A Graph-Based Approach to Symmetry Detection

Abstract

Symmetry detection aims at discovering redundancy in the form of reoccurring structures in geometric objects. In this paper, we present a new symmetry detection algorithm for geometry represented as point clouds that is based on analyzing a graph of surface features. We combine a general feature detection scheme with a RANSAC-based randomized subgraph searching algorithm in order to reliably detect reoccurring patterns of locally unique structures. A subsequent segmentation step based on a simultaneous region growing variant of the ICP algorithm is applied to verify that the actual point cloud data supports the pattern detected in the feature graphs. We apply our algorithm to synthetic and real-world 3D scanner data sets, demonstrating robust symmetry detection results in the presence of scanning artifacts and noise. The modular and flexible nature of the graph-based detection scheme allows for easy generalizations of the algorithm, which we demonstrate by applying the same technique to other data modalities such as images or triangle meshes.