Abstract: As a concise representation of shapes,skeletons preserve both the geometric characteristics and complete topological structure of the shapes.Among skeleton computation methods,the potential field-based approach suggests that skeletons are located in the region of singular points on the potential field surface and are capable of providing a topologically correct and con-tinuous representation of skeletons.However,the skeletons derived from this method still have some limitations,such as high sensitivity to noise and isometric transformations.To address these issues,this paper assumes that charges are evenly distributed on the shape boundary and defines a novel potential field inside the shape for the computation of 2D skeletons.Unlike traditional potential fields that use Euclidean distance,this paper utilizes heat kernel functions to approximate the geodesic distance within the shape,and then calculates the novel electric potential distribution within the shape.Due to the smoothness of the heat kernel geodesic distance,it exhibits stronger robustness against shape noise and isometric transformations.Furthermore,based on the Nyström distance interpolation technique,a fast computation method for the defined potential field is proposed.Extensive experiments are conducted on two shape datasets,and the parameters of this method are thoroughly analyzed,demonstrating that the proposed method can generate stable and concise shape skeletons,outperforming state-of-the-art competitors in the robustness of noise.

Key words: Shape representation, Skeleton computation, Generalized electric potential, Heat kernel, Smoothed geodesic distance