Rotational symmetry is a nice play around thingy. Simply said, an approach that you could use is template based matching. There are some general steps to take in order to perform this.
- Rotate a given image (imgBase) for some degrees and call it imgRotated
- For the first image, define some interesting points by performing an interesting feature point detector like SURF, SIFT, ORB, ...
- Use a set of features defined on the imgBase as locations for test. Feed regions of interest around those points as templates to a descriptor and create a representation for it. Many aproaches are here possible, look at this link : http://docs.opencv.org/modules/gpu/doc/feature_detection_and_description.html
- Apply same descriptor at same locations in imgRotated
- Match the descriptors for each point and define the amount of equality which will be an amount of rotational symmetry.
I do not have a solution, but given this comments, I think you got some starting points right.
