Precise particle tracking against a complicated background: polynomial fitting with Gaussian weight

We present a new particle tracking software algorithm designed to accurately track the motion of low-contrast particles against a background with large variations in light levels. The method is based on a polynomial fit of the intensity around each feature point, weighted by a Gaussian function of the distance from the centre, and is especially suitable for tracking endogeneous particles in the cell, imaged with bright field, phase contrast or fluorescence optical microscopy. Furthermore, the method can simultaneously track particles of all different sizes, and allows significant freedom in their shape. The algorithm is evaluated using the quantitative measures of accuracy and precision of previous authors, using simulated images at variable signal-to-noise ratios. To these we add new tests: the error due to a non-uniform background, and the error due to two particles approaching each other. Finally the tracking of particles in real cell images is demonstrated. The method is made freely available for non-commercial use as a software package with a graphical user-interface, which can be run within the Matlab programming environment.     

Optimising the precision for localising fluorescent proteins in living cells by 2D Gaussian fitting of digital images: application to COPII-coated endoplasmic reticulum exit sites

An insight into the operation of molecular motors has already been obtained under in vitro conditions from single-molecule tracking of proteins. It remains to analyse the effects of these motors on the position and secretion of specific organelles in the environment of the cell. For this purpose, we have investigated the accuracy of a standard algorithm to enable the tracking of particles in live-cell microscopy. The results have been applied to an example study into the role of the microtubule-motor kinesin on the function of COPII-coated secretory-cargo exit sites forming part of the mammalian endoplasmic reticulum. These exit sites are marked with multiple EYFP-tagged proteins to produce bright fluorescent particles, and a demonstration of the motility of vesicles, under different conditions in the cell, is described here. It is essential to use a low-level expression of fluorescent protein-tagged cellular components to ensure faithful replication for the behaviour of endogenous protein. However, this leads to a lower ratio for the signal-to-noise than is desired for the sub-pixel tracking of objects in digital images. This has driven the present effort to develop a computational model of the experiment in order to estimate the precision for localization of a fluorescent particle. Our work gives a greater insight, than has been managed in the past, into the accuracy and precision of particle tracking from live-cell imaging under a variety of different conditions, and it takes into consideration the current standards in digital technology for optical microscopy.

Tracking single particles: a user-friendly quantitative evaluation

As our knowledge of biological processes advances, we are increasingly aware that cells actively position sub-cellular organelles and other constituents to control a wide range of biological processes. Many studies quantify the position and motion of, for example, fluorescently labeled proteins, protein aggregates, mRNA particles or virus particles. Both differential interference contrast (DIC) and fluorescence microscopy can visualize vesicles, nuclei or other small organelles moving inside cells. While such studies are increasingly important, there has been no complete analysis of the different tracking methods in use, especially from the practical point of view. Here we investigate these methods and clarify how well different algorithms work and also which factors play a role in assessing how accurately the position of an object can be determined. Specifically, we consider how ultimate performance is affected by magnification, by camera type (analog versus digital), by recording medium (VHS and SVHS tape versus direct tracking from camera), by image compression, by type of imaging used (fluorescence versus DIC images) and by a variety of sources of noise. We show that most methods are capable of nanometer scale accuracy under realistic conditions; tracking accuracy decreases with increasing noise. Surprisingly, accuracy is found to be insensitive to the numerical aperture, but, as expected, it scales with magnification, with higher magnification yielding improved accuracy (within limits of signal-to-noise). When noise is present at reasonable levels, the effect of image compression is in most cases small. Finally, we provide a free, robust implementation of a tracking algorithm that is easily downloaded and installed.     

Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules.

We have developed a technique to detect, recognize, and track each individual low density lipoprotein receptor (LDL-R) molecule and small receptor clusters on the surface of human skin fibroblasts. Molecular recognition and high precision (30 nm) simultaneous automatic tracking of all of the individual receptors in the cell surface population utilize quantitative time-lapse low light level digital video fluorescence microscopy analyzed by purpose-designed algorithms executed on an image processing work station. The LDL-Rs are labeled with the biologically active, fluorescent LDL derivative dil-LDL. Individual LDL-Rs and unresolved small clusters are identified by measuring the fluorescence power radiated by the sub-resolution fluorescent spots in the image; identification of single particles is ascertained by four independent techniques. An automated tracking routine was developed to track simultaneously, and without user intervention, a multitude of fluorescent particles through a sequence of hundreds of time-lapse image frames. The limitations on tracking precision were found to depend on the signal-to-noise ratio of the tracked particle image and mechanical drift of the microscope system. We describe the methods involved in (i) time-lapse acquisition of the low-light level images, (ii) simultaneous automated tracking of the fluorescent diffraction limited punctate images, (iii) localizing particles with high precision and limitations, and (iv) detecting and identifying single and clustered LDL-Rs. These methods are generally applicable and provide a powerful tool to visualize and measure dynamics and interactions of individual integral membrane proteins on living cell surfaces.     

