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

This paper addresses the problem of detecting mirror symportion to be analyzed needs to be segmented and to inmetries of 3D shapes. Unlike previous methods, which involve clude the overall 2D shape. Moment analysis cannot thereoverall 3D shape data, our method uses a range image obtained fore be applied to locally symmetric shapes or incomplete from one viewpoint. Also, the proposed method can be applied data such as occluded shapes. On the other hand, while to detection of local as well as global symmetries. The method the latter approach is suitable both for detecting local symconsists of two stages. First, initial estimates of symmetric plane metry and handling incomplete data, pointwise local symcandidates are obtained using the Hough transform. As local metry detection is often sensitive to noise. fragments aggregated by the Hough transform, we use the local In order to identify 3D symmetry, a method based on symmetry points determined by point pairs between occluding moment analysis has been proposed for detecting various contour points and surface points. Next, the iteratively reweighted least-squares method is applied in order to perform global symmetries from octree data [7]. This method, hownonmaximum suppression and refinement of the parameter ever, suffers from the same problems as 2D moment-based values. The method is further extended so as to extract curved methods. For example, symmetry detection is impossible as well as planar symmetries. Two kinds of extensions are using a range image from one viewpoint, such as is obtained proposed—fitting a quadratic function instead of fitting a using a typical range scanner [8]. A 3D shape description plane, and extracting smoothed local surface symmetries, which scheme based on local symmetry analysis also has been represent a 3D extension of smoothed local symmetries. Experireported [9], which is a 3D extension of the symmetric axis mental results involving synthesized and real range images are transform [1]. However, this work concentrated on the presented.  1996 Academic Press, Inc. theoretical aspects of the scheme and did not actually dem-