Point Cloud Synthesis Using Inner Product Transforms

TL;DR

This paper introduces a new point cloud synthesis method that uses inner product transforms to efficiently encode geometric features, resulting in faster inference and high-quality generation, reconstruction, and interpolation.

Contribution

The paper presents a novel inner product transform-based encoding for point clouds, offering a highly-efficient and expressive representation integrated into deep learning models.

Findings

Inference times are orders of magnitude faster than existing methods.

High-quality results in reconstruction, generation, and interpolation tasks.

Provable expressivity properties of the encoding.

Abstract

Point cloud synthesis, i.e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have been devised. We develop a novel method that encodes geometrical-topological characteristics of point clouds using inner products, leading to a highly-efficient point cloud representation with provable expressivity properties. Integrated into deep learning models, our encoding exhibits high quality in typical tasks like reconstruction, generation, and interpolation, with inference times orders of magnitude faster than existing methods.