基于自适应模糊C均值与后处理的图像分割算法 
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Image Segmentation Based on Adaptive Fuzzy C-Means and Post Processing Correction
1 河北地质大学信息工程学院, 河北 石家庄 050031
2 河北地质大学河北省光电信息与地球探测技术重点实验室, 河北 石家庄 050031
图 & 表
图 1. 3×3含噪区域。(a)(b)高斯噪声;(c)(d)混合噪声
Fig. 1. 3×3 window with noise. (a)(b) Gaussian noise; (c)(d) mixed noise
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图 2. 某邻域隶属度和分类标签。(a)标签为1的隶属度;(b)标签为2的隶属度;(c)分类标签
Fig. 2. Membership andcluster label of neighborhood. (a) membership of label 1; (b) membership of label 2; (c) cluster label
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图 3. 添加高斯噪声(0,0.03)的合成图像分割图。(a)原始图像;(b)高斯噪声图像;(c) FCM_S1算法;(d) FCM_S2算法;(e) EnFCM算法;(f) FGFCM算法;(g) FLICM算法;(h) NDFCM_P算法;(i) FNDFCM_P算法
Fig. 3. Segmentation of synthetic image with Gaussian noise(0, 0.03). (a) Original image; (b) image with Gaussian noise (0, 0.03); (c) FCM_S1algorithm; (d) FCM_S2 algorithm; (e) EnFCM algorithm; (f) FGFCM algorithm; (g) FLICM algorithm; (h) NDFCM_P algorithm; (i) FNDFCM_P algorithm
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图 4. 添加椒盐噪声(0.1)的合成图像分割图。(a)原始图像;(b)高斯噪声图像;(c) FCM_S1算法;(d) FCM_S2算法; (e) EnFCM算法;(f) FGFCM算法;(g) FLICM算法;(h) NDFCM_P算法;(i) FNDFCM_P算法
Fig. 4. Segmentation of synthetic image with salt & pepper noise (0.1). (a) Original image; (b) image with salt & pepper noise (0.1); (c) FCM_S1 algorithm; (d) FCM_S2 algorithm; (e) EnFCM algorithm; (f) FGFCM algorithm; (g) FLICM algorithm; (h) NDFCM_P algorithm; (i) FNDFCM_P algorithm
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图 5. 不同邻域的人工合成分割结果对比图。(a) NDFCM_P算法;(b) FNDFCM_P算法
Fig. 5. Comparison of synthetic segmentation results in different neighborhoods. (a) NDFCM_P algorithm; (b) FNDFCM_P algorithm
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图 6. #42049分割结果。(a)原图;(b)加噪图;(c)标准人工分割图;(d) FCM_S1算法;(e) FCM_S2算法;(f) EnFCM算法;(g) FGFCM算法;(h) FLICM算法;(i) NDFCM_P算法;(j) FNDFCM_P算法
Fig. 6. Segmentation results of #42049 (a) Original image; (b) image with mixed noise; (c) standard manual segmentation; (d) FCM_S1 algorithm; (e) FCM_S2 algorithm; (f) EnFCM algorithm; (g) FGFCM algorithm; (h) FLICM algorithm; (i) NDFCM_P algorithm; (j) FNDFCM_P algorithm
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图 7. #238001分割结果。(a)原图;(b)加噪图;(c)标准人工分割图;(d) FCM_S1算法;(e) FCM_S2算法;(f) EnFCM算法;(g) FGFCM算法;(h) FLICM算法;(i) NDFCM_P算法;(j) FNDFCM_P算法
Fig. 7. Segmentation results of #238001. (a) Original image; (b) image with Salt & Pepper noise; (c) standard manual segmentation; (d) FCM_S1 algorithm;(e) FCM_S2 algorithm; (f) EnFCM algorithm; (g) FGFCM algorithm; (h) FLICM algorithm; (i) NDFCM_P algorithm; (j) FNDFCM_P algorithm
