Shape Matching Based On Parabolic Fitting Of Curvature Scale Space Maps

In the field of computer vision, shape matching is comprised of two steps, i.e., shape representation and shape similarity computation. The curvature scale space (CSS) technique is a modern technique for shape representation, and has been selected in MPEG-7 due to a set of nice properties. For this technique, firstly the coordinates of the highest point of each arch-shaped trajectory in the CSS map are recorded, and then the compared shapes are matched. However, since the information of the other points of the trajectory is omitted, this representation cannot fully represent all the features of the object shape. To overcome the difficulty, a new representation of the CSS map, called parabolic-fitting CSS representation, is introduced in the present paper. In the new representation, each arc-shape CSS trajectory is fitted by a pair of parabolas, with which more dominant information of the CSS map can be saved. Therefore, a more efficient description of the object shape is achieved. Based on the parabolic-fitting CSS representation, we further proposed a method for computing the similarity between two shapes, and formulated a new shape matching algorithm. First, the fitted CSS maps are shifted horizontally so that their highest parabolas locate at the left of axis, and the parabolas between two compared CSS maps are matched with each other. Then, a mathematical model for measuring the shape similarity is established, and a matching value is obtained, which decided whether a shape could be matched to the other one. Numerical experiments are finally conducted, which show that the new algorithm based on the parabolic-fitting CSS representation has a good performance.