On semiautomatic estimation of surface area

In this paper, we propose a semiautomatic procedure for estimation of particle surface area. It uses automatic segmentation of the boundaries of the particle sections and applies different estimators depending on whether the segmentation was judged by a supervising expert to be satisfactory. If the segmentation is correct the estimate is computed automatically, otherwise the expert performs the necessary measurements manually. In case of convex particles we suggest to base the semiautomatic estimation on the so‐called flower estimator, a new local stereological estimator of particle surface area. For convex particles, the estimator is equal to four times the area of the support set (flower set) of the particle transect. We study the statistical properties of the flower estimator and compare its performance to that of two discretizations of the flower estimator, namely the pivotal estimator and the surfactor. For ellipsoidal particles, it is shown that the flower estimator is equal to the pivotal estimator based on support function measurements along four perpendicular rays. This result makes the pivotal estimator a powerful approximation to the flower estimator. In a simulation study of prolate and oblate ellipsoidal particles, the surfactor also performs well for particles which are not extremely elongated. In particular, the surfactor is not very much affected by the singularity in the surfactor formula or by possible inaccuracies in the necessary angle measurements. We also assess the performance of the semiautomatic procedure in a study of somatostatin positive inhibitory interneurons from mice hippocampi. Only 35% of the cells needed to be analysed manually and an important decrease in workload was obtained by using the semiautomatic approach.     

Design-based estimation of surface area in thick tissue sections of arbitrary orientation using virtual cycloids

Surface area is a first‐order stereological parameter with important biological applications, particularly at the intersection of biological phases. To deal with the inherent anisotropy of biological surfaces, state‐of‐the‐art design‐based methods require tissue rotation around at least one axis prior to sectioning. This paper describes the use of virtual cycloids for surface area estimation of objects and regions in thick, transparent tissue sections cut at any arbitrary (convenient) orientation. Based on the vertical section approach of Baddeley et al., the present approach specifies the vertical axis as the direction of sectioning (i.e. the direction perpendicular to the tissue section), and applies computer‐generated cycloids (virtual cycloids) with their minor axis parallel to the vertical axis. The number of surface‐cycloid intersections counted on focal planes scanned through the z‐axis is proportional to the surface area of interest in the tissue, with no further assumptions about size, shape or orientation. Optimal efficiency at each x–y location can be achieved by three virtual cycloids orientated with their major axes (which are parallel to the observation planes) mutually at an angle of 120°. The major practical advantage of the present approach is that estimates of total surface area (S) and surface density (S_V) can be obtained in tissue sections cut at any convenient orientation through the reference space.     

Geometrical characterization of fluorescently labelled surfaces from noisy 3D microscopy data

Modern fluorescence microscopy enables fast 3D imaging of biological and inert systems alike. In many studies, it is important to detect the surface of objects and quantitatively characterize its local geometry, including its mean curvature. We present a fully automated algorithm to determine the location and curvatures of an object from 3D fluorescence images, such as those obtained using confocal or light‐sheet microscopy. The algorithm aims at reconstructing surface labelled objects with spherical topology and mild deformations from the spherical geometry with high accuracy, rather than reconstructing arbitrarily deformed objects with lower fidelity. Using both synthetic data with known geometrical characteristics and experimental data of spherical objects, we characterize the algorithm's accuracy over the range of conditions and parameters typically encountered in 3D fluorescence imaging. We show that the algorithm can detect the location of the surface and obtain a map of local mean curvatures with relative errors typically below 2% and 20%, respectively, even in the presence of substantial levels of noise. Finally, we apply this algorithm to analyse the shape and curvature map of fluorescently labelled oil droplets embedded within multicellular aggregates and deformed by cellular forces.     

基于MATLAB的不规则平面立体表面积计算

在空间坐标系中,不规则平面立体的各个坐标点易知,表面积难求;为了找到一种方便、高效的求表面积的方法,以MATLAB为平台,对不规则平面立体的表面积计算做了研究.空间任意平面可由多个空间三角形组合而成,利用空间向量叉乘得到任意三角形面积,进而得到空间平面面积,则易求不规则立方体表面积;利用MATLAB卓越的数值计算能力,建立数据连接表,实现计算不规则表面积的通用平台.在此平台上,仅需输入所求平面立体的各点坐标,即可得到其表面积数据,结果显示,对于不规则立体表面的计算时间不超过三秒,而误差率不大于0.00001.     

