A splitting-based algorithm for multi-view stereopsis of textureless objects

International audienceWe put forward a simple, yet eective splitting strategy for multi-view stereopsis. It recasts the minimization of the classic photo-consistency + gradient regularization functional as a sequence of simple problems which can be solved eciently. This framework is able to handle various photo-consistency measures and regularization terms, and can be used for instance to estimate either a minimal-surface or a shading-aware solution. The latter makes the proposed approach very eective for dealing with the well-known problem of textureless objects 3D-reconstruction. 1 Introduction Multi-view stereopsis consists in reconstructing dense 3D-geometry from multi-view images. A common approach to this problem is to estimate a mapping (depth) between pixels in a reference view and 3D-geometry, by maximizing the photo-consistency of the reference image with the others. To measure photo-consistency, the reference image is warped to the other views using the estimated depth map and the (known) relative poses, and compared against the target images. However, photo-consistency is not signicant in textureless areas (see Figure 1): the optimization problem needs to be regularized by constraining variations in the 3D-geometry. If z : Ω ⊂ R 2 → R + \{0} denotes the unknown depth map, with Ω the image domain, surface variations under perspective projection can be measured as a function of z z = log z : Ω → R 2. Multi-view stereo can then be formulated in a classic and generic manner [13] as the minimization of the sum of a delity term f inversely proportional to photo-consistency, and of a regularization term g. We thus consider in this work the following variational problem: min z f (z) + g(log z) (1) (the choice of applying regularization in log-space is discussed in Section 2)