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Introducing the Dahu Pseudo-Distance

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Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10225))

Abstract

The minimum barrier (MB) distance is defined as the minimal interval of gray-level values in an image along a path between two points, where the image is considered as a vertex-valued graph. Yet this definition does not fit with the interpretation of an image as an elevation map, i.e. a somehow continuous landscape. In this paper, based on the discrete set-valued continuity setting, we present a new discrete definition for this distance, which is compatible with this interpretation, while being free from digital topology issues. Amazingly, we show that the proposed distance is related to the morphological tree of shapes, which in addition allows for a fast and exact computation of this distance. That contrasts with the classical definition of the MB distance, where its fast computation is only an approximation.

E. Carlinet is now with DxO, France.

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Notes

  1. 1.

    As a consequence (and despite how frustrating it might be for the reader), due to limited space, this paper does not address the following aspects of our work: practical applications that follow from this new distance definition, a quantitative comparison with the MB distance, considerations about the sampling grid and continuity, implementation details and execution times; last, some proofs have also been omitted.

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Acknowledgments

The authors want to thank Guillaume Tochon (new evangelist with ) and Laurent W. Najman for their valuable comments on an erstwhile version of this paper, and the reviewers for their helpful remarks. This work has been conducted within the mobidem project, part of the “Systematic Paris-Region” and “Images & Network” Clusters. This project is partially funded by the French Government and its economic development agencies.

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Authors and Affiliations

  1. EPITA Research and Development Laboratory (LRDE), Le Kremlin-Bicêtre, France

    Thierry Géraud, Yongchao Xu, Edwin Carlinet & Nicolas Boutry

  2. Institut Mines Telecom, Telecom ParisTech, Paris, France

    Yongchao Xu

  3. Université Paris-Est, LIGM, Équipe A3SI, ESIEE, Champs-sur-Marne, France

    Nicolas Boutry

Authors
  1. Thierry Géraud
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  2. Yongchao Xu
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  3. Edwin Carlinet
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  4. Nicolas Boutry
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Corresponding author

Correspondence to Thierry Géraud .

Editor information

Editors and Affiliations

  1. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Jesús Angulo

  2. MINES ParisTech, PSL-Research University , Fontainebleau, France

    Santiago Velasco-Forero

  3. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Fernand Meyer

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Géraud, T., Xu, Y., Carlinet, E., Boutry, N. (2017). Introducing the Dahu Pseudo-Distance. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science(), vol 10225. Springer, Cham. https://doi.org/10.1007/978-3-319-57240-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-57240-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57239-0

  • Online ISBN: 978-3-319-57240-6

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