Hausdorff Distance Calculation Between Curves And Surfaces And Research In Shape Matching

As a method of similarity measure, Hausdorff distance(HD) can effectively measure the accuracy of approximating or non-matching between two geometric objects, it have been widely used in the geometrical approximation, mesh simplification and image matching. For the Hausdorff distance between discrete geometry objects, it mainly used in image matching, we can solve it directly according to the Hausdorff distance’s definition or its improved form. So far, it has been extensively used in many areas such as face recognition, license plate recognition, collision detection, etc. Compared to the research and applications of Hausdorff distance in the image matching, due to the high computational complexity and the proposed methods are difficult to achieve, the calculation methods and applications of Hausdorff distance are fairly little between continuous geometry. Aiming at this problem, we put the Hausdorff distance as the research object and mainly analyze the methods of calculating the Hausdorff distance between continuous geometric objects and its applications.The method of calculating the Hausdorff distance between curved surfaces is mainly proposed in this paper. In view of the high computational complexity and less related calculation methods between surfaces, a triangular patch bounding box method is proposed to quickly measure the approximate value of Hausdorff distance between parametric surfaces. The method of discretizing triangular patches from surfaces is a good way to approach the surface, so the Hausdorff distance between surfaces can be approximated by the Hausdorff distance between triangles. In order to improve computational efficiency,bounding box technology is used to eliminate the invalid triangles in the process of computing. At the same time, in order to further simplify the distance calculation between two triangles, an approximate calculation method of sampling points is put forward and the error is under control. The experiments show that the proposed method is simpler, easier to implement and has a higher exclusion rate compared with the surface surrounded bounding box method, also the computational efficiency is significantly improved without affecting the results, so the method has a wide application value. On this basis, this method is extended to compute the Hausdorff distance between curve and surface, and we can prove the validity and practicability of this method through the experimental examples.In addition, the shape matching based on the Hausdorff distance and its solving method between discrete point set and continuous geometry object such as polygon geometry, curves and surfaces are researched. And the method of similarity measure of Hausdorff distance is proposed to use in reduced order error measurement of curves and surfaces. We can also judge the effectiveness of the order reduction method throughcalculating the error metrics for degree reduction examples of curves and surfaces using our proposed method.