Properly constrained orthonormal functional maps for intrinsic symmetries

Intrinsic symmetry detection, phrased as finding intrinsic self-isometries, courts much attention in recent years. However, extracting dense global symmetry from the shape undergoing moderate non-isometric deformations is still a challenge to the state-of-the-art methods. To tackle this problem, we develop an automatic and robust global intrinsic symmetry detector based on functional maps. The main challenges of applying functional maps lie in how to amend the previous numerical solution scheme and construct reliable and enough constraints. We address the first challenge by formulating the symmetry detection problem as an objective function with descriptor, regional and orthogonality constraints and solving it directly. Compared with refining the functional map by a post-processing, our approach does not break existing constraints and generates more confident results without sacrificing efficiency. To conquer the second challenge, we extract a sparse and stable symmetry-invariant point set from shape extremities and establish symmetry electors based on the transformation, which is constrained by the symmetric point pairs from the set. These electors further cast votes on candidate point pairs to extract more symmetric point pairs. The final functional map is generated with regional constraints constructed from the above point pairs. Experimental results on TOSCA and SCAPE Benchmarks show that our method is superior to the state-of-the-art methods.