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.     

Advantages and pitfalls of using free‐hand sections of frozen needles for three‐dimensional analysis of mesophyll by stereology and confocal microscopy

The anatomical structure of mesophyll tissue in the leaf is tightly connected with many physiological processes in plants. One of the most important mesophyll parameters related to photosynthesis is the internal leaf surface area, i.e. the surface area of mesophyll cell walls exposed to intercellular spaces. An efficient design‐based stereological method can be applied for estimation of this parameter, using software‐randomized virtual fakir test probes in stacks of optical sections acquired by a confocal microscope within thick physical free‐hand sections (i.e. acquired using a hand microtome), as we have shown in the case of fresh Norway spruce needles recently. However, for wider practical use in plant ecophysiology, a suitable form of sample storage and other possible technical constraints of this methodology need to be checked. We tested the effect of freezing conifer needles on their anatomical structure as well as the effect of possible deformations due to the cutting of unembedded material by a hand microtome, which can result in distortions of cutting surfaces. In the present study we found a higher proportion of intercellular spaces in mesophyll in regions near to the surface of a physical section, which means that the measurements should be restricted only to the middle region of the optical section series. On the other hand, the proportion of intercellular spaces in mesophyll as well as the internal needle surface density in mesophyll did not show significant difference between fresh and frozen needles; therefore, we conclude that freezing represents a suitable form of storage of sampled material for proposed stereological evaluation.     

The optical rotator

The optical rotator is an unbiased, local stereological principle for estimation of cell volume and cell surface area in thick, transparent slabs. The underlying principle was first described in 1993 by Kiêu &38; Jensen ( J. Microsc170, 45–51) who also derived an estimator of length. In this study we further discuss the methods derived from this principle and present two new local volume estimators.
The optical rotator benefits from information obtained in all three dimensions in thick sections but avoids over-/underprojection problems at the extremes of the cell. Using computer-assisted microscopes the extra measurements demand minimal extra effort and make this estimator even more efficient when it comes to estimation of individual cell size than many of the previous local estimators. We demonstrate the principle of the optical rotator in an example (the cells in the dorsal root ganglion of the rat), evaluate its efficiency and compare it with other unbiased, local stereological principles available for estimation of cell volume and surface area.     

自由曲面孔域数据的拟实填补与曲面重建

为解决具有孔域的自由曲面在逆向设计中存在的数据空洞，提出了孔域测量数据的填实方法，通过孔域边界数据的光顺，截面测量曲线的端点 闭合处理，孔域的截面数据延拓，母面设计和曲面裁剪等技术，解决了自由曲面孔域数据填补和曲面的重建问题，实例应用表明，该方法可应用于逆向工程中对具有孔域的自由曲面的测量和造型，并能保证曲面重建的品质。     

Volume estimation from projections

We describe a new estimator of the volume of axially convex objects from total vertical projections with known position of the vertical axis. The estimator combines the Cavalieri method with the known formula for area in terms of the support function of a convex body. We examine the accuracy of the proposed estimator for ellipsoidal objects having exactly known support function and volume. In addition, we illustrate practical problems of accuracy by implementing the method for some biological products.     

Searching surface orientation of microscopic objects for accurate 3D shape recovery

In this article, we propose a new shape from focus (SFF) method to estimate 3D shape of microscopic objects using surface orientation cue of each object patch. Most of the SFF algorithms compute the focus value of a pixel from the information of neighboring pixels lying on the same image frame based on an assumption that the small object patch corresponding to the small neighborhood of a pixel is a plane parallel to the focal plane. However, this assumption fails in the optics with limited depth of field where the neighboring pixels of an image have different degree of focus. To overcome this problem, we try to search the surface orientation of the small object patch corresponding to each pixel in the image sequence. Searching of the surface orientation is done indirectly by principal component analysis. Then, the focus value of each pixel is computed from the neighboring pixels lying on the surface perpendicular to the corresponding surface orientation. Experimental results on synthetic and real microscopic objects show that the proposed method produces more accurate 3D shape in comparison to the existing techniques.     

