Component-Trees and Multivalued Images: Structural Properties

Article

Abstract

Component-trees model the structure of grey-level images by considering their binary level-sets obtained from successive thresholdings. They also enable to define anti-extensive filtering procedures for such images. In order to extend this image processing approach to any (grey-level or multivalued) images, both the notion of component-tree, and its associated filtering framework, have to be generalised. In this article we deal with the generalisation of the component-tree structure. We define a new data structure, the component-graph, which extends the notion of component-tree to images taking their values in any (partially or totally) ordered set. The component-graphs are declined in three variants, of increasing richness and size, whose structural properties are studied.

Keywords

Mathematical morphology Component-tree Multivalued images Anti-extensive filtering Component-graph 

Notes

Acknowledgements

The research leading to these results has received funding from the French Agence Nationale de la Recherche (Grant Agreement ANR-10-BLAN-0205).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.CReSTICUniversité de Reims Champagne-ArdenneReimsFrance
  2. 2.ICube, CNRSUniversité de StrasbourgStrasbourgFrance

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