Robust point cloud registration based on topological graph and Cauchy weighted [formula omitted] norm
Point Cloud Registration (PCR) is a fundamental and important issue in photogrammetry and computer vision. Its goal is to find rigid transformations that register multiple 3D point sets. This paper proposes a robust and efficient PCR method based on topological graph and Cauchy weighted lq norm. Our method does not require initializations and is highly robust to outliers and partial overlaps. It contains two major steps: (1) correspondence based coarse registration, which is called Weighted lq Coarse Registration (WlqCR) In the WlqCR method, we represent feature point sets as topological graphs and transform the point matching problem to an edge matching problem. We build a mathematical model for edge correspondence maximization. We also present an edge voting strategy to distinguish potential correct matches from mismatches. Then, we define a concept called edge vector, which has a property that it is invariant to translations. Based on this property, six Degrees of Freedoms (DoF) PCR problem can be simplified into two three DoF subproblems, i.e. rotation estimation and translation estimation. (2) fine registration based on Weighted lq Iterative Closest Point (WlqICP) We propose a new ICP method called WlqICP, which is much more robust to partial overlaps compared with traditional ICP. In both rotation estimation and WlqICP, we use a new Cauchy weighted lq norm (0<q<1) instead of l2 norm for object function construction, which has a high degree of robustness. Extensive experiments on both simulated and real data demonstrate the power of the proposed method, i.e. our method is more robust (is able to tolerate up to 99% of outliers) and much faster than compared state of the art methods (WlqCR is almost two orders of magnitude faster than RANdom SAmple Consesus (RANSAC) and its variants under 95% of outliers) The source code will be made publicly available in http:/www.escience.cn/people/lijiayuan/index.html.