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  Unsupervised learning of a steerable basis for invariant image representations

Bethge, M., Gerwinn, S., & Macke, J. (2007). Unsupervised learning of a steerable basis for invariant image representations. In B. Rogowitz, T. Pappas, & S. Daly (Eds.), Human Vision and Electronic Imaging XII: Proceedings of the SPIE Human Vision and Electronic Imaging Conference 2007 (pp. 1-12). Bellingham, WA, USA: SPIE.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-CEB9-6 Version Permalink: https://hdl.handle.net/21.11116/0000-0003-E8C0-E
Genre: Conference Paper

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https://www.spiedigitallibrary.org/proceedings/Download?fullDOI=10.1117%2F12.711119 (Publisher version)
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 Creators:
Bethge, M1, 2, Author           
Gerwinn, S1, 2, 3, Author           
Macke, JH1, 2, 3, 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              
3Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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 Abstract: There are two aspects to unsupervised learning of invariant representations of images: First, we can reduce the dimensionality of the representation by finding an optimal trade-off between temporal stability and informativeness. We show that the answer to this optimization problem is generally not unique so that there is still considerable freedom in choosing a suitable basis. Which of the many optimal representations should be selected? Here, we focus on this second aspect, and seek to find representations that are invariant under geometrical transformations occuring in sequences of natural images. We utilize ideas of steerability and Lie groups, which have been developed in the context of filter design. In particular, we show how an anti-symmetric version of canonical correlation analysis can be used to learn a full-rank image basis which is steerable with respect to rotations. We provide a geometric interpretation of this algorithm by showing that it finds the two-dimensional eigensubspaces of the avera
ge bivector. For data which exhibits a variety of transformations, we develop a bivector clustering algorithm, which we use to learn a basis of generalized quadrature pairs (i.e. complex cells) from sequences of natural images.

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 Dates: 2007-02
 Publication Status: Issued
 Pages: -
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 Rev. Type: -
 Identifiers: DOI: 10.1117/12.711119
BibTex Citekey: 4305
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Title: SPIE Human Vision and Electronic Imaging Conference 2007
Place of Event: San Jose, CA, USA
Start-/End Date: 2007-01-28 - 2007-02-01

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Title: Human Vision and Electronic Imaging XII: Proceedings of the SPIE Human Vision and Electronic Imaging Conference 2007
Source Genre: Proceedings
 Creator(s):
Rogowitz, BE, Editor
Pappas, TN, Editor
Daly, SJ, Editor
Affiliations:
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Publ. Info: Bellingham, WA, USA : SPIE
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1 - 12 Identifier: ISBN: 978-0-8194-6605-1

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Title: Proceedings of the SPIE
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Pages: - Volume / Issue: 6492 Sequence Number: - Start / End Page: - Identifier: ISSN: 0277-786X