SIAM-AMS Proceedings Volume 13 1981
Overview. When I accepted the invitation to participate in this symposium, I promised to discuss some representative models of perception. It soon became apparent that the mathematical models currently being proposed are so numerous and so complex that it would require volumes to do justice to even one subspeciality, such as color vision or binocular vision. For example, simple linear matrix operations sufficed for the theory of color mixture for 100 years ( Wyszecki and Stiles [ 1967]); today's more comprehensive theories of color perception invoke additional nonlinear operations (e.g. Pugh and Mollon [ 1979]).2 There are new developments in theories such as factor analysis, multidimensional scaling, and cluster analysis which have been used to describe the mapping of physical stimuli (such as simple color patches but also much more complex stimuli) into psychologically significant space ( Shepard [ 1980]). Measurement theory has evolved as a branch of mathematics to describe the mapping of physical stimulus dimensions (most often intensity) into psychological dimensions ( Krantz, Luce, Suppes, and Tversky [ 1971], Roberts [ 1979]).
In sensory psychology, particularly in the study of vision and of hearing, linear equations have been used with considerable success to describe the receptors, i.e., the optical properties of the lens of the eye ( Fry [ 1955], Krauskopf [ 1962]) and the transducer properties of the outer, middle, and inner ear (basilar membrane, Allen [ 1977a], [ 1977b]). Sine wave stimulus patterns and linear theory are widely used to describe the first order psychological properties of sensory systems ( Licklider [ 1961], Graham [ 1981]). But in these domains, familiar engineering methods have been all but exhausted; current theories deal with complex, nonlinear sensory mechanisms ( Schroeder [ 1975], Victor, Shapley, and Knight [ 1977]). In fact, process models (such as models of the presumed
© 1981 American Mathematical Society____________________
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