Markovian fields and variational methods applied to low-level vision tasks.

Summary In many situations, image processing comes down to the translation of a given problem in the form of an energy minimization. The main difficulty then lies in the quality of this translation, i.e. in the construction of an energy whose minimum represents the information that we wish to extract or reconstruct. This thesis presents two different approaches to this problem, depending on whether we place ourselves in the probabilistic framework of Markov fields or in the deterministic framework of variational calculus. The first part deals with the detection of valley lines on a pair of noisy images degraded by a strong luminosity gradient. The valley background lines are represented by their discrete version and modeled by a Markov field. The bayes-markov approach leads to minimize an energy composed of two terms. The first one represents the a priori model on the discrete curves and integrates the regularity (low curvature) and length constraints. The second one is deduced from the noise model and is controlled by a parameter defining the minimal signal-to-noise ratio from which a detection is performed on the pair of recalibrated images. This energy is minimized by a stochastic algorithm of type mpm. The second part concerns the automatic reconstruction of the silhouette of an object placed on a noisy homogeneous background. The framework used is that of snakes, a method derived from variational computing. The contour is obtained by minimizing an energy by means of a deterministic gradient algorithm using several levels of resolution. Finally, this work also presents a study on the Lambertian illumination model. We propose a semi-local approach to estimate the reflectance and local orientation of objects when the direction of the incident light is unknown.