From 2D to 3D: Component Description for Partial Matching of Point Clouds

We present a method to compute the descriptor of components of point clouds, therefore, a novel component-oriented partial matching of point clouds is achieved based on the component descriptor. We observe that 3D components can be constructed by stacking 2D shapes using certain criteria so that the centers of the 2D shapes form a curve called a skeletal curve that is the trajectory of the 2D shapes. In addition, the scaling factors of the 2D shapes also impact the shape of the 3D components. Motivated by these observations, the computation of the component descriptor that is termed 2to3SSC (from 2D to 3D: 2D Shape and Skeletal Curve) is formulated as a 2D shape and skeletal curve extraction problem, and the component-oriented partial matching of the point clouds is based on the dissimilarity measure of 2to3SSCs of the components. Furthermore, for the 2D shape matching, which is crucial to the matching of the components, we present a novel 2D shape descriptor called VDTL (Vertical Distances to the Tangent Line). The proposed method outperforms previously proposed methods because it simultaneously encodes the local and global features of the components as opposed to only encoding the local or partial features as in previous studies. Finally, the effectiveness and performance of 2to3SSCs are compared with those of state-of-the-art feature description and matching methods for different point cloud datasets. Further, the benefits and the applicability of the proposed method are demonstrated; favorable results are obtained for real-world point clouds of Terracotta fragments.