拐点计数法及其在材料科学中的应用

采用集合论的形式对一种体视学新方法,即拐点计数法及相应的体视学基本关系式进行了描述和推导,使之更加条统、准确和明瞭。并进而讨论了它们在材料科学中的各种可能应用及有关问题。     

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.     

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.     

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.     

Automated identification of neurons in 3D confocal datasets from zebrafish brainstem

Many kinds of neuroscience data are being acquired regarding the dynamic behaviour and phenotypic diversity of nerve cells. But as the size, complexity and numbers of 3D neuroanatomical datasets grow ever larger, the need for automated detection and analysis of individual neurons takes on greater importance. We describe here a method that detects and identifies neurons within confocal image stacks acquired from the zebrafish brainstem. The first step is to create a template that incorporates the location of all known neurons within a population – in this case the population of reticulospinal cells. Once created, the template is used in conjunction with a sequence of algorithms to determine the 3D location and identity of all fluorescent neurons in each confocal dataset. After an image registration step, neurons are segmented within the confocal image stack and subsequently localized to specific locations within the brainstem template – in many instances identifying neurons as specific, individual reticulospinal cells. This image-processing sequence is fully automated except for the initial selection of three registration points on a maximum projection image. In analysing confocal image stacks that ranged considerably in image quality, we found that this method correctly identified on average ∼80% of the neurons (if we assume that manual detection by experts constitutes 'ground truth'). Because this identification can be generated approximately 100 times faster than manual identification, it offers a considerable time savings for the investigation of zebrafish reticulospinal neurons. In addition to its cell identification function, this protocol might also be integrated with stereological techniques to enhance quantification of neurons in larger databases. Our focus has been on zebrafish brainstem systems, but the methods described should be applicable to diverse neural architectures including retina, hippocampus and cerebral cortex.     

Statistical analysis of labelling patterns of mammary carcinoma cell nuclei on histological sections

It is of central interest for tumour biology to explore the mechanisms of tumour cell proliferation. In this study, methods of spatial statistics were used to study the spatial distribution of proliferating cells within tumour tissue quantitatively and objectively. Mammary cancer tissue was studied as an example. It was attempted to clarify whether cell division occurs entirely at random (random labelling), i.e. the process of division occurs at random, independently from the state of the neighbouring nuclei, or whether the spatial distribution of proliferation is more complex, e.g. in the form of actively proliferating clusters alternating with relatively silent zones. In the case of random labelling, the reduced second moment functions K(r) of the labelled and the unlabelled nuclei would be identical. The same would hold for the pair correlation functions g(r) . The alternative hypothesis is that the second‐order properties of the processes of the labelled and the unlabelled nuclei are different. Twenty cases of invasive ductal mammary carcinomas were studied. The nuclei of proliferating cells were stained immunohistochemically with the monoclonal antibody MIB‐1, which detects specifically the proliferation‐associated nuclear antigen Ki 67. The planar coordinates of the tumor cell nucleus profiles from two rectangular visual fields per case were recorded. For each visual field, the following investigations were performed: estimation of the explorative summary characteristics K(r) and g(r) , fitting of the parameters of a stationary Strauss hard‐core model to the observed point patterns, estimation of two distance‐dependent Simpson indices and Monte Carlo tests of all individual patterns on the null hypothesis of random labelling. Significant differences between the mean K‐functions and the mean g‐functions of the labelled and the unlabelled nuclei were found. Moreover, the mean interaction parameter γ of the stationary Strauss hard‐core model was significantly higher for the labelled nuclei than for the unlabelled nuclei. The estimates of the two distance‐dependent Simpson indices showed a tendency of points with the same label towards a positive spatial correlation. In the Monte Carlo tests, the null hypothesis of random labelling was rejected for the majority of the visual fields. These four lines of investigation led to the concordant conclusion that the labelling of mammary carcinoma nuclei by MIB‐1 is not simply random. The data suggest that the second‐order properties of the point process of the labelled nuclei are significantly different from those of the unlabelled nuclei. In particular, the process of the labelled nuclei shows a higher degree of clustering (increased strength of interaction) than the process of the unlabelled points.     

New variance expressions for systematic sampling: the filtering approach

We present a collection of variance models for estimators obtained by geometric systematic sampling with test points, quadrats, and n‐boxes in general, on a bounded domain in n‐dimensional Euclidean space ?ⁿ, n = 1, 2, ... , and for systematic rays and sectors on the circle. The approach adopted ? termed the filtering approach ? is new and different from the current transitive approach. This report is only preliminary, however, because it includes only variance models in terms of the covariogram of the measurement function. The estimation step is in preparation.     

Precision of stereological planar area predictors

Total planar area can be estimated based on sampling by a lattice of figures (e.g. point patterns, line segments, quadrats). General formulae are provided for the approximation of mean squared errors. The approximation formulae are products of the boundary length and of a parameter that depends only on the sampling scheme. An R package is provided by the authors for the numerical computation of the mean squared error formulae. The speed of convergence of the mean squared error approximation is assessed on the basis of several simulations. Several sampling schemes are compared in view of the approximated mean squared errors.     

Reconstruction of the rose of directions from a digital microhologram of fibres

Digital holography makes it possible to acquire quickly the interference patterns of objects spread in a volume. The digital processing of the fringes is still too slow to achieve on line analysis of the holograms. We describe a new approach to obtain information on the direction of illuminated objects. The key idea is to avoid reconstruction of the volume followed by classical three-dimensional image processing. The hologram is processed using a global analysis based on autocorrelation. A fundamental property of diffraction patterns leads to an estimate of the mean geometric covariogram of the objects projections. The rose of directions is connected with the mean geometric covariogram through an inverse problem. In the general case, only the two-dimensional rose of the object projections can be reconstructed. The further assumption of unique-size objects gives access with the knowledge of this size to the three-dimensional direction information. An iterative scheme is suggested to reconstruct the three-dimensional rose in this special case. Results are provided on holograms of paper fibres.