Shape from silhouettes based on a centripetal pentahedron model

In this paper we present a novel volumetric shape from silhouette (SfS) algorithm based on a centripetal pentahedron model (pent-model). The pent-model is an object-centered volumetric model composed of a set of pentahedrons cut from the centripetal triangular pyramids, which together partition the 3D space. The SfS algorithm first computes the pyramids by constructing a geodesic sphere. These pyramids are then projected onto the image planes of all cameras. The intersections between the projected pyramids and the silhouettes, which are a set of hexagons, are computed. This process can be performed very efficiently with pre-computed polar silhouette graphs (PSGs) and reduced PSGs. The hexagons are then back-projected into the 3D space, where the intersections are calculated and the pent-model is derived. After that, a mesh surface model can be extracted by marching pentahedrons. Our algorithm has the combined advantages of robustness, speediness and preciseness. Experimental results based on both synthetic images and real photos are presented.