David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Axiomathes 13 (3-4):347-363 (2003)
We present a neuro-geometrical model for generating the shape of Kanizsa's modal subjective contours which is based on the functional architecture of the primary areas of the visual cortex. We focus on V1 and its pinwheel structure and model it as a discrete approximation of a continuous fibration π: R × P → P with base space the space of the retina R and fiber the projective line P of the orientations of the plane. The horizontal cortico-cortical connections of V1 implement what the geometers call the contact structure of the fibration π, and defines therefore an integrability condition which can be shown to correspond to Field's, Hayes', and Hess' psychophysical concept of association field. We present then a variational model of curved modal illusory contours (in the spirit of previous models due to Ullman, Horn, and Mumford) based on the idea that virtual contours are “geodetic” integral curves of the contact structure.
|Keywords||Contact structure Pinwheels Functional architecture Fibration Horizontal connections Lie group Association field Illusory contour Variational model|
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Peer F. Bundgaard (2011). The Grammar of Aesthetic Intuition: On Ernst Cassirer's Concept of Symbolic Form in the Visual Arts. Synthese 179 (1):43 - 57.
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