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Background Notions

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Morphological Image Analysis

Abstract

Mathematical morphology stems from set theory and if one wishes to get an insight into its theoretical basis, some knowledge on set theory and topology is required. However, if we restrict our attention to the digital framework, only simple mathematical concepts such as set unions and intersections are necessary. It is the scope of this chapter to present these background notions. Moreover, we will see that many definitions related to the geometry of a Euclidean object do not apply to discrete objects. For example, how should we define the neighbours of a point and what is the best approximation of a line on a raster grid? There is therefore a need to introduce a few principles of discrete geometry.

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Authors and Affiliations

  1. Silsoe Research Institute, Wrest Park, MK45 4HS, Silsoe Bedfordshire, UK

    Dr. Ir. habil. Pierre Soille

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  1. Dr. Ir. habil. Pierre Soille
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© 1999 Springer-Verlag Berlin Heidelberg

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Soille, P. (1999). Background Notions. In: Morphological Image Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03939-7_2

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  • DOI: https://doi.org/10.1007/978-3-662-03939-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03941-0

  • Online ISBN: 978-3-662-03939-7

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