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G-images refer to image data defined on irregular graph domains. This article elaborates on a similarity-preserving Fuzzy <italic>C</italic>-Means (FCM) algorithm for G-image segmentation and aims to develop techniques and tools for segmenting G-images. To preserve the membership similarity between an arbitrary image pixel and its neighbors, a Kullback&#x2013;Leibler divergence term on partition matrix is introduced as a part of FCM. As a result, similarity-preserving FCM is developed by considering spatial information of image pixels for its robustness enhancement. Due to superior characteristics of a wavelet space, the proposed FCM is performed in this space rather than the Euclidean one used in conventional FCM to secure its high robustness. Experiments on synthetic and real-world G-images demonstrate that it indeed achieves higher robustness and performance than the state-of-the-art segmentation algorithms. Moreover, it requires less computation than most of them.

G-Image Segmentation: Similarity-Preserving Fuzzy C-Means With Spatial Information Constraint in Wavelet Space