Locally Planar and Affine Deformable Surface Reconstruction from Video

Abstract

We present new solutions to tackle the problem of reconstructing a deforming surface viewed in monocular videos without a template, by exploiting the fact that many deforming surfaces are on the local scale approximately rigid and planar. The reconstruction task can then be seen, from bottom up as first multi-plane based pose estimation then dense surface reconstruction from planar samples. In practice there are major obstacles to overcome. In this paper we specifically target computing stable orientation estimates at small surface regions from interview image motion. We achieve this using local affine projection models which are stable and accurate when local perspective effects are small. Our core theoretical contributions are closed form solutions to multiview orthographic planar pose estimation in both the minimal and overdetermined cases. We use this to efficiently construct a weak deformable template; an undirected graph with nodes holding the surface's local planar structure and edges denoting physical deformation constraints. The template can then be used to recover dense 3D shape very efficiently from affine image motion via unambiguous planar pose estimation combined with surface regularisation.