Reconstruction et alignement en vision 3D : points, droites, plans et caméras

This thesis deals with the reconstruction of 3D models of scenes from images taken by cameras. It is common to reconstruct from subsets of images and to merge the partial 3D models, based on a 3D alignment step. Reconstruction and alignment algorithms rely on point or line correspondences between the images. The position of these features in the images is affected by noise, which influences the quality of the reconstructed 3D models. This thesis focuses on obtaining optimal results and on the problems of representation which are induced. The first part of this thesis tackles the problem of reconstructing 3D models. Calibrated and uncalibrated cameras are dealt with. We develop methods for the reconstruction of points, lines and cameras. The incorporation of geometric coplanarity constraints allows simultaneous reconstruction of planes. Our main contributions are the development and the comparison of methods for the optimal 3D reconstruction of points, lines, planes and cameras. The second part of this thesis is concerned with the problem of aligning 3D models, or equivalently, estimating the geometric transformation relating two 3D models. Existing methods are based on point correspondences. We study the case of line correspondences. Calibrated and uncalibrated cameras are dealt with. Our major contributions in this domain are, from a theoretical point of view, the study of geometric transformations of 3D lines. More precisely, we extend the standard matrix representation, suitable for points, to a representation suitable for lines. From a practical point of view, we develop and compare numerous linear and non-linear alignment methods. Finally, we propose methods for the reconstruction of 3D models for non-rigid scenes and a method for the automatic detection of planar surfaces within a 3D model.