In this paper, we present a regularization approach on discrete graph spaces for perceptual image segmentation via semisupervised learning. In this approach, first, a spectral clustering method is embedded and extended into regularization on discrete graph spaces. In consequence, the spectral graph clustering is optimized and smoothed by integrating top-down and bottom-up processes via semi-supervised learning. Second, a designed nonlinear diffusion filter is used to maintain semi-supervised

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... rning, labeling and differences between foreground or background regions. Furthermore, the spectral segmentation is penalized and adjusted using labeling prior and optimal window-based affinity functions in a regularization framework on discrete graph spaces. Experiments show that the algorithm achieves perceptual and optimal image segmentation. The algorithm is robust in that it can handle images that are formed in variational environments.