STEREOLOGY OF ARBITRARY PARTICLES - A REVIEW OF UNBIASED NUMBER AND SIZE ESTIMATORS AND THE PRESENTATION OF SOME NEW ONES, IN MEMORY OF THOMPSON,WILLIAM,R.
STEREOLOGY OF ARBITRARY PARTICLES - A REVIEW OF UNBIASED NUMBER AND SIZE ESTIMATORS AND THE PRESENTATION OF SOME NEW ONES, IN MEMORY OF THOMPSON,WILLIAM,R.
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DOI：
10.1111/j.1365-2818.1986.tb02764.x
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发表时间：
1986-07-01
影响因子：
2
通讯作者：
GUNDERSEN, HJG
中科院分区：
文献类型：
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作者：
GUNDERSEN, HJG
本文讨论三维空间中孤立的、可数项，通常称为粒子。它的实质是对这些粒子的数量、高度、表面和体积进行无偏见的体视学估计，而不对它们的形状做出任何假设。描述了各种估计量，其中有些是第一次，有些是改进的形式，几个是一个以上的版本，所有这些都是在一个单一的、绝对的要求下进行的，即人们实际上可以识别出人们在截面上量化的是什么。就用于分析的最小截面数量而言，估计器可分类如下：在单个截面上可以估计v̄V，即体积加权或筛分分布中颗粒的平均体积。在相隔已知距离的两个平行截面上，存在普通数分布中的颗粒数量和所有平均尺寸(高度、表面和体积)的估计器，以及颗粒体积数分布的标准偏差sDn(V)的估计器。如果包含空间是相对透明的，这些部分可以是一个厚的物理部分中的两个光学部分。在一堆平行的部分上，至少与最大的粒子一样高，并被已知的距离分开，人们可以得到12个平均尺寸和12个单独尺寸的分布：三个尺寸的所有组合：高度、表面和体积，四种不同类型的分布：数量、高度、表面和体积。为了满足上述两个估计原则的抽样要求，最近已经证明，通过将它们结合起来，甚至可以估计具有恒定但未知间隔的一堆截面中任意颗粒的平均尺寸和数量。最后，描述了样品中物品总数的唯一的、无偏的估计器，使用该估计器，人们不需要测量截面之间的距离、其厚度或样品的体积，也不需要假设任何关于收缩/膨胀、切片压缩或丢失盖子的情况。这就是分馏塔。
This paper deals with isolated, countable items, often termed particles, in three‐dimensional space. Its substance is the unbiased stereological estimation of the number, height, surface and volume of such particleswithout any assumptions about their shape. The full range of estimators is described, some of them for the first time, some in an improved form, several in more than one version, and all of them under the single, absolute requirement that one can in fact identify what one is quantifying on sections. In terms of the minimal number of sections for the analysis, the estimators may be classified as follows:On a single section it is possible to estimate v̄V, the mean volume of particles in the volume‐weighted or ‘sieving’‐distribution.On two parallel sections, separated by a known distance, estimators exist of particle number and of all mean sizes (height, surface and volume) in the ordinary number distribution, as well as of SDN(v), the standard deviation in the number distribution of particle volumes. If the containing space is relatively transparent the sections may be two optical sections within one thick physical section.On a stack of parallel sections, at least as high as the largest particle, and separated by known distances, one can get twelve mean sizes and twelve distributions of individual sizes: all combinations of three sizes: height, surface and volume in four different types of distributions: number, height, surface and volume. Fulfilling the sampling requirements of the above two estimation principles it has been shown very recently that by combining them one may even estimate mean sizes and number of arbitrary particles in a stack of sections with constant but unknown separation.Finally, a unique, unbiased estimator of the total number of items in a specimen is described for the use of which one need not measure the distance between sections, nor their thickness, nor the volume of the specimen, nor assume anything about shrinkage/swelling, sectioning compression or lost caps. It is the fractionator.