A Caltech Library Service

Toward a mathematical theory of perception

Kajiya, James Thomas (1979) Toward a mathematical theory of perception. Computer Science Technical Reports, 1979.4116. California Institute of Technology , Pasadena, CA. (Unpublished)

PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


A new technique for the modelling of perceptual systems called formal modelling is developed. This technique begins with qualitative observations about the perceptual system, the so-called perceptual symmetries, to obtain through mathematical analysis certain model structures which may then be calibrated by experiment. The analysis proceeds in two different ways depending upon the choice of linear or nonlinear models. For the linear case, the analysis proceeds through the methods of unitary representation theory. It begins with a unitary group representation on the image space and produces what we have called the fundamental structure theorem. For the nonlinear case, the analysis makes essential use of infinite-dimensional manifold theory. It begins with a Lie group action on an image manifold and produces the fundamental structure formula. These techniques will be used to study the brightness perception mechanism of the human visual system. Several visual groups are defined and their corresponding structures for visual system models are obtained. A new transform called the Mandala transform will be deduced from a certain visual group and its implications for image processing will be discussed. Several new phenomena of brightness perception will be presented. New facts about the Mach band illusion along with new adaptation phenomena will be presented. Also a new visual illusion will be presented. A visual model based on the above techniques will be presented. It will also be shown how use of statistical estimation theory can be made in the study of contrast adaptation. Furthermore, a mathematical interpretation of unconscious inference and a simple explanation of the Tolhurst effect without mutual channel inhibition will be given. Finally, image processing algorithms suggested by the model will be used to process a real-world image for enhancement and for "form" and texture extraction.

Item Type:Report or Paper (Technical Report)
Additional Information:Copyright © James T. Kajiya 1979. A dissertation submitted to the faculty of the University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Group:Computer Science Technical Reports
Series Name:Computer Science Technical Reports
Issue or Number:1979.4116
Record Number:CaltechAUTHORS:20120424-144344175
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:30300
Deposited On:01 May 2012 21:00
Last Modified:03 Oct 2019 03:49

Repository Staff Only: item control page