Methods for Digital Particle Image Sizing (DPIS): Comparisons and improvements

This paper explores the accuracy of particle image sizing using direct processing of digitally recorded images. Traditional methods for particle image sizing were considered and, four new algorithms were developed to deliver improved accuracy and robustness. Statistical error analysis was performed using Monte Carlo simulations in order to quantify the dependence of these methods on noise, discretization, and particle size distribution. The performance of these methods were compared against Phase Doppler Analyzer measurements of spray atomization.We introduce a novel two-dimensional four-point Gaussian estimator and an alternative Gaussian estimator based on a local least squares (LLS) fit. These methods were further advanced to account for pixel discretization effects using integral formulations (continuous methods). All new methods were compared against conventional pixel counting and the established three-point Gaussian estimator. The new methods significantly reduced the total error in the diameter estimation compared to the three-point Gaussian estimator and pixel counting. The least squares Gaussian estimator and its continuous version demonstrated almost identical results and superior performance for diameters over 4 pixels. For smaller diameters, the continuous four-point Gaussian estimator delivered the highest accuracy. For uniform particle size distribution between 2–14 pixels image diameter, the least squares estimators delivered error less than 5% with respect to the true diameter for 80% of the particles. The remaining methods demonstrated error of 5% (or better) for less than 60% of the particles. Validation in an experiment of high-pressure spray atomization showed that the Gaussian local least squares methods and the continuous four-point method delivered similar particle size distribution compared to PDA. The particle mean diameter estimated by the two methods differed only by 3% and 6% respectively with respect to the PDA measurements.The novel particle image sizing schemes developed here can deliver accurate, robust, and computationally efficient apparent diameter measurement, thus providing a viable, simple and inexpensive solution for performing sizing on conventional particle image velocimetry images. This capability enables simultaneous measurements of both velocity and particle size for a wide range of multi-phase flows.     

Experimental ultra fast X-ray computed tomography with a linearly scanned electron beam source

We devised and tested a computed tomography approach that utilises a scanned electron beam X-ray source to produce fast tomographic image sequences of transient density distributions. Potential application areas for this technique are the visualisation and measurement of two-phase and particle flows in thermofluid dynamics research, chemical processes, or transport systems for fluids and bulk solids. In our setup we used a linear deflection pattern for the electron beam and a non-annular detector arc to record transmission data of an object from different projection angles. This approach gives the highest achievable axial resolution and is comparatively moderate in effort and costs. For the inverse problem we applied iterative image reconstruction techniques to reconstruct the density distribution from a limited data set. The method has been experimentally tested on static and dynamic phantoms with a frame rate of 1000 images per second and a spatial resolution of approximately 1 mm in plane and axial.     

Exit wave reconstruction at atomic resolution

An iterative method for exit wave function reconstruction based on wave function propagation in free space is presented. The method, which has the potential for application to many forms of microscopy, has been tailored to work with a through focal series of images measured in a high-resolution transmission electron microscope. Practical difficulties for exit wave reconstruction which are pertinent in this experimental environment are the slight incoherence of the electron beam, sample drift and its effect upon the defocus step size that can be utilised, and the number of image measurements that need to be made. To gauge the effectiveness of the method it is applied to experimental data that has been analysed previously using a maximum likelihood formalism (the MAL method).     

An FFT-based method for attenuation correction in fluorescence confocal microscopy

A problem in three-dimensional imaging using a confocal scanning laser microscope (CSLM) in the (epi)fluorescence mode is the darkening of the deeper layers due to absorption and scattering of both the excitation and the fluorescence light. A new method is proposed to correct for these effects. The approach, valid for weak attenuation, consists of multiplying the measured fluorescence intensity by a correction factor involving a convolution integral of the measured signal, which can be computed efficiently by the fast Fourier transform. Analytical and numerical estimates are given for the degree of attenuation under which the method is valid, and the method is applied to various test images. A real CSLM image is restored. Finally, the method is compared with a recent iterative method with regard to numerical accuracy and computational efficiency.     

