Matching Geometric Shapes in 4D Space Incorporating Curvature Information

The Iterative Closest Point (ICP) algorithm and its variants are widely used in matching different patches of 3-Dimensional (3D) scanning data. In this paper, a 4-Dimensional (4D) based approach is proposed to improve the robustness of the ICP algorithm. Considering curvatures of the given geometries as an extra dimension, the existing ICP algorithm can be extended to 4D space. The reason of using this additional information is that it introduces an extra dimension of similarity in the shape matching algorithm, thus improves the effectiveness of the optimization process. Using a variant of the Laplacian smoothing tool, high frequency noise and interferences in the curvature domain are suppressed and the principal geometric features are addressed. By a 4D to 3D orthogonal projection, the matched geometries are projected back to 3D space, where the existing ICP algorithm in 3D is applied as a fine-tuning tool. Numerical implementations on several sets of scanning data demonstrate the robustness of the proposed method. The converging process and the speed of the propose method are investigated as well.