Jaccard Index-Based Detection of Order 2 Rotational Quasi-Symmetry Focus for Binary Images

Finding the exact position of the rotational quasi-symmetry focus using the Jaccard index for binary images was not considered so far. The focus is the point at which the Jaccard index reaches its maximum as the figure rotates. In this paper, we deal with only order 2 rotational symmetry images. A basic extensive focus search procedure is proposed, and the symmetry function profile is subsequently estimated in the vicinity of the maximum. With the search problem analysis, we proposed a computationally efficient procedure for finding the rotational symmetry function maximum based on the quadratic approximation of the symmetry function. The seed point of the search area is the center of mass of the figure. The proposed procedure correctly identified the true rotational symmetry focus for the test image set while the performance was significantly improved compared to the extensive reference procedure.