Normalized Cut Meets MRF

We propose a new segmentation or clustering model that combines Markov Random Field (MRF) and Normalized Cut (NC) objectives. Both NC and MRF models are widely used in machine learning and computer vision, but they were not combined before due to significant differences in the corresponding optimization, e.g. spectral relaxation and combinatorial max-flow techniques. On the one hand, we show that many common applications for multi-label MRF segmentation energies can benefit from a high-order NC term, e.g. enforcing balanced clustering of arbitrary high-dimensional image features combining color, texture, location, depth, motion, etc. On the other hand, standard NC applications benefit from an inclusion of common pairwise or higher-order MRF constraints, e.g. edge alignment, bin-consistency, label cost, etc. To address NC+MRF energy, we propose two efficient multi-label combinatorial optimization techniques, spectral cut and kernel cut, using new unary bounds for different NC formulations.