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On the Axioms of Scale Space Theory

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Abstract

We consider alternative scale space representations beyond the well-established Gaussian case that satisfy all “reasonable” axioms. One of these turns out to be subject to a first order pseudo partial differential equation equivalent to the Laplace equation on the upper half plane {(x, s) ∈ ℝd × ℝ | s > 0}. We investigate this so-called Poisson scale space and show that it is indeed a viable alternative to Gaussian scale space. Poisson and Gaussian scale space are related via a one-parameter class of operationally well-defined intermediate representations generated by a fractional power of (minus) the spatial Laplace operator.

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Authors and Affiliations

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

    Remco Duits

  2. Eindhoven University of Technology, Den Dolech 2, NL-5600 MB, The Netherlands

    Luc Florack

  3. Eindhoven University of Technology, Den Dolech 2, NL-5600 MB, The Netherlands

    Jan de Graaf

  4. Eindhoven University of Technology, Den Dolech 2, NL-5600 MB, The Netherlands

    Bart ter Haar Romeny

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  1. Remco Duits
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  2. Luc Florack
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  3. Jan de Graaf
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  4. Bart ter Haar Romeny
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Duits, R., Florack, L., de Graaf, J. et al. On the Axioms of Scale Space Theory. Journal of Mathematical Imaging and Vision 20, 267–298 (2004). https://doi.org/10.1023/B:JMIV.0000024043.96722.aa

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