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In this paper, C-means algorithm is fuzzified and regularized by incorporating both local data and membership information. The local membership information is incorporated via two membership relative entropy (MRE) functions. These MRE functions measure the information proximity of the membership function of each pixel to the membership average in the immediate spatial neighborhood. Then minimizing these MRE functions pushes the membership function of a pixel toward its average in the pixel vicinity. The resulting algorithm is called the Local Membership Relative Entropy based FCM (LMREFCM). The local data information is incorporated into the LMREFCM algorithm by adding to the standard distance a weighted distance computed from the locally smoothed data. The final resulting algorithm, called the Local Data and Membership Relative Entropy based FCM (LDMREFCM), assigns a pixel to the cluster more likely existing in its immediate neighborhoods. This provides noise immunity and results in clustered images with piecewise homogeneous regions. Simulation results of segmentation of synthetic and real-world noisy images are presented to compare the performance of the proposed LMREFCM and LDMREFCM algorithms with several FCM-related algorithms

In this paper, C-means algorithm is fuzzified and regularized by incorporating both local data and membership information. The local membership information is incorporated via two membership relative entropy (MRE) functions. These MRE functions measure the information proximity of the membership function of each pixel to the membership average in the immediate spatial neighborhood. Then minimizing these MRE functions pushes the membership function of a pixel toward its average in the pixel vicinity. The resulting algorithm is called the Local Membership Relative Entropy based FCM (LMREFCM). The local data information is incorporated into the LMREFCM algorithm by adding to the standard distance a weighted distance computed from the locally smoothed data. The final resulting algorithm, called the Local Data and Membership Relative Entropy based FCM (LDMREFCM), assigns a pixel to the cluster more likely existing in its immediate neighborhoods. This provides noise immunity and results in clustered images with piecewise homogeneous regions. Simulation results of segmentation of synthetic and real-world noisy images are presented to compare the performance of the proposed LMREFCM and LDMREFCM algorithms with several FCM-related algorithms

In this paper, a fuzzy clustering technique for image segmentation is developed by incorporating a hybrid of local spatial membership and data information into the conventional hard C-means (HCM) algorithm. This incorporation is a threefold procedure. (1) The membership function of a pixel is spatially smoothed in the pixel vicinity. (2) The Kullback-Leibler (KL) divergence between the pixel membership function and the smoothed one is added to the HCM objective function for fuzzification. (3) The resulting fuzzified HCM is regularized by adding a weighted HCM-like function where the original pixel data are replaced by locally smoothed ones. Thereby the weight is proportional to the residual of the locally smoothed membership. This residual decreases when many pixels existing in the pixel vicinity belong to the same cluster. Thus, the weighted distance decreases, allowing the pixel membership to follow the dominant membership in the pixel vicinity. The simulation results of segmenting synthetic, medical and media images have shown that the proposed algorithm provides better performance compared to several previously developed algorithms. For example, in a synthetic image, with added white Gaussian noise having a variance of 0.3, the proposed algorithm provides accuracy, sensitivity and specificity of 92%, 84% and 94.7% respectively, while the algorithm with the closest results provides 81.9% of accuracy, 62.2% of sensitivity and 86.8% of specificity. In addition, the proposed algorithm shows the capability to identify the number of clusters.

In this paper, a fuzzy clustering technique for image segmentation is developed by incorporating a hybrid of local spatial membership and data information into the conventional hard C-means (HCM) algorithm. This incorporation is a threefold procedure. (1) The membership function of a pixel is spatially smoothed in the pixel vicinity. (2) The Kullback-Leibler (KL) divergence between the pixel membership function and the smoothed one is added to the HCM objective function for fuzzification. (3) The resulting fuzzified HCM is regularized by adding a weighted HCM-like function where the original pixel data are replaced by locally smoothed ones. Thereby the weight is proportional to the residual of the locally smoothed membership. This residual decreases when many pixels existing in the pixel vicinity belong to the same cluster. Thus, the weighted distance decreases, allowing the pixel membership to follow the dominant membership in the pixel vicinity. The simulation results of segmenting synthetic, medical and media images have shown that the proposed algorithm provides better performance compared to several previously developed algorithms. For example, in a synthetic image, with added white Gaussian noise having a variance of 0.3, the proposed algorithm provides accuracy, sensitivity and specificity of 92%, 84% and 94.7% respectively, while the algorithm with the closest results provides 81.9% of accuracy, 62.2% of sensitivity and 86.8% of specificity. In addition, the proposed algorithm shows the capability to identify the number of clusters.

In this paper, a fuzzy clustering technique for image segmentation is developed by incorporating a hybrid of local spatial membership and data information into the conventional hard C-means (HCM) algorithm. This incorporation is a threefold procedure. (1) The membership function of a pixel is spatially smoothed in the pixel vicinity. (2) The Kullback-Leibler (KL) divergence between the pixel membership function and the smoothed one is added to the HCM objective function for fuzzification. (3) The resulting fuzzified HCM is regularized by adding a weighted HCM-like function where the original pixel data are replaced by locally smoothed ones. Thereby the weight is proportional to the residual of the locally smoothed membership. This residual decreases when many pixels existing in the pixel vicinity belong to the same cluster. Thus, the weighted distance decreases, allowing the pixel membership to follow the dominant membership in the pixel vicinity. The simulation results of segmenting synthetic, medical and media images have shown that the proposed algorithm provides better performance compared to several previously developed algorithms. For example, in a synthetic image, with added white Gaussian noise having a variance of 0.3, the proposed algorithm provides accuracy, sensitivity and specificity of 92%, 84% and 94.7% respectively, while the algorithm with the closest results provides 81.9% of accuracy, 62.2% of sensitivity and 86.8% of specificity. In addition, the proposed algorithm shows the capability to identify the number of clusters.

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