ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Clouds
This work addresses a fundamental symmetry challenge in processing 2D point clouds, which is crucial for applications like computer vision, but it is incremental as it builds on existing equivariance concepts.
The paper tackled the problem of rotation equivariance in 2D point clouds by proposing a universal neural network architecture that approximates any continuous rotation equivariant and permutation invariant function, and demonstrated its application in estimating essential matrices for stereo vision.
In this paper, we are concerned with rotation equivariance on 2D point cloud data. We describe a particular set of functions able to approximate any continuous rotation equivariant and permutation invariant function. Based on this result, we propose a novel neural network architecture for processing 2D point clouds and we prove its universality for approximating functions exhibiting these symmetries. We also show how to extend the architecture to accept a set of 2D-2D correspondences as indata, while maintaining similar equivariance properties. Experiments are presented on the estimation of essential matrices in stereo vision.