Efficiency of 2D alignment methods

In single particle analysis, the alignment of two-dimensional images is a fundamental step aimed at bringing into register various particle views of biological macromolecules observed with the electron microscope. The computational efficiency of this step is a deciding factor in design of alignment strategies for large sets of noisy data and in development of three-dimensional structure refinement methods. In addition, the accuracy of the alignment method varies depending on the numerical solutions adopted to efficiently perform exhaustive searches for three orientation parameters. The selected alignment methods are analyzed in terms of their computational complexity and the estimates of numbers of arithmetic operations for each method are given. The tests of alignment accuracy are performed using images simulated in accordance with the linear theory of image formation in the electron microscope. It is demonstrated that the efficiency of the alignment methods can be improved if approximate centers of gravity of particle views are known. The accuracy of the methods considered is largely affected, particularly for high noise levels, by the order in which interpolation steps are applied.     

高阶混合正则化图像盲复原方法

提出了一种高阶混合正则化图像盲复原方法,用于实现模糊噪声图像的清晰化盲复原。根据自然图像边缘的稀疏特性,对图像的边缘细节成分进行了全变差(total variation TV)正则化约束,根据自然图像同性质平滑区域内像素值的变化规律,将一种高阶的类Tikhonov正则化约束运用于图像的平滑区域中,提出了一种新的高阶混合正则化模型。最后,提出一种多变量分裂布雷格曼(Multi-variable Split Bregman MSB)最优化迭代策略对提出的模型进行最优化求解。实验结果表明,提出的方法能够很好地保护图像的边缘细节,同时有效地消除图像平滑区域内的阶梯和假边缘瑕疵。与近几年的一些较好的图像盲复原方法相比,本文方法的信噪比增量(increase of the signal to noise ratio ISNR)增加了0.03~2.5 dB。     

A multiscale optimal filter method for micro-motion measurement with high accuracy

Micro-motion measurement plays an important role in technologies such as micro/nanomanufacturing and biomedicine. In this paper, micro-motion measurement is viewed as a signal processing problem, and the measured image gradients are estimated using the filter methods. A class of optimal filters for image gradient calculation is designed according to Parks-McClellan algorithm. In combination with multiscale approach, a multiscale optimal filter method for micro-motion measurement is proposed. In such a method, the larger motions are converted into multiple small motions to measure, thus the measurement accuracy can be further improved. The maximal bias magnitude of this proposed method reached 0.0064 pixels for the motions near 2 pixels. Experimental simulations show this proposed multiscale optimal filter method can measure the micro-motion with high accuracy.     

视觉注意机制下的粒子窗快速目标检测

针对传统滑动窗目标检测方法需要在全图像范围内穷举搜索的缺点,提出了一种基于视觉注意机制的粒子窗检测方法,旨在保持较高检测精度的同时减少计算量。该方法将目标显著性作为先验知识引入搜索过程,采用"图像签名"方法生成显著图,然后通过阈值门限提取出包含有目标真实位置的局部区域。利用蒙特卡洛采样在显著目标对应的图像范围内均匀生成粒子窗,并依据分类器的响应对粒子进行重采样,以凸显真实目标区域、避免滑动窗方法对搜索步长的依赖。建立了Adaboost+类Harr特征(HLF)和支持向量机(SVM)+方向梯度直方图(HOG)的多级分类器结构,前级分类器用于大范围目标的快速筛选,后级分类器用于小范围目标的精确定位。将本文目标检测模型与传统滑动窗法和粒子窗法进行了比较,结果表明本文方法的受试者工作特征曲线(ROC)包含的面积更大,耗时仅为滑动窗法的1/3到1/4,粒子窗法的1/2,在保持较高检测精度的条件下显著提升了检测速度,实现了快速准确的目标检测。     

Segmentation of virus particle candidates in transmission electron microscopy images

In this paper, we present an automatic segmentation method that detects virus particles of various shapes in transmission electron microscopy images. The method is based on a statistical analysis of local neighbourhoods of all the pixels in the image followed by an object width discrimination and finally, for elongated objects, a border refinement step. It requires only one input parameter, the approximate width of the virus particles searched for. The proposed method is evaluated on a large number of viruses. It successfully segments viruses regardless of shape, from polyhedral to highly pleomorphic.     

