Partial Intrinsic Reflectional Symmetry of 3D Shapes


Kai Xu, Hao Zhang, Andrea Tagliasacchi, Ligang Liu, Guo Li, Min Meng, Yueshan Xiong

While many 3D objects exhibit various forms of global symmetries, prominent intrinsic symmetries which exist only on parts of an object are also well recognized. Such partial symmetries are often seen as more natural compared to a global one, especially on a composite shape. We introduce algorithms to extract partial intrinsic reflectional symmetries (PIRS) of a 3D shape. Given a closed 2-manifold mesh, we develop a voting scheme to obtain an intrinsic reflectional symmetry axis (IRSA) transform, which computes a scalar field over the mesh so as to accentuate prominent IRSAs of the shape. We then extract a set of explicit IRSA curves on the shape based on a refined measure of local reflectional symmetry support along a curve. The iterative refinement procedure combines IRSA-induced region growing and region-constrained symmetry support refinement to improve accuracy and address potential issues due to rotational symmetries in the shape. We show how the extracted IRSA curves can be incorporated into a conventional mesh segmentation scheme so that the implied symmetry cues can be utilized to obtain more meaningful results. We also demonstrate the use of IRSA curves for symmetry-driven part repair.