Can animals detect symmetry? (Translation of 「動物に対称性は見えるか」)

First, let us see a picture by Jurgen Otto who shows many photographies of spiders. The 6th picture exhibits an admirable mimesis of a spider.

The color and the texture are very good as a camouflage. However, we can easily find its strange figure by the clue of the symmetric part of the picture. That is line symmetric (or plane symmetric considering thickness), while the vein of the bark is not symmetric in the scale of the spider.

We don't need the mathematical notion of symmetry. Intuitively it appeals to our sense by an unnatural shape making contrast with the irregularly shaped ambient. Symmetry is a character of animals. (Not unique to animals. Flowers and crystals are also symmetric.) Since these spiders survive, this camouflage is successful in spite of its outstanding symmetry.

Although I cannot explain well, optical recognition of symmetry is more difficult or higer task than that of higher, lower, left, right, near or far. Thus we reach the following general question:
``Can a monkey, a dog, a cat, a bird or a fish detect symmetry?"

An idea of experiment to answer this question is the following.
Make cookies of two kinds, one dog's favorite ones, the other passable ones. Shape the former non-symmetric and the latter symmetric. Let dogs choose them repeatedly not allowing them to distinguish by smell. Do the dogs develop their skill to choose favorite cookies? Please try and let me know the result because I have neither a dog nor a cat. If it is accurately described, it would be an interesting ethological report.