A Simple Deconvolutional Mechanism for Point Clouds and Sparse Unordered Data

This paper presents a novel deconvolution mechanism, called the Sparse Deconvolution, that generalizes the classical transpose convolution operation to sparse unstructured domains, enabling the fast and accurate generation and upsampling of point clouds and other irregular data. Specifically, the approach uses deconvolutional kernels, which each map an input feature vector and set of trainable scalar weights to the feature vectors of multiple child output elements. Unlike previous approaches, the Sparse Deconvolution does not require any voxelization or structured formulation of data, it is scalable to a large number of elements, and it is capable of utilizing local feature information. As a result, these capabilities allow for the practical generation of unstructured data in unsupervised settings. Preliminary experiments are performed here, where Sparse Deconvolution layers are used as a generator within an autoencoder trained on the 3D MNIST dataset.