Canonical and Compact Point Cloud Representation for Shape Classification
This work addresses the need for efficient shape classification in computer vision, though it appears incremental as it builds on existing representation methods with specific improvements.
The authors tackled the problem of creating a compact and invariant representation for 3D point clouds by developing a method that parametrizes a distance field into a unique vector using singular value decomposition and neural networks, achieving shape classification on 3D datasets with minimal augmentation and simple networks.
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.