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Morphological Processing of Univariate Gaussian Distribution-Valued Images Based on Poincaré Upper-Half Plane Representation

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Geometric Theory of Information

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

Mathematical morphology is a nonlinear image processing methodology based on the application of complete lattice theory to spatial structures. Let us consider an image model where at each pixel is given a univariate Gaussian distribution. This model is interesting to represent for each pixel the measured mean intensity as well as the variance (or uncertainty) for such measurement. The aim of this work is to formulate morphological operators for these images by embedding Gaussian distribution pixel values on the Poincaré upper-half plane. More precisely, it is explored how to endow this classical hyperbolic space with various families of partial orderings which lead to a complete lattice structure. Properties of order invariance are explored and application to morphological processing of univariate Gaussian distribution-valued images is illustrated.

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Author information

Authors and Affiliations

  1. CMM-Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES ParisTech, Paris, France

    Jesús Angulo

  2. Department of Mathematics, National University of Singapore, Buona Vista, Singapore

    Santiago Velasco-Forero

Authors
  1. Jesús Angulo
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  2. Santiago Velasco-Forero
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Corresponding author

Correspondence to Jesús Angulo .

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Editors and Affiliations

  1. Laboratoire d'Informatique (LIX), Polytechnique School, Palaiseau Cedex, France

    Frank Nielsen

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Angulo, J., Velasco-Forero, S. (2014). Morphological Processing of Univariate Gaussian Distribution-Valued Images Based on Poincaré Upper-Half Plane Representation. In: Nielsen, F. (eds) Geometric Theory of Information. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-05317-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-05317-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05316-5

  • Online ISBN: 978-3-319-05317-2

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