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Second Order Structure of Scale-Space Measurements

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Abstract

The second-order structure of random images f :ℝd→ℝN is studied under the assumption of stationarity of increments, isotropy and scale invariance. Scale invariance is defined via linear scale space theory. The results are formulated in terms of the covariance structure of the jet consisting of the scale space derivatives at a single point. Operators describing the effect in jet space of blurring and scaling are investigated. The theory developed is applicable in the analysis of naturally occurring images of which examples are provided.

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Authors and Affiliations

  1. Department of Natural Sciences, Faculty of Life Sciences, University of Copenhagen, Copenhagen, Denmark

    Bo Markussen

  2. Department of Computer Science, University of Copenhagen, Universitetsparken 1, 2100, Copenhagen, Denmark

    Kim Steenstrup Pedersen & Marco Loog

  3. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands

    Marco Loog

Authors
  1. Bo Markussen
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  2. Kim Steenstrup Pedersen
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  3. Marco Loog
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Corresponding author

Correspondence to Kim Steenstrup Pedersen.

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Markussen, B., Pedersen, K.S. & Loog, M. Second Order Structure of Scale-Space Measurements. J Math Imaging Vis 31, 207–220 (2008). https://doi.org/10.1007/s10851-008-0080-7

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  • DOI: https://doi.org/10.1007/s10851-008-0080-7

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