Simultaneous point matching and 3D deformable surface reconstruction

It has been shown that the 3D shape of a deformable surface in an image can be recovered by establishing correspondences between that image and a reference one in which the shape is known. These matches can then be used to set-up a convex optimization problem in terms of the shape parameters, which is easily solved. However, in many cases, the correspondences are hard to establish reliably. In this paper, we show that we can solve simultaneously for both 3D shape and correspondences, thereby using 3D shape constraints to guide the image matching and increasing robustness, for example when the textures are repetitive. This involves solving a mixed integer quadratic problem. While optimizing this problem is NP-hard in general, we show that its solution can nevertheless be approximated effectively by a branch-and-bound algorithm.