Image-EELS: Simultaneous recording of multiple electron energy-loss spectra from series of electron spectroscopic images

A new approach for element microanalysis with energy-filtering transmission electron microscopy (EFTEM) is presented which was accomplished with the CEM 902 electron microscope (Zeiss, Germany). This method is called Image-EELS, because it is a synthesis of electron energy-loss spectroscopy (EELS) and electron spectroscopic imaging (ESI). Series of energy-filtered images at increasing energy losses are recorded from one area with a TV camera. In a second step the intensity of selected regions in the image stack is measured with an image analysis system and plotted as a function of the energy loss. Thus many spectra from different objects can be calculated from one image series and compared with each other. The spatial resolution of EELS is considerably enhanced, the noise is decreased because many pixels from irregular objects are integrated, and the information from ESI can be analysed as a function of the energy loss.     

Imaging a dense nanodot assembly by phase retrieval from TEM images

Phase retrieval is a classical inverse problem in many fields dealing with waves that is becoming of increasing interest in transmission electron microscopy (TEM). A non-interferometric approach is here applied to TEM images. Phase retrieval possibilities given by the transport intensity equation are compared to the ones deriving from the weak phase object approximation. In the limit of small angles, both methods lead to a similar equation between the phase and a set of defocus images. This equation can be solved by an image processing equivalent to using a specific filter in Fourier space. This processing leads to phase images with a spatial resolution here essentially limited by the defocus amount between images. A dense assembly of silicon nanodots is used as a model case to illustrate the interest of this approximate phase retrieval method which can be carried out on standard equipment. The dot heights estimated using the phase images are found to be in good agreement with ones measured by atomic force microscopy. Since image noise and large defocus values may strongly affect the solution given by the approximate method, an iterative phase retrieval method is also used as a test for working conditions.     

Combination of thresholding and fitting methods for measuring nanoparticle sizes and size distributions in (S)TEM

The practical need for a simple and reliable tool for routine size analysis of nanoparticles with diameters down to a few nm embedded in a polymer matrix motivated the development of a new approach. The idea underlying the method proposed in this work is to combine intensity thresholding and contrast fitting procedures in the same software for particle recognition and measurements of sizes and size distributions of nanoparticles in transmission and scanning transmission electron microscopy images. Particle recognition in images is performed in an interactive process of manual setting the numerical threshold level after image preprocessing. We show that fitting the calculated gray level distribution to the real images is able to provide a maximum accuracy in measurements of the particle diameters in contrast to thresholding approaches. The fitting procedure is applied in the vicinity of nanoparticle images with the mass‐thickness, diffraction, and chemical contrast. The grayscale function associated to the nanoparticle thickness is described using polynomial with degree ? 2 and undetermined coefficients. The program for particle detection and size measurement— An alyzer of Na noparticles ( AnNa )—has been written and is described here. It was successfully tested on systems containing Ag nanoparticles grown and stabilized in aqueous solutions of different polymers for biomedical use and is available from the authors.     

An iterative algorithm for cell segmentation using short-time Fourier transform

In this paper, an iterative cell image segmentation algorithm using short-time Fourier transform magnitude vectors as class features is presented. The cluster centroids of the magnitude vectors are obtained by the K-means clustering method and used as representative class features. The initial image segmentation classifies only those image pixels whose surrounding closely matches a class centroid. The subsequent procedure iteratively classifies the remaining image pixels by combining their spatial distance from the regions already segmented and the similarities between their corresponding magnitude vectors and the cluster centroids. Experimental results of the proposed algorithm for segmenting real cell images are provided.     

Entropy‐assisted image segmentation for nano‐ and micro‐sized networks

Image analysis is an important tool for characterizing nano/micro network structures. To understand the connection, organization and proper alignment of network structures, the knowledge of the segments that represent the materials inside the image is very necessary. Image segmentation is generally carried out using statistical methods. In this study, we developed a simple and reliable masking method that improves the performance of the indicator kriging method by using entropy. This method selectively chooses important pixels in an image (optical or electron microscopy image) depending on the degree of information required to assist the thresholding step. Reasonable threshold values can be obtained by selectively choosing important pixels in a complex network image composed of extremely large numbers of thin and narrow objects. Thus, the overall image segmentation can be improved as the number of disconnected objects in the network is minimized. Moreover, we also proposed a new method for analyzing high‐pixel resolution images on a large scale and optimized the time‐consuming steps such as covariance estimation of low‐pixel resolution image, which is rescaled by performing the affine transformation on high‐pixel resolution images. Herein, image segmentation is executed in the original high‐pixel resolution image. This entropy‐based masking method of low‐pixel resolution significantly decreases the analysis time without sacrificing accuracy.     

高温下小区域变形长时测量方法的研究及其应用

对于高温下服役的构件，焊缝区域较为狭小，焊缝以及热影响区（HAZ）的高温变形难以用传统的方法测量。文中利用石英光纤和数字图象处理技术，研究开发一种能在高温下长时测量局部变形的新方法和测量系统，分析讨论了测量精度，并用HK40炉管焊缝长时蠕变变形的测量，分析比较了焊缝和母材的蠕变性能差异。     

超声乳腺肿瘤图像中种子点的自动定位研究

利用种子区域增长对超声乳腺肿瘤图像进行分割是一种常用的计算机辅助诊断方法。为实现种子点的自动快速定位,满足实时在线分割图像的需求,根据超声乳腺肿瘤图像的结构特征,综合图像的灰度因素和空间因素,提出了一种基于迭代四叉树分解的算法。该算法将满足特定阈值的图像分裂转化为寻找种子区域,以实现种子点的自动定位。对105幅超声乳腺肿瘤图像进行了实验验证,结果表明,该算法准确率能够达到94.28%,平均耗时2.97 s,不但满足了种子点的自动定位于图像肿瘤内部,而且需要调整的参数少,其定位效率要高于人工选择。     

Projected potential profiles across interfaces obtained by reconstructing the exit face wave function from through focal series

An iterative method for reconstructing the exit face wave function from a through focal series of transmission electron microscopy image line profiles across an interface is presented. Apart from high-resolution images recorded with small changes in defocus, this method works also well for a large defocus range as used for Fresnel imaging. Using the phase-object approximation the projected electrostatic as well as the absorptive potential profiles across an interface are determined from this exit face wave function. A new experimental image alignment procedure was developed in order to align images with large relative defocus shift. The performance of this procedure is shown to be superior to other image alignment procedures existing in the literature. The reconstruction method is applied to both simulated and experimental images.     

稳健李代数旋转平均用于GPS辅助无人机影像三维重建

针对最小二乘的旋转平均方法对粗差敏感,求解影像旋转参数不够精确的问题,提出了一种稳健的旋转平均方法。先利用李群和李代数之间的映射关系,将旋转矩阵的乘积运算简化为李代数中的减法运算,推导出旋转平均迭代解算的线性化方程;然后利用L1范数优化和迭代加权最小二乘相结合的方法求解全局一致旋转最优解;最后采用迭代策略剔除粗差,得到精确的旋转矩阵。实验结果表明,与传统最小二乘方法相比,提出方法的旋转参数求解精度更高,稳健性更好,用于三维重建可以得到更密集均匀的点云,重建完整性更好。旋转平均的精度优于0.15度,计算时间不超过0.31s,光束法平差后,重投影误差在1.3个像素以内。基本满足快速稳健三维重建的要求。     

EELS elemental mapping with unconventional methods. II. Applications to biological specimens

This article presents two applications of image analysis and processing using the unconventional methods described in the companion paper (part I). Both the information analysis via relative entropy measurement and mapping and the factorial analysis of correspondence are demonstrated to be valuable tools for building an elemental map from a set of noisy energy-filtered images recorded in an analytical transmission electron microscope. Although the only technique considered here is electron energy loss spectroscopy, there is no doubt that such methods can be applied to a wide variety of similar problems: only a reduced number of underlying hypotheses are needed.     

纳米二氧化硅粒径分析

本文对2个系列的纳米二氧化硅样品进行粒径分析。对单分散的纳米二氧化硅颗粒分别采用透射电镜和图像分析法、X射线小角散射法和动态光散射法测定其粒径,得到一致的结果。采用2种图像分析软件对另一纳米二氧化硅颗粒的透射电镜照片统计其粒径,得到一致的结果。