Local Reflectional Symmetry Detection in Point Clouds Using a Simple PCA-Based Shape Descriptor

Symmetry is a commonly occurring feature in real world objects and its knowledge can be useful in various applications. Different types of symmetries exist but we only consider the reflectional symmetry which is probably the most common one. Multiple methods exist that aim to find the global reflectional symmetry of a given 3D object and although this task on its own is not easy, finding symmetries of objects that are merely parts of larger scenes is much more difficult. Such symmetries are often called local symmetries and they commonly occur in real world 3D scans of whole scenes or larger areas. In this paper we propose a simple PCA-based local shape descriptor that can be easily used for potential symmetric point matching in 3D point clouds and, building on previous work, we present a new method for detecting local reflectional symmetries in 3D point clouds which combines the PCA descriptor point matching with the density peak location algorithm. We show the results of our method for several real 3D scanned scenes and demonstrate its computational efficiency and robustness to noise.