Extraction of symmetry properties using correlation with rotated and reflected images

Abstract

AbstractThe symmetrical properties of an image or a figure are important in visual psychology and computer vision.This paper proposes a new method to extract the properties of rotational symmetry and reflectional symmetry from planar two‐dimensional images. In the detection of the rotational symmetry, first, the original image for a quantized range of angles of rotation is rotated. The rotated results are convolved with the image using directional features. Then a set of affine transformations is applied to the parameter space to obtain the correlation results using each pixel as the center of rotation.The periodicity of the correlation along the rotation angle for each point is evaluated. Finally, the local maximum correlation is determined that indicates the center and the number of folds of the rotational symmetry. In the detection of the reflectional symmetry, the image for the lines in the possible quantized directions is reflected. Then the correlation between the resulting images and the original image is calculated.The transformation that maximizes the correlation directly indicates the direction of the axis of the reflectional symmetry and the translation amount of the glide symmetry. This method does not require any segmentation nor knowledge of the centroid position.The method in this paper evaluates the transformation that matches the images even though the match is a partial one; thus, it can extract the symmetrical property that exists only partially.Although a large amount of computation and storage capacity is required, the method is fundamental, versatile, and suited to the parallel computation.