Information recovery in missing angular data cases: an approach by the convex projections method in three dimensions

We have studied the method of projections on to convex sets (POCS) for the restoration of three-dimensional signals, especially applied for the degraded information obtained in three-dimensional (3-D) reconstructions by electron microscopy due to the limited tilting angular range of the sample that is obtainable in practice. A computer generated specimen has been used as a test object. Several noise levels were added to the specimen, obtaining signal-to-noise ratios (signal power/noise power) of between 12 and 0·5 dB. Different missing data angular regions of 30° and 10° zenithal angle have been considered. Our results illustrate the possibilities of POCS to restore incomplete 3-D data in the absence and the presence of noise, and offer ways for further applications to improve the quality of 3-D reconstructions based on real data.     

Improvement in the resolution of three-dimensional data sets collected using optical serial sectioning

In this paper an approach for improving the quality of 3-D microscopic images obtained through optical serial sectioning is described and implemented. A serially sectioned image is composed of a sequence of 2-D images obtained by incrementing the focusing plane of the microscope through the specimen of interest; ideally, the image obtained at each focusing plane should be in focus, and should contain information lying only within that plane. In practice, however, the images obtained contain redundant information from neighbouring focusing planes and are blurred by a three-dimensional low-pass distortion. These degradations are a consequence of the limited aperture of any optical system; using principles of geometric optics and allowing for the passage of light through the specimen, we are able to demonstrate that the microscope distortion can be described as a linear system, if the absorption of the specimen is assumed to be linear and non-diffractive. The transfer function of the microscope is found to zero a biconic region of 3-D spatial frequencies orientated along the optical axis; a closed-form expression is derived for the low-pass transfer function of the microscope outside the region of missing frequencies. The planar resolution of the serial sections can be greatly improved by convolving the image obtained with the inverse of the low-pass distortion function, although the missing cone of frequencies is not recoverable. The reconstruction technique is demonstrated using both simulated images, to demonstrate more clearly the effects of the distortion and the accuracy of the subsequent reconstruction, and actual experiments with a pollen grain and a stained preparation of human cerebellum tissue.     

A nondestructive method for three-dimensional reconstruction of luminescence materials: Principles,data acquisition,image processing

In the study presented here we have tried to state the principles and calculate and visualize models of three-dimensional (3-D)-cathodoluminescence reconstruction of luminescence structures by scanning electron microscopy (SEM). The new technique does not destroy the specimen and uses the variable energy of the electron beam to penetrate to different depths in the specimen volume. The SEM in color cathodoluminescence mode (CCL-SEM) detects integrated panchromatic CL-images for different energies of the electron beam. The use of electron scattering theory in solids and theories of cathodoluminescence and color allow the production of problem-oriented software for the routine processing of primary images. Processed images represent the CCL-SEM displays of separated layers (without CL information from other layers) up to the maximum depth penetrated by the beam. The 3-D reconstruction is carried out through algorithms developed using a personal computer, software, and a set of processed two-dimensional (2-D) images. The first experimental work was accomplished using a multilayer SiC mesastructure. The final reconstructed image of SiC material demonstrates separated epitaxial layers of different SiC polytypes and Z sections (YOZ and XOZ sections). The 3-D image represents the space distribution of CL-spectral data in color CL interpretation.     

Morphometrical study of plant vacuolar dynamics in single cells using three-dimensional reconstruction from optical sections

In higher plants, vacuoles increase their volumes in accordance with cell enlargement and occupy most of the cell volume. However, quantitative analyses of vacuolar contributions during changes in cell morphology have been hampered by the inadequacies and frequent artifacts associated with current three-dimensional (3-D) reconstruction methods of images derived from light microscopy. To overcome the limitations of quantifying 3-D structures, we have introduced 3-D morphometrics into light microscopy, adopting a contour-based approach for which we have developed an interpolation method. Using this software, named REANT, the morphological and morphometrical changes in protoplasts and vacuoles during plasmolysis could be investigated. We employed the tobacco (Nicotiana tabacum) BY-2 cell line No.7, expressing a GFP-AtVam3p fusion protein, BY-GV7, using GFP as a marker of vacuolar membranes (VMs). By vital staining of the plasma membrane (PM) of cells, we simultaneously obtained optical sections of both the PM and VM. We, therefore, reconstructed the 3-D structures of protoplasts and vacuoles before and after plasmolysis. We were able to identify the appearance of elliptical structures of VMs in the vacuolar lumen, and to determine that they were derived from cytoplasmic strands. From the 3-D structures, the volumes and surface areas were measured at the single cell level. The shrinkage of vacuoles accounted for most of the decrease in protoplast volume, while the surface area of the vacuoles remained mostly unchanged. These morphometrical analyses suggest that the elliptical structures are reservoirs for excess VMs that result from the response to rapid decreases in vacuolar and protoplast volumes.     

