Translation symmetry detection in a fronto-parallel view

In this paper, we present a method of detecting translation symmetries from a fronto-parallel image. The proposed method automatically detects unknown multiple repetitive patterns of arbitrary shapes, which are characterized by translation symmetries on a plane. The central idea of our approach is to take advantage of the interesting properties of translation symmetries in both image space and the space of transformation group. We first detect feature points in input image as sampling points. Then for each sampling point, we search for the most probable corresponding lattice structures in the image and transform spaces using scale-space similarity maps. Finally, using a MRF formulation, we optimally partition the graph of all sampling points associated with the estimated lattices into subgraphs of sampling points and lattices belonging to the same symmetry pattern. Our method is robust because of the joint analysis in image and transform spaces, and the MRF optimization. We demonstrate the robustness and effectiveness of our method on a large variety of images.