Quadratic Markovian Probability Fields for Image Binary Segmentation

We present a Markov random field model for image binary segmentation that computes the probability that each pixel belongs to a given class. We show that the computation of a real valued field has noticeable computational and performance advantages with respect to the computation of binary valued field; the proposed energy function is efficiently minimized with standard fast linear order algorithms as conjugate gradient or multigrid Gauss-Seidel schemes. By providing a good initial guesses as starting point we avoid to construct from scratch a new solution, accelerating the computational process, and allow us to naturally implement efficient multigrid algorithms. For applications with limited computational time, a good partial solution can be obtained by stopping the iterations even if the global optimum is not yet reached. We present a meticulous comparison with state of the art methods: graph cut, random walker and GMMF The algorithms´ performance are compared using a cross-validation procedure and an automatics algorithm for learning the parameter set.