Component-trees and multivalued images: Structural properties

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.
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Nicolas Passat, Benoît Naegel. Component-trees and multivalued images: Structural properties. Journal of Mathematical Imaging and Vision, Springer Verlag, 2014, 49 (1), pp.37-50. ⟨10.1007/s10851-013-0438-3⟩. ⟨inria-00611714v3⟩

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