ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Clouds

TL;DR

ZZ-Net introduces a universal neural network architecture that achieves rotation equivariance and permutation invariance for 2D point cloud processing, with proven universality and extensions for correspondence data, demonstrated on stereo vision tasks.

Contribution

The paper presents a novel, universal neural network architecture for 2D point clouds that guarantees rotation equivariance and permutation invariance, extending to correspondence data.

Findings

Proves the universality of ZZ-Net for rotation equivariant functions.

Extends architecture to handle 2D-2D correspondences.

Demonstrates effectiveness on essential matrix estimation in stereo vision.

Abstract

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.