2D Gaussian Function Research Articles

Latent Local Feature Extraction for Low-Resolution Virus Image Classification

Virus image classification is a significant and challenging issue in both clinical virology and medical image processing. Due to the low-resolution virus images in the original dataset, there is tricky difficulty in extracting useful features from this kind of poor quality images adopting the traditional feature extraction methods. In this paper, we propose an effective and robust method, which eliminates the drawbacks of traditional local feature extraction methods and conducts latent local texture feature extraction thus to promote the accuracy of virus image classification. Firstly, the multi-scale principal component analysis (PCA) filters are learned from all original images. Then, it establishes a scale space for each PCA-filtered image by 2D Gaussian function. Finally, some typical feature descriptors are employed to extract texture features from all images, which include the original image and its filtered images by PCA and Gaussian filters. Aiming at the classification of low-resolution images, the proposed method solves the difficulty in extracting the essential feature from the original image and captures its latent and principal texture information from different perspectives in different filtered images. Experimental results show that the classification accuracy of the proposed method is much higher than state-of-the-art methods in the same low-resolution virus dataset, reaching 88.00%.

A High-Efficiency Super-Resolution Reconstruction Method for Ultrasound Microvascular Imaging

The emergence of super-resolution imaging makes it possible to display the microvasculatures clearly using ultrasound imaging, which is of great importance in the early diagnosis of cancer. At present, the super-resolution performance can only be achieved when the sampling signal is long enough (usually more than 10,000 frames). Thus, the imaging time resolution is not suitable for clinical use. In this paper, we proposed a novel super-resolution reconstruction method, which is proved to have a satisfactory resolution using shorter sampling signal sequences. In the microbubble localization step, the integrated form of the 2D Gaussian function is innovatively adopted for image deconvolution in our method, which enhances the accuracy of microbubble positioning. In the trajectory tracking step, for the first time the averaged shifted histogram technique is presented for the visualization, which greatly improves the precision of reconstruction. In vivo experiments on rabbits were conducted to verify the effectiveness of the proposed method. Compared to the conventional reconstruction method, our method significantly reduces the Full-Width-at-Half-Maximum (FWHM) by 50% using only 400-frame signals. Besides, there is no significant increase in the running time using the proposed method. Considering its imaging performance and used frame number, the conclusion can be drawn that the proposed method advances the application of super-resolution imaging to the clinical use with a much higher time resolution.

SU‐C‐BRC‐04: Efficient Dose Calculation Algorithm for FFF IMRT with a Simplified Bivariate Gaussian Source Model

Purpose:To develop an efficient and accurate independent dose calculation algorithm with a simplified analytical source model for the quality assurance and safe delivery of Flattening Filter Free (FFF)‐IMRT on an Elekta Versa HD.Methods:The source model consisted of a point source and a 2D bivariate Gaussian source, respectively modeling the primary photons and the combined effect of head scatter, monitor chamber backscatter and collimator exchange effect. The in‐air fluence was firstly calculated by back‐projecting the edges of beam defining devices onto the source plane and integrating the visible source distribution. The effect of the rounded MLC leaf end, tongue‐and‐groove and interleaf transmission was taken into account in the back‐projection. The in‐air fluence was then modified with a fourth degree polynomial modeling the cone‐shaped dose distribution of FFF beams. Planar dose distribution was obtained by convolving the in‐air fluence with a dose deposition kernel (DDK) consisting of the sum of three 2D Gaussian functions. The parameters of the source model and the DDK were commissioned using measured in‐air output factors (Sc) and cross beam profiles, respectively. A novel method was used to eliminate the volume averaging effect of ion chambers in determining the DDK. Planar dose distributions of five head‐and‐neck FFF‐IMRT plans were calculated and compared against measurements performed with a 2D diode array (MapCHECK™) to validate the accuracy of the algorithm.Results:The proposed source model predicted Sc for both 6MV and 10MV with an accuracy better than 0.1%. With a stringent gamma criterion (2%/2mm/local difference), the passing rate of the FFF‐IMRT dose calculation was 97.2±2.6%.Conclusion:The removal of the flattening filter represents a simplification of the head structure which allows the use of a simpler source model for very accurate dose calculation. The proposed algorithm offers an effective way to ensure the safe delivery of FFF‐IMRT.

