I'm not sure whether this question belongs here, so I apologize in advance if it does not, however, I think it's worth a try. Also please excuse my poor English, I am not native English speaker.
My question is:
How do people recognize symmetric shapes?
By "symmetry" I mean only reflection with respect to axis in two dimensions and reflection with respect to a plane in three dimensions.
I try to specify what I have in mind.
I don't find strange that one can recognize the same shape rotated in some way, since one has plenty experience "from real life" by which this ability can be justified (If I see the letter "F" written on a piece of paper, after rotating the paper by hand, I still see the same object even though now it looks different). So one could argue that the ability to recognize some shape after a rotation is an evolutionarily developed skill.
However, I don't think that this kind of argument can be applied to reflections. The only experience with this can be obtained by (versions of) observing mirrored images of things. And even though the "skill to recognize a reflection of a tiger on a surface of a pond" can be a good skill contributing to survival, this still does not explain why it is easier to recognize symmetric shapes than recognizing the same shapes, when one of them is rotated in some non-trivial way.
In particular, what I find really puzzling is this: Suppose I know a person with a strangely shaped scar on his left cheek. Someone shows me a reflected picture of that person (so on the picture, the scar is seemingly on the right cheek, etc.) and I still recognize him immediately, and probably I would not even realize the image is reflected. It seems to me that the ability to "ignore" the differences between the original image and reflected image is much stronger than the ability to ignore the difference between an image and the same image rotated.
Are there some explanations of this from evolutionary and/or cognitive science's point of view?
I would also like to stress that this is not a question about the ability to recognize oneself in a mirror.
Also, I would appreciate any references, where similar kinds of questions are addressed.