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Toward a theory of patterns

Part of the Lecture Notes in Mathematics book series (LNM,volume 31)

Abstract

The purpose of this paper is to present a mathematical model intended for the description and analysis of patterns. As buildingblocks for this model will serve certain simple but foundamental concepts: signs, configurations, and images. These are related by similarity, synonymity and deformation transformations. Using these concepts it is shown how patterns can be analysed into elementary parts, both pure patterns and deformed ones. As a result of such an analysis one gets a grammatical description of the image presented to the observer. For didactic reasons the grammatical construction is limited to a special but typical case; a more general grammer of patterns will be treated elsewhere. The introduction of the mathematical model is accompanied by a number of illustrative examples.

Keywords

  • Contrast Pattern
  • Recognition Procedure
  • Recognition Function
  • Background Space
  • Euclidean Transformation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1967 Springer-Verlag

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Grenander, U. (1967). Toward a theory of patterns. In: Symposium on Probability Methods in Analysis. Lecture Notes in Mathematics, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061111

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  • DOI: https://doi.org/10.1007/BFb0061111

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-03902-0

  • Online ISBN: 978-3-540-34970-9

  • eBook Packages: Springer Book Archive