Calibrating Parameters of Cost Functionals in Computer Vision

We propose a new framework for calibrating parameters of energy functionals, as used in image analysis. The method learns parameters from a family of correct examples, and given a probabilistic construct for generating wrong examples from correct ones. We introduce a measure of frustration to penalize cases in which wrong responses are preferred to correct ones, and we design a stochastic gradient algorithm which converges to parameters which minimize this measure of frustration. We also present a rst set of experiments in this context, and introduce possible extensions to deal with data-dependent energies. 1. Description of the method Many problems in computer vision are addressed through the minimization of a cost functional. Typically, one is given a large, but nite, set (for example the set of pictures with given dimensions), and one tries to obtain an element x 2 which minimizes a given real-valued functional x 7 ! E(x). Most of the time, the energy is designed as a combination of several terms, each of them corresponding to a precise property which much be satissed by the optimal solution. For example, the cost function in 5], which is used to segment and smooth an observed picture, is the combination of three terms, one which ensures that the smoothed picture is not be too diierent from the observed one, another which states that the derivative of the smoothed picture should be small, except, possibly, on a discontinuity set, and a last one which ensures that the discontinuity set has small length. These terms are weighted 1