Superpixelizing Binary MRF for Image Labeling Problems

Superpixels have become prevalent in computer vision. They have been used to achieve satisfactory performance at a significantly smaller computational cost for various tasks. People have also combined superpixels with Markov random field (MRF) models. However, it often takes additional effort to formulate MRF on superpixellevel, and to the best of our knowledge there exists no principled approach to obtain this formulation. In this paper, we show how generic pixel-level binary MRF model can be solved in the superpixel space. As the main contribution of this paper, we show that a superpixel-level MRF can be derived from the pixel-level MRF by substituting the superpixel representation of the pixelwise label into the original pixel-level MRF energy. The resultant superpixel-level MRF energy also remains submodular for a submodular pixel-level MRF. The derived formula hence gives us a handy way to formulate MRF energy in superpixel-level. In the experiments, we demonstrate the efficacy of our approach on several computer vision problems.