Digital image tiles: a method for the processing of large sections

Segmentation of large areas of light microscopic slides into N by N fields, and each of these fields into M digital image tiles, allows the scanning, storage and digital processing of large images. Any of the original N² fields or composites of M adjacent tiles can be recalled to the video display for analysis. Developed procedures for use on a microscope equipped with a precision scanning stage allow registration of the image coordinates (X-Y) for any original or composite field and the alignment of one of these fields along the depth (Z) axis by means of external, machined fiducial marks in serial sections. To facilitate work whenever unavoidable, we have incorporated methods for digital image panning and zooming (changes of magnification) and discuss their use and implications.     

A method using an on-line digital computer for the improvement of resolution of backscattered electron images

In principle, the resolution of backscattered electron (BSE) images can be little improved, even though an infinitely small beam size is achieved by various improvements in the intrinsic instrument. In order to circumvent this problem, a method is proposed which utilizes an on-line digital computer for the image recording and processing. The major image-processing tools are reduction, expansion, super-imposition with matching of the images, and high-emphasis filtering in the Fourier domain. By using various combinations of these techniques, the resolution of BSE images has been significantly improved. The validity of these improved images has been confirmed. In the case of a BSE image with too wide a dynamic range, both the present method and digital homomorphic filtering provide successful results.     

The projection of a negatively-stained filamentous object down its central axis as revealed by image reconstruction from tilt series

Helical reconstructions of negatively stained biological objects contain distortions arising from filament flattening and the non-cylindrical profile of the stain envelope. Current methods of estimating flattening do not make full use of the information available in electron micrographs. We have applied the more rigorous approach of reconstructing the density profile from tilt series using digital image processing techniques. Tilt series were collected for tobacco mosaic viruses (TMV) and seven independent reconstructions were calculated using equatorial data out as far as ～1/9·3 nm^—1. They indicated that the filaments were flattened with an axial ratio of about 2·4:1, which was probably closer to 3:1 in the original specimen, because the limited resolution caused flattening to be underestimated. The stain envelope around TMV and some indication of the underlying carbon substrate were also observed. This information could enable correction factors for flattening to be developed, which could be useful when calculating helical reconstructions or indexing helical diffraction patterns. This method could also be extended to non-equatorial layer planes, which would provide three-dimensional information on a wide range of macromolecules that possess a one-dimensional repeat.     

Serial sectioning and digitization of porous media for two- and three-dimensional analysis and reconstruction

A procedure is proposed for serial sectioning of impregnated porous media, for photographing the sections under the microscope, and for digitizing the image using an IBM PC (XT) with a digitizing board. The result is a three-dimensional matrix containing the enhanced digitized image in a binary form of O's and I's which represent solid and pore spaces respectively. The procedure was tested on three different porous materials: (1) a pack of glass beads, 170–350 μm; (2) Berca sandstone; and (3) Elora clay loam soil. Each of these was impregnated, forty-six to eighty cross-sections were prepared by close parallel polishing of 10–50 μm per section, and then the sections were photographed and digitized. Examples of the real and digitized cross-sectioned samples are given as well as an example of reconstructed images in a plane perpendicular to the plane of sampling. It is proposed that the method of serial sectioning and automated digitization of porous media provides a powerful tool for further three-dimensional geometrical and topological investigation of pore space to be used in models of fluid transport phenomena.     

