3-d Symmetry Detection Using the Pseudo-polar Fourier Transform

Symmetry detection in 3D images is an important task in many fields such as computer vision, pattern recognition to name a few. An algebraic based 3D symmetry detection algorithm is presented. The 3D volume is transformed to the Fourier domain by using the pseudo-polar Fourier transform. The pseudo-polar representation enables to analyze angular properties such as finite symmetric properties that stay invariant under the transform. The algorithm is based on analysis of the angular correspondence rate of the given volume and its rotated and rotated-inverted replicas in their pseudo-polar representations. Initially, the algorithm detects the rotations symmetry group of the given volume. This group enables to detect the rest of the symmetries. The complexity of the algorithm is O ( Nlog(N) ) , where N × N × N is the volumetric size. The complexity of the proposed algorithm is independent of the number of detected symmetries. Different types of objects were tested. The results demonstrate that all the symmetries, including imperfect ones, are detected by the proposed algorithm.