Detection of the Optimal Reflection Symmetry Axis with the Jaccard Index and the Radon Transform

This study determines the optimal reflection symmetry axis of an object in a binary image using the Jaccard index. We propose to find the global optimum on the grid by estimating the upper bounds of the Jaccard index with the Radon transform. Several approaches to improving the Jaccard index computation for a given line are considered. It is shown that for the shear symmetry the optimal skew for a candidate symmetry axis can be found analytically. Some strategies for enumerating possible symmetry axes and selecting the initial approximation are proposed. The experiments show that the Jaccard index for the optimal axis found by the proposed method is not inferior to the exhaustive brute-force of the axes passing through the points of the object contour considering the rasterization error. In terms of speed, the proposed method significantly exceeds the previously developed methods for limiting the exhaustive search.