Two-dimensional Gaussian Fitting Research Articles

A comparison of digital centering algorithms for high Earth orbital space debris

The applications of digital centering algorithms have a major impact on precise astrometry. In optical observations of space debris, due to the observing strategies and methods, the image degradation is distinct, which affects the centroid computing of CCD images. Adopting the four widely-used centering algorithms, including modified moment, one-dimensional Gaussian fit, two-dimensional Gaussian fit and median, tests are made on raw CCD images of space debris. With the observation positions obtained by astronomical calibration and the reference ones from ephemeris, the precision of variable algorithms and the influence of different threshold settings are acquired. The results indicate that the median reveals performs best for right ascension coordinates and others reveals a better results for declination coordinates. For Gaussian fit, no threshold may improve the centering precision.

An adaptive threshold method for improving astrometry of space debris CCD images

Optical survey is a main technique for observing space debris, and precisely measuring the positions of space debris is of great importance. Due to several factors, e.g. the angle object normal to the observer, the shape as well as the attitude of the object, the variations of observed characteristics for low earth orbital space debris are distinct. When we look at optical CCD images of observed objects, the size and brightness are varying, hence it’s difficult to decide the threshold during centroid measurement and precise astrometry. Traditionally the threshold is given empirically and constantly in data reduction, and obviously it’s not suitable for data reduction of space debris. Here we offer a solution to provide the threshold. Our method assumes that the PSF (point spread function) is Gaussian and estimates the signal flux by a directly two-dimensional Gaussian fit, then a cubic spline interpolation is performed to divide each initial pixel into several sub-pixels, at last the threshold is determined by the estimation of signal flux and the sub-pixels above threshold are separated to estimate the centroid. A trail observation of the fast spinning satellite Ajisai is made and the CCD frames are obtained to test our algorithm. The calibration precision of various threshold is obtained through the comparison between the observed equatorial position and the reference one, the latter are obtained from the precise ephemeris of the satellite. The results indicate that our method reduces the total errors of measurements, it works effectively in improving the centering precision of space debris images.

Performance of correlation approaches for the evaluation of spatial distortion reductions

The analysis of optical remote sensing images often requires a perfect pixel alignment between single bands. Even smallest deviations may degrade the accuracy of subsequent parameter retrieval or lead to the detection of non-existing structures caused by artificial gradients. Hence, a careful pre-processing is essential for minimizing spatial non-uniformities such as erroneous co-registration. The results need to be validated and assigned with a quality flag that is unfortunately still not a common practice. In this letter, four broadly used global correlation approaches, a two-dimensional Gaussian peak fit, a poly phase technique, an iterative phase approach and its proposed enhancement, were tested for their capacity to serve either as an evaluation tool for preceding spatial distortion reductions, e.g. by co-registration, or as a global minimizer for generic reduction approaches. For this eight broadly used test images, three Landsat 7 and three Landsat 8 samples were sub pixel shifted artificially and degraded by different noise levels resulting in more than 200,000 noise and shift scenarios. Additionally, one state-of-the-art approach was enhanced by 50% on average for all scenarios and by 280% on average for all non-degraded images. This study indicates that three out of four approaches can serve as evaluation tools for spatial distortion reductions or as a global minimizer even for highly degraded images, whereas proposed enhancement offers highest accuracy and the poly phase approach offers best overall performance with regard to considered criteria.

Plasmon point spread functions: How do we model plasmon-mediated emission processes?

A major challenge with studying plasmon-mediated emission events is the small size of plasmonic nanoparticles relative to the wavelength of light. Objects smaller than roughly half the wavelength of light will appear as diffraction-limited spots in far-field optical images, presenting a significant experimental challenge for studying plasmonic processes on the nanoscale. Super-resolution imaging has recently been applied to plasmonic nanosystems and allows plasmon-mediated emission to be resolved on the order of ∼5 nm. In super-resolution imaging, a diffraction-limited spot is fit to some model function in order to calculate the position of the emission centroid, which represents the location of the emitter. However, the accuracy of the centroid position strongly depends on how well the fitting function describes the data. This Perspective discusses the commonly used two-dimensional Gaussian fitting function applied to super-resolution imaging of plasmon-mediated emission, then introduces an alternative model based on dipole point spread functions. The two fitting models are compared and contrasted for super-resolution imaging of nanoparticle scattering/luminescence, surface-enhanced Raman scattering, and surface-enhanced fluorescence.

