PubMed Health⌕ Search

Biomedical subjects

D Stoyan

Publications and source records attributed to D Stoyan.

8 recordsLinked to original sources
PubMed2005

Morphological characterization of point patterns.

A triplet of function s for the statistical characterization of planar point patterns is introduced. They are related to the integral-geometric quantities area, boundary length and Euler number of patterns of discs centred at the given points. These functions are able to give information on the distribution of a given point pattern which the traditional summary statistics of point process theory do not offer and so can lead to an improved statistical description. The paper describes the statistical estimation of the new characteristics. Some examples illustrate their application in the exploratory analysis of point patterns of tree positions in forests, in comparison to results obtained by means of second-order and distance characteristics.

Agriculture↗
PubMed2005

Statistical characterization of TEM images of silica-filled rubber.

Transmission electron microscopy is used to study the micro-dispersion of silica fillers within the polymer matrix of rubber. The resulting grey-value images are interpreted as realizations of random fields and are characterized by means of variograms. The so-called Cauchy class is a suitable model for this purpose. Statistical analysis shows that different filler dispersion properties are reflected in different variogram parameters. As a case study, the random field approach is demonstrated for four exemplary rubber compounds.

Algorithms↗
PubMed2004

Second-order stereology of spatial fibre systems.

This paper describes methods for second-order stereology of spatial fibre systems. For stationary and isotropic fibre processes it gives practicable estimators of the K-function and the pair correlation function, which are based on planar sections. The second-order methods are applied in transmission electron microscopy analysis of blood capillaries in the rat thyroid. They lead to the result that the capillaries show an inhibitory pattern of their spatial arrangement, with a hard-core distance of about 2.6 microm. There is a close relationship to three-dimensional size characteristics estimated recently for these elliptical capillaries.

Algorithms↗
PubMed2003

On the estimation variance for the specific Euler-Poincaré characteristic of random networks.

The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.

Humans↗
PubMed2000

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.

Animals↗
PubMed1999

Stereological analysis and modelling of gradient structures

Gradient structures are inhomogeneous along a particular gradient direction but homogeneous perpendicular to that direction. Consequently, structural parameters such as volume fraction or surface area density are local characteristics which depend on the 'vertical' coordinate with respect to the 'vertical' gradient axis. Analogously, models for gradient structures have model parameters depending on the vertical coordinate z. For example, a Voronoi tessellation with a gradient is generated by a gradient point process with a local intensity which is a function of z. Similarly, a gradient germ grain model is obtained from a gradient point process where the grain size distribution may also depend on z. For a gradient Boolean model, local volume fraction VV(z) and local surface area density SV(z) can be calculated from the model parameters. Stereological methods for gradient structures are based on vertical sections parallel to the gradient direction. Estimation of VV(z), SV(z) and local length density LV(z) is done by lineal analysis using horizontal test lines with vertical coordinate z. Similarly, lineal analysis is used to estimate local mean cell volume of gradient tessellations. For the estimation of local particle number density and size in the spirit of the Wicksell problem the use of kernel methods and distributional assumptions is required.

Journal Article↗
PubMed1985

The pair correlation function for point and fibre systems and its stereological determination by planar sections.

Traditional stereology consists nearly completely in the determination of particle size distributions and mean values such as Vv and Sv. However, for the description of the 'inner' structure of random structures second-order characteristics such as the pair correlation function or reduced second moment function are useful. In the present paper stereological estimation of second-order quantities for centres of random sphere systems and for random fibre systems are considered. In the case of sphere systems stereological formulae are given which connect the pair correlation function of the sphere centres with quantities available from planar, linear and thin sections. For random fibre systems some exact and approximate stereological methods are suggested which enable the determination of second-order quantities from planar and thin intersections.

Capillaries↗