Confocal laser microscopy and three-dimensional reconstruction of nucleus-associated microtubules in the division plane of vacuolated plant cells

The way in which transvacuolar strands radiating from the cell nucleus reorganize to form the phragmosome, within which division occurs, has been thoroughly studied in epidermal explants of Nautilocalyx lynchii. In recent years it has been established that the movement of the nucleus into the centre of large vacuolated cells such as these, in preparation for division, involves actin filaments. In the present study, the appearance and gradual reorganization of nucleus-associated microtubules (NAMTs) over the premitotic period is described. Epidermal explants fluorescently labelled with anti-tubulin were optically sectioned by confocal scanning laser microscopy, the sections reconstructed by an image processing computer and projected as rotating stereo pairs. This revealed that the NAMTs are a major component of the phragmosome, and that they change from a radiating to a planar distribution concomitantly with the ‘bunching’ of cortical MTs to form the pre-prophase band. The continuity of the two sets of MTs indicates that the band contains newly polymerized microtubules. Other recent studies on the division of vacuolated cells are reviewed and factors affecting the alignment of the division plane are discussed.     

Three-dimensional reconstruction from a single-exposure,random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli

We present a new reconstruction method that takes advantage of the fact that many biological macromolecular assemblies show a preferred orientation with respect to the plane of the specimen grid in the electron microscopic preparation. From one micrograph taken of such a specimen tilted by a large angle, a conical tilt series with random azimuthal angles can be extracted and used for a three-dimensional reconstruction. Our technique allows the determination of the molecular structure under low-dose conditions, which are not achievable with reconstruction methods that use conventional tilt series. The reconstruction method combines a number of existing image processing techniques with a newly developed weighted back-projection algorithm designed for three-dimensional reconstruction from projections taken with arbitrary projecting directions. The method is described as it was applied to the three-dimensional reconstruction of the structure of the 50S ribosomal subunit of Escherichia coli (E. coli).     

High-precision distance measurements and volume-conserving segmentation of objects near and below the resolution limit in three-dimensional confocal fluorescence microscopy

This study presents a method for high-precision distance measurements and for the volume-conserving segmentation of fluorescent objects with a size of the order of the microscopic observation volume. The segmentation was performed via a model-based approach, using an algorithm that was calibrated by the microscopic point spread function. Its performance was evaluated for three different fluorochromes using model images and fluorescent microspheres as test targets. The fundamental limits which the microscopic imaging process imposes on the accuracy of volume and distance measurements were evaluated in detail. A method for the calibration of the axial stepwidth of a confocal microscope is presented. The results suggest that in biological applications, 3D distances and radii of objects in cell nuclei can be determined with an accuracy of ≤ 60 nm. Using objects of different spectral signature, 3D distance measurements substantially below the lateral half width of the confocal point spread function are feasible. This is shown both theoretically and experimentally.     

Study of the structure of the air and blood capillaries of the gas exchange tissue of the avian lung by serial section three-dimensional reconstruction

We have previously reconstructed the gas exchange tissue of the adult muscovy duck, Cairina moschata using a method of manually aligning sections and tracing the contours of the components of the gas exchange tissue. This reconstruction method demonstrated that the air capillaries are comprised of an expanded globular part interconnected by narrow air channels. The blood capillaries completely surround the air capillaries forming an anastomosing meshwork of short segments. However, the resulting reconstruction was limited in scope because of the laborious process of tracing the profiles of each component through the sequence of micrographs. We have now reconstructed a larger proportion of the exchange tissue by using a cross-correlation based alignment strategy and have demonstrated that the staining intensity of each of the exchange tissue components is sufficiently different to allow them to be identified by simple filtering and thresholding. The resulting reconstructions sample a much larger proportion of the exchange tissue and demonstrate the heterogeneity of structures from different locations in the parabronchus. We have shown that a sheet-flow-type arrangement of blood capillaries surrounds the infundibulum; this represents an unexpected functional convergence with the arrangement of blood capillaries surrounding the mammalian alveoli. It is feasible, using this reconstruction strategy, to analyse the exchange tissue of a large number of avian species in order to determine structural correlates of function. The resulting reconstructions could be analysed in order to determine the basis of the functional efficiency and rigidity of the avian lung.     

An improved scanning method based on characteristics of the human visual system for scanning electron microscopy

An improved scanning method for the scanning electron microscope (SEM) is proposed. Here, quincuncial scanning (sampling) instead of a conventional (raster) scanning is used. This scanning method is very effective for quality improvement of an SEM image obtained under undersampling conditions (rough sampling). The present study focuses on characteristics of the human visual system, specifically the low response of eyes in diagonal directions. When using this method coupled with a high-precision interpolation, the number of pixels necessarily doubles. It is not surprising that it is advantageous for printing. A more important advantage is the fact that SEM images can be acquired with a shorter recording time. Hence, this type of scanning will be helpful for quick and frequent recordings in a "snapshot" mode, which up to now has not been achieved successfully by SEM.     