Quantitative annular dark-field STEM images of a silicon crystal using a large-angle convergent electron probe with a 300-kV cold field-emission gun

Annular dark-field scanning transmission electron microscope (ADF-STEM) images of an Si (001) crystal were obtained by using an aberration-corrected electron microscope, at 30-mrad convergent probe and cold field-emission gun at 300kV. The intensity of ADF-STEM images, that is, the number of scattered electrons relative to the incident electrons, obtained for specimen thickness from 10 to 50nm was compared quantitatively with absorptive multi-slice simulation. The column and background intensities were analyzed by column-by-column two-dimensional Gaussian fitting. These intensities were found to increase linearly with the sample thicknesses. However, the simulated image gave higher column intensity and lower background intensity for all the sample thickness. We found that experimental images were reproduced by the simulation with Gaussian convolution of 70pm full-width at half-maximum for all the sample thicknesses from 10 to 50nm. The possible factors accounted for this Gaussian convolution is discussed.

Nanometer displacement measurement of a multiwalled carbon nanotube cantilever under aqueous conditions

In this study, we report nanometer displacement measurement of an individual multiwalled nanotube (MWNT) in liquid, based on the high accuracy localization of individual fluorescent nanoparticles. In order to visualize a MWNT cantilever in liquid, a fluorescent polystyrene nanoparticle with an amine conjugate was selectively attached at the end of a nanotube by noncovalent hydrogen bonding between amine and carboxylic groups. Physical absorption of ethylenediamine gas vapor onto an as-fabricated MWNT cantilever renders the nanotube hydrophilic, enabling manipulation of the MWNT cantilever in liquid without bending or breaking. A fluorescent nanoparticle was localized by a two-dimensional Gaussian fit for the fluorescence intensity of the particle. During the manipulation of the nanotube cantilever in liquid, the displacement was determined by the positional change of the localized nanoparticle. The measurement technique was evaluated by measuring the displacement of a MWNT cantilever subjected to controlled manipulation such as a single line scan, step and stair response. The positional accuracy of the measurement was experimentally found to be 7 nm. The fluorescence measurement of a hydrophilic MWNT cantilever can be further used in biological applications such as biochemical sensors and single molecule force spectroscopy.

Image Analysis with Rapid and Accurate Two-Dimensional Gaussian Fitting

A computationally rapid image analysis method, weighted overdetermined regression, is presented for two-dimensional (2D) Gaussian fitting of particle location with subpixel resolution from a pixelized image of light intensity. Compared to least-squares Gaussian iterative fitting, which is most exact but prohibitively slow for large data sets, the precision of this new method is equivalent when the signal-to-noise ratio is high and approaches it when the signal-to-noise ratio is low, while enjoying a more than 100-fold improvement in computational time. Compared to another widely used approximation method, nine-point regression, we show that precision and speed are both improved. Additionally, weighted regression runs nearly as fast and with greatly improved precision compared to the simplest method, the moment method, which, despite its limited precision, is frequently employed because of its speed. Quantitative comparisons are presented for both circular and elliptical Gaussian intensity distributions. This new image analysis method may be useful when dealing with large data sets such as those frequently met in astronomy or in single-particle and single-molecule tracking using microscopy and may facilitate advances such as real-time quantification of microscopy images.

Kinesin‐1 (uKHC/KIF5B) is Required for Bidirectional Motility of ER Exit Sites and Efficient ER‐to‐Golgi Transport

Transport of proteins and lipids between intracellular compartments is fundamental to the organization and function of eukaryotic cells. The efficiency of this process is greatly enhanced through coupling of membranes to microtubules. This serves two functions, organelle positioning and vesicular transport. In this study, we show that in addition to the well-known role for the minus-end motor dynein in endoplasmic reticulum (ER)-to-Golgi transport, the plus-end-directed motor kinesin-1 is involved in positioning coat protein II-coated ER exit sites (ERES) in cells as well as the formation of transport carriers and their movement to the Golgi. Using two-dimensional Gaussian fitting to determine their location at high spatial resolution, we show that ERES undergo short-range bidirectional movements. Bidirectionality depends on both kinesin-1 and dynein. Suppression of kinesin-1 (KIF5B) also inhibits ER-to-Golgi transport and affects the morphology of ER-to-Golgi transport carriers. Furthermore, we show that suppression of dynein heavy chain expression increases the range of movement of ERES, suggesting that dynein might anchor ERES, or the ER itself, to microtubules. These data implicate kinesin-1 in the spatial organization of the ER/Golgi interface as well as in traffic outside the ER.

