Statistical Study of Stereology for the Spatial Correlation of Point Patterns

通常的立体学（fOA）的主要任务是从二维截面信息中估计三维空间中物体的形态特征（如大小、形状和方向）。然而，以细胞为例，生物组织的功能与细胞在空间中的分布密切相关。因此，有必要发展能够提取物体空间相关信息的统计学和立体学方法。在这个研究项目中，我们的目标是开发上述的方法。我们的研究进展如下：1。通过生成三维点图，通过计算机模拟，得到了若干参数下三维径向分布函数与二维径向分布函数的经验关系。建立了硬球系统径向分布函数的立体理论，并通过计算机仿真对其进行了验证。这项工作是作为国际合作研究进行的，并准备发表。个人电脑图像处理软件已部分完成。通过我们设计的似然法，从三维点图的横截面估计了相互作用势。然后，研究了三维模拟中使用的相互作用势与截面估计的相互作用势之间的关系。从立体学的观点出发，研究了随机填充和随机镶嵌与空间维数的关系。我们已经开始开发一维点模式的似然方法。这与项目的主题密切相关，并进行了一些应用。调查结果已在一些国际会议和其他会议上发表，部分结果已发表。这个领域的研究才刚刚开始。还有许多课题有待研究。我们想继续这个有趣的研究领域。少

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