a perfect score of one.
- After the proposed ensemble approach, the DoG filter and the top-hat operation exhibited the best detection performance on average.
- Background-detection-based methods had the worst results compared with other methods because they cannot detect non-moving colloids and colloids that move slowly. Additionally, these methods produce a lot of noise in the detection process, necessitating post-processing algorithms.
- Since small colloids do not have enough information to identify them, the dilation operation, by expanding the boundaries and increasing the size of small colloids, can improve their distinguishing features for detection and subsequent research on porous media, such as colloid tracking.
- The presented results confirmed that morphology-based methods perform the process of detecting colloids in porous media more effectively and are more useful in this field compared with the methods of the other three categories.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Types of Methods | Ranking |
---|---|
Top-hat | 2.34 |
DoG | 2.42 |
k-Means | 2.50 |
Otsu | 3.94 |
Laplacian | 4.44 |
Dilation | 5.36 |
FDBS | 7.20 |
MFD | 7.80 |
I | Methods | p-Value | Holm |
---|---|---|---|
1 | DoG vs. Top-hat | 0.908073 | 0.05 |
2 | k-Means vs. DoG | 0.908073 | 0.025 |
3 | k-Means vs. Top-hat | 0.817361 | 0.016667 |
4 | Otsu vs. Laplacian | 0.470486 | 0.0125 |
5 | FDBS vs. MDF | 0.386476 | 0.01 |
6 | Laplacian vs. Dilation | 0.184209 | 0.008333 |
7 | Otsu vs. Dilation | 0.040404 | 0.007143 |
8 | k-Means vs. Otsu | 0.037667 | 0.00625 |
9 | Otsu vs. DoG | 0.02824 | 0.005556 |
10 | Otsu vs. Top-hat | 0.020291 | 0.005 |
11 | FDBS vs. Dilation | 0.007912 | 0.004545 |
12 | k-means vs. Laplacian | 0.005108 | 0.004167 |
13 | Laplacian vs. DoG | 0.00355 | 0.003846 |
14 | Laplacian vs. Top-hat | 0.002437 | 0.003571 |
15 | MDF vs. Dilation | 0.000429 | 0.003333 |
16 | FDBS vs. Laplacian | 0.000068 | 0.003125 |
17 | k-Means vs. Dilation | 0.000037 | 0.002941 |
18 | DoG vs. Dilation | 0.000022 | 0.002778 |
19 | Dilation vs. Top-hat | 0.000013 | 0.002632 |
20 | Otsu vs. FDBS | 0.000003 | 0.0025 |
21 | MDF vs. Laplacian | 0.000001 | 0.002381 |
22 | Otsu vs. MDF | < | 0.002273 |
23 | k-Means vs. FDBS | < | 0.002174 |
24 | FDBS vs. DoG | < | 0.002083 |
25 | FDBS vs. Top-hat | < | 0.002 |
26 | k-Means vs. MDF | < | 0.001923 |
27 | MDF vs. DoG | < | 0.001852 |
28 | MDF vs. Top-hat | < | 0.001786 |
Types of Methods | Metrics | ||||
---|---|---|---|---|---|
Precision | Recall | F-Measure | TCR | ||
Segmentation-based | k-Means | 0.9949 (0.007) | 0.9799 (0.010) | 0.9873 (0.007) | 0.9752 (0.014) |
Otsu | 1.0000 (0.000) | 0.9646 (0.013) | 0.9819 (0.007) | 0.9646 (0.013) | |
Background-detection-based | FDBS | 1.0000 (0.000) | 0.7127 (0.062) | 0.8309 (0.044) | 0.7127 (0.062) |
MFD | 0.8905 (0.057) | 0.7301 (0.038) | 0.8005 (0.018) | 0.6933 (0.024) | |
Filter-based | Laplacian | 1.0000 (0.000) | 0.9595 (0.016) | 0.9793 (0.008) | 0.9595 (0.016) |
DoG | 0.9754 (0.008) | 1.0000 (0.000) | 0.9875 (0.004) | 0.9761 (0.008) | |
Morphology-based | Dilation | 0.9843 (0.006) | 0.9543 (0.026) | 0.9689 (0.015) | 0.9411 (0.029) |
Top-hat | 0.9752 (0.000) | 1.0000 (0.000) | 0.9874 (0.000) | 0.9758 (0.000) | |
Ensemble | 1.0000 (0.000) | 1.0000 (0.000) | 1.0000 (0.000) | 1.0000 (0.000) |
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Mirzaei, B.; Nezamabadi-pour, H.; Raoof, A.; Nikpeyman, V.; de Vries, E.; Derakhshani, R. A Novel Image Processing Approach for Colloid Detection in Saturated Porous Media. Sensors 2024, 24, 5180. https://doi.org/10.3390/s24165180
Mirzaei B, Nezamabadi-pour H, Raoof A, Nikpeyman V, de Vries E, Derakhshani R. A Novel Image Processing Approach for Colloid Detection in Saturated Porous Media. Sensors. 2024; 24(16):5180. https://doi.org/10.3390/s24165180
Chicago/Turabian StyleMirzaei, Behzad, Hossein Nezamabadi-pour, Amir Raoof, Vahid Nikpeyman, Enno de Vries, and Reza Derakhshani. 2024. "A Novel Image Processing Approach for Colloid Detection in Saturated Porous Media" Sensors 24, no. 16: 5180. https://doi.org/10.3390/s24165180