1988 Fiscal Year Final Research Report Summary
Statistical Study of Stereology for the Spatial Correlation of Point Patterns
| Project/Area Number |
62530017
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
統計学
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
TANEMURA Masaharu The Institute of Statistical Mathematics, Associate Professor, 調査実験解析研究系, 助教授 (80000214)
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| Co-Investigator(Kenkyū-buntansha) |
OGATA Yoshihiko The Institute of Statistical Mathematics, Associate Professor, 統計基礎研究系, 助教授 (70000213)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Dimension 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 |
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| 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
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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
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Research Products
(14 results)
