A 3D Surface Matching Method Using Keypoint- Based Covariance Matrix Descriptors

A 3D surface is considered one of the most promising tools for representing and recognizing 3D objects. Therefore, 3D surface matching is widely applied to 3D object recognition, retrieval, and so on. In this paper, a 3D surface matching method using a keypoint-based covariance matrix descriptor is proposed, whose purpose is to find correspondences between 3D surfaces (e.g., 3D model and scene) by matching feature points, which are highly repeatable keypoints described by a multi-scale covariance matrix descriptor. A keypoint is detected by analyzing the surface variation index and eigenvalue variation index of a local neighborhood centered at a point. A multi-scale covariance matrix descriptor of a keypoint describes the geometric relation, surface variation gradient, and eigenvalue variation gradient between the keypoint and its neighborhood. The rationale for adopting the keypoint-based covariance matrix descriptor in our proposed 3D surface matching method is that a small number of keypoints with high repeatability can greatly enhance the matching effect of a 3D surface, after being described by a multi-scale covariance matrix descriptor with high descriptiveness. The experimental results also show that our proposed keypoint detection algorithm has higher repeatability than the surface variation index-based and eigenvalue variation index-based detection algorithms; our proposed multi-scale covariance matrix descriptor has higher descriptiveness than spin image, PFH, and 3DSC; our proposed bidirectional nearest-neighbor distance ratio algorithm can obtain better feature matching effect than the nearest-neighbor-based and nearest-neighbor distance-ratio-based feature matching. Finally, our proposed 3D surface matching method has a better matching effect than 3D surface matching methods based on spin image, PFH, and 3DSC on the Stanford 3D Scanning Repository, UWA data set and Bologna data set.