Geometrical Models for Early Vision
Dr. L.M.J. Florack
Technische Universiteit Eindhoven


In several seminal papers Koendrink has introduced a geometric rationale in vision, which lends itself not only for a mathematical assessment of visual processes, but also for "biomimicking" (simulating visual processes) in image analysis. A prerequisite for the geometric rationale in vision and image analysis is an embodiment of well-posed differential operators in the brain, respectively an implementation in terms of linear filters.
I will discuss two paradigms for the operationalization of classical differential calculus: Tikhonov regularization and distribution theory. I will establish an exact relation between scale space theory, a particular instance of distribution theory, and certain Tikhonov regularization schemes. Subsequently I will address some biologically relevant aspects, notably temporal causality, nonlinear retino-cortical transfer, and retino-cortical magnification, and show how these can be accounted for within the "canonical" scale space paradigm (or suitable Tikhonov scheme). Finally I will give simple scheme for generating complete sets of scalar differential invariants, which capture geometrically meaningful local image structure up to some predefined order.

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