KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation
Abstract
:1. Introduction
2. Related Work
2.1. Fuzzy C-Means
2.2. Local Spatial Fuzzy C-Means
2.3. Cluster Ensemble
3. KL Divergence-Based Fuzzy Cluster Ensemble
3.1. Formulation of the Fuzzy Cluster Ensemble Problem
3.2. Fuzzy Cluster Ensemble Based on KL Divergence ()
3.3. Spatial Information-Based
Algorithm 1: |
Input: Normalized partitions , values of the fuzzification coefficient m, maximum iteration number and a small enough error Output: The consensus clustering;
|
4. Experiment Results
4.1. Synthetic Images
4.2. Real Images
5. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
Fuzzy cluster ensemble method based on KL divergence | |
Spatial |
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0.7 | 0.2 | 0.1 | 0.1 | 0.7 | 0.2 | 0.7 | 0.2 | 0.1 | 0.1 | 0.7 | 0.2 | 0.35 | 0.10 | 0.05 | 0.05 | 0.35 | 0.10 | ||||
0.9 | 0.1 | 0.0 | 0.0 | 0.8 | 0.2 | 0.9 | 0.1 | 0.0 | 0.0 | 0.8 | 0.2 | 0.45 | 0.05 | 0.00 | 0.00 | 0.40 | 0.10 | ||||
0.2 | 0.6 | 0.2 | 0.1 | 0.1 | 0.8 | 0.2 | 0.6 | 0.2 | 0.1 | 0.1 | 0.8 | 0.10 | 0.30 | 0.10 | 0.05 | 0.05 | 0.40 | ||||
0.1 | 0.9 | 0.0 | 0.2 | 0.1 | 0.7 | 0.1 | 0.9 | 0.0 | 0.2 | 0.1 | 0.7 | 0.05 | 0.45 | 0.00 | 0.10 | 0.05 | 0.35 | ||||
0.1 | 0.2 | 0.7 | 0.6 | 0.2 | 0.2 | 0.1 | 0.2 | 0.7 | 0.6 | 0.2 | 0.2 | 0.05 | 0.10 | 0.35 | 0.30 | 0.10 | 0.10 |
SA | SFCM | SSCM | NLSFCM | NLSSCM | ||
---|---|---|---|---|---|---|
1% Gaussian | ||||||
3% Gaussian | ||||||
5% Gaussian | ||||||
10% Gaussian | 0.9992 | 0.9992 | 0.9996 | 0.9996 | 0.9996 | |
15% Gaussian | 0.9984 | 0.9980 | 0.9992 | 0.9992 | 0.9992 | |
20% Gaussian | 0.9928 | 0.9932 | 0.9988 | 0.9988 | 0.9988 | |
30% Gaussian | 0.9732 | 0.9760 | 0.9976 | 0.9976 | 0.9956 | |
50% Gaussian | 0.9100 | 0.9148 | 0.9916 | 0.9916 | 0.9808 | |
1% Rician | ||||||
3% Rician | ||||||
5% Rician | ||||||
10% Rician | ||||||
15% Rician | ||||||
20% Rician | ||||||
30% Rician | 0.9956 | 0.9960 | 0.9988 | 0.9988 | 0.9988 | |
50% Rician | 0.8640 | 0.8664 | 0.9744 | 0.9828 | 0.9678 |
SA | SFCM | SSCM | NLSFCM | NLSSCM | ||
---|---|---|---|---|---|---|
10% Gaussian | 0.9817 | 0.9878 | 0.9946 | 0.9951 | 0.9966 | |
12% Gaussian | 0.9563 | 0.9712 | 0.9893 | 0.9817 | 0.9922 | |
15% Gaussian | 0.8979 | 0.9348 | 0.9800 | 0.9670 | 0.9797 | |
18% Gaussian | 0.8420 | 0.8896 | 0.9624 | 0.9138 | 0.9631 | |
20% Gaussian | 0.8218 | 0.8457 | 0.9290 | 0.8937 | 0.9468 | |
25% Gaussian | 0.7729 | 0.7773 | 0.7847 | 0.7813 | 0.9026 | |
30% Gaussian | 0.6860 | 0.7446 | 0.7341 | 0.7539 | 0.7239 | |
10% Rician | 0.9839 | 0.9917 | 0.9919 | 0.9934 | 0.9954 | |
12% Rician | 0.8782 | 0.9768 | 0.9817 | 0.9888 | 0.9897 | |
15% Rician | 0.7578 | 0.7136 | 0.9209 | 0.9670 | 0.9758 | |
18% Rician | 0.7114 | 0.7112 | 0.7886 | 0.9526 | 0.9570 | |
20% Rician | 0.6799 | 0.7085 | 0.7598 | 0.8413 | 0.9377 | |
25% Rician | 0.6650 | 0.6775 | 0.7681 | 0.7531 | 0.8472 | |
30% Rician | 0.6287 | 0.6406 | 0.6914 | 0.6818 | 0.7832 |
SA | SFCM | SSCM | NLSFCM | NLSSCM | ||
---|---|---|---|---|---|---|
25% Rician | 0.8523 | 0.8125 | 0.8438 | 0.9543 | 0.9692 | |
27% Rician | 0.8473 | 0.8117 | 0.8411 | 0.8504 | 0.9669 | |
30% Rician | 0.8405 | 0.8070 | 0.8391 | 0.8411 | 0.9605 | |
32% Rician | 0.8373 | 0.8026 | 0.8393 | 0.8339 | 0.9559 | |
35% Rician | 0.8321 | 0.7966 | 0.8390 | 0.8317 | 0.9485 | |
40% Rician | 0.8160 | 0.7903 | 0.8395 | 0.8249 | 0.9361 | |
50% Rician | 0.7804 | 0.7784 | 0.8610 | 0.7911 | 0.9074 |
12% Rician Noise | SFCM | SSCM | NLSFCM | NLSSCM | ||
---|---|---|---|---|---|---|
SA | 0.7293 | 0.7400 | 0.7181 | 0.7163 | 0.7247 | |
0.7463 | 0.7530 | 0.7297 | 0.7247 | 0.7381 | ||
0.7099 | 0.7256 | 0.7055 | 0.7073 | 0.7098 |
15% Rician Noise | SFCM | SSCM | NLSFCM | NLSSCM | ||
---|---|---|---|---|---|---|
SA | 0.7079 | 0.7237 | 0.7023 | 0.7093 | 0.7098 | |
0.7281 | 0.7431 | 0.7248 | 0.7421 | 0.7369 | ||
0.6844 | 0.7012 | 0.6758 | 0.6670 | 0.6763 |
18% Rician Noise | SFCM | SSCM | NLSFCM | NLSSCM | ||
---|---|---|---|---|---|---|
SA | 0.6744 | 0.7014 | 0.6879 | 0.7028 | 0.6953 | |
0.7031 | 0.7268 | 0.7205 | 0.7584 | 0.7338 | ||
0.6395 | 0.6708 | 0.6467 | 0.6139 | 0.6438 |
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Wei, H.; Chen, L.; Guo, L. KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation. Entropy 2018, 20, 273. https://doi.org/10.3390/e20040273
Wei H, Chen L, Guo L. KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation. Entropy. 2018; 20(4):273. https://doi.org/10.3390/e20040273
Chicago/Turabian StyleWei, Huiqin, Long Chen, and Li Guo. 2018. "KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation" Entropy 20, no. 4: 273. https://doi.org/10.3390/e20040273
APA StyleWei, H., Chen, L., & Guo, L. (2018). KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation. Entropy, 20(4), 273. https://doi.org/10.3390/e20040273