TH‐CD‐207B‐09: Task‐Driven Fluence Field Modulation Design for Model‐Based Iterative Reconstruction in CT

Purpose:There has been increasing interest in integrating fluence field modulation (FFM) devices with diagnostic CT scanners for dose reduction purposes. Conventional FFM strategies, however, are often either based on heuristics or the analysis of filtered‐backprojection (FBP) performance. This work investigates a prospective task‐driven optimization of FFM for model‐based iterative reconstruction (MBIR) in order to improve imaging performance at the same total dose as conventional strategies.Methods:The task‐driven optimization framework utilizes an ultra‐low dose 3D scout as a patient‐specific anatomical model and a mathematical formation of the imaging task. The MBIR method investigated is quadratically penalized‐likelihood reconstruction. The FFM objective function uses detectability index, d’, computed as a function of the predicted spatial resolution and noise in the image. To optimize performance throughout the object, a maxi‐min objective was adopted where the minimum d’ over multiple locations is maximized. To reduce the dimensionality of the problem, FFM is parameterized as a linear combination of 2D Gaussian basis functions over horizontal detector pixels and projection angles. The coefficients of these bases are found using the covariance matrix adaptation evolution strategy (CMA‐ES) algorithm. The task‐driven design was compared with three other strategies proposed for FBP reconstruction for a calcification cluster discrimination task in an abdomen phantom.Results:The task‐driven optimization yielded FFM that was significantly different from those designed for FBP. Comparing all four strategies, the task‐based design achieved the highest minimum d’ with an 8–48% improvement, consistent with the maxi‐min objective. In addition, d’ was improved to a greater extent over a larger area within the entire phantom.Conclusion:Results from this investigation suggests the need to re‐evaluate conventional FFM strategies for MBIR. The task‐based optimization framework provides a promising approach that maximizes imaging performance under the same total dose constraint.

TFG Promotes Organization of Transitional ER and Efficient Collagen Secretion.

SummaryCollagen is the most abundant protein in the animal kingdom. It is of fundamental importance during development for cell differentiation and tissue morphogenesis as well as in pathological processes such as fibrosis and cancer cell migration. However, our understanding of the mechanisms of procollagen secretion remains limited. Here, we show that TFG organizes transitional ER (tER) and ER exit sites (ERESs) into larger structures. Depletion of TFG results in dispersion of tER elements that remain associated with individual ER-Golgi intermediate compartments (ERGICs) as largely functional ERESs. We show that TFG is not required for the transport and packaging of small soluble cargoes but is necessary for the export of procollagen from the ER. Our work therefore suggests a key relationship between the structure and function of ERESs and a central role for TFG in optimizing COPII assembly for procollagen export.

Experimentally validated pencil beam scanning source model in TOPAS

The presence of a low-dose envelope, or ‘halo’, in the fluence profile of a proton spot can increase the output of a pencil beam scanning field by over 10%. This study evaluated whether the Monte Carlo simulation code, TOPAS 1.0-beta 8, based on Geant4.9.6 with its default physics list, can predict the spot halo at depth in phantom by incorporating a halo model within the proton source distribution. Proton sources were modelled using three 2D Gaussian functions, and optimized until simulated spot profiles matched measurements at the phantom surface out to a radius of 100 mm. Simulations were subsequently compared with profiles measured using EBT3 film in Solidwater® phantoms at various depths for 100, 115, 150, 180, 210 and 225 MeV proton beams. Simulations predict measured profiles within a 1 mm distance to agreement for 2D profiles extending to the 0.1% isodose, and within 1 mm/1% Gamma criteria over the integrated curve of spot profile as a function of radius. For isodose lines beyond 0.1% of the central spot dose, the simulated primary spot sigma is smaller than the measurement by up to 15%, and can differ by over 1 mm. The choice of particle interaction algorithm and phantom material were found to cause ~1 mm range uncertainty, a maximal 5% (0.3 mm) difference in spot sigma, and maximal 1 mm and ~2 mm distance to agreement in isodoses above and below the 0.1% level, respectively. Based on these observations, therefore, the selection of physics model and the application of Solidwater® as water replacement material in simulation and measurement should be used with caution.

