Residual-Sparse Fuzzy C-Means Clustering Incorporating Morphological Reconstruction and Wavelet Frame

Cong Wang, Witold Pedrycz, Zhiwu Li, Mengchu Zhou, Jun Zhao

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


In this article, we develop a residual-sparse Fuzzy C-Means (FCM) algorithm for image segmentation, which furthers FCM's robustness by realizing the favorable estimation of the residual (e.g., unknown noise) between an observed image and its ideal version (noise-free image). To achieve a sound tradeoff between detail preservation and noise suppression, morphological reconstruction is used to filter the observed image. By combining the observed and filtered images, a weighted sum image is generated. Tight wavelet frame decomposition is used to transform the weighted sum image into its corresponding feature set. Taking such feature set as data for clustering, we impose an ell _0 regularization term on residual to FCM's objective function, thus resulting in residual-sparse FCM, where spatial information is introduced for improving its robustness and making residual estimation more reliable. To further enhance segmentation accuracy of the proposed FCM, we employ morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, a segmented image is reconstructed by using tight wavelet frame reconstruction. Experimental results regarding synthetic, medical, and real-world images show that the proposed algorithm is effective and efficient, and outperforms its peers.

Original languageEnglish (US)
Pages (from-to)3910-3924
Number of pages15
JournalIEEE Transactions on Fuzzy Systems
Issue number12
StatePublished - Dec 1 2021

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


  • Fuzzy C -Means
  • image segmentation
  • machine learning
  • morphological reconstruction
  • residual sparse
  • wavelet frame


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