Finding Approximate Convex Shapes in RGBD Images

Abstract. We propose a novel method to find approximate convex 3D shapes from single RGBD images. Convex shapes are more general than cuboids, cylinders, cones and spheres. Many real-world objects are near-convex and every non-convex object can be represented using convex parts. By finding approximate convex shapes in RGBD images, we ex-tract important structures of a scene. From a large set of candidates generated from over-segmented superpixels we globally optimize the se-lection of these candidates so that they are mostly convex, have small intersection, have a small number and mostly cover the scene. The opti-mization is formulated as a two-stage linear optimization and efficiently solved using a branch and bound method which is guaranteed to give the global optimal solution. Our experiments on thousands of RGBD images show that our method is fast, robust against clutter and is more accurate than competing methods.