Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions
In various stereological problems a n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a random section is studied. This distribution i...
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| Format: | Article |
| Language: | English |
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Slovenian Society for Stereology and Quantitative Image Analysis
2023-10-01
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| Series: | Image Analysis and Stereology |
| Subjects: | |
| Online Access: | https://www.ias-iss.org/ojs/IAS/article/view/2923 |
| _version_ | 1797404305254252544 |
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| author | Thomas van der Jagt Geurt Jongbloed Martina Vittorietti |
| author_facet | Thomas van der Jagt Geurt Jongbloed Martina Vittorietti |
| author_sort | Thomas van der Jagt |
| collection | DOAJ |
| description | In various stereological problems a n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions. |
| first_indexed | 2024-03-09T02:53:03Z |
| format | Article |
| id | doaj.art-4443c36fb1bf4412877d841d266f9a9c |
| institution | Directory Open Access Journal |
| issn | 1580-3139 1854-5165 |
| language | English |
| last_indexed | 2024-03-09T02:53:03Z |
| publishDate | 2023-10-01 |
| publisher | Slovenian Society for Stereology and Quantitative Image Analysis |
| record_format | Article |
| series | Image Analysis and Stereology |
| spelling | doaj.art-4443c36fb1bf4412877d841d266f9a9c2023-12-05T08:17:32ZengSlovenian Society for Stereology and Quantitative Image AnalysisImage Analysis and Stereology1580-31391854-51652023-10-0142317118410.5566/ias.29231998Existence and Approximation of Densities of Chord Length- and Cross Section Area DistributionsThomas van der Jagt0https://orcid.org/0000-0002-9597-9949Geurt Jongbloed1https://orcid.org/0000-0003-4708-5868Martina Vittorietti2https://orcid.org/0000-0002-7695-3209Delft University of TechnologyDelft University of TechnologyUniversità degli Studi di PalermoIn various stereological problems a n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions.https://www.ias-iss.org/ojs/IAS/article/view/2923absolute continuitychord length distributioncross section area distributionstereology |
| spellingShingle | Thomas van der Jagt Geurt Jongbloed Martina Vittorietti Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions Image Analysis and Stereology absolute continuity chord length distribution cross section area distribution stereology |
| title | Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions |
| title_full | Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions |
| title_fullStr | Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions |
| title_full_unstemmed | Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions |
| title_short | Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions |
| title_sort | existence and approximation of densities of chord length and cross section area distributions |
| topic | absolute continuity chord length distribution cross section area distribution stereology |
| url | https://www.ias-iss.org/ojs/IAS/article/view/2923 |
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