  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.
