Dual Transformation and Manifold Distances Voting for Outlier Rejection in Point Cloud Registration

We present a novel outlier rejection scheme for point cloud registration using SE(3) voting on local transformation estimates with a dual consensus constraint. Point cloud registration is commonly performed by matching key-points in both point clouds and estimating the transformation parameters from these matches. In the presented method, each putative matching pair of points is equipped with a local transformation estimate using the Rigid Transformation Universal Manifold Embedding. Putative matching pairs with similar local estimates are then clustered together and the global transformation between point clouds is estimated for each cluster. Finally, the cluster with the majority of the votes such that the average of local transformations agrees with its associated global transformation is selected for completing the registration. This approach successfully deals with up to 99.5% outliers where state of the art fails.

1. Introduction

Registration of point cloud measurements of 3D objects has been an active research subject with a vast range of applications in computer vision, robotics, autonomous navigation and more. A point cloud is a finite set of points in ℝ³. In many applications these points are samples from a physical object, (we may think of it as a surface in 3D). Viewing point clouds as sets of samples, the registration problem may be formulated as follows: Let be a physical object and T (x) = Rx + t a rigid map (R ∈ SO(3) is a rotation matrix and t ∈ ℝ³ is a translation vector). We consider the transformed object . Let and be two point clouds sampled from the object and the transformed object , respectively. In the registration problem, addressed in this paper, the goal is to estimate the transformation parameters R and t given only and .