Blended convolution and synthesis for efficient discrimination of 3D shapes

Existing models for shape analysis directly learn feature representations on 3D point clouds. 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-pronged 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 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, we propose a novel 3D convolution operator functioning inside the unit ball to extract useful volumetric features. We 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.