Planar Curve Fitting And Matching Algrithm

Fitting curve to planar point clouds and planar curve matching is an important problem in the fields of computer graphics and computer aided design. In this article, we give a survey on the study of curve fitting and matching algorithm, and then we propose our resolution with previous research.In the B-spline curve fitting section. Concerned with the problem of current B-spline curve fitting technical: PDM, TDM and SDM, A principal curve based approach for fitting open B-spline curve to planar point clouds is presented. First, principal curve is extracted from planar point clouds and curvatures at every vertex of the principal curve are calculated. Then we determine the initial control polygon by the curvature maxima. Finally, we fit the open B-spline curve using SDM method to the point clouds. Experiments with real data show that the proposed method can obtain fairly good initial fitting curve, and improve the robust of curve fitting.In the curve matching section. First we introduce several partial curve matching algorithm, include: line search algorithm, curve matching based on longest common subsequence, iterative closest point algorithm and probabilistic matching of curves. Then a partial matching algorithm for planar curve is proposed. The algorithm divide curve matching into global search and local matching. In the global search section, a sub-matrix matching algorithm is used to determine the candidate partial matches between curves. In local matching, curvatures are compared to validate the matches and the accuracy is guaranteed. At last, a rigid body transformation is computed. For curves with few feature points, we divide them into small curve segments according to curvature maxima and make use of a local line search method to find the matches. Experimental results show that the method can efficiently find correct partial matches between curves under rigid body transformation.With the planar B-spline curve fitting algorithm and partial matching algorithm, we also provided a curve matching based revolution retrieval system, on the purpose of computer-aided fragment-stitch, which can be used to classify and query relic fragments.