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Detecting Planar and Curved Symmetries of 3D Shapes from a Range Image

This paper addresses the problem of detecting mirror symmetries of 3D shapes. Unlike previous methods, which involve overall 3D shape data, our method uses a range image obtained from one viewpoint. Also, the proposed method can be applied to detection of local as well as global symmetries. The method consists of two stages. First, initial estimates of symmetric plane candidates are obtained using the Hough transform. As local fragments aggregated by the Hough transform, we use the local symmetry points determined by point pairs between occluding contour points and surface points. Next, the iteratively reweighted least-squares method is applied in order to perform nonmaximum suppression and refinement of the parameter values. The method is further extended so as to extract curved as well as planar symmetries. Two kinds of extensions are proposed?fitting a quadratic function instead of fitting a plane, and extracting smoothed local surface symmetries, which represent a 3D extension of smoothed local symmetries. Experimental results involving synthesized and real range images are presented.