Detecting Bilateral Symmetry in Perspective

A method is presented for efficiently detecting bilateral symmetry on planar surfaces under perspective projection. The method is able to detect local or global symmetries, locate symmetric surfaces in complex backgrounds, and detect multiple incidences of symmetry. Symmetry is simultaneously evaluated across all locations, scales, orientations and under perspective skew. Feature descriptors robust to local affine distortion are used to match pairs of symmetric features. Feature quadruplets are then formed from these symmetric feature pairs. Each quadruplet hypothesises a locally planar 3D symmetry that can be extracted under perspective distortion. The method is posed independently of a specific feature detector or descriptor. Results are presented demonstrating the efficacy of the method for detecting bilateral symmetry under perspective distortion. Our unoptimised Matlab implementation, running on a standard PC, requires of the order of 20 seconds to process images with 1,000 feature points.