Notes on Perceptual Geometries.

by Fred S. Roberts

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Discusses some mathematical models of visual perception; proposes terminology; asks several basic theoretical questions; and introduces a new approach based on the way that human beings actually perceive spatial relationships. What subjects see as straight or parallel or perpendicular may not be physically so. A useful approach is based on Zeeman's notion of a tolerance space within which objects can move before we notice any difference. A tolerance geometry could be obtained from classical Euclidean geometry by substituting closeness for identity; ordinary betweenness is replaced by epsilon-betweenness, an approach developed further in P-4430. Perhaps the simplest example is an indifference graph (in the graph theory sense). To account for inconsistency in judgment, it may be necessary to use probabilistic rather than deterministic models, like the probabilistic consistency in preference theory. (Prepared for the NSFsponsored Workshop on Perceptual Geometries in Miami, August-September 1970.) 20 pp. Ref. (MW)

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