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Digital Steiner sets and Matheron semi-groups

Abstract : The Euclidean hierarchies of openings satisfy Matheron semi-groups law $ gamma _{lambda }gamma _{mu }=gamma _{max (lambda ,mu )}$ , where $ lambda$ is a size factor. One finds this law when the $ gamma_{lambda }$ are adjunction openings by Steiner convex sets, i.e. by Minkowki sums of segments. The conditions under which, in $ Z^{n}$ , the law remains valid, and the Steiner sets are convex, and connected, are established.
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Contributor : Jean Serra Connect in order to contact the contributor
Submitted on : Monday, September 12, 2011 - 10:56:50 AM
Last modification on : Saturday, January 15, 2022 - 3:57:53 AM


  • HAL Id : hal-00622190, version 1


Jean Serra. Digital Steiner sets and Matheron semi-groups. International Symposium on Mathematical Morphology - International Symposium on Mathematical Morphology'07, 8th International Symposium, Proceedings, 2007, France. pp.75-86. ⟨hal-00622190⟩



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