Semi-Supervised Normalized Cuts for Image Segmentation

Since its introduction as a powerful graph-based method for image segmentation, the Normalized Cuts (NCuts) algorithm has been generalized to incorporate expert knowledge about how certain pixels or regions should be grouped, or how the resulting segmentation should be biased to be correlated with priors. Previous approaches incorporate hard must-link constraints on how certain pixels should be grouped as well as hard cannot-link constraints on how other pixels should be separated into different groups. In this paper, we reformulate NCuts to allow both sets of constraints to be handled in a soft manner, enabling the user to tune the degree to which the constraints are satisfied. An approximate spectral solution to the reformulated problem exists without requiring explicit construction of a large, dense matrix, hence, computation time is comparable to that of unconstrained NCuts. Using synthetic data and real imagery, we show that soft handling of constraints yields better results than unconstrained NCuts and enables more robust clustering and segmentation than is possible when the constraints are strictly enforced.