Kullback-Leibler Divergence-Based Fuzzy C-Means Clustering Incorporating Morphological Reconstruction and Wavelet Frames for Image Segmentation

In this article, we elaborate on a Kullback-Leibler (KL) divergence-based Fuzzy C-Means (FCM) algorithm by incorporating a tight wavelet frame transform and morphological reconstruction (MR). To make membership degrees of each image pixel closer to those of its neighbors, a KL divergence term on the partition matrix is introduced as a part of FCM, thus resulting in KL divergence-based FCM. To make the proposed FCM robust, a filtered term is augmented in its objective function, where MR is used for image filtering. Since tight wavelet frames provide redundant representations of images, the proposed FCM is performed in a feature space constructed by tight wavelet frame decomposition. To further improve its segmentation accuracy (SA), a segmented feature set is reconstructed by minimizing the inverse process of its objective function. Each reconstructed feature is reassigned to the closest prototype, thus modifying abnormal features produced in the reconstruction process. Moreover, a segmented image is reconstructed by using tight wavelet frame reconstruction. Finally, supporting experiments coping with synthetic, medical, and real-world images are reported. The experimental results exhibit that the proposed algorithm works well and comes with better segmentation performance than other peers. In a quantitative fashion, its average SA improvements over its peers are 4.06%, 3.94%, and 4.41%, respectively, when segmenting synthetic, medical, and real-world images. Moreover, the proposed algorithm requires less time than most of the FCM-related algorithms.

Automated summary

This article introduces a Fuzzy C-Means (FCM) algorithm based on KL divergence, incorporating tight wavelet frame transform and morphological reconstruction. By introducing a KL divergence term on the partition matrix to make membership degrees closer, the algorithm improves image segmentation accuracy. Experimental results show that the proposed algorithm outperforms its peers in synthetic, medical, and real-world image segmentation, while also being faster than most FCM-related algorithms.