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SaidAchmiz comments on Being Wrong about Your Own Subjective Experience - Less Wrong
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Consider this: programming a computer to perceive a coin-viewed-at-an-angle as an ellipse is algorithmically and computationally trivial. Programming the same computer to perceive said coin as a circle is far less trivial; algorithmic sophistication, and more processing power, is required.
Furthermore, our brains are designed to resolve a two-dimensional visual grid into a representation of a three-dimensional scene. The correct 3D representation of the scene is one that includes a circular (well, thin cylindrical) coin. Therefore a brain that perceives the coin as circular regardless of orientation is working as designed.
It may not be that complicated- a brain could just retain the memory of roundness from looking at the coin and look up the memory in place of actual processing, which must be what I was thinking of when I doubted my brain's spatial processing. Would a person who has never seen a coin or similar object perform as well?