Detecting Rotational Symmetry in Polar Domain Based on SIFT

Symmetry is everywhere, found in objects around us, whether artificial or natural, and acts as a mid-level cue for both human and machine perception of the chaotic real world. From real-world symmetries, humans take advantage of various tasks, but their computational treatment remains elusive. This study proposes a novel approach for detecting rotational symmetry and the order of rotation within a single object digital image. The proposed method relies on the extraction of Scale Invariant Features Transform (SIFT) features and the robust centroid point. The centroid is computed on the basis of extracted features, to be drawn in xy-plan so that the centroid is on the origin. Later on, converted to the polar domain to facilitate the extraction of rotationally symmetric pairs and the order of rotation. The symmetry exhibited by each pair in the transform domain is the function of the features' location, orientation, magnitude, and descriptor vector. Experimental results show that the approach correctly identifies the rotational symmetry if enough features are detected and the centroid is robust one.