颗粒群特征的定量体视学分析方法

根据定量体视学原理，应用Ｑｕａｎｔｉｍｅｔ６００图象分析仪，对颗粒群特征参数进行了定量分析，并对定量体视学方法实验参数：最小样本数、图像优化方法及二值化灰度阀值等进行了实验研究．实验结果表明：定量体视学图像分析方法可同时获得矿渣微粉试样的级配和颗粒形状因子（圆度）等一系列颗粒群特征参数     

Combining quantitative 2D and 3D image analysis in the serial block face SEM: application to secretory organelles of pancreatic islet cells

A combination of two‐dimensional (2D) and three‐dimensional (3D) analyses of tissue volume ultrastructure acquired by serial block face scanning electron microscopy can greatly shorten the time required to obtain quantitative information from big data sets that contain many billions of voxels. Thus, to analyse the number of organelles of a specific type, or the total volume enclosed by a population of organelles within a cell, it is possible to estimate the number density or volume fraction of that organelle using a stereological approach to analyse randomly selected 2D block face views through the cells, and to combine such estimates with precise measurement of 3D cell volumes by delineating the plasma membrane in successive block face images. The validity of such an approach can be easily tested since the entire 3D tissue volume is available in the serial block face scanning electron microscopy data set. We have applied this hybrid 3D/2D technique to determine the number of secretory granules in the endocrine α and β cells of mouse pancreatic islets of Langerhans, and have been able to estimate the total insulin content of a β cell.     

Block bootstrap methods for the estimation of the intensity of a spatial point process with confidence bounds

This paper deals with the estimation of the intensity of a planar point process on the basis of a single point pattern, observed in a rectangular window. If the model assumptions of stationarity and isotropy hold, the method of block bootstrapping can be used to estimate the intensity of the process with confidence bounds. The results of two variants of block bootstrapping are compared with a parametric approximation based on the assumption of a Gaussian distribution of the numbers of points in deterministic subwindows of the original pattern. The studies were performed on patterns obtained by simulation of well‐known point process models (Poisson process, two Matérn cluster processes, Matérn hardcore process, Strauss hardcore process). They were also performed on real histopathological data (point patterns of capillary profiles of 12 cases of prostatic cancer). The methods are presented as worked examples on two cases, where we illustrate their use as a check on stationarity (homogeneity) of a point process with respect to different fields of vision. The paper concludes with various methodological discussions and suggests possible extensions of the block bootstrap approach to other fields of spatial statistics.     

The efficiency of systematic sampling in stereology — reconsidered

In the present paper, we summarize and further develop recent research in the estimation of the variance of stereological estimators based on systematic sampling. In particular, it is emphasized that the relevant estimation procedure depends on the sampling density. The validity of the variance estimation is examined in a collection of data sets, obtained by systematic sampling. Practical recommendations are also provided in a separate section.     

Global spatial sampling with isotropic virtual planes: estimators of length density and total length in thick, arbitrarily orientated sections

Existing design-based direct length estimators require random rotation around at least one axis of the tissue specimen prior to sectioning to ensure isotropy of test probes. In some tissue it is, however, difficult or even impossible to define the region of interest, unless the tissue is sectioned in a specific, nonrandom orientation. Spatial uniform sampling with isotropic virtual planes circumvents the use of physically isotropic or vertical sections. The structure that is contained in a thick physical section is investigated with software-randomized isotropic virtual planes in volume probes in systematically sampled microscope fields using computer-assisted stereological analysis. A fixed volume of 3D space in each uniformly sampled field is probed with systematic random, isotropic virtual planes by a line that moves across the computer screen showing live video images of the microscope field when the test volume is scanned with a focal plane. The intersections between the linear structure and the virtual probes are counted with columns of two dimensional disectors.
Global spatial sampling with sets of isotropic uniform random virtual planes provides a basis for length density estimates from a set of parallel physical sections of any orientation preferred by the investigator, i.e. the simplest sampling scheme in stereology. Additional virtues include optimal conditions for reducing the estimator variance, the possibility to estimate total length directly using a fractionator design and the potential to estimate efficiently the distribution of directions from a set of parallel physical sections with arbitrary orientation.
Other implementations of the basic idea, systematic uniform sampling using probes that have total 3D × 4π freedom inside the section, and therefore independent of the position and the orientation of the physical section, are briefly discussed.     

