Image Representation by Complex Cell Responses

Authors:
Ingo J. Wundrich;Christoph J. Von Der Malsburg;Rolf P. Würtz
Affiliations:
Institut für Neuroinformatik, Ruhr-Universität Bochum, D-44780 Bochum, Germany;Institut für Neuroinformatik, Ruhr-Universität Bochum, D-44780 Bochum, Germany, and Department of Computer Science, University of Southern California, Los Angeles, CA 90089, U.S.A.;Institut für Neuroinformatik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
Venue:
Neural Computation
Year:
2004

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Abstract

We present an analysis of the representation of images as the magnitudes of their transform with complex-valued Gabor wavelets. Such a representation is a model for complex cells in the early stage of visual processing and of high technical usefulness for image understanding, because it makes the representation insensitive to small local shifts. We show that if the images are band limited and of zero mean, then reconstruction from the magnitudes is unique up to the sign for almost all images.