Feature-Preserving Fuzzy Clustering for Blurred G-Image Segmentation

G-images, defined as graph-structured data with complex topologies, have played a significant role in various fields. Current research mainly focuses on denoising and segmenting observed G-images. However, due to sampling or information degradation, they often contain blurred texture information. Therefore, reconstructing and segmenting them accurately is a critical challenge. To address this issue, this work elaborates a feature-preserving FuzzyC-Means (FCM) algorithm by the aid of a wavelet frame transform, which is aimed at segmenting observed G-images with noise and blur. Given the superior performance of tight wavelet frames in feature extraction, this work leverages the proposed algorithm in a wavelet space, thus incorporating both the original and rectified features of G-images to maintain high robustness. To improve segmentation accuracy, it also uses the local binary pattern code to identify and enhance the blurred features. Additionally, to preserve the similarity between any vertex and its adjacent nodes, it introduces a Kullback-Leibler divergence term as a part of FCM’s objective function. Moreover, convergence analysis establishes that the entire sequence of iterates generated by the algorithm is globally convergent to a critical point. Finally, numerical experiments are conducted by comparing the proposed algorithm with other peers on both synthetic and real-world G-images with noise and blur of different levels. Experimental evidence shows that the proposed algorithm exhibits superior effectiveness and robustness compared to existing peers.