Abstract
The impossible objects originally meant imaginary 3D structures that could be represented only by 2D pictures, called impossible figures. However, several tricks were found to construct actual objects whose appearances match impossible figures, and now the impossible objects mean actual 3D objects whose behaviors look impossible because of optical illusion. In this talk we review various classes of newest impossible objects, and consider why our vision systems cannot avoid such illusions. Mathematically we have two kinds of ambiguity in interpreting a 2D picture as a 3D structure. One is the freedom in choosing the viewpoint from which we see the picture, and the other is the freedom in choosing depth for each fixed viewpoint. Psychologically, on the other hand, our vision systems have several strong preferences such as a preference to rectangles over other angles. We will explain the impossible object illusions by the interaction between those mathematical and psychological properties.
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