A method of PSF generation for 3D brightfield deconvolution

This paper addresses the problem of 3D deconvolution of through focus widefield microscope datasets (Z‐stacks). One of the most difficult stages in brightfield deconvolution is finding the point spread function. A theoretically calculated point spread function (called a ‘synthetic PSF’ in this paper) requires foreknowledge of many system parameters and still gives only approximate results. A point spread function measured from a sub‐resolution bead suffers from low signal‐to‐noise ratio, compounded in the brightfield setting (by contrast to fluorescence) by absorptive, refractive and dispersal effects. This paper describes a method of point spread function estimation based on measurements of a Z‐stack through a thin sample. This Z‐stack is deconvolved by an idealized point spread function derived from the same Z‐stack to yield a point spread function of high signal‐to‐noise ratio that is also inherently tailored to the imaging system. The theory is validated by a practical experiment comparing the non‐blind 3D deconvolution of the yeast Saccharomyces cerevisiae with the point spread function generated using the method presented in this paper (called the ‘extracted PSF’) to a synthetic point spread function. Restoration of both high‐ and low‐contrast brightfield structures is achieved with fewer artefacts using the extracted point spread function obtained with this method. Furthermore the deconvolution progresses further (more iterations are allowed before the error function reaches its nadir) with the extracted point spread function compared to the synthetic point spread function indicating that the extracted point spread function is a better fit to the brightfield deconvolution model than the synthetic point spread function.     

Shack-Hartmann wave front measurements in cortical tissue for deconvolution of large three-dimensional mosaic transmitted light brightfield micrographs

We present a novel approach for deconvolution of 3D image stacks of cortical tissue taken by mosaic/optical‐sectioning technology, using a transmitted light brightfield microscope. Mosaic/optical‐sectioning offers the possibility of imaging large volumes (e.g. from cortical sections) on a millimetre scale at sub‐micrometre resolution. However, a blurred contribution from out‐of‐focus light results in an image quality that usually prohibits 3D quantitative analysis. Such quantitative analysis is only possible after deblurring by deconvolution. The resulting image quality is strongly dependent on how accurate the point spread function used for deconvolution resembles the properties of the imaging system. Since direct measurement of the true point spread function is laborious and modelled point spread functions usually deviate from measured ones, we present a method of optimizing the microscope until it meets almost ideal imaging conditions. These conditions are validated by measuring the aberration function of the microscope and tissue using a Shack‐Hartmann sensor. The analysis shows that cortical tissue from rat brains embedded in Mowiol and imaged by an oil‐immersion objective can be regarded as having a homogeneous index of refraction. In addition, the amount of spherical aberration that is caused by the optics or the specimen is relatively low. Consequently the image formation is simplified to refraction between the embedding and immersion medium and to 3D diffraction at the finite entrance pupil of the objective. The resulting model point spread function is applied to the image stacks by linear or iterative deconvolution algorithms. For the presented dataset of large 3D images the linear approach proves to be superior. The linear deconvolution yields a significant improvement in signal‐to‐noise ratio and resolution. This novel approach allows a quantitative analysis of the cortical image stacks such as the reconstruction of biocytin‐stained neuronal dendrites and axons.     

Blind deconvolution of 3D fluorescence microscopy using depth‐variant asymmetric PSF

The 3D wide‐field fluorescence microscopy suffers from depth‐variant asymmetric blur. The depth‐variance and axial asymmetry are due to refractive index mismatch between the immersion and the specimen layer. The radial asymmetry is due to lens imperfections and local refractive index inhomogeneities in the specimen. To obtain the PSF that has these characteristics, there were PSF premeasurement trials. However, they are useless since imaging conditions such as camera position and refractive index of the specimen are changed between the premeasurement and actual imaging. In this article, we focus on removing unknown depth‐variant asymmetric blur in such an optical system under the assumption of refractive index homogeneities in the specimen. We propose finding few parameters in the mathematical PSF model from observed images in which the PSF model has a depth‐variant asymmetric shape. After generating an initial PSF from the analysis of intensities in the observed image, the parameters are estimated based on a maximum likelihood estimator. Using the estimated PSF, we implement an accelerated GEM algorithm for image deconvolution. Deconvolution result shows the superiority of our algorithm in terms of accuracy, which quantitatively evaluated by FWHM, relative contrast, standard deviation values of intensity peaks and FWHM. Microsc. Res. Tech. 79:480–494, 2016. © 2016 Wiley Periodicals, Inc.     