一种用于曲面快速测量的激光片光源的研究

与快速成形技术有关的自由曲面快速反求工程中,测绘曲面所用的被称为光刀或片光的细长光条的质量是至关重要的。介绍一种应用柱面反射镜单向扩展光束形成激光片光的方法,并根据常用Ｈｅ－Ｎｅ激光为高斯光束的特性,应用长焦距透镜压缩其发散角,使激光片光具有很大焦深。激光光强的高斯分布使光刀宽度的中心具有极大值,使得片光的质量具有优良的特性,非常容易实现,并有利于摄像机采集。介绍了这种片光源的工作原理、片光的性能     

Stereology of isolated objects with the invariator

The invariator is a new stereological design to generate motion invariant test lines in three dimensions on an isotropic plane through a fixed point. The theory has been published recently. The purpose of this paper is to illustrate the application of the invariator on a group of rat brains to estimate brain volume and external surface area. Each brain was first split into its two hemispheres and then embedded into a ball filled with agar following a configuration named the antithetic isector, with the idea of reducing the error variance. After rolling the ball at random it was scanned by magnetic resonance imaging into a stack of parallel systematic sections: this is the isotropic Cavalieri design which, combined with the antithetic isector idea, proves to be very accurate. The invariator used only an equatorial section of the ball, and in the present case the coefficient of error of the volume and surface area estimators of an individual brain was about 30%. As it is design unbiased, the invariator may prove its strength mainly to estimate population means.     

Flowers and wedges for the stereology of particles

Recently, a new decomposition has been found for the motion invariant density of straight lines in, with applications in stereology. The new principle, called the invariator, leads to new rotational formulae which express the surface area and the volume of a bounded subset (called a 'particle') in terms of an observable functional defined in an isotropically oriented section (called a pivotal section) through a fixed point (called the pivotal point). The results have been extended to intrinsic volumes of manifolds in general space forms. The purpose of this paper is to present new results and computational formulae for three-dimensional particles. Explicit estimators are obtained for a convex polyhedral particle with a pivotal point in its interior, in terms of the coordinates of the vertices of the pivotal section. The results are applied to a population of polyhedral grains from a cemented carbide which was studied earlier by alternative methods.     

Influence of the phase effect on gradient‐based and statistics‐based focus measures in bright field microscopy

Autofocusing is essential to high throughput microscopy and live cell imaging and requires reliable focus measures. Phase objects such as separated single Chinese hamster ovary cells are almost invisible at the optical focus position in bright field microscopy images. Because of the phase effect, defocused images of phase objects have more contrast. In this paper, we show that widely used focus measures exhibit an untypical behaviour for such images. In the case of homogeneous cells, that is, when most cells tend to lie in the same focal plane, both gradient‐based and statistics‐based focus measures tend to have a local minimum instead of a global maximum at the optical focus position. On the other hand, if images show inhomogeneous cells, gradient‐based focus measures tend to yield typical focus curves, whereas statistics‐based focus measures deliver curves similar to the case of homogeneous cells. These results were interpreted using the equation describing the phase effect and patch‐wise analysis of the focus curves. Bioprocess engineering experts are also influenced by the phase effect. Forty‐four focus positions selected by them led to the conclusion that they prefer to look at defocused images instead of those at the optical focus.     

Stereological estimation of surface area and barrier thickness of fish gills in vertical sections

Previous morphometric methods for estimation of the volume of components, surface area and thickness of the diffusion barrier in fish gills have taken advantage of the highly ordered structure of these organs for sampling and surface area estimations, whereas the thickness of the diffusion barrier has been measured orthogonally on perpendicularly sectioned material at subjectively selected sites. Although intuitively logical, these procedures do not have a demonstrated mathematical basis, do not involve random sampling and measurement techniques, and are not applicable to the gills of all fish. The present stereological methods apply the principles of surface area estimation in vertical uniform random sections to the gills of the Brazilian teleost Arapaima gigas. The tissue was taken from the entire gill apparatus of the right‐hand or left‐hand side (selected at random) of the fish by systematic random sampling and embedded in glycol methacrylate for light microscopy. Arches from the other side were embedded in Epoxy resin. Reference volume was estimated by the Cavalieri method in the same vertical sections that were used for surface density and volume density measurements. The harmonic mean barrier thickness of the water‐blood diffusion barrier was calculated from measurements taken along randomly selected orientation lines that were sine‐weighted relative to the vertical axis. The values thus obtained for the anatomical diffusion factor (surface area divided by barrier thickness) compare favourably with those obtained for other sluggish fish using existing methods.     

