A registration method for free-form surfaces

This paper presents a method for fast surface matching. The algorithm handles all six degrees of freedom and is based on the curvature of a surface. Two surfaces are sampled at discrete points and represented as a set of threedimensional verteces. The sampling rate is supposed to be at least the double of the nyquist frequency. Steps in the surface lead to a curvature value higher than a threshold. The related verteces are marked and not taken into account for any further calculation. The gaussian curvature of the two surfaces is computed. Then a certain number of feature points are extracted out of the surfaces. These feature points are connected to create triangles. Similar triangles found in both surfaces are compared. If they match the rotation between these two triangles can be computed. A transformation histogram determines the rotation with the highest probability and a sequencing displacement calculation specifies a displacement between the triangles with the best likelyhood. Only the displacement between the triangles contributing to the calculated orientation vote for the correct displacement. The exact matching is done by a least square optimization procedure considering only the triangles connected with the initial transformation and possessing the same parameters in both surfaces such as size and form. The proposed method is applicable on range images without any edges or known reference points as it is based on free-farm surface inherent features.