3D light scanning macrography

The technique of 3D light scanning macrography permits the non-invasive surface scanning of small specimens at magnifications up to 200×. Obviating both the problem of limited depth of field inherent to conventional close-up macrophotography and the metallic coating required by scanning electron microscopy, 3D light scanning macrography provides three-dimensional digital images of intact specimens without the loss of colour, texture and transparency information. This newly developed technique offers a versatile, portable and cost-efficient method for the non-invasive digital and photographic documentation of small objects. Computer controlled device operation and digital image acquisition facilitate fast and accurate quantitative morphometric investigations, and the technique offers a broad field of research and educational applications in biological, medical and materials sciences.     

Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution

Confocal laser scanning microscopy is a powerful and popular technique for 3D imaging of biological specimens. Although confocal microscopy images are much sharper than standard epifluorescence ones, they are still degraded by residual out-of-focus light and by Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm, which computes maximum likelihood estimation adapted to Poisson statistics. As this algorithm tends to amplify noise, regularization constraints based on some prior knowledge on the data have to be applied to stabilize the solution. Here, we propose to combine the Richardson-Lucy algorithm with a regularization constraint based on Total Variation, which suppresses unstable oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results as compared with the unregularized Richardson-Lucy algorithm, both visually and quantitatively.     

Iterative,constrained 3-D image reconstruction of transmitted light bright-field micrographs based on maximum likelihood estimation

We present several image reconstruction algorithms for generating three-dimensional (3-D) renderings of bright-field micrographs that are founded on maximum likelihood estimation (MLE) theory. The basic principle of the algorithms is in estimating the values of the optical densities of the specimen. A computer simulation and initial experimental testing of a steepest ascent version of the algorithm is presented. The computer simulation demonstrates that the MLE algorithm has an advantage over previously used inverse filtering techniques in that it partially restores the zeroed Fourier components in the well-known missing-cone region. We present 3-D reconstructions from real biological data to show the potential of the algorithm in practical applications.     

3D deconvolution of spherically aberrated images using commercial software

Refractive index mismatch between the specimen and the objective immersion oil results in spherical aberration, which causes distortion and spreading of the point spread function, as well as incorrect readings of the axial coordinates. These effects have to be taken into account when performing three-dimensional restoration of wide-field fluorescence images. By using objects with well-defined geometry (fluorescently stained Escherichia coli or actin filaments) separated from a cover slip by a layer of oil with known refractive index, we investigated the accuracy of three-dimensional shape restoration by the commercial programs Huygens and Autoquant. Aberration correction available in the software dramatically reduced the axial blur compared to deconvolution that ignored the refractive index mismatch. At the same time, it failed to completely recover the cylindrical symmetry of bacteria or of actin fibres, which showed up to a three to five times larger width along the optical axis compared to the lateral plane. The quality of restoration was only moderately sensitive to the exact values of the specimen refractive index but in some cases improved significantly by assuming a reduced NA of the objective. Because image restoration depends on the knowledge of the vertical scale, we also performed detailed measurements of the axial scaling factor and concluded (in agreement with some previous authors) that scaling is adequately described by the simple paraxial formula, even when high-NA oil-immersion objectives are used.     