Errors in two particle tracking at close distances

Tracking single and multiple particles is of great importance for many physical investigations in a variety of different areas. It is essential to find and eliminate sources of systematic errors in the particle position determination (PPD) and to determine the limits of its applicability to a given problem. Particularly when measuring the interactions between colloids at close distances, artifacts in the image taking process pose a great problem. By means of a simulation technique, we investigated the accuracy of the PPD using two-dimensional Gaussian and Gaussian-like fitting functions. For the distance between the two colloidal particles this revealed a systematic overestimation of the inter-particle distance of up to 1.9% of the particle diameter for the Gaussian fitting function. This deviation can be explained by the differences between the intensity distribution of the overlap of the simulated particles and the linear superposition of the Gaussian functions. Modifications of the fitting functions can reduce the systematic error significantly.

A Single Mechanism Can Explain the Speed Tuning Properties of MT and V1 Complex Neurons

A recent study by Priebe et al., (2006) has shown that a small proportion (27%) of primate directionally selective, complex V1 neurons are tuned for the speed of image motion. In this study, I show that the weighted intersection mechanism (WIM) model, which was previously proposed to explain speed tuning in middle temporal neurons, can also explain the tuning found in complex V1 neurons. With the addition of a contrast gain mechanism, this model is able to replicate the effects of contrast on V1 speed tuning, a phenomenon that was recently discovered by Priebe et al., (2006). The WIM model simulations also indicate that V1 neuron spatiotemporal frequency response maps may be asymmetrical in shape and hence poorly characterized by the symmetrical two-dimensional Gaussian fitting function used by Priebe et al., (2006) to classify their cells. Therefore, the actual proportion of speed tuning among directional complex V1 cells may be higher than the 27% estimate suggested by these authors.

A quantitative study of three-dimensional Lagrangian particle tracking algorithms

A neural network particle finding algorithm and a new four-frame predictive tracking algorithm are proposed for three-dimensional Lagrangian particle tracking (LPT). A quantitative comparison of these and other algorithms commonly used in three-dimensional LPT is presented. Weighted averaging, one-dimensional and two-dimensional Gaussian fitting, and the neural network scheme are considered for determining particle centers in digital camera images. When the signal to noise ratio is high, the one-dimensional Gaussian estimation scheme is shown to achieve a good combination of accuracy and efficiency, while the neural network approach provides greater accuracy when the images are noisy. The effect of camera placement on both the yield and accuracy of three-dimensional particle positions is investigated, and it is shown that at least one camera must be positioned at a large angle with respect to the other cameras to minimize errors. Finally, the problem of tracking particles in time is studied. The nearest neighbor algorithm is compared with a three-frame predictive algorithm and two four-frame algorithms. These four algorithms are applied to particle tracks generated by direct numerical simulation both with and without a method to resolve tracking conflicts. The new four-frame predictive algorithm with no conflict resolution is shown to give the best performance. Finally, the best algorithms are verified to work in a real experimental environment.

A single-molecule study of polycrystalline microstructure by fluorescence polarization spectroscopy

The structure of n-hexadecane polycrystalline matrices is examined with single molecule fluorescence spectroscopy at a temperature of 1.7 K. Some single chromophores exhibit spectral dynamics during experiments: their resonances either jump between two frequencies or split into two components. By means of polarization measurements, we investigate the molecular spectra in order to distinguish between the case of two spatially unresolved molecules and the case of chromophore — two level system (TLS) pair. For closely spaced molecules two-dimensional Gaussian function fitting is applied to extract the spatial coordinates of the molecules. For TLS-chromophore systems, parameters of the TLSs are estimated.

Fluorescence Imaging with One Nanometer Accuracy: Application to Molecular Motors

We introduce the technique of FIONA, fluorescence imaging with one nanometer accuracy. This is a fluorescence technique that is able to localize the position of a single dye within approximately 1 nm in the x-y plane. It is done simply by taking the point spread function of a single fluorophore excited with wide field illumination and locating the center of the fluorescent spot by a two-dimensional Gaussian fit. We motivate the development of FIONA by unraveling the walking mechanism of the molecular motors myosin V, myosin VI, and kinesin. We find that they all walk in a hand-over-hand fashion.

