Statistical Study of Stereology for the Spatial Correlation of Point Patterns

通常的体视学的主要主题是从二维横截面信息中估计物体在三维空间中的形态特征(如大小、形状和方向)。然而，例如，细胞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性信息的统计和体视学方法。在本研究项目中，我们的目标是发展上述方法。我们的研究进展如下：1.通过生成三维点模式，通过计算机模拟，得到了几个参数的三维径向分布函数与二维径向分布函数之间的经验关系。建立了硬球系统径向分布函数的体视学理论，并用计算机SIMU…进行了验证更多的废话。这项工作是作为国际合作研究完成的，并准备出版。在PC机上完成了部分图像处理软件的开发。通过我们设计的似然方法，从三维点图案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上估计的相互作用势之间的关系。从体视学的角度，研究了随机填充和随机镶嵌与空间维度的关系。我们已经开始发展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公布，其中一些也发表了。这一领域的研究才刚刚起步。还有许多课题有待调查。我们希望继续这一有趣的研究领域。较少

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