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

• Published in: IEEE transactions on cybernetics Vol. 52; no. 8; pp. 7612 - 7623
• Main Authors: Wang, Cong, Pedrycz, Witold, Li, Zhiwu, Zhou, Mengchu
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.08.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Clustering; Clustering algorithms; Frames (data processing); Fuzzy <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">C -means (FCMs); Image filters; Image reconstruction; Image segmentation; Kullback–Leibler divergence; Linear programming; Matrix partitioning; morphological reconstruction (MR); Morphology; Partitioning algorithms; Prototypes; wavelet frame; Wavelet transforms
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2021.3099503

In this article, we elaborate on a Kullback-Leibler (KL) divergence-based Fuzzy <inline-formula> <tex-math notation="LaTeX">{C} </tex-math></inline-formula>-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.