A Method Based On Functional Maps For Intrinsic Symmetries

Symmetry is the cornerstone of nature. Extracting the symmetries, especially the intrinsic symmetries from 3D shapes is one of basic problems in the field of computer graphics, which has much applications and blueprints such as shape recognition, matching, synthesis and reconstruction. It is easy to extract symmetries from 3D rigid shapes. However, extracting dense global symmetry from the shape undergoing moderate non-isometric deformations is still a challenge work. Many researches for this part aim to keep the intrinsic variables (such as Gaussian curvature, global or local geodesic distance), but all the results are not good.The functional maps method, as a new method to extract the symmetries, finds the maps of feature functions between shapes themselves instead of getting the feature descriptors. At last, it only needs to solve a linear optimization in order to greatly decrease computational complexity. In this paper, we develop an automatic and robust global intrinsic symmetry detector based on functional maps:firstly we get some relative accurate landmark correspondences using the diffusional pruning technique, and then put them into the linear system constructed by the functional maps method as a constraint condition, and finally solve a linear optimization with several constrains to get a matrix which can easily return the dense symmetries. Experimental results show that the proposed method is much better than the functional maps without any other constrain and competitive to the other methods.