Canonical and Compact Point Cloud Representation for Shape Classification

TL;DR

This paper introduces a new compact, invariant point cloud representation for shape classification that uses a shape-embedded neural network to encode distance fields, reducing the need for data augmentation.

Contribution

A novel shape representation method that is invariant to scale, coordinate change, and point permutation, using a shape-embedded neural network trained with an ELM for efficient shape classification.

Findings

Effective shape classification with minimal data augmentation

Invariant representation reduces complexity compared to previous methods

Shape-embedded network parameters are highly descriptive for shape recognition

Abstract

We present a novel compact point cloud representation that is inherently invariant to scale, coordinate change and point permutation. The key idea is to parametrize a distance field around an individual shape into a unique, canonical, and compact vector in an unsupervised manner. We firstly project a distance field to a $4$D canonical space using singular value decomposition. We then train a neural network for each instance to non-linearly embed its distance field into network parameters. We employ a bias-free Extreme Learning Machine (ELM) with ReLU activation units, which has scale-factor commutative property between layers. We demonstrate the descriptiveness of the instance-wise, shape-embedded network parameters by using them to classify shapes in $3$D datasets. Our learning-based representation requires minimal augmentation and simple neural networks, where previous approaches demand numerous representations to handle coordinate change and point permutation.