The Geometry of Visual Space: About the Incompatibility between Science and Mathematics

We address the problem of a geometrical model of vision. This problem is interesting for at least two reasons. First, any theory of vision (human or computer) must decide which geometry should be used to represent perceived objects (e.g., Euclidean vs projective). We believe that this representation should be compatible with geometrical properties of the imaging device (eye or camera). Second, the analysis of geometrical properties of vision will examine the usefulness of standard geometries and can lead to progress in mathematics itself. We analyze the geometry of image formation and show that human vision appears to involve a new branch of geometry whose properties are quite different from the properties of traditional geometries. We formulate these properties and use them to derive models of shape perception. Finally, we provide perceptual interpretations for our theoretical analyses.

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