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In Collection A Transformation for Extracting New Descriptors of Shape

Author(s): Harry Blum.
In Collection: Models for the Perception of Speech and Visual Form, MIT Press, Weiant Wathen-Dunn, pp. 362--380, Cambridge, 1967.
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Abstract:
I have approached the problem of shape by assuming that the current mathematical tools were somehow missing essential elements of the problem. For despite more than two millenia of geometry, no formulation which appears natural for the biological problem has emerged. This is not surprising perhaps when one recognizes that geometry has been born of surveying and has grown in close collaboration with physical science and its nesuration problems. A corollary to this position is that there is some central difference between the biological problem that we are trying to deal with and the physical problem that we have been dealing with. Consequently, such an approach requires a restudy of visual function to assess what such a geometry should indeed try to accomplish. Unfortunately, the problem of exploring function is not easy to do in isolation, since the visual shapes and their functional value to an organism may reflect the cultural bias of the experimenter to a large degree. I have chosen to enter the problem from the middle hypothesizing simple shape processing mechanisms, and then exploring together the geometry and visual function that result. One such mechanism is presented in this paper. Since it leads to a drastic reformulation of a number of notions implicit in our views and experiments.

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