###### Abstract  
This paper presents a robust point cloud registration method based on a multi-scale covariance matrix descriptor and an accurate transformation estimation. Compared with state-of-the-art feature descriptors, such as FPH, 3 DSC, spin image, etc., our proposed multi-scale covariance matrix descriptor is superior for dealing with registration problems in a higher noise environment since the mean operation in generating the covariance matrix can filter out most of the noise-damaged samples or outliers and also make itself robust to noise. Compared with transformation estimation, such as feature matching, clustering, ICP, RANSAC, etc., our transformation estimation is able to find a better optimal transformation between a pair of point clouds since our transformation estimation is a multi-level point cloud transformation estimator including feature matching, coarse transformation estimation based on clustering, and a fine transformation estimation based on ICP. Experiment findings reveal that our proposed feature descriptor and transformation estimation outperforms state-of-the-art feature descriptors and transformation estimation, and registration effectiveness based on our registration framework of point cloud is extremely successful in the Stanford 3D Scanning Repository, the SpaceTime dataset, and the Kinect dataset, where the Stanford 3D Scanning Repository is known for its comprehensive collection of high-quality 3D scans, and the SpaceTime dataset and the Kinect dataset are captured by a SpaceTime Stereo scanner and a low-cost Microsoft Kinect scanner, respectively.  
point cloud registration; feature descriptor; multi-scale covariance matrix; boundary point detection; transformation estimation +
Footnote †: journal: Medical  
global optimum during the distance-minimization process. Therefore, a coarse transformation estimation should be carried out initially to obtain the correct initial transformation parameters, which include a rotation matrix and a translation vector with six degrees of freedom. Finding geometric features and the correspondence between these features are two crucial jobs that must be completed for point clouds in any initial orientation or position during coarse registration. However, the aforementioned tasks may be hindered by some significant obstacles, such as noise and outliers, various types of occlusions, varying densities, low overlap, and so on.  
In this paper, we propose a local descriptor based on a multi-scale covariance matrix for point cloud registration which is robust to noise and invariant to rigid transformation, and we also put forward an accurate transformation estimation method by multi-level estimating point cloud transformations. The following is a summary of the contributions.  
(1) A multi-scale covariance matrix feature descriptor is proposed, which can describe the geometrical relationship, eigenvalue variation gradient, and surface variation gradient between a keypoint and its neighboring points. The feature descriptor can filter out most of the noise samples by the mean operation in the process of producing covariance and make it very robust to noise.  
(2) A method for detecting boundary points is put forward, which can efficiently extract points on the border. By utilizing this approach, nearby keypoints may be successfully eliminated, improving the descriptiveness of the keypoint by our proposed feature descriptor.  
(3) An accurate transformation estimation between a pair of point clouds is brought upon. In this method, we obtain corresponding keypoint pairs by feature matching, estimate an initial transformation using a coarse transformation estimation method based on clustering via these correspondences, and finally obtain an accurate transformation by a fine transformation estimation, such as ICP's variants.