Spatially varying regularization of deconvolution in 3D microscopy

Confocal microscopy has become an essential tool to explore biospecimens in 3D. Confocal microcopy images are still degraded by out‐of‐focus blur and Poisson noise. Many deconvolution methods including the Richardson–Lucy (RL) method, Tikhonov method and split‐gradient (SG) method have been well received. The RL deconvolution method results in enhanced image quality, especially for Poisson noise. Tikhonov deconvolution method improves the RL method by imposing a prior model of spatial regularization, which encourages adjacent voxels to appear similar. The SG method also contains spatial regularization and is capable of incorporating many edge‐preserving priors resulting in improved image quality. The strength of spatial regularization is fixed regardless of spatial location for the Tikhonov and SG method. The Tikhonov and the SG deconvolution methods are improved upon in this study by allowing the strength of spatial regularization to differ for different spatial locations in a given image. The novel method shows improved image quality. The method was tested on phantom data for which ground truth and the point spread function are known. A Kullback–Leibler (KL) divergence value of 0.097 is obtained with applying spatially variable regularization to the SG method, whereas KL value of 0.409 is obtained with the Tikhonov method. In tests on a real data, for which the ground truth is unknown, the reconstructed data show improved noise characteristics while maintaining the important image features such as edges.     

The point-spread function of a confocal microscope: its measurement and use in deconvolution of 3-D data

We have measured the point-spread function (PSF) for an MRC-500 confocal scanning laser microscope using subresolution fluorescent beads. PSFs were measured for two lenses of high numerical aperture—the Zeiss plan-neofluar 63 × water immersion and Leitz plan-apo 63 × oil immersion—at three different sizes of the confocal detector aperture. The measured PSFs are fairly symmetrical, both radially and axially. In particular there is considerably less axial asymmetry than has been demonstrated in measurements of conventional (non-confocal) PSFs. Measurements of the peak width at half-maximum peak height for the minimum detector aperture gave approximately 0·23 and 0·8 μm for the radial and axial resolution respectively (4·6 and 15·9 in dimensionless optical units). This increased to 0·38 and 1·5 μm (7·5 and 29·8 in dimensionless units) for the largest detector aperture examined. The resulting optical transfer functions (OTFs) were used in an iterative, constrained deconvolution procedure to process three-dimensional confocal data sets from a biological specimen—pea root cells labelled in situ with a fluorescent probe to ribosomal genes. The deconvolution significantly improved the clarity and contrast of the data. Furthermore, the loss in resolution produced by increasing the size of the detector aperture could be restored by the deconvolution procedure. Therefore for many biological specimens which are only weakly fluorescent it may be preferable to open the detector aperture to increase the strength of the detected signal, and thus the signal-to-noise ratio, and then to restore the resolution by deconvolution.     

3D boundary extraction of confocal cellular images using higher order statistics

In recent years, cell biologists have benefited greatly from using confocal microscopy to study intracellular organelles. For high-level image analysis, 3D boundary extraction of cell structure is a preliminary requisite in confocal cellular imaging. To detect the object boundaries, most investigators have used gradient/Laplacian operator as a principal tool. In this paper we propose a higher order statistics (HOS) based boundary extraction algorithm for confocal cellular image data set using kurtosis. After the initial pre-processing, kurtosis boundary map is estimated locally for the entire volume using a cubic sliding window and subsequently the noisy kurtosis value is removed by thresholding. Voxels having positive kurtosis value with zero-crossing on its surface are then identified as boundary voxels. Typically used in signal processing, kurtosis for 3D cellular image processing is a novel application of HOS. Its reliable and robust nature of computing makes it very suitable for volumetric cellular boundary extraction.     

Confocal bi-protocol: a new strategy for isotropic 3D live cell imaging

The conventional approach for microscopic 3D cellular imaging is based on axial through-stack image series which has some significant limitations such as anisotropic resolution and axial aberration. To overcome these drawbacks, we have recently introduced an alternative approach based on micro-rotation image series. Unfortunately, this new technique suffers from a huge burden of computation that makes its use quite difficult for current applications. To address these problems we propose a new imaging strategy called bi-protocol, which consists of coupling micro-rotation acquisition and conventional z-stack acquisition. We experimentally prove bi-protocol 3D reconstruction produces similar quality to that of pure micro-rotation, but offers the advantage of reduced computation burden because it uses the z-stack volume to accelerate the registration of the micro-rotation images.     

