dorsal/arxiv
View SchemaVector- and tensor-valued descriptors for spatial patterns
| Authors | Claus Beisbart, Robert Dahlke, Klaus Mecke, Herbert Wagner |
|---|---|
| Categories | |
| ArXiv ID | physics/0203072 |
| URL | https://arxiv.org/abs/physics/0203072 |
Abstract
Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The properties of these extensions are described in detail. We show the versatility of these measures by using simple toy models as well as real data. Our applications cover the morphology of galaxy clusters, the structure of spiral galaxies, and the geometry of molecules. Furthermore, we consider a physical ansatz closely related to higher-rank Minkowski valuations, the Rosenfeld functional known from density functional theory.
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"date_created": "2026-03-02T18:00:39.034000Z",
"date_modified": "2026-03-02T18:00:39.034000Z",
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"abstract": "Higher-rank Minkowski valuations are efficient means for describing the\ngeometry and connectivity of spatial patterns. We show how to extend the\nframework of the scalar Minkowski valuations to vector- and tensor-valued\nmeasures. The properties of these extensions are described in detail. We show\nthe versatility of these measures by using simple toy models as well as real\ndata. Our applications cover the morphology of galaxy clusters, the structure\nof spiral galaxies, and the geometry of molecules. Furthermore, we consider a\nphysical ansatz closely related to higher-rank Minkowski valuations, the\nRosenfeld functional known from density functional theory.",
"arxiv_id": "physics/0203072",
"authors": [
"Claus Beisbart",
"Robert Dahlke",
"Klaus Mecke",
"Herbert Wagner"
],
"categories": [
"physics.data-an",
"astro-ph",
"cond-mat.stat-mech",
"math.GM"
],
"title": "Vector- and tensor-valued descriptors for spatial patterns",
"url": "https://arxiv.org/abs/physics/0203072"
},
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"execution_id": "f78e1154-77f6-45fd-b7ce-faef5d313f35",
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"type": "Model",
"variant": "snapshot-2026-03-01",
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