A Graph-based Error Correction Model Using Lie-algebraic Cohomology and Its Application on Global Consistent Indoor Scene Reconstruction

Abstract

We present a novel, effective method for global indoor scene reconstruction problems by geometric topology. Based on point cloud pairwise registration methods (e.g ICP) or IMU, 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 graph optimation, 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 indoor scene. The experimental results also demonstrate that our global registration method runs quickly and provides accurate reconstructions.