Objective Evaluation of Fabric Pilling Using Image Analysis Techniques

For quality control of textiles, it is necessary to develop an objective method to evaluate fabric pilling, rather than subjective, to improve reliability and reproducibility. This paper presents a new method to extract pill features from fabric images. In this work, we apply a two-dimensional Gaussian fit theory to train a pill template using actual pill images for pill template matching, and determine a reasonable threshold for image segmentation using a histogram-fitting technique. We then extract five parameters to describe pill properties—pill number, mean area of pills. total area of pills. contrast. and density—and establish formulas to calculate objective grades with these parameters. The results show that a good correlation can be achieved between objective and subjective data.

Two sub-pixel processing algorithms for high accuracy particle centre estimation in low seeding density particle image velocimetry

This article presents two algorithms for spatial processing of low seeding density PIV (particle image velocimetry) images which lead to sub-pixel precision in particle positioning. The particle centres are estimated to accuracies of the order of 0.1 pixel, yielding 1% error in velocity calculation. The first algorithm discriminates valid particles from the rest of the image and determines their centres in Cartesian coordinates by using a two-dimensional Gaussian fit. The second algorithm performs local correlation between particle pairs and determines instantaneous two-dimensional velocities. The methods have been applied initially to simulated data. Gaussian noise and distortion has then been added to simulate experimental conditions. It is shown that, in comparison with conventional methods, the new algorithms offer up to an order of magnitude higher accuracy for particle centre estimation. Finally, the Gaussian fit approach has been used to map an experimental transonic flow field from the stator trailing edge wake region of a cascade with an estimated error of 1%. The experimental results are found to be in good agreement with previous theoretical steady-state viscous calculations.

Circumstellar OH maser observation of OH 17.7-2.0

We used the Parkes 64-m radio telescope to observe the circumstellar OH maser of OH 17.7-2.0. We found three peaks, two belong to a previously known strong source, one is a new, weak source. Using two-dimensional gaussian fit, we found the position of two strong peaks to agree with that of an IRAS point source, while the weak source is located to the SW. The velocity and-peak flux of the strong source are found to be rather stable.

Maximum Likelihood Estimation of Digital Image Center

A algorithm for digital image centering with the maximum likelihood method is described. The astrometric accuracy of this algorithm is similar to the two-dimensional Gaussian fitting. For saturated images, this algorithm is better than the Gaussian fitting. With the maximum likelihood method, some systematic effect, such as coma and magnitude equation, can be reduced significantly.

The QUEST System for Quantitative Analysis of Two-dimensional Gels

The strategies and methods used by the QUEST system for two-dimensional gel analysis are described, and the performance of the system is evaluated. Radiolabeled proteins, resolved on two-dimensional gels and detected using calibrated exposures to film, are quantified in units of disintegrations per minute or as a fraction of the total protein radioactivity applied to the gel. Spot quantitation and resolution of overlapping spots is performed by two-dimensional gaussian fitting. Pattern matching is carried out for groups of gels called matchsets, and within each matchset every gel is matched to every other gel. During the matching process, spots are automatically added to each pattern at positions where unmatched spots were detected in other patterns. This results in enhanced accuracy for both spot detection and for matching. The spot fitting procedure is repeated after matching. Tests show that up to 97% of spots in each pattern can be matched and that fewer than 1% of the spots are matched inconsistently. Approximately 2000 proteins are detected from typical gels. Of these 1600 are high quality spots. Tests to measure the coefficient of variation of spot quantitation versus spot quality show that the average coefficient of variation for high quality spots is 21%. The intensities of the detected proteins range from 4 to 20,000 ppm of total protein synthesis. The QUEST analysis system has been used to build a quantitative database for the proteins of normal and transformed REF52 cells, as presented in the accompanying reports (Garrels, J., and Franza, B. R., Jr. (1989) J. Biol. Chem. 264, 5283-5298, 5299-5312).

The analysis of simultaneous mass and charge data from damped heavy-ion reactions

Procedures are described to identify simultaneously the mass and charge of projectile-like fragments produced in damped heavy-ion reactions and derived from data recorded with a ΔE− E time-of-flight telescope. Corrections for the effects of particle emission from the primary reaction products are also discussed. The average properties of the resultant charge, neutron and mass distributions can be described by six parameters obtained from a two-dimensional Gaussian fit. These parameters, which are a function of kinetic energy damping, summarize the properties of nucleon exchange in the damped process. After the effects of experimental resolution (in two dimensions, charge and mass) and the effects of binning of the data have been taken into account, most physically relevant quantities of interest and their uncertainties can be calculated with the formulas presented.