Estimation of average particle size from vertical projections

A new stereological relationship is derived for the estimation of average size (average width) of a collection of convex particles in a 3D microstructure. The average size is estimated from measurements performed on projected images of the microstructure generated by total vertical projections. The stereological relationship is as follows: D = Ī _C /(2 N ₀β). D is the average width, ¯ I _C is the average absolute number of intersections between the specifically oriented and regularly spaced cycloid shape test lines and particle boundaries observed in the total vertical projections, N ₀ is the total number of particles observed in the total vertical projection and the parameter β is a characteristic of the measurement grid; it has units of reciprocal of length. The result is applicable to any arbitrary collection of convex particles; the particle orientations need not be isotropic. Only 'intersection counts' are required; it is not necessary to measure sizes of the particles in the projected images.     

Classification of spatial textures in benign and cancerous glandular tissues by stereology and stochastic geometry using artificial neural networks

Stereology and stochastic geometry can be used as auxiliary tools for diagnostic purposes in tumour pathology. Whether first-order parameters or stochastic-geometric functions are more important for the classification of the texture of biological tissues is not known. In the present study, volume and surface area per unit reference volume, the pair correlation function and the centred quadratic contact density function of epithelium were estimated in three case series of benign and malignant lesions of glandular tissues. The information provided by the latter functions was summarized by the total absolute areas between the estimated curves and their horizontal reference lines. These areas are considered as indicators of deviation of the tissue texture from a completely uncorrelated volume process and from the Boolean model with convex grains, respectively. We used both areas and the first-order parameters for the classification of cases using artificial neural networks (ANNs). Learning vector quantization and multilayer feedforward networks with backpropagation were applied as neural paradigms. Applications included distinction between mastopathy and mammary cancer (40 cases), between benign prostatic hyperplasia and prostatic cancer (70 cases) and between chronic pancreatitis and pancreatic cancer (60 cases). The same data sets were also classified with linear discriminant analysis. The stereological estimates in combination with ANNs or discriminant analysis provided high accuracy in the classification of individual cases. The question of which category of estimator is the most informative cannot be answered globally, but must be explored empirically for each specific data set. Using learning vector quantization, better results could often be obtained than by multilayer feedforward networks with backpropagation.     

Improved estimation of the pair correlation function of random sets

The texture of binary spatial structures can be characterized by second-order methods of spatial statistics. The pair correlation function, which describes the structure in terms of spatial correlation as a function of distance, is of central importance in this context. Conventionally, the pair correlation function of stationary and isotropic random sets is estimated as the ratio of the covariance to the square of volume fraction of the phase of interest. In the present paper, an improved estimator of the pair correlation function is presented, where the covariance is divided by the square of a distance-adapted estimator of volume fraction. The new estimator is explained mathematically and applied to simulated images of the Boolean model and to microscopic images from neoplastic and non-neoplastic human glandular tissues. It leads to a considerable reduction of bias and variance of estimated pair correlation functions, in particular for large distances.     

Unbiased and efficient estimation of the total number of terminal bronchiolar duct endings in lung: a modified physical disector

A novel modification of the physical disector is described which was used to estimate the total number of terminal bronchiolar duct endings (TBDEs) in human infant lung. TBDEs are closed three-dimensional space curves of complex shape that are inherently difficult to count from histological sections. However, careful consideration of the microanatomy of the terminal duct endings provides us with the opportunity to define a very simple and unbiased counting rule. To apply the rule in practice we also need to determine a suitable disector height. Owing to the complex shape of the TBDE we had no prior knowledge of what disector height would be suitable for counting the TBDE structures. Exhaustive serial sectioning of complete TBDE structures was carried out and showed that any disector height under 90 μm would give unbiased counts. A further empirical study was then undertaken to determine the most efficient disector height. This was found to be 50 μm.
The total number of TBDEs in the upper lobe of the right lung of six human infants aged between 13 and 25 weeks was also estimated. The estimates of numerical density obtained with our modification of the physical disector were multiplied by estimates of lung lobe volume obtained using Cavalieri's Principle. The total number of TBDEs in the lobes ranged from 15 323 to 57 768, with a mean of 40 306. The average coefficient of error of the number estimates was 19%, which was deemed precise enough given the biological coefficient of variation between TBDE number of 36%.     

An integral-geometric approach for the Euler–Poincaré characteristic of spatial images

The determination of the Euler–Poincaré characteristic of a set can be based on observations of a digitized image of that set. In the present paper the correctness of the method is proved due to a strict integral-geometric approach. Our result also provides a link to the methods which are used in image analysis and are based on graph theory.