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Statistical Study of Stereology for the Spatial Correlation of Point Patterns

Research Project

Project/Area Number 62530017
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 統計学
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

TANEMURA Masaharu  The Institute of Statistical Mathematics, Associate Professor, 調査実験解析研究系, 助教授 (80000214)

Co-Investigator(Kenkyū-buntansha) OGATA Yoshihiko  The Institute of Statistical Mathematics, Associate Professor, 統計基礎研究系, 助教授 (70000213)
Project Period (FY) 1987 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1988: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1987: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsDimension of Space / Interaction Potential / Likelihood Procedure / Radial Distribution Function / Random Packing / Random Tessellation / Spatial Correlation / ステレオロジー / 尤度法 / 空間的相関 / 剛体球系
Research Abstract

The main subject of the usual stereology, so fOA, was to estimate the morphological characters (such as size, shape and direction) of objects in three-dimensional space, from the informations of two-dimensional cross sections. However, the functions of biological tissue of cells, for instance, are closely related to how the cells are distributed in space. Then it is necessary to develop statistical and stereological methodologies which can extract informations of spatial correlation of objects.
In this research project, we aimed to develop such methodologies just stated above. The progress of our research has been such as follows:
1. By generating three-dimensional point patterns, through computer simulations, for several parameters, we obtained the empirical relationship between three-dimensional radial distribution functions and two-dimensional ones.
2. We have built a stereological theory for the radial distribution functions of hard sphere system, and justified it by the computer simu … More lation. This work was done as the international coperative research, and was prepared for publication.
3. The softwares for image processing on personal computer were partly finished.
4. The interaction potentials were estimated, through the likelihood method we have devised, from the cross sections of three-dimensional point patterns. Then, the relation of interaction potentials between those used in three-dimensional simulation and those estimated in cross sections, was investigated.
5. From the stereological point of interest, the random packings and random tessellations were investigated in their relation to the dimension of space.
6. we have started to develop the likelihood method for one-dimensional point patterns. This is closely related to the theme of the project, and some applications were done.
7. The results of investigation have been presented in some international conferences and other meetings, and also some of them were published. The research of this field has just started. and there remains many subjects to be investigated. We would like to continue this interesting field of research. Less

Report

(3 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1987 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] Masaharu Tanemura: Acta Stereologica. 6. 129-134 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 尾形良彦: 統計数理. 35. 257-274 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Masaharu Tanemura: Journal of Microscopy. 151. 247-255 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 種村正美: 物性研究. 51. 89-96 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Yosihiko Ogata: Annals of the Institute of Statistical Mathematics. 41. (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Masaharu Tanemura.: Annals of the Institute of Statistical Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 小川泰 編: "かたちの科学" 朝倉書店, 200 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Masaharu Tanemura: "On the Stereology of Spatial Structure of Interacting Particle Systems" Acta Stereologica. 6. 129-134 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Yosihiko Ogata: "Likelihhod Analysis for Gibbsian Point Patterns" Proceedings of the Institute of Statistical Mathematics. 35. 257-274 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Masaharu Tanemura: "Random Packing and Random Tessellation in Relation to the Dimension of Space" Journal of Microscopy. 151. 247-255 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Masaharu Tanemura: "Random Packing by Two Species of Cells" Bussei Kenkyu (mimeographed circular in Japanese). 51. 89-96 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Yosihiko Ogata: "Likeihood Estimation of Soft-Core Interaction Potentials for Gibbsian Point Patterns" Annals of the Institute of Statistical Mathematics. 41. (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Masaharu Tanemura: "On the Density of Strict Random Complete Parking by Discs" Annals of the Institute of Statistical Mathematics.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Tohru Ogawa (Editor): Science of Form. Asakura Publishing Company, 200 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] M.Tanemura.: Journal of Microscopy. 151. 247-255 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 種村正美: 物性研究. 51. 89-96 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Y. Ogata.: Annals of the Instirute of Statistical Mathematics. 41. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] M.Tanemura.: Annals of the Institute of Statistical Mathematics.

    • Related Report
      1988 Annual Research Report
  • [Publications] Masanaru Tanemura: Acta Stereologica. 6. 129-134 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] Yosihiko Ogata: Annals of the Institute of Statistical Mathematics (Research Memorandum No. 338, The Inst. Statist.Math.). (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] Masaharu Tanemura: Journal of Microscopy (Research Memorandum No. 339, The Inst. Statist. Math.). (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] 小川 泰 (編集): "かたちの科学" 朝倉書店, 200 (1987)

    • Related Report
      1987 Annual Research Report

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Published: 1987-04-01   Modified: 2016-04-21  

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