Computing the α-channel with probabilistic segmentation for image colorization

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).