Global Consistent Point Cloud Registration Based on Lie-algebraic Cohomology

TL;DR

This paper introduces a novel global point cloud registration method leveraging Lie-algebraic cohomology and geometric topology to eliminate accumulated errors efficiently, resulting in accurate and fast 3D reconstructions.

Contribution

It proposes a linear error elimination technique based on solving a Poisson equation, ensuring global consistency in point cloud registration.

Findings

The method effectively reduces accumulated registration errors.

Experiments show high accuracy on real-world RGBD datasets.

The approach is computationally efficient and suitable for large-scale scenes.

Abstract

We present a novel, effective method for global point cloud registration problems by geometric topology. Based on many point cloud pairwise registration methods (e.g ICP), we focus on the problem of accumulated error for the composition of transformations along any loops. The major technical contribution of this paper is a linear method for the elimination of errors, using only solving a Poisson equation. We demonstrate the consistency of our method from Hodge-Helmhotz decomposition theorem and experiments on multiple RGBD datasets of real-world scenes. The experimental results also demonstrate that our global registration method runs quickly and provides accurate reconstructions.