SPP tomography: A simple wide‐field nanoscope

We explore the wide‐field optical nanoimaging capabilities of the surface plasmon polariton (SPP) tomography technique. We show that nanofeatures with lateral dimensions smaller than λ/20 can be observed in the surface emission (SE) images of plasmonic crystals with a period of 300 nm. Moreover, as a proof‐of‐concept, we demonstrate that SPP tomography permits to resolve two single objects with a center‐to‐center separation of 200 nm and edge‐to‐edge separation as small as λ/7. We present a comprehensive discussion about the nanoimaging capabilities of the SPP tomography technique. In contrast to other optical subwavelength resolution techniques, in our approach for imaging nanosize features, enhanced evanescent waves are coupled to the far‐field via leakage radiation associated with SPPs excited by near‐field fluorescence; therefore wide‐field images, which are not out‐of‐plane diffraction‐limited, are formed directly in the microscope's camera. We also discuss additional imaging processing capabilities associated with the fact that SPP tomography SE images are formed by the microscope lenses through an analog tomography process. SCANNING 35: 246‐252, 2013. © 2012 Wiley Periodicals, Inc.     

Atomic force microscopy wear characterization of biomedical polymer coatings

Atomic force microscopy (AFM) has become established as a powerful and versatile tool for investigating local mechanical properties. In addition, through the AFM tip–sample interaction, it has become possible to study the effects of perturbations and modifications to the surface of soft samples, such as polymers. The accurate knowledge of their response to continuous AFM scanning could help to design new materials having desirable mechanical properties. In this paper, we present the results obtained by applying a new methodology to investigate wear properties on two different type of polymer, poly(methyl‐methacrylate) and poly(l ‐lactic acid). These polymers have been widely employed in biomedical applications and have recently been considered as good candidates for coronary metallic stent coatings. Copyright © 2006 John Wiley & Sons, Ltd.     

Stereological reconstruction of polycrystalline materials

Laguerre tessellations are suitable models for many polycrystalline materials. In this work, we present a reconstruction‐based approach to fit a spatial Laguerre tessellation model to a plane section of a cellular material under the condition that one section of the model resembles the observed section of the material. To account for this special requirement, we introduce a novel Euclidean distance‐based criterion for the model fitting. The model fitting itself is based on Simulated Annealing. If the structure under consideration is a Laguerre tessellation, we found a nearly perfect reconstruction of its spatial cell characteristics in the model. Even for a real sample of a sintered alumina the observed section is captured quite well by the model.     

Surface plasmon-assisted widefield non-linear imaging of gold structures

In this paper, we demonstrate how the confinement and enhancement of optical fields by surface plasmon resonance can allow non‐linear microscopy to be performed in a simple, cost‐effective widefield configuration, rather than the more usual laser‐scanning arrangement. We present second harmonic and two‐photon luminescence widefield images of dielectric and gold samples obtained with both prism‐based and high numerical aperture objective (‘prismless’) microscope arrangements.     

Authentication of bee pollen grains in bright‐field microscopy by combining one‐class classification techniques and image processing

A novel method for authenticating pollen grains in bright‐field microscopic images is presented in this work. The usage of this new method is clear in many application fields such as bee‐keeping sector, where laboratory experts need to identify fraudulent bee pollen samples against local known pollen types. Our system is based on image processing and one‐class classification to reject unknown pollen grain objects. The latter classification technique allows us to tackle the major difficulty of the problem, the existence of many possible fraudulent pollen types, and the impossibility of modeling all of them. Different one‐class classification paradigms are compared to study the most suitable technique for solving the problem. In addition, feature selection algorithms are applied to reduce the complexity and increase the accuracy of the models. For each local pollen type, a one‐class classifier is trained and aggregated into a multiclassifier model. This multiclassification scheme combines the output of all the one‐class classifiers in a unique final response. The proposed method is validated by authenticating pollen grains belonging to different Spanish bee pollen types. The overall accuracy of the system on classifying fraudulent microscopic pollen grain objects is 92.3%. The system is able to rapidly reject pollen grains, which belong to nonlocal pollen types, reducing the laboratory work and effort. The number of possible applications of this authentication method in the microscopy research field is unlimited. Microsc. Res. Tech. 2012. © 2012 Wiley Periodicals, Inc.