Methods and algorithms for finding central symmetry in binary images

Jaccard index for estimating the degree of symmetry

Real world objects that are perceived as symmetrical may not be so in the strict sense. The reasons are natural defects of the figure, optical distortions, the presence of noise and others.
A suitable way to estimate the measure of symmetry of the figure (set of pixels), which returns a value in the range [0,1], is the Jaccard index:
Description image №1
A is the original shape, A' is the rotated shape.
Description image №2

Obviously, rotation relative to different points provides different values of the Jaccard index. Therefore, the task is to find a focus that maximizes the Jaccard index when turning at given angles.