Image Segmentation by Convex Quadratic Programming

A quadratic programming formulation for multiclass image segmentation is investigated. It is proved that, in the convex case, the non-negativity constraint on the recent reported Quadratic Markov Measure Field model can be neglected and the solution preserves the probability measure property. This allows one to design efficient optimization algorithms. Additionally, it is proposed a (free parameter) inter-pixel affinity measure which is more related with classes memberships than with color or gray gradient based standard methods. Moreover it is introduced a formulation for computing the pixel likelihoods by taking into account local context and texture properties.