Functional map-based reflection intrinsic symmetry detection and symmetrization for 2D deformable shapes

Abstract

Symmetry is widely prevalent in both natural phenomena and man-made objects. Detecting and enhancing the symmetry of shapes is crucial in fields like art and engineering. However, symmetry detection and shape symmetrization based on it for 2D deformable shapes have long been a challenge. In this paper, we propose a 2D intrinsic symmetry detection method based on functional maps. By leveraging constraints from feature-symmetric point pairs and functional maps framework, our approach formulates an optimization problem for detecting intrinsic symmetry in 2D deformable shapes. We employ spectral upsampling techniques, iteratively optimizing the functional map matrix and symmetric point-to-point mapping matrix in both frequency and spatial domains. Then we perform rapid symmetrization guided by the extracted backbone and shape symmetry. The backbone is detected by mapping skeletons, and projecting it onto a straight line segment drives automatic mesh deformation to symmetrize the 2D shape. We have tested our method on a variety of 2D shapes, and the results have demonstrated its effectiveness.