High-resolution solid modeling of biological samples imaged with 3D fluorescence microscopy

Optical-sectioning, digital fluorescence microscopy provides images representing temporally- and spatially-resolved molecular-scale details of the substructures of living cells. To render such images into solid models for further computational analyses, we have developed an integrated system of image acquisition, processing, and rendering, which includes a new empirical technique to correct for axial distortions inherent in fluorescence microscopy due to refractive index mismatches between microscope objective immersion medium, coverslip glass, and water. This system takes advantage of the capabilities of ultra-high numerical aperture objectives (e.g. total internal reflection fluorescence microscopy) and enables faithful three-dimensional rendering of living cells into solid models amenable to further computational analysis. An example of solid modeling of bovine aortic endothelial cells and their nuclei is presented. Since many cellular level events are temporally and spatially confined, such integrated image acquisition, processing, rendering, and computational analysis, will enable, in silico, the generation of new computational models for cell mechanics and signaling.     

基于激光共焦扫描显微镜方法的磨损表面三维数字化描述

表面形貌的精确描述在许多领域诸如材料、生物医学、摩擦学和机器状态监测等领域变得越来越重要。开发了一种基于激光共焦显微镜和图像处理技术的研究磨损表面及表面参数的新方法。首先用B io-rad Rad iance 2000激光共焦显微镜方法获得精确的三维表面形貌,然后用计算机辅助图像分析技术自动计算出表面特征参数。应用示例表明本文所研究的方法是可靠的,能对工程表面的表面粗糙度特征进行精确描述。     

Application of confocal laser microscopy and three-dimensional Voronoi diagrams for volume and surface estimates of interphase chromosomes

This study demonstrates the use of Voronoi tessellation procedures to obtain quantitative morphological data for chromosome territories in the cell nucleus. As a model system, chromosomes 7 and X were visualized in human female amniotic fluid cell nuclei by chromosomal in situ suppression hybridization with chromosome-specific composite probes. Light optical serial sections of 18 nuclei were obtained with a confocal scanning laser fluorescence microscope. A three-dimensional (3-D) tessellation of the image volumes defined by the stack of serial sections was then performed. For this purpose a Voronoi diagram, which consists of convex polyhedra structured in a graph environment, was built for each nucleus. The chromosome territories were extracted by applying the Delaunay graph, the dual of the Voronoi diagram, which describes the neighbourhood in the Voronoi diagram. The chromosome territories were then described by three morphological parameters, i.e. volume, surface area and a roundness factor (shape factor). The complete evaluation of a nucleus, including the calculation of the Voronoi diagram, 3-D visualization of extracted territories using computer graphic methods and parameterization was carried out on a Silicon Graphics workstation and was generally completed within 5 min. The geometric information obtained by this procedure revealed that both X- and 7-chromosome territories were similar in volume. Roundness factors indicated a pronounced variability in interphase shape for both pairs of chromosomes. Surface estimates showed a significant difference between the two X-territories but not between chromosome 7-territories.     

An automatic method for identifying appropriate gradient magnitude for 3D boundary detection of confocal image stacks

Gradients play an important role in 2D image processing. Many edge detection algorithms are gradient‐based. We are interested in 3D boundary detection which can be considered as an extension of 2D edge detection in 3D space. In this paper, an algorithm to automatically and quantitatively measure the suitability of gradient magnitudes in detection of 3D boundary points of confocal image stacks is presented. A Measurement Function is defined to evaluate the suitability of each gradient magnitude chosen to be the threshold for 3D boundary detection. The application of Gauss's Divergence Theorem provides a solution to calculate the Measurement Function numerically. The gradient magnitude at which the maximum of the Measurement Function is achieved can be utilized as the most appropriate threshold for gradient‐based boundary detection and other operations like volume visualization.     

