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

Abstract:

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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