Quantitative Analysis of Intracellular Fluorescent Foci in Live Bacteria

Fluorescence microscopy has revolutionized in vivo cellular biology. Through the specific labeling of a protein of interest with a fluorescent protein, one is able to study movement and colocalization, and even count individual proteins in a live cell. Different algorithms exist to quantify the total intensity and position of a fluorescent focus. Although these algorithms have been rigorously studied for in vitro conditions, which are greatly different than the in-homogenous and variable cellular environments, their exact limits and applicability in the context of a live cell have not been thoroughly and systematically evaluated. In this study, we quantitatively characterize the influence of different background subtraction algorithms on several focus analysis algorithms. We use, to our knowledge, a novel approach to assess the sensitivity of the focus analysis algorithms to background removal, in which simulated and experimental data are combined to maintain full control over the sensitivity of a focus within a realistic background of cellular fluorescence. We demonstrate that the choice of algorithm and the corresponding error are dependent on both the brightness of the focus, and the cellular context. Expectedly, focus intensity estimation and localization accuracy suffer in all algorithms at low focus to background ratios, with the bacteroidal background subtraction in combination with the median excess algorithm, and the region of interest background subtraction in combination with a two-dimensional Gaussian fit algorithm, performing the best. We furthermore show that the choice of background subtraction algorithm is dependent on the expression level of the protein under investigation, and that the localization error is dependent on the distance of a focus from the bacterial edge and pole. Our results establish a set of guidelines for what signals can be analyzed to give a targeted spatial and intensity accuracy within a bacterial cell.     

Tracking single particles and elongated filaments with nanometer precision

Recent developments in image processing have greatly advanced our understanding of biomolecular processes in vitro and in vivo. In particular, using Gaussian models to fit the intensity profiles of nanometer-sized objects have enabled their two-dimensional localization with a precision in the one-nanometer range. Here, we present an algorithm to precisely localize curved filaments whose structures are characterized by subresolution diameters and micrometer lengths. Using surface-immobilized microtubules, fluorescently labeled with rhodamine, we demonstrate positional precisions of ∼2 nm when determining the filament centerline and ∼9 nm when localizing the filament tips. Combined with state-of-the-art single particle tracking we apply the algorithm 1), to motor-proteins stepping on immobilized microtubules, 2), to depolymerizing microtubules, and 3), to microtubules gliding over motor-coated surfaces.     

Ultrafast,accurate, and robust localization of anisotropic dipoles

The resolution of single molecule localization imaging techniques largely depends on the precision of localization algorithms. However, the commonly used Gaussian function is not appropriate for anisotropic dipoles because it is not the true point spread function. We derived the theoretical point spread function of tilted dipoles with restricted mobility and developed an algorithm based on an artificial neural network for estimating the localization, orientation and mobility of individual dipoles. Compared with fitting-based methods, our algorithm demonstrated ultrafast speed and higher accuracy, reduced sensitivity to defocusing, strong robustness and adaptability, making it an optimal choice for both two-dimensional and threedimensional super-resolution imaging analysis.     

Feature point tracking and trajectory analysis for video imaging in cell biology

This paper presents a computationally efficient, two-dimensional, feature point tracking algorithm for the automated detection and quantitative analysis of particle trajectories as recorded by video imaging in cell biology. The tracking process requires no a priori mathematical modeling of the motion, it is self-initializing, it discriminates spurious detections, and it can handle temporary occlusion as well as particle appearance and disappearance from the image region. The efficiency of the algorithm is validated on synthetic video data where it is compared to existing methods and its accuracy and precision are assessed for a wide range of signal-to-noise ratios. The algorithm is well suited for video imaging in cell biology relying on low-intensity fluorescence microscopy. Its applicability is demonstrated in three case studies involving transport of low-density lipoproteins in endosomes, motion of fluorescently labeled Adenovirus-2 particles along microtubules, and tracking of quantum dots on the plasma membrane of live cells. The present automated tracking process enables the quantification of dispersive processes in cell biology using techniques such as moment scaling spectra.     