Modelling and analysis of 3-D arrangements of particles by point processes with examples of application to biological data obtained by confocal scanning light microscopy

Within the concept of point processes, a review is presented of quantities which can be used in studies of three-dimensional (3-D) aggregates of particles. Suitable characteristics and estimators are given for both unmarked and marked point processes. To demonstrate the feasibility of such quantitative approaches, an application in histology, dealing with 3-D arrangements of cell nuclei in rat liver, is described. Using a confocal scanning light microscope, 3-D images are recorded and image analysis used to obtain the coordinates of the centroid, together with the volume and DNA content, of each cell nucleus. Examples of results are given, using both unmarked and marked point processes. In the latter case, cell type, nuclear volume and ploidy group are suitable marks.     

Deconvolution improves colocalization analysis of multiple fluorochromes in 3D confocal data sets more than filtering techniques

Background and noise impair image quality by affecting resolution and obscuring image detail in the low intensity range. Because background levels in unprocessed confocal images are frequently at about 30% maximum intensity, colocalization analysis, a typical segmentation process, is limited to high intensity signal and prone to noise‐induced, false‐positive events. This makes suppression or removal of background crucial for this kind of image analysis. This paper examines the effects of median filtering and deconvolution, two image‐processing techniques enhancing the signal‐to‐noise ratio (SNR), on the results of colocalization analysis in confocal data sets of biological specimens. The data show that median filtering can improve the SNR by a factor of 2. The technique eliminates noise‐induced colocalization events successfully. However, because filtering recovers voxel values from the local neighbourhood false‐negative (‘dissipation’ of signal intensity below threshold value) as well as false‐positive (‘fusion’ of noise with low intensity signal resulting in above threshold intensities), results can be generated. In addition, filtering involves the convolution of an image with a kernel, a procedure that inherently impairs resolution. Image restoration by deconvolution avoids both of these disadvantages. Such routines calculate a model of the object considering various parameters that impair image formation and are able to suppress background down to very low levels (< 10% maximum intensity, resulting in a SNR improved by a factor 3 as compared to raw images). This makes additional objects in the low intensity but high frequency range available to analysis. In addition, removal of noise and distortions induced by the optical system results in improved resolution, which is of critical importance in cases involving objects of near resolution size. The technique is, however, sensitive to overestimation of the background level. In conclusion, colocalization analysis will be improved by deconvolution more than by filtering. This applies especially to specimens characterized by small object size and/or low intensities.     

Robust incremental compensation of the light attenuation with depth in 3D fluorescence microscopy

Fluorescent signal intensities from confocal laser scanning microscopes (CLSM) suffer from several distortions inherent to the method. Namely, layers which lie deeper within the specimen are relatively dark due to absorption and scattering of both excitation and fluorescent light, photobleaching and/or other factors. Because of these effects, a quantitative analysis of images is not always possible without correction. Under certain assumptions, the decay of intensities can be estimated and used for a partial depth intensity correction. In this paper we propose an original robust incremental method for compensating the attenuation of intensity signals. Most previous correction methods are more or less empirical and based on fitting a decreasing parametric function to the section mean intensity curve computed by summing all pixel values in each section. The fitted curve is then used for the calculation of correction factors for each section and a new compensated sections series is computed. However, these methods do not perfectly correct the images. Hence, the algorithm we propose for the automatic correction of intensities relies on robust estimation, which automatically ignores pixels where measurements deviate from the decay model. It is based on techniques adopted from the computer vision literature for image motion estimation. The resulting algorithm is used to correct volumes acquired in CLSM. An implementation of such a restoration filter is discussed and examples of successful restorations are given.     

桥式起重机运行环境三维建图偏振光降噪研究

在桥式起重机运行环境双目视觉三维建图任务中,为减少因反光耀斑所造成的建图误差,文中对双目相机采集的图像使用偏振滤镜对偏振光进行过滤,使用搭建的实验台进行了实验,比较了偏振滤镜对三维地图精度的影响.结果表明:偏振滤镜可以有效过滤物体表面反光,减小建图误差,提高建图结果的鲁棒性.