Matching contours in images using curvature information

The work here described consists in searching for the optimum global matching between contours of two objects represented in images, which are sampled by equal or different number of points. Thus, to determine the optimum global matching between the points of two contours, it is used curvature information, that is totally invariant to rigid transformations. For the case of contours sampled by different numbers of points, two approaches are proposed to exclude, from the matching process, the additional points. In the last section of this paper, a method for the determination of the rigid transformation associated to two contours that is based in the same solution considered in our matching process is also described. methodologiemethotodology. of a contour 2 correspond the amplitude of angle i θ . Consequently, along these two contours to be matched, it can be considered the association between each point and the angle of its curvature. It should be noted that the sequences of angles obtained for each contour depends only on its shape, and not on its scale or position in the original image. The following step of our matching methodology consists in searching for the correspondences between angles of the two contours with the minor global matching cost associated. That is, the goal of this step is to minimize the sum of absolute values of the angular differences between matched points. Thus, we have an assignment problem, but with a fundamental constraint that prevent the application of the traditional assignment algorithms: the order of the points that defines the two contours should be maintained. Therefore, the methodology proposed in (Maciel 2002), for instance, can not be used. For that reason, it is necessary to develop a new matching algorithm that we explain next. Let us consider that the two contours to be matched are sampled by n points. Using our approach, we obtain two sequences of angular amplitudes associated with the curvature along each contour to be matched: n α α α ,..., , 2 1 and n θ θ θ ,..., , 2 1 . The next step is to test the n matching hypotheses successively, figure 3, saving the associated matching values in the following matrix of costs: