Estimating surface area by the isotropic fakir method from thick slices cut in an arbitrary direction

The proposed fakir method for estimating surface area is based on counting the intersections between the surface lying within a thick slice, and an isotropic spatial grid consisting of a combination of linear probes called fakir probes. An unbiased procedure using a directly randomized spatial grid rather than sections with randomized directions is presented. The method is applicable if perfectly registered serial sections of the surface are available in a thick slice while the direction of the slice can be arbitrary. The efficiency of the fakir method using different arrangements of orthogonal triplets of fakir probes is evaluated and it is shown that mutually shifted probes are superior to non-shifted ones. The application software for interactive counting of intersections between computer-generated fakir probes and the surface within the stack of digitized images is described and demonstrated by two examples: estimation of the surface area of individual tobacco cell chains using a confocal microscope, and estimation of the total area of exposed surface of mesophyll cells in a barley leaf using a wide-field transmission microscope.     

Measuring the surface area of a cell by the method of the spatial grid with a CSLM—a demonstration

The spatial grid is a method for estimating the surface area of particles. A stack of perfectly registered sections is the essential prerequisite for its use. The confocal scanning light microscope provides such a stack by optical sectioning. The spatial grid method is briefly described and applied to an osteocyte lacuna in dry mineralized human mandible. This type of cell was chosen because of its very complex shape. The variance of the area estimate is studied and compared with the results of a simulation.     

Stereological analysis of the spatial Poisson–Voronoi tessellation

Stereological model tests and parameter estimators for the spatial Poisson–Voronoi tessellation are discussed. The tests aim to discriminate the Poisson–Voronoi tessellation from more regular or more irregular tessellations. The power of the model tests under some special parametric alternative hypotheses is investigated by simulation. Among the tests considered, the most powerful test is based on the variance of the section cell areas. Various stereological estimators for the model parameter of the spatial Poisson–Voronoi tessellation are compared with respect to their bias and variance by means of a Monte–Carlo study. Formulae are given for variance prediction. An estimator based on vertex counting is found to be the best. Robustness is investigated by applying the estimators to Voronoi tessellations generated by other point process models.     

Confocal microscopy and stereology: estimating volume, number, surface area and length by virtual test probes applied to three-dimensional images

The opportunities of confocal microscopy applied to morphometry of microscopical structures are presented and demonstrated on stereological methods based on evaluation of optical sections within a thick slice and using computer-generated virtual test probes. Such methods, allowing arbitrary orientation of the thick slice, can be used for estimating volume, number, surface area, and length. The methods using spatial grid of points, disector, fakir, and slicer probes are described and illustrated by different examples using our freeware 3DTOOLS software and their variance and applicability are discussed. It is shown that shifted triple or quadruple spatial grids of lines are very efficient for the surface area and volume estimation by the fakir method.     

Estimating mean particle volume and number from random sections by sampling profile boundaries

We describe some new shape-independent stereological estimates of particle mean volume and surface area. Finding volumes or surface areas of cell nuclei, from electron micrographs of random thin sections, is a central problem of biological stereology. The well-known point-sampled intercept (PSI) method samples profile interiors to find the volume-weighted mean volume. This can be used in place of the true mean volume, but to do so introduces bias when volumes vary a great deal, as they do in fixed specimens. Jensen and Gundersen quite recently extended the PSI estimator to provide particle surface area, with no bias in the case of uniform surface areas. Here we extend the PSI volume estimator in a different way, sampling profile boundaries rather than their interiors. We obtain a boundary-sampled intercept (BSI) volume estimator, simpler than the PSI surface area estimator, but also unbiased for uniform surface areas. Both of these estimators are attractive, for example, in measuring and counting cell nuclei, where membrane surface area varies less than volume. Furthermore, they have no shape bias whatsoever. This paper also examines the general relationship between boundary- and area-sampled estimates, and we clarify the formal connection between our volume estimator and the PSI surface area estimator. We also calculate and compare their theoretical efficiencies.     

