Cross ratio arrays: A descriptor invariant to severe projective deformation and robust to occlusion for planar shape recognition

Abstract

Recognizing planar objects such as characters, symbols and logos is considered a hard problem in computer vision due to the possibility of these shapes suffer from different kinds of disturbances: projective or other nonlinear deformations, occlusions and spurious insertions. Different planar descriptors have been proposed by taking advantage of geometric features that are invariant to certain image transformations, usually linear ones such as scaling, rotation and affinity. In this work, a new descriptor of planar shapes robust to projective deformations is proposed: Cross Ratio Arrays (CRA). The descriptor is based on tracing rays across the images and collecting their intersections with the borders of the shapes to assemble arrays of computed cross ratios, one of the most fundamental projective invariants. Higher level arrays are built out of these sets of arrays from both query and template shapes, which ultimately allows us to identify correspondences in these shapes to estimate how projectively deformed one shape is from the other. Experiments with synthetic shapes as well as real world scene shapes suffering from severe projective deformations were conducted, with CRA outperforming state-of-the-art descriptors. In addition, tests were performed with different levels of occlusion and weak nonlinear deformations to evidence CRA’s robustness to such cases.