利用归一化互相关算法去除吸收强度涨落调制血管造影图像模糊

吸收强度涨落调制成像（AIFM）方法是基于血红细胞和背景组织对低相干光照明的吸收差异,通过在频域分离动态的血红细胞信号和静态的背景信号,实现对近透明活体生物样本全场无标记的光学血管造影成像. 但此成像方法需采集较长的原始图像序列,系统漂移或生物抖动会造成图像模糊,难以实现对某些特定区域的血管造影成像. 本文提出一种结合AIFM成像和归一化互相关算法的新方法来提升血管造影图像的质量：原始的图像序列被分成若干短时序列,每个短时序列先利用AIFM成像算法重构得到全场的血管造影图像;再利用归一化的互相关算法将所有的短时重构图像与第一帧重构图像相匹配,并融合得到最终的血管造影片. 我们以活体鸡蛋胚胎为样品,通过实验验证了利用短时归一化互相关AIFM成像方法,能够消除鸡胚胎心跳引起的图像模糊,从而获得高分辨率和信噪比的心血管造影片,对研究活体动物心脑血管疾病具有重要应用价值.     

A guide to accurate fluorescence microscopy colocalization measurements

Biomolecular interactions are fundamental to the vast majority of cellular processes, and identification of the major interacting components is usually the first step toward an understanding of the mechanisms that govern various cell functions. Thus, statistical image analyses that can be performed on fluorescence microscopy images of fixed or live cells have been routinely applied for biophysical and cell biological studies. These approaches measure the fraction of interacting particles by analyzing dual color fluorescence images for colocalized pixels. Colocalization algorithms have proven to be effective, although the dynamic range and accuracy of these measurements has never been well established. Spatial image cross-correlation spectroscopy (ICCS), which cross-correlates spatial intensity fluctuations recorded in images from two detection channels simultaneously, has also recently been shown to be an effective measure of colocalization as well. Through simulations, imaging of fluorescent antibodies adsorbed on glass and cell measurements, we show that ICCS performs much better than standard colocalization algorithms at moderate to high densities of particles, which are often encountered in cellular systems. Furthermore, it was found that the density ratio between the two labeled species of interest plays a major role in the accuracy of the colocalization analysis. By applying a direct and systematic comparison between the standard, fluorescence microscopy colocalization algorithm and spatial ICCS, we show regimes where each approach is applicable, and more importantly, where they fail to yield accurate results.     

A Highlights from MBoC Selection: Cega: a single particle segmentation algorithm to identify moving particles in a noisy system

Improvements to particle tracking algorithms are required to effectively analyze the motility of biological molecules in complex or noisy systems. A typical single particle tracking (SPT) algorithm detects particle coordinates for trajectory assembly. However, particle detection filters fail for data sets with low signal-to-noise levels. When tracking molecular motors in complex systems, standard techniques often fail to separate the fluorescent signatures of moving particles from background signal. We developed an approach to analyze the motility of kinesin motor proteins moving along the microtubule cytoskeleton of extracted neurons using the Kullback-Leibler divergence to identify regions where there are significant differences between models of moving particles and background signal. We tested our software on both simulated and experimental data and found a noticeable improvement in SPT capability and a higher identification rate of motors as compared with current methods. This algorithm, called Cega, for “find the object,” produces data amenable to conventional blob detection techniques that can then be used to obtain coordinates for downstream SPT processing. We anticipate that this algorithm will be useful for those interested in tracking moving particles in complex in vitro or in vivo environments.     

A Novel Tracking Algorithm via Feature Points Matching

Visual target tracking is a primary task in many computer vision applications and has been widely studied in recent years. Among all the tracking methods, the mean shift algorithm has attracted extraordinary interest and been well developed in the past decade due to its excellent performance. However, it is still challenging for the color histogram based algorithms to deal with the complex target tracking. Therefore, the algorithms based on other distinguishing features are highly required. In this paper, we propose a novel target tracking algorithm based on mean shift theory, in which a new type of image feature is introduced and utilized to find the corresponding region between the neighbor frames. The target histogram is created by clustering the features obtained in the extraction strategy. Then, the mean shift process is adopted to calculate the target location iteratively. Experimental results demonstrate that the proposed algorithm can deal with the challenging tracking situations such as: partial occlusion, illumination change, scale variations, object rotation and complex background clutter. Meanwhile, it outperforms several state-of-the-art methods.     

Precise nanometer localization analysis for individual fluorescent probes

Calculation of the centroid of the images of individual fluorescent particles and molecules allows localization and tracking in light microscopes to a precision about an order of magnitude greater than the microscope resolution. The factors that limit the precision of these techniques are examined and a simple equation derived that describes the precision of localization over a wide range of conditions. In addition, a localization algorithm motivated from least-squares fitting theory is constructed and tested both on image stacks of 30-nm fluorescent beads and on computer-generated images (Monte Carlo simulations). Results from the algorithm show good agreement with the derived precision equation for both the simulations and actual images. The availability of a simple equation to describe localization precision helps investigators both in assessing the quality of an experimental apparatus and in directing attention to the factors that limit further improvement. The precision of localization scales as the inverse square root of the number of photons in the spot for the shot noise limited case and as the inverse of the number of photons for the background noise limited case. The optimal image magnification depends on the expected number of photons and background noise, but, for most cases of interest, the pixel size should be about equal to the standard deviation of the point spread function.     

Comparison of photo‐matching algorithms commonly used for photographic capture–recapture studies

Photographic capture–recapture is a valuable tool for obtaining demographic information on wildlife populations due to its noninvasive nature and cost‐effectiveness. Recently, several computer‐aided photo‐matching algorithms have been developed to more efficiently match images of unique individuals in databases with thousands of images. However, the identification accuracy of these algorithms can severely bias estimates of vital rates and population size. Therefore, it is important to understand the performance and limitations of state‐of‐the‐art photo‐matching algorithms prior to implementation in capture–recapture studies involving possibly thousands of images. Here, we compared the performance of four photo‐matching algorithms; Wild‐ID, I3S Pattern+, APHIS, and AmphIdent using multiple amphibian databases of varying image quality. We measured the performance of each algorithm and evaluated the performance in relation to database size and the number of matching images in the database. We found that algorithm performance differed greatly by algorithm and image database, with recognition rates ranging from 100% to 22.6% when limiting the review to the 10 highest ranking images. We found that recognition rate degraded marginally with increased database size and could be improved considerably with a higher number of matching images in the database. In our study, the pixel‐based algorithm of AmphIdent exhibited superior recognition rates compared to the other approaches. We recommend carefully evaluating algorithm performance prior to using it to match a complete database. By choosing a suitable matching algorithm, databases of sizes that are unfeasible to match “by eye” can be easily translated to accurate individual capture histories necessary for robust demographic estimates.     

Computer-assisted tracking of actin filament motility.

In vitro motility assays, in which fluorescently labeled actin filaments are propelled by myosin molecules adhered to a glass coverslip, require that actin filament velocity be determined. We have developed a computer-assisted filament tracking system that reduced the analysis time, minimized investigator bias, and provided greater accuracy in locating actin filaments in video images. The tracking routine successfully tracked filaments under experimental conditions where filament density, size, and extent of photobleaching varied dramatically. Videotaped images of actin filament motility were digitized and processed to enhance filament image contrast relative to background. Once processed, filament images were cross correlated between frames and a filament path was determined. The changes in filament centroid or center position between video frames were then used to calculate filament velocity. The tracking routine performance was evaluated and the sources of noise that contributed to errors in velocity were identified and quantified. Errors originated in algorithms for filament centroid determination and in the choice of sampling interval between video frames. With knowledge of these error sources, the investigator can maximize the accuracy of the velocity calculation through access to user-definable computer program parameters.     

Global analysis of fluorescence lifetime imaging microscopy data

Global analysis techniques are described for frequency domain fluorescence lifetime imaging microscopy (FLIM) data. These algorithms exploit the prior knowledge that only a limited number of fluorescent molecule species whose lifetimes do not vary spatially are present in the sample. Two approaches to implementing the lifetime invariance constraint are described. In the lifetime invariant fit method, each image in the lifetime image sequence is spatially averaged to obtain an improved signal-to-noise ratio. The lifetime estimations from these averaged data are used to recover the fractional contribution to the steady-state fluorescence on a pixel-by-pixel basis for each species. The second, superior, approach uses a global analysis technique that simultaneously fits the fractional contributions in all pixels and the spatially invariant lifetimes. In frequency domain FLIM the maximum number of lifetimes that can be fit with the global analysis method is twice the number of lifetimes that can be fit with conventional approaches. As a result, it is possible to discern two lifetimes with a single-frequency FLIM setup. The algorithms were tested on simulated data and then applied to separate the cellular distributions of coexpressed green fluorescent proteins in living cells.     

Quantifying Intracellular Particle Flows by DIC Object Tracking

Label-free imaging techniques such as differential interference contrast (DIC) allow the observation of cells and large subcellular structures in their native, unperturbed states with minimal exposure to light. The development of robust computational image-analysis routines is vital to quantitative label-free imaging. The reliability of quantitative analysis of time-series microscopy data based on single-particle tracking relies on accurately detecting objects as distinct from the background, i.e., segmentation. Typical approaches to segmenting DIC images either involve converting images to those resembling phase contrast, mimicking the optics of DIC object formation, or using the morphological properties of objects. Here, we describe MATLAB based, single-particle tracking tool with a GUI for mobility analysis of objects from in vitro and in vivo DIC time-series microscopy. The tool integrates contrast enhancement with multiple modified Gaussian filters, automated threshold detection for segmentation and minimal distance-based two-dimensional single-particle tracking. We compare the relative performance of multiple filters and demonstrate the utility of the tool for DIC object tracking (DICOT). We quantify subcellular dynamics of a time series of Caenorhabditis elegans embryos in the one-celled stage by detecting birefringent yolk granules in the cytoplasm with high precision. The resulting two-dimensional map of oscillatory dynamics of granules quantifies the cytoplasmic flows driven by anaphasic spindle oscillations. The frequency of oscillations across the anterior-posterior (A-P) and transverse axes of the embryo correspond well with the reported frequency of spindle oscillations. We validate the quantitative accuracy of our method by tracking the in vitro diffusive mobility of micron-sized beads in glycerol solutions. Estimates of the diffusion coefficients of the granules are used to measure the viscosity of a dilution series of glycerol. Thus, our computational method is likely to be useful for both intracellular mobility and in vitro microrheology.     

Sizing-up finite fluorescent particles with nanometer-scale precision by convolution and correlation image analysis

Determining the positions, shapes and sizes of finite living particles such as bacteria, mitochondria or vesicles is of interest in many biological processes. In fluorescence microscopy, algorithms that can simultaneously localize such particles as a function of time and determine the parameters of their shapes and sizes at the nanometer scale are not yet available. Here we develop two such algorithms based on convolution and correlation image analysis that take into account the position, orientation, shape and size of the object being tracked, and we compare the precision of the two algorithms using computer simulations. We show that the precision of both algorithms strongly depends on the objects size. In cases where the diameter of the object is larger than about four to five times the beam waist radius, the convolution algorithm gives a better precision than the correlation algorithm (it leads to more precise parameters), while for smaller object diameters, the correlation algorithm gives superior precision. We apply the convolution algorithm to sequences of confocal laser scanning micrographs of immobile Escherichia coli bacteria, and show that the centroid, the front end, the rear end, the left border and the right border of a bacterium can be determined with a signal-to-noise-dependent precision down to ~5 nm.     

Influence of device accuracy and choice of algorithm for species distribution modelling of seabirds: a case study using black‐browed albatrosses

Species distribution models (SDM) based on tracking data from different devices are used increasingly to explain and predict seabird distributions. However, different tracking methods provide different data resolutions, ranging from < 10 m to > 100 km. To better understand the implications of this variation, we modeled the potential distribution of black‐browed albatrosses Thalassarche melanophris from South Georgia that were simultaneously equipped with a platform terminal transmitter (PTT) (high resolution) and a global location sensor (GLS) logger (coarse resolution), and measured the overlap of the respective potential distribution for a total of nine different SDM algorithms. We found slightly better model fits for the PTT than for GLS data (AUC values 0.958 ± 0.048 vs 0.95 ± 0.05) across all algorithms. The overlaps of the predicted distributions were higher between device types for the same algorithm, than among algorithms for either device type. Uncertainty arising from coarse‐resolution location data is therefore lower than that associated with the modeling technique. Consequently, the choice of an appropriate algorithm appears to be more important than device type when applying SDMs to seabird tracking data. Despite their low accuracy, GLS data appear to be effective for analyzing the habitat preferences and distribution patterns of pelagic species.