Stereological estimation of mean linear intercept length using the vertical sections and trisector methods

A method for estimating the mean linear intercept length of anisotropic microstructures using vertical sections is presented. A test system of cycloids and points is overlaid on the vertical sections, and the mean linear intercept length is estimated from a simple counting procedure — no length measurements are required. The vertical direction is either arbitrarily chosen or chosen perpendicular to most of the surface boundaries of the objects of interest. A design with the latter choice of the vertical direction and three vertical sections — a trisector — will optimize the precision of the estimate from only three vertical sections. The method was applied to two metallic structures, but it may also be used in a biomedical context.     

Precision of area estimation: a numerical study

After listing some general formulae for sampling in n-dimensional space, the author considers the one-dimensional case: the estimation of the length of a line segment by counting the number of points that happen to fall within the segment. If the points are equidistantly located, the variance of the estimate is a strictly periodic function of the length of the segment. This systematic sample has a higher efficiency than simple and stratified random samples of the same intensity. With some modifications, the results carry over to the two-dimensional case: the estimation of the area of a plane figure by counting the number of sample points falling inside the figure. However, the strict periodicity of the variance in the one-dimensional systematic case is replaced by a ‘Zitterbewegung’. The magnitude of this oscillation is seen to be very different for figures of different shapes. Some results are presented also for the estimation of areas by line transects, and for the estimation of volumes by aid of lattices of points in R³, and R⁴. Some comments are also given on the practical implications of the results for sampling in the plane.     

凸显尖锐特征的点-线-面递进式曲面重建

针对现有曲面重建算法不能很好地重建出点云模型尖锐特征的缺陷,提出了一种凸显点云尖锐特征的点-线-面递进式曲面重建算法。首先,根据近邻点的欧氏距离、法向偏差和曲面变分,采用主成分分析算法和k-近邻点迭代加权法获取点云准确法向;接着,依据特征点位于多个平面交线上的原则,利用法向聚类和平面拟合从候选特征点中筛选特征点;然后,依据特征点生长方向和主方向的相互关系重建特征线,并按照最小二乘原理采用矩阵法修复角点;最后,以特征线为约束重建尖锐特征点云曲面。实验结果表明：本文算法计算的点云准确法向与理论法向偏差接近于0,特征重建效果优于其他算法,算法耗时短且与点云数量呈线性关系。算法不仅能够准确计算尖锐特征区域的点云法向,还能准确提取出点云模型的特征点并凸显模型的尖锐特征。     

Stereological stereometry: Simplified approaches to volumetry by SEM

New approximate methods for the measurement of volumes of pits in otherwise flat substrates are outlined: all are based on taking parallax measurements from SEM stereo-pair images. The measured points lie at pre-set intervals in a grid, the grid corresponding to the usual 2-D array used in stereology and being used for the same purpose – that of determining area. Depth below the original surface is derived from the parallax at each point. Several practical alternatives for parallax measurement are considered, all involving relatively inexpensive instruments. The cheapest – and it remains to be determined whether also the most efficient – involves the use of a stereo-pair grid overlay, called a “2D-3D” grid. This grid exists physically in only two dimensions, but is seen to exist apparently in three dimensions.     

曲面造型中一种快速的曲面跟踪求交算法

提出了一种新的曲面求交算法,采用精度好、效率高、计算稳定的迭代方法求得等参数网格线在曲面上的交点,并通过跟踪获得两曲面的交线。本算法由三个子算法组成,一个是求曲面上到固定点距离最近的点,一个是求参数网格线与曲面的交点,一个是求曲面与曲面的交点。为保证不遗漏交点,利用第一个算法对参数网格点进行分类,跟踪交点时利用第三个求下一个交点。与离散法求交相比,本算法具有计算稳定性、可靠性好,速度快,精度高的优点     

Measuring fractal dimension and complexity — an alternative approach with an application

Fractal dimension has often been applied as a parameter of complexity, related to, for example, surface roughness, or for classifying textures or line patterns. Fractal dimension can be estimated statistically, if the pattern is known to be self-similar. However, the fractal dimension of more general patterns cannot be estimated, even though the concept may be retained to characterize complexity. We here show that the usual statistical methods, e.g. the box counting method, are not appropriate to measure complexity. A recently developed approach, the extended counting method, whose properties are closer to what fractal dimension means, is considered here in more detail. The methods are applied to geometric and to blood vessel patterns. The weak assumptions about the structure, and the lower variance of the estimate, suggest that the extended counting method has beneficial properties for comparing complexity of naturally occurring patterns.     

Automated techniques for the study of lung alveolar stereological parameters with the IBAS image analyser on optical microscopy sections

In the case of lung alveoli, the good contrast of the features allows the use of a fully automated image analysing procedure, yielding many of the desirable stereological parameters which can be estimated on optical microscopy slides: alveolar volume and surface densities, a form factor and average mean integral curvature. With our program, specially designed for the IBAS image analyser (Kontron Bildanalyse, Munich, B.R.D.), the whole automated process takes an average of 28 s per field. The image analyser-obtained stereological estimates compare well with those given by point and intersection counting methods. Some difficulties inherent in image analysers arise when measuring alveolar boundary lengths: a scheme is therefore proposed which eliminates the image-edge errors, with no sampling bias, by comparing three different frames inside each field. A solution to the problem of estimating automatically the positive and negative tangent counts, necessary for the curvature calculations, is also proposed. Our program has been applied routinely to the study of premature newborn rabbit lung alveoli, as part of a work dealing with an evaluation of the possibility of preventing the respiratory distress syndrome by the administration of heterologous surfactant.     

立体网状静电传感器空间灵敏特性研究

提出一种全新的立体网状静电传感器,以克服现有静电传感器对流场内速度分布无法测量的不足。通过建立立体网状静电传感器的三维仿真模型,利用有限元分析法获得了立体网状静电传感器的灵敏度空间分布规律,并对其动态灵敏度进行了分析。结果表明:立体网状静电传感器具有局部敏感特性,对于管内颗粒分布比较敏感。而且由于其极棒间相互交错的特性,可以探测到颗粒的运动方向;传感器的动态灵敏度可以反映带电颗粒在各个极棒间的空间位置及其速度,即带电颗粒距离极棒交织点越近,速度越快,动态灵敏度越大。最后通过重力输送颗粒实验,证明理论分析的结果与实验结果一致,从而为立体网状静电传感器实现颗粒流动参数测量提供了理论依据。     

The spatial rotator

This paper presents a new local volume estimator, the spatial rotator, which is based on measurements on a virtual 3D probe, using computer assisted microscopy. The basic design of the probe builds upon the rotator principle which requires only a few manual intersection markings, thus making the spatial rotator fast to use. Since a 3D probe is involved, it is expected that the spatial rotator will be more efficient than the the nucleator and the planar rotator, which are based on measurements in a single plane. An extensive simulation study shows that the spatial rotator may be more efficient than the traditional local volume estimators. Furthermore, the spatial rotator can be seen as a further development of the Cavalieri estimator, which does not require randomization of sectioning or viewing direction. The tissue may thus be sectioned in any arbitrary direction, making it easy to identify the specific tissue region under study. In order to use the spatial rotator in practice, however, it is necessary to be able to identify intersection points between cell boundaries and test rays in a series of parallel focal planes, also at the peripheral parts of the cell boundaries. In cases where over‐ and underprojection phenomena are not negligible, they should therefore be corrected for if the spatial rotator is to be applied. If such a correction is not possible, it is needed to avoid these phenomena by using microscopy with increased resolution in the focal plane.     

