DYNAMIC PROGRAMMING FOR CURVED REFLECTION SYMMETRY DETECTION IN SEGMENTED IMAGES

Abstract. This study proposes a method for detecting curved reflection symmetry in binary and grayscale images. The crucial step is to construct a curvilinear symmetry axis generating a nonlinear transformation of the image coordinates that projects the curve on the Y axis and makes the image maximally symmetric about this axis in terms of the Jaccard index. We proposed analytical estimations for the symmetry axis curvature to make the transform bijective. We applied dynamic programming to construct the curvilinear symmetry axis. The axis points are generated one by one with a local direction change at each point. To improve the computational efficiency of the method for images of a given size, we construct a graph of possible transitions in advance. To estimate the symmetry in grayscale images, we proposed two analogs to the Jaccard index. The experiments with image libraries demonstrated that the method correctly handles images containing a single object on a homogeneous background.