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图 8. 不同邻域时#42049的分割结果对比图。(a) NDFCM_P算法;(b) FNDFCM_P算法
Fig. 8. Comparison of #42049 segmentation results in different neighborhoods. (a) NDFCM_P algorithm; (b) FNDFCM_P algorithm
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图 9. 不同算法的石头山图像分割图。(a)原始图像;(b)混合噪声图像;(c) FCM_S1算法;(d) FCM_S2算法; (e) EnFCM算法;(f) FGFCM算法;(g) FLICM算法;(h) NDFCM_P算法;(i) FNDFCM_P算法
Fig. 9. Segmentation of stone mountain image by different algorithms. (a) Original image; (b) image corrupted by mixed noise; (c) FCM_S1algorithm; (d) FCM_S2 algorithm; (e) EnFCM algorithm; (f) FGFCM algorithm; (g) FLICM algorithm; (h) NDFCM_P algorithm; (i) FNDFCM_P algorithm
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图 10. 不同算法的硬币图像分割图。(a)原始图像;(b)椒盐噪声图像;(c) FCM_S1算法;(d) FCM_S2算法; (e) EnFCM算法;(f) FGFCM算法;(g) FLICM算法; (h) NDFCM_P算法; (i) FNDFCM_P算法
Fig. 10. Segmentation of coin image by different algorithms. (a) Original image; (b) image corrupted by salt & pepper noise; (c) FCM_S1 algorithm; (d) FCM_S2 algorithm; (e) EnFCM algorithm; (f) FGFCM algorithm; (g) FLICM algorithm; (h) NDFCM_P algorithm; (i) FNDFCM_P algorithm
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表 1后处理执行框架
Table1. Diagram of post processing
| Step 1: extraction of potentially misclassified pixels | Step 2: reclassification of the extracted pixels (xl) |
|---|
| 1 l← 1 | 1 for all extracted pixels xl do | | 2 for all pixels xj of the image do | 2 for ∀ xj∈xl, do | | 3 if [label (xj)≠label (3×3 neighbourhood)] then | 3 Find arg max (Ji) by using formula (23) | | 4 xl=xj | 4 end for | | 5 l← l+1 | 5 end for | | 6 end if | 6 return segmentation results | | 7 end for | | | 8 return xl | |
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表 2不同分割算法的参数设置
Table2. Parameters setting for different segmentation algorithms
| Algorithm | Parameter setting |
|---|
| m | α | λs | λg | T | ε |
|---|
| FCM_S1 | 2 | 4 | | | 300 | 10-5 | | FCM_S2 | 2 | 4 | | | 300 | 10-5 | | EnFCM | 2 | 4 | | | 300 | 10-5 | | FGFCM | 2 | | 3 | 3 | 300 | 10-5 | | FLICM | 2 | | | | 300 | 10-5 | | NDFCM_P | 2 | | 3 | 3 | 300 | 10-5 | | FNDFCM_P | 2 | | 3 | 3 | 300 | 10-5 |
|
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表 3不同噪声水平下各分割算法的指标对比
Table3. Comparison of indices of different segmentation algorithms under different noise levels
| Noise level | Index | FCM_S1 | FCM_S2 | EnFCM | FGFCM | FLICM | NDFCM_P | FNDFCM_P |
|---|
