I work with images, as a Laue pattern, that consists of spots distributed in an image. The pattern could have a certain symmetry (refelction symmetry, rotational symmetry, inversion center, ...) that we as human easily detect. I am currently working with a symmetry algorithm that uses Hough transformation to detect those symmetries. Important is that the algorithm has some kind of flexibility in finding the center for symmetries and also not checking perfectly each pixel mapped on corresponding pixels to show symmetries.
One problem is beeing encountered:
2-fold symmetric patterns get detected as 4-fold rotational symmetric. The algorithm computes it correctly, there is just a situation that I did not consider and gets misclassified. In the 2-fold case, there is a big cross, which is detected and therefore missleades to 4-fold symmetry.
First of all, I checked for similar questions, but none of them was applicable and well suiting the problem.
I tired also to rotate the image and compare it each angle with the initial image to search for peaks. -> is to static and less felxibel
I tried to use binary openings and dilations to abstract to relevant information. -> non-uniform spot generation, not good
I tried as well some summations and sructural similarity comparisons. -> differences less visible than expected
I also tried to work with the centers of the found spots. But none of them worked out. -> not all are spotted
Does anyone have an idea how one could look for rotational symmetries in general or distinguish 2-fold and 4-fold rotational symmetries?
Example of a 4-fold rot. symmetry:
Example of a 2-fold rot. symmetry:
