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  Hierarchical Modeling of Local Image Features through Lp-Nested Symmetric Distributions

Sinz, F., Simoncelli, E., & Bethge, M. (2010). Hierarchical Modeling of Local Image Features through Lp-Nested Symmetric Distributions. In Y. Bengio, D. Schuurmans, J. Lafferty, C. Williams, & A. Culotta (Eds.), Advances in Neural Information Processing Systems 22 (pp. 1696-1704). Red Hook, NY, USA: Curran.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C0C8-7 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-93C4-A
Genre: Conference Paper

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 Creators:
Sinz, F1, 2, Author              
Simoncelli, EP, Author
Bethge, M1, 2, Author              
Affiliations:
1Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497805              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: We introduce a new family of distributions, called Lp-nested symmetric distributions, whose densities are expressed in terms of a hierarchical cascade of Lp- norms. This class generalizes the family of spherically and Lp-spherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family includes the Independent Subspace Analysis (ISA) model as a special case, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. Lp-nested distributions are relatively easy to estimate and allow us to explore the variety of models between ISA and the Lp-spherically symmetric models. By fitting the generalized Lp-nested model to 8 by 8 image patches, we show that the subspaces obtained from ISA are in fact more dependent than the individual filter coefficients within a subspace. When first applying contrast gain control as preprocessing, however, there are no dependencies left that could be exploited by ISA. This suggests that complex cell modeling can only be useful for redundancy reduction in larger image patches.

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 Dates: 2010-04
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: BibTex Citekey: 6047
 Degree: -

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Title: 23rd Annual Conference on Neural Information Processing Systems (NIPS 2009)
Place of Event: Vancouver, BC, Canada
Start-/End Date: 2009-12-07 - 2009-12-10

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Title: Advances in Neural Information Processing Systems 22
Source Genre: Proceedings
 Creator(s):
Bengio, Y, Editor
Schuurmans, D, Editor
Lafferty, J, Editor
Williams, C, Editor
Culotta, A, Editor
Affiliations:
-
Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1696 - 1704 Identifier: ISBN: 978-1-615-67911-9