Learning Shape Primitives via Implicit Convexity Regularization.

Shape primitives decomposition has been an important and long-standing task in 3D shape analysis. Prior arts heavily rely on 3D point clouds or voxel data for shape primitives extraction, which are less practical in real-world scenarios. This paper proposes to learn shape primitives from multi-view images by introducing implicit surface rendering. It is challenging since implicit shapes have a high degree of freedom, which violates the simplicity property of shape primitives. In this work, a novel regularization term named Implicit Convexity Regularization (ICR) imposed on implicit primitive learning is proposed to tackle this problem. We start with the convexity definition of general 3D shapes, and then derive the equivalent expression for implicit shapes represented by signed distance functions (SDFs). Further, instead of directly constraining the output SDF values which cause unstable optimization, we alternatively impose constraint on second order directional derivatives on line segments inside the shapes, which proves to be a tighter condition for 3D convexity. Implicit primitives constrained by the proposed ICR are combined into a whole object via softmax-weighted-sum operation over all primitive SDFs. Experiments on synthetic and real-world datasets show that our method is able to decompose objects into simple and reasonable shape primitives without the need of segmentation labels or 3D data. Code and data is publicly available in https://github.com/seanywang0408/ICR.