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Global Topological Properties of Images Derived from Local Curvature Features

Erhardt BarthContact Information, Mario FerraroContact Information and Christoph ZetzscheContact Information

(6)  Institute for Signal Processing, University of Lübeck, Ratzeburger Allee 160, 23538 Lübeck, Germany
(7)  Dipartimento di Fisica Sperimentale and INFM, via Giuria 1, Torino, Italy
(8)  Institut für Medizinische Psychologie, Goethestr. 31, 80336 München, Germany
Abstract
In this paper we show that all images are topologically equivalent. Nevertheless, one can define useful pseudo-topological properties that are related to what is usually referred to as topological perception. The computation of such properties involves low-level structures, which correspond to end-stopped and dot-responsive visual neurons. Our results contradict the common belief that the ability for perceiving topological properties must involve higher-order, cognitive processes.

Keywords  Topology - Euler number - closure - curvature - visual perception


Contact Information Erhardt Barth
Email: barth@isip.mu-luebeck.de
URL: http://www.isip.mu-luebeck.de

Contact Information Mario Ferraro
Email: ferraro@to.infn.it

Contact Information Christoph Zetzsche
Email: chris@imp.med.uni-muenchen.de
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