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Proceedings Paper

Geometry of the perceptual space
Author(s): Amir H. Assadi; Stephen Palmer; Hamid Eghbalnia; John Carew
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Paper Abstract

The concept of space and geometry varies across the subjects. Following Poincare, we consider the construction of the perceptual space as a continuum equipped with a notion of magnitude. The study of the relationships of objects in the perceptual space gives rise to what we may call perceptual geometry. Computational modeling of objects and investigation of their deeper perceptual geometrical properties (beyond qualitative arguments) require a mathematical representation of the perceptual space. Within the realm of such a mathematical/computational representation, visual perception can be studied as in the well-understood logic-based geometry. This, however, does not mean that one could reduce all problems of visual perception to their geometric counterparts. Rather, visual perception as reported by a human observer, has a subjective factor that could be analytically quantified only through statistical reasoning and in the course of repetitive experiments. Thus, the desire to experimentally verify the statements in perceptual geometry leads to an additional probabilistic structure imposed on the perceptual space, whose amplitudes are measured through intervention by human observers. We propose a model for the perceptual space and the case of perception of textured surfaces as a starting point for object recognition. To rigorously present these ideas and propose computational simulations for testing the theory, we present the model of the perceptual geometry of surfaces through an amplification of theory of Riemannian foliation in differential topology, augmented by statistical learning theory. When we refer to the perceptual geometry of a human observer, the theory takes into account the Bayesian formulation of the prior state of the knowledge of the observer and Hebbian learning. We use a Parallel Distributed Connectionist paradigm for computational modeling and experimental verification of our theory.

Paper Details

Date Published: 23 September 1999
PDF: 11 pages
Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); doi: 10.1117/12.364087
Show Author Affiliations
Amir H. Assadi, Univ. of Wisconsin/Madison (United States)
Stephen Palmer, Univ. of California/Berkeley (United States)
Hamid Eghbalnia, Univ. of Wisconsin/Madison (United States)
John Carew, Univ. of Wisconsin/Madison (United States)

Published in SPIE Proceedings Vol. 3811:
Vision Geometry VIII
Longin Jan Latecki; Robert A. Melter; David M. Mount; Angela Y. Wu, Editor(s)

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