Blended Convolution and Synthesis for Efficient Discrimination of 3D Shapes (1908.10209v2)

Abstract: Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve inter-class discrimination efficiently. In this paper, we propose a two-faceted solution to this problem that is seamlessly integrated in a single `Blended Convolution and Synthesis' layer. This fully differentiable layer performs two critical tasks in succession. In the first step, it projects the input 3D point clouds into a latent 3D space to synthesize a highly compact and more inter-class discriminative point cloud representation. Since, 3D point clouds do not follow a Euclidean topology, standard 2/3D Convolutional Neural Networks offer limited representation capability. Therefore, in the second step, it uses a novel 3D convolution operator functioning inside the unit ball ($\mathbb{B}^3$) to extract useful volumetric features. We extensively derive formulae to achieve both translation and rotation of our novel convolution kernels. Finally, using the proposed techniques we present an extremely light-weight, end-to-end architecture that achieves compelling results on 3D shape recognition and retrieval.