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 4D 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 3D 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.
@article{arxiv.1809.04820,
title = {Canonical and Compact Point Cloud Representation for Shape Classification},
author = {Kent Fujiwara and Ikuro Sato and Mitsuru Ambai and Yuichi Yoshida and Yoshiaki Sakakura},
journal= {arXiv preprint arXiv:1809.04820},
year = {2018}
}