A Bayesian Formulation of Coherent Point Drift.

Osamu Hirose

doi:10.1109/tpami.2020.2971687

Abstract

Coherent point drift is a well-known algorithm for solving point set registration problems, i.e., finding corresponding points between shapes represented as point sets. Despite its advantages over other state-of-the-art algorithms, theoretical and practical issues remain. Among theoretical issues, (1) it is unknown whether the algorithm always converges, and (2) the meaning of the parameters concerning motion coherence is unclear. Among practical issues, (3) the algorithm is relatively sensitive to target shape rotation, and (4) acceleration of the algorithm is restricted to the use of the Gaussian kernel. To overcome these issues and provide a different and more general perspective to the algorithm, we formulate coherent point drift in a Bayesian setting. The formulation brings the following consequences and advances to the field: convergence of the algorithm is guaranteed by variational Bayesian inference; the definition of motion coherence as a prior distribution provides a basis for interpretation of the parameters; rigid and non-rigid registration can be performed in a single algorithm, enhancing robustness against target rotation. We also propose an acceleration scheme for the algorithm that can be applied to non-Gaussian kernels and that provides greater efficiency than coherent point drift.

Highlights

T HE goal of point set registration is to find pairs of corresponding points between shapes represented as point sets
We propose a Bayesian formulation of Coherent point drift (CPD) and derive an algorithm called Bayesian coherent point drift (BCPD)
We show that iterative closest point (ICP) is a special case of BCPD regarding the estimation of corresponding points

Summary

Introduction

T HE goal of point set registration is to find pairs of corresponding points between shapes represented as point sets. Algorithms for finding shape correspondences have been actively studied in computer vision and computer graphics. We begin with a summary concerning some of the active research fields in which point set registration arises. A goal of computer vision and graphics is to reconstruct the entire 3D surface of an object from range images, i.e., 2D images with depth information, captured at different camera positions. To this end, range images are typically converted into point sets, called point clouds. If every point cloud partially overlaps with some of the others, point set registration finds overlaps of the point clouds and aligns them in a global coordinate system

Objectives

Methods

Results

Conclusion