Constraints and their satisfaction in the recovery of local surface structure

This thesis deals with the problem of recovering the local structure of surfaces from discrete range data. It is assumed that this recovery is done mostly in a bottom-up fashion, that is, without the help of a priori knowledge about the viewed surface.Because the problem is ill-posed, we nevertheless need to place constraints on the recovered structure to get a unique solution. In a bottom-up approach, these constraints must come from generic assumptions that apply to all surfaces.Many methods of bottom-up surface reconstruction have been proposed up to now, some of them dealing with intensity surfaces, some with range surfaces. Each of these methods either explicitly or implicitly applies a set of constraints on the data. The way in which the constraints are applied also varies from method to method. The main contribution of this thesis is some success at unifying a number of those methods under a common formalism of energy minimization, which will permit to better compare the choice of constraints between methods. We also show that the most successful surface reconstruction methods form idempotent operators, which we argue is to be expected.One method, Sander's curvature consistency, is studied in more detail than the others because it has not been studied much elsewhere yet