Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics

Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions...

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Autores principales:	John R. Jungck, Michael J. Pelsmajer, Camron Chappel, Dylan Taylor
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	graph theory computational geometry spatial statistics image analysis tessellations Voronoi polygons Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/602b9fc6624440328a791ed0f285c26d
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id	oai:doaj.org-article:602b9fc6624440328a791ed0f285c26d
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spelling	oai:doaj.org-article:602b9fc6624440328a791ed0f285c26d2021-11-11T18:16:46ZSpace: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics10.3390/math92127262227-7390https://doaj.org/article/602b9fc6624440328a791ed0f285c26d2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2726https://doaj.org/toc/2227-7390Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi polygons; Delaunay triangulations; perpendicular bisectors; circumcenters; convex hulls; minimal spanning trees; Ulam trees; Pitteway violations; circularity; Clark-Evans spatial statistics; variance to mean ratios; Gabriel graphs; and, minimal spanning trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation.John R. JungckMichael J. PelsmajerCamron ChappelDylan TaylorMDPI AGarticlegraph theorycomputational geometryspatial statisticsimage analysistessellationsVoronoi polygonsMathematicsQA1-939ENMathematics, Vol 9, Iss 2726, p 2726 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	graph theory computational geometry spatial statistics image analysis tessellations Voronoi polygons Mathematics QA1-939
spellingShingle	graph theory computational geometry spatial statistics image analysis tessellations Voronoi polygons Mathematics QA1-939 John R. Jungck Michael J. Pelsmajer Camron Chappel Dylan Taylor Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics
description	Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi polygons; Delaunay triangulations; perpendicular bisectors; circumcenters; convex hulls; minimal spanning trees; Ulam trees; Pitteway violations; circularity; Clark-Evans spatial statistics; variance to mean ratios; Gabriel graphs; and, minimal spanning trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation.
format	article
author	John R. Jungck Michael J. Pelsmajer Camron Chappel Dylan Taylor
author_facet	John R. Jungck Michael J. Pelsmajer Camron Chappel Dylan Taylor
author_sort	John R. Jungck
title	Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics
title_short	Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics
title_full	Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics
title_fullStr	Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics
title_full_unstemmed	Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics
title_sort	space: the re-visioning frontier of biological image analysis with graph theory, computational geometry, and spatial statistics
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/602b9fc6624440328a791ed0f285c26d
work_keys_str_mv	AT johnrjungck spacetherevisioningfrontierofbiologicalimageanalysiswithgraphtheorycomputationalgeometryandspatialstatistics AT michaeljpelsmajer spacetherevisioningfrontierofbiologicalimageanalysiswithgraphtheorycomputationalgeometryandspatialstatistics AT camronchappel spacetherevisioningfrontierofbiologicalimageanalysiswithgraphtheorycomputationalgeometryandspatialstatistics AT dylantaylor spacetherevisioningfrontierofbiologicalimageanalysiswithgraphtheorycomputationalgeometryandspatialstatistics
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Space: The Re-Visioning Frontier of Biological Image Analysis with Graph Theory, Computational Geometry, and Spatial Statistics

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