We propose a gray scale image colorization method based on a Bayesian segmentation framework in which the classes are established from scribbles made by a user on the image. These scribbles can be considered as a multimap (multilabels map) that defines the boundary conditions of a probability measure field to be computed in each pixel. The components of such a probability measure field express the degree of belonging of each pixel to spatially smooth classes. In a first step we obtain the probability measure field by computing the global minima of a positive definite quadratic cost function with linear constraints. Then color is introduced in a second step through a pixelwise operation. The computed probabilities (memberships) are used for defining the weights of a simple linear combination of user provided colors associated to each class. An advantage of our method is that it allows us to re-colorize part or the whole image in an easy way, without need of recomputing the memberships (or /sp alpha/-channels).

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.