Edge effect elimination in the recursive implementation of Gaussian filters

The paper discusses a general methodology to the design of recursive Gaussian filters to be used for separating the form, waviness and roughness components of the surface texture. By selecting appropriate initial values for the filter difference equations, it is possible to eliminate the so-called edge effect and evaluate the whole registered profile. Two ways of filter implementation were considered: series and parallel. The incremental difference operator is applied in place of the usual shift operator z to describe the filter transfer function. This increases the accuracy of the representation of filter parameters and decreases the number of rounding errors. The results of the analysis were illustrated using 2D and 3D roughness profiles of a ball bearing race. The data show that the mean line and the mean surface were correctly determined for the whole area of the measured profile.     

Effects of distribution of surface slopes and flow pressures of contact asperities on contact between solid surfaces

An analysis of the mechanism of contact between two solids was carried out considering the distribution of the surface slopes of conical asperities and the variation of the flow pressure of each contact asperity due to work-hardening and the work-hardened layer of the softer surface. From the analysis, where the distributions of the surface heights and the surface slopes are Gaussian the number of contact points decreases and their mean radius increases with increasing ranges of the distribution of the surface slopes for a given value of the mean surface slope. The number of contact points, the total real area, the separation and the radius of the contact points are influenced by the variation of the flow pressure of each contact asperity due to work-hardening of the contact asperities or the work-hardened layer of the softer surface.The validity of the theory was checked by comparing the theoretical and experimental results of the number, the separation and the distribution of the radii of contact points.     

The avoidance of cutter gouging in five-axis machining with a fillet-end milling cutter

This paper proposes a new method of automatic detection and elimination of cutter gouging when using the fillet-end milling cutter to produce a complex surface on the five-axis computer numerical control machine tool. To avoid local cutter gouging at the point where the cutter and part surface make contact with each other, the method of exact curvature matching between the cutter and part surface is presented. The size of cutter radii is more easily determined by this method. To detect if a rear cutter gouging occurs near the contact point, a square grid with horizontal and vertical points is used for illustrating the checking area and checking points. The technique of automatic generation of the square grid points and the method of detection and avoidance of rear cutter gouging are investigated throughout this article. In the end, the studied methodology and algorithms are inspected and verified by using an example of nonuniform rational B spline surface.     

A novel method for mean cell volume estimation

A novel method is described for the estimation of the mean cell volume of cell populations grown in suspension. The cells are filtered onto a nitrocellulose filter to form a cylindrical pellet which is embedded in epoxy resin. Using estimates of pellet height and radius, the number of cells in the pellet and of the volume density of the cells in the pellet, it is possible to produce an unbiased estimate of the mean cell volume. This method is compared, using cell suspensions of the blood parasite Trypanosoma brucei, with mean cell volume estimation using a Coulter channellizer. A Coulter channellizer was also used to compare the mean cell volume of living trypanosomes with that of aldehyde-fixed populations, and the values obtained were compared with those obtained using the new method. The estimated mean cell volume of a T. brucei clone was used to derive values from volume densities obtained by point and intersection counts for the absolute volumes of the flagellar pocket, the nucleus, and endocytic organelles containing internalized horseradish peroxidase and transferrin-gold after 30-min incubations at 310 K. Estimated values for the surface area of the flagellar pocket and the surface area of a cell were also obtained. From known data on the total amount of variant surface glycoprotein molecules per cell and the known packing density of membrane proteins, it was estimated that approximately 80% of the molecules must reside in intracellular compartments. It was estimated that the equivalent of 5% of the surface membrane may be internalized per minute, an amount which is almost the size of the entire flagellar pocket membrane.     

Tactile sensing of constructional differences in fabrics with a polymeric finger tip

There have been many attempts for quantitative assessment of constructional differences of woven fabrics in view of perceived touch. This research focuses on quantifying the tactile perception of minor changes in constructional parameters (yarn density, yarn fineness and pattern) of fabrics by rubbing with an artificial finger tip at achievable preload and velocity. Experiments show the viability of sensing constructional differences and confirm the significance of scanning direction in asymmetrical patterns. Friction coefficients primarily rely on the number of intersection points and total area of flow yarns taking place in a unit pattern area in the direction of scanning.