Geodesic Mean Shift

In this paper we introduce a versatile and robust method for analyzing the feature space associated with a given surface. The method is based on the mean-shift operator which was shown to be successful in image and video processing. Its strength stems from the fact that it works in a single space of joint geometry and attributes called the feature-space. The feature-space attributes can be scalar or vector, and are either given (e.g. temperature, pressure) or extracted (e.g. curvature, geodesic centricity). The procedure works as a gradient descent that finds maxima of an estimated probability density function in feature-space. Using this technique on surfaces introduces several difficulties. First, meshes as opposed to images do not present a regular and uniform sampling of the feature-space. Second, on boundary embedded surfaces the shifting procedure must be constrained to stay on the surface, obeying geodesic distances. Based on local parameterizations scheme, we generalize the meanshift procedure to unstructured embedded boundary meshes. Furthermore, we also support piecewise linear attribute definitions and not only piecewise constant by employing hardware-supported area sampling using rasterization. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Boundary representations; I.4.6 [Image Processing And Computer Vision ]: Segmentation—Region growing, partitioning G.3 [Probability And Statistics]: Statistical computing