Patch-based reconstruction of surfaces undergoing different types of deformations

Abstract

We deal with the reconstruction of surfaces that deform under a variety of conditions. The deformation can range from no extension to a certain degree of extensibility. The deformed surface is reconstructed from a single image, given a 3D reference shape. This shape corresponds to the undeformed state of the surface and can be computed using any appropriate technique. In particular, we use homographies defined from two views of the surface. To proceed with the 3D reconstruction of the deformed surface, we assume that the deformations are locally homogeneous and that the overall surface deformation can be obtained by combining the local homogeneous deformations. For this purpose, the surface is split into small patches. For each patch, a mapping between the undeformed and the deformed shapes is computed. The mapping is specified by using the quadratic deformation model Fayad et al. (Proceedings of British Machine Vision Conference (BMVC), 2004). As a result, given the undeformed shape, we define an optimization procedure whose goal is to estimate the 3D positions of deformed points in each image. The optimization is performed on each patch, independently of the others. The experimental results show that this approach allows precise reconstruction of a wide class of real deformations.

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