Une approche statistique multi-échelle au recalage rigide de surfaces : Application à l'implantologie dentaire

The main subject of this work is the rigid registration of surfaces dedicated to VirtualScope, aper-operative guiding system designed for oral implants surgery.It is based on a purely statistical approach. We first show how to compute and maximize a likelihood,based on a model of the data noise, for the landmarks registration problem. This approach justifies theuse of the ICP algorithm, and a new multi-scale variant named ICP/EM, which improves accuracy, speedand robustness. We introduce new noise models specifically designed for the registration of sampled andnoised surfaces. We discuss about the theoretical prediction of the registration accuracy, and use it forguiding the data acquisition. We analyze in detail the experimental performances of the algorithm, andprovide methods for setting optimally the parameters and ensuring the correctness of registration results.The resulting algorithm is perfectly suited to the VirtualScope application.The second part of this work deals with the more general problem of the statistical modelisationof sampled and noised curves and surfaces. Based on previous works on Saliency and Tensor Votingnotions, it defines a vote field that represent the probability of a curve or surface element, knowinganother element. We provide basic yet easy to implement examples of such a field, which can handle thesurface shape, the sampling strategy and the measurement errors. We apply them successfully to theregistration problem, and suggest to use them to derive Bayesian methods to virtually all other computervision problems involving sampled and noised curves and surfaces. This work could lead to the design ofa common statistical and multi-scale framework for these various methods.