| Gaussian noise (0,0.03) | SA | 0.9224 | 0.9358 | 0.9249 | 0.9476 | 0.9543 | 0.9845 | 0.9825 | | ARI | 0.8966 | 0.9144 | 0.8999 | 0.9302 | 0.9391 | 0.9792 | 0.9767 | | Gaussian noise (0,0.04) | SA | 0.8957 | 0.8899 | 0.8983 | 0.9257 | 0.9413 | 0.9731 | 0.9714 | | ARI | 0.8613 | 0.8666 | 0.8644 | 0.9011 | 0.9217 | 0.9641 | 0.9619 | | Salt & pepper noise (0.1) | SA | 0.8962 | 0.9586 | 0.9575 | 0.9703 | 0.8725 | 0.9966 | 0.9934 | | ARI | 0.8616 | 0.9448 | 0.9434 | 0.9604 | 0.8300 | 0.9954 | 0.9911 | | Gaussian noise (0,0.02) &salt & pepper noise (0.1) | SA | 0.8502 | 0.9170 | 0.9189 | 0.9341 | 0.8426 | 0.9837 | 0.9790 | | ARI | 0.8002 | 0.8894 | 0.8919 | 0.9122 | 0.7901 | 0.9784 | 0.9720 |
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表 4Berkeley图像各分割算法的指标对比
Table4. Comparison of indices of different segmentation algorithms on Berkeley image
| Image | Noise level | Index | FCM_S1 | FCM_S2 | EnFCM | FGFCM | FLICM | NDFCM_P | FNDFCM_P |
|---|
| #42049 | Gaussiannoise (0,0.05) | SA | 0.9407 | 0.9392 | 0.9417 | 0.9483 | 0.9529 | 0.9547 | 0.9539 | | ARI | 0.8815 | 0.8783 | 0.8834 | 0.8966 | 0.9058 | 0.9094 | 0.9078 | | Salt & peppernoise (0.2) | SA | 0.8918 | 0.9529 | 0.8917 | 0.9465 | 0.9373 | 0.9601 | 0.9563 | | ARI | 0.7836 | 0.9058 | 0.7833 | 0.8929 | 0.8346 | 0.9202 | 0.9127 | | Gaussian noise(0,0.04) & Salt &pepper noise (0.1) | SA | 0.9072 | 0.9292 | 0.9147 | 0.9416 | 0.9454 | 0.9525 | 0.9531 | | ARI | 0.8144 | 0.8584 | 0.8295 | 0.8832 | 0.8908 | 0.9050 | 0.9062 | | #238001 | Gaussiannoise (0,0.02) | SA | 0.5926 | 0.5740 | 0.8938 | 0.9153 | 0.8447 | 0.9475 | 0.9495 | | ARI | 0.3890 | 0.3611 | 0.8408 | 0.8731 | 0.7671 | 0.9212 | 0.9242 | | Salt & peppernoise (0.1) | SA | 0.7083 | 0.9071 | 0.7673 | 0.9146 | 0.6634 | 0.9610 | 0.9585 | | ARI | 0.5625 | 0.8606 | 0.6509 | 0.8719 | 0.4951 | 0.9415 | 0.9378 | | Gaussian noise(0,0.01) & Salt &pepper noise (0.05) | SA | 0.6285 | 0.6005 | 0.6592 | 0.9422 | 0.7031 | 0.9578 | 0.9578 | | ARI | 0.4428 | 0.4008 | 0.4888 | 0.9134 | 0.5547 | 0.9367 | 0.9368 |
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表 5不同分割算法的运行时间对比
Table5. Comparison of execution time by different segmentation algorithms
| Image | Size /(pixel×pixel) | Cluster | Time /s |
|---|
| FCM_S1 | EnFCM | FLICM | NDFCM_P | FNDFCM_P |
|---|
| Synthetic image | 128×128 | 4 | 0.25 | 0.06 | 16.59 | 0.95 | 0.81 | | #42049 image | 481×321 | 2 | 0.76 | 0.04 | 121.63 | 108.61 | 112.28 | | Coin image | 308×242 | 3 | 4.52 | 0.04 | 39.46 | 29.65 | 30.80 |
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朱占龙, 王军芬. 基于自适应模糊C均值与后处理的图像分割算法[J]. 激光与光电子学进展, 2018, 55(1): 011004. Zhu Zhanlong, Wang Junfen. Image Segmentation Based on Adaptive Fuzzy C-Means and Post Processing Correction[J]. Laser & Optoelectronics Progress, 2018, 55(1): 011004.
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