A geometric model for the functional circuits of the visual front-end

Abstract

This paper reviews a biologically-inspired geometric model for the functional circuits of the visual front-end. An axiomatic approach is taken towards the filters and their tasks in early vision. A highdimensional Lie-group based approach models the convolutions of the receptive fields in a multi-scale, multi-orientation, multi-velocity, multispatial frequency, multi-disparity and multi-color framework. In these new, and essentially invertible, extra-dimensional expansions new geometric reasoning can be developed. They give a feasible approach to the understanding of context, Gestalt, and association fields and enable full exploitation of adaptive, geometry-driven strategies, such as for contour completion and convection. The high-dimensionality leads to high computational costs, but, just as in human vision, this can be solved by massively parallel implementations, which is one of the goals of the EU Human brain project.