# 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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Conference papers
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https://hal-upec-upem.archives-ouvertes.fr/hal-00622190
Contributor : Jean Serra <>
Submitted on : Monday, September 12, 2011 - 10:56:50 AM
Last modification on : Wednesday, February 26, 2020 - 7:06:05 PM

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• HAL Id : hal-00622190, version 1

### Citation

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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