Measuring Shape Relations Using r-Parallel Sets

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Standard

Measuring Shape Relations Using r-Parallel Sets. / Stephensen, Hans Jacob Teglbjærg; Svane, Anne Marie; Villanueva, Carlos Benitez; Goldman, Steven Alan; Sporring, Jon.

In: Journal of Mathematical Imaging and Vision, Vol. 63, 2021, p. 1069–1083.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Stephensen, HJT, Svane, AM, Villanueva, CB, Goldman, SA & Sporring, J 2021, 'Measuring Shape Relations Using r-Parallel Sets', Journal of Mathematical Imaging and Vision, vol. 63, pp. 1069–1083. https://doi.org/10.1007/s10851-021-01041-3

APA

Stephensen, H. J. T., Svane, A. M., Villanueva, C. B., Goldman, S. A., & Sporring, J. (2021). Measuring Shape Relations Using r-Parallel Sets. Journal of Mathematical Imaging and Vision, 63, 1069–1083. https://doi.org/10.1007/s10851-021-01041-3

Vancouver

Stephensen HJT, Svane AM, Villanueva CB, Goldman SA, Sporring J. Measuring Shape Relations Using r-Parallel Sets. Journal of Mathematical Imaging and Vision. 2021;63:1069–1083. https://doi.org/10.1007/s10851-021-01041-3

Author

Stephensen, Hans Jacob Teglbjærg ; Svane, Anne Marie ; Villanueva, Carlos Benitez ; Goldman, Steven Alan ; Sporring, Jon. / Measuring Shape Relations Using r-Parallel Sets. In: Journal of Mathematical Imaging and Vision. 2021 ; Vol. 63. pp. 1069–1083.

Bibtex

@article{c63b791ec32247b0a6fc5f6c1528850c,
title = "Measuring Shape Relations Using r-Parallel Sets",
abstract = "Geometrical measurements of biological objects form the basis of many quantitative analyses. Hausdorff measures such as the volume and the area of objects are simple and popular descriptors of individual objects; however, for most biological processes, the interaction between objects cannot be ignored, and the shape and function of neighboring objects are mutually influential. In this paper, we present a theory on the geometrical interaction between objects inspired by K -functions for spatial point-processes. Our theory describes the relation between two objects: a reference and an observed object. We generate the r -parallel sets of the reference object, calculate the intersection between the r -parallel sets and the observed object, and define measures on these intersections. The measures are simple, like the volume or surface area, but describe further details about the shape of individual objects and their pairwise geometrical relation. Finally, we propose a summary-statistics. To evaluate these measures, we present a new segmentation of cell membrane, mitochondria, synapses, vesicles, and endoplasmic reticulum in a publicly available FIB-SEM 3D brain tissue data set and use our proposed method to analyze key biological structures herein.",
author = "Stephensen, {Hans Jacob Teglbj{\ae}rg} and Svane, {Anne Marie} and Villanueva, {Carlos Benitez} and Goldman, {Steven Alan} and Jon Sporring",
year = "2021",
doi = "10.1007/s10851-021-01041-3",
language = "English",
volume = "63",
pages = "1069–1083",
journal = "Journal of Mathematical Imaging and Vision",
issn = "0924-9907",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Measuring Shape Relations Using r-Parallel Sets

AU - Stephensen, Hans Jacob Teglbjærg

AU - Svane, Anne Marie

AU - Villanueva, Carlos Benitez

AU - Goldman, Steven Alan

AU - Sporring, Jon

PY - 2021

Y1 - 2021

N2 - Geometrical measurements of biological objects form the basis of many quantitative analyses. Hausdorff measures such as the volume and the area of objects are simple and popular descriptors of individual objects; however, for most biological processes, the interaction between objects cannot be ignored, and the shape and function of neighboring objects are mutually influential. In this paper, we present a theory on the geometrical interaction between objects inspired by K -functions for spatial point-processes. Our theory describes the relation between two objects: a reference and an observed object. We generate the r -parallel sets of the reference object, calculate the intersection between the r -parallel sets and the observed object, and define measures on these intersections. The measures are simple, like the volume or surface area, but describe further details about the shape of individual objects and their pairwise geometrical relation. Finally, we propose a summary-statistics. To evaluate these measures, we present a new segmentation of cell membrane, mitochondria, synapses, vesicles, and endoplasmic reticulum in a publicly available FIB-SEM 3D brain tissue data set and use our proposed method to analyze key biological structures herein.

AB - Geometrical measurements of biological objects form the basis of many quantitative analyses. Hausdorff measures such as the volume and the area of objects are simple and popular descriptors of individual objects; however, for most biological processes, the interaction between objects cannot be ignored, and the shape and function of neighboring objects are mutually influential. In this paper, we present a theory on the geometrical interaction between objects inspired by K -functions for spatial point-processes. Our theory describes the relation between two objects: a reference and an observed object. We generate the r -parallel sets of the reference object, calculate the intersection between the r -parallel sets and the observed object, and define measures on these intersections. The measures are simple, like the volume or surface area, but describe further details about the shape of individual objects and their pairwise geometrical relation. Finally, we propose a summary-statistics. To evaluate these measures, we present a new segmentation of cell membrane, mitochondria, synapses, vesicles, and endoplasmic reticulum in a publicly available FIB-SEM 3D brain tissue data set and use our proposed method to analyze key biological structures herein.

U2 - 10.1007/s10851-021-01041-3

DO - 10.1007/s10851-021-01041-3

M3 - Journal article

VL - 63

SP - 1069

EP - 1083

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

SN - 0924-9907

ER -

ID: 273011957