The Lie transformation group model of visual perception

The Lie transformation group model of neuropsychology (LTG/NP) purports to represent and explain how the locally smooth processes observed in the visual field, and their integration into the global field of visual phenomena, are consequences of special properties of the underlying neuronal complex. These properties are modeled by a specific set of mathematical structures that account both for local (infinitesimal) operations and for their generation of the “integral curves” that are visual contours. The purpose of this tutorial paper is to expound, as nontechnically as possible, the mathematical basis for LTG/NP, and to evaluate that model against a reasonable set of criteria for a neuropsychological theory. It is shown that this approach to spatial vision is closer to the mainstream of current theoretical work than might be assumed; recent experimental support for LTG/NP is described.

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