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Ubiquity of the Distance Function in Mathematical Morphology

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Space, Structure and Randomness

Part of the book series: Lecture Notes in Statistics ((LNS,volume 183))

Abstract

Distance has been the key notion for usual Euclidean geometry and the definition of geometrical objects. For instance, a circle is the locus of points at the same distance of a given one, an ellipsis is the locus of points whose sum of distances to two given points is a constant, a parabola is the locus of points whose sum of distances to a given point and a given straight line is a constant. Also, the shortest path between two points is the line segment.

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Author information

Authors and Affiliations

  1. Ecole Nationale Supérieure des Mines de Paris, 60 Boulevard Saint-Michel, 75272, Paris cedex 06

    Michel Schmitt

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  1. Michel Schmitt
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Editor information

Editors and Affiliations

  1. Centre de Morphologie Mathématique, Ecole des Mines de Paris, 35 rue Saint Honoré, 77305, Fontainebleau, France

    Michel Bilodeau  & Fernand Meyer  & 

  2. Direction des recherches, Ecole des Mines de Paris, 60 Boulevard Saint Michel, 75272, Paris Cedex 06, France

    Michel Schmitt

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Schmitt, M. (2005). Ubiquity of the Distance Function in Mathematical Morphology. In: Bilodeau, M., Meyer, F., Schmitt, M. (eds) Space, Structure and Randomness. Lecture Notes in Statistics, vol 183. Springer, New York, NY. https://doi.org/10.1007/0-387-29115-6_14

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