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Deep Structure from a Geometric Point of View

  • Conference paper
Deep Structure, Singularities, and Computer Vision (DSSCV 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3753))

Abstract

The geometry of “empty” scale space is investigated. By virtue of the proposed geometric axioms the generating PDE, the linear isotropic heat equation, can be presented in covariant, or geometrical form. The postulate of a metric for scale space cannot be upheld, as it is incompatible with the generating equation. Two familiar instances of scale spaces consistent with the geometric axioms are considered by way of example, viz. classical, homogeneous scale space, and foveal scale space.

This work is part of the DSSCV project supported by the IST Program of the European Union (IST-2001-35443). The Netherlands Organisation for Scientific Research (NWO) is gratefully acknowledged for financial support.

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Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Eindhoven University of Technology, Den Dolech 2, NL-5600 MB, Eindhoven, The Netherlands

    Luc Florack

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  1. Luc Florack
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Editors and Affiliations

  1. IT University of Copenhagen, Rued Langgaardsvej 7, 2300, Copenhagen South, Denmark

    Ole Fogh Olsen

  2. Technische Universiteit Eindhoven, P.O. Box 513, 5600, Eindhoven, MB, The Netherlands

    Luc Florack

  3. Radon Institute for Computational and Applied Mathematics, Linz, Austria

    Arjan Kuijper

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Florack, L. (2005). Deep Structure from a Geometric Point of View. In: Fogh Olsen, O., Florack, L., Kuijper, A. (eds) Deep Structure, Singularities, and Computer Vision. DSSCV 2005. Lecture Notes in Computer Science, vol 3753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11577812_12

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  • DOI: https://doi.org/10.1007/11577812_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29836-6

  • Online ISBN: 978-3-540-32097-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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