一种新的周期信号的高速数据采集方法研究

本文介绍了一种新颖、简单的针对周期信号的高速数据采集方法，论证了该方法的可行性，完成了一个基于该方法的、采用CPLD和单片机的系统设计，并给出了硬件设计框图。实验表明，该系统工作稳定，满足实际应用的需要，适用于高速数字信号处理。     

A simple method for the handling and orientation of small specimens for electron microscopy

Cyanoacrylic glue (Eastman 910) was used to affix small pieces of nasal scrapings to lens paper immediately before fixation in the glutaraldehyde. The lens paper not only served to hold specimens together so that they were not lost during tissue processing, but also functioned as a ‘landmark’ for the specimens, so that specimens could be oriented in a specific manner during embedding and subsequent sectioning.     

Three-dimensional morphometry in scanning electron microscopy: a technique for accurate dimensional and angular measurements of microstructures using stereopaired digitized images and digital image analysis

A method for accurate dimensional and angular measurements of microstructures analysed in the scanning electron microscope is described. The method considers central and parallel projections and involves (a) digital image acquisition of stereopaired images from the scanning electron microscope's photodisplay, (b) generation of 3D-image representations, (c) setting of measuring points in the digitized stereopaired images, (d) computation of exact space coordinates ( x / y / z ) from the corresponding point coordinates ( x _L/ y _L; x _R/ y _R), (e) determination of distances and angles between consecutive corresponding points using vector equations, and (f) transfer of computed data into spreadsheets of the data analysis software using dynamic data exchange with simultaneous graphical display of the frequency distribution of variables.
Measurements performed on specimens with known dimensions (grid with 10 μm wide square meshes, polystyrene beads with 0.33 μm diameter) and angles (synthetic crystals of K(Al,Cr)[SO₄], CuSO₄.5H₂O and NaCl) revealed a high accuracy in dimensional as well as angular measurements (total error 1 ± 0.5%).
In Monte Carlo experiments the overall error was found to depend strongly on the size of the measured structure relative to the size of the measurement field (field width).     

Serial section reconstruction using a computer graphics system: Applications to intracellular structures in yeast cells and to the periodontal structure of dogs' teeth

A computer graphics system for reconstruction from serial section micrographs was applied to intracellular details of a yeast target cell (Saccharomyces cerevisiae cell) induced by the α factor mating pheromone and was also applied to a periodontal structure of a dog tooth moved orthodontically. In the former, intracellular organelles and a distribution of vesicles could be clearly observed through the cell membrane using the transparent display method in which the smoothing of the reconstructed outer cell membrane surface by computer processing was applied to the transparent display. In the latter case, by cutting through a reconstructed dog tooth and its periodontal tissues, labiolingual and mesiodistal cut surfaces of the tooth and of adjacent alveolar bone could be observed with fine details (232 sections were used).     

A combination of topographical contrast and stereoscopy for the reconstruction of surface topographies in SEM

The reconstruction of three-dimensional surface topographies can be done in two principally different ways: conventional stereoscopy and ‘shape from shading’. In conventional stereoscopy the depth information is obtained from two perspective views of the specimen. For that, perspectively corresponding features have to be identified in both views to determine depth from perspective shift. Conventional stereoscopy normally results in a relatively sparse set of irregularly distributed points whose elevations are known precisely. The shape-from-shading approach determines the local surface orientation from the local surface luminosity. Over a limited range of surface inclinations the emission of secondary (SE) and back-scattered (BSE) electrons depends uniquely on the angle between electron beam and local surface normal of the specimen. Shape from shading uses this relationship to determine the surface normal with multiple detectors mounted in different take-off directions. Contrary to conventional stereoscopy shape from shading yields depth information from each surface point, but this method is less accurate than stereoscopy. In this paper we propose a combination of both approaches, in which the dense, but less accurate results from shape from shading are used to fill the gaps in the sparsely distributed, but very accurately known, depth information obtained from stereoscopy.