NegCut: Automatic Image Segmentation based on MRF-MAP

Solving the Maximum a Posteriori on Markov Random Field, MRF-MAP, is a prevailing method in recent interactive image segmentation tools. Although mathematically explicit in its computational targets, and impressive for the segmentation quality, MRF-MAP is hard to accomplish without the interactive information from users. So it is rarely adopted in the automatic style up to today. In this paper, we present an automatic image segmentation algorithm, NegCut, based on the approximation to MRF-MAP. First we prove MRF-MAP is NP-hard when the probabilistic models are unknown, and then present an approximation function in the form of minimum cuts on graphs with negative weights. Finally, the binary segmentation is taken from the largest eigenvector of the target matrix, with a tuned version of the Lanczos eigensolver. It is shown competitive at the segmentation quality in our experiments.