Investigation of a single dielectric barrier discharge in submillimeter air gaps: Uniform field

The characteristics of a single discharge in 0.01–0.2-cm air gaps are investigated under atmospheric pressure between the metal electrodes and in the presence of a polymer barrier on one of the electrodes. The experimentally determined surface charge density distributions are satisfactorily described by a 2D Gaussian function with the proposed parameters. In the uniform field, the breakdown voltage weakly depends on the presence of a dielectric barrier. At the same time, the change from the positive to negative polarity of the metal electrode leads to a manifold increase in the discharge current and in the surface charge. The breakdown occurs under considerable overvoltage; the estimates indicate the streamer mechanism of the breakdown.

Nearest Neighbor Interactions Attenuate Intrinsic Amino Acid Conformational Preferences: A Combined Vibrational and NMR Study

Contrary to the isolated pair hypothesis, a pivotal ingredient of the random coil model, conformational distributions of amino acid residues in unfolded proteins cannot be considered as isolated from their nearest neighbors. To enable structural predictions of unfolded proteins or peptides (IDPs) knowledge about intrinsic propensities of amino acid residues must be complemented by information on nearest-neighbor interactions. To explore this influence, we preformed a joint vibrational and 2D-NMR spectroscopy study of selected “GxyG” host-guest peptides in aqueous solution: GDyG, GSyG, GxLG, GxVG, where x/y={A,K,LV}. The choice of D and S (L and V) for the x (y) position was motivated by their documented ability to drastically change the distribution of alanine in xAy tripeptides of truncated coil libraries. The observed spectral information were analyzed in terms of superpositions of 2D-Gaussian functions in the Ramachandran space, representing sub-ensembles of pPII-, β-strand-, helical-, and turn-like conformations. Results reveal that “turn forming residues” and hydrophobic residues have very strong effects on the conformation of their nearest neighbors. A direct comparison of the conformational distribution for S and D in GSAG ,GSLG, and GDAG with corresponding distributions in GxG peptiess reveals that hydrophobic neighbors cause drastic reductions of turn propensities. As a neighbor, K eliminates the asx turn propensity of D. In addition, insertion of these 'turn forming' residues (S, and D) causes conformational redistributions of L, A, and K from pPII to more extended β strand-like conformations while at the same time increasing the overall turn content. Concomitantly, the positions of pPII and particularly of β distributions are shifted to lower ψ values. Taken together, our results indicate that Dx and Sx motifs might act as conformational randomizers in proteins, attenuating intrinsic propensities of neighboring residues.

An automated approach applying 2D Gaussian fitting to quantitatively analyze the dynamic feature of immunoreceptor microclusters

An automated approach applying 2D Gaussian fitting to quantitatively analyze the dynamic feature of immunoreceptor microclusters

Kinematic decomposition and classification of octopus arm movements.

The octopus arm is a muscular hydrostat and due to its deformable and highly flexible structure it is capable of a rich repertoire of motor behaviors. Its motor control system uses planning principles and control strategies unique to muscular hydrostats. We previously reconstructed a data set of octopus arm movements from records of natural movements using a sequence of 3D curves describing the virtual backbone of arm configurations. Here we describe a novel representation of octopus arm movements in which a movement is characterized by a pair of surfaces that represent the curvature and torsion values of points along the arm as a function of time. This representation allowed us to explore whether the movements are built up of elementary kinematic units by decomposing each surface into a weighted combination of 2D Gaussian functions. The resulting Gaussian functions can be considered as motion primitives at the kinematic level of octopus arm movements. These can be used to examine underlying principles of movement generation. Here we used combination of such kinematic primitives to decompose different octopus arm movements and characterize several movement prototypes according to their composition. The representation and methodology can be applied to the movement of any organ which can be modeled by means of a continuous 3D curve.

How do Nearest-Neighbor Interactions Effect the Conformational Distributions in Peptides?

For structural predictions of intrinsically disordered proteins (IDPs), knowledge about intrinsic propensities of amino acids must be complimented by information on nearest-neighbor interactions. To explore the influence of nearest-neighbors on conformational distributions of amino acid residues, we preformed a joint vibrational and 2D-NMR study of selected GxyG host-guest peptides: GDyG, GSyG, GxLG, GxVG, where x/y={A,K,LV}. The choice of D and S (L/V) for the x (y) position was motivated by their documented ability to drastically change the distribution of alanine in xAy tripeptide sequences in truncated coil libraries. Five J-coupling constants and amide I’ profiles of the respective IR, polarized Raman and Vibrational Circular Dichroism spectra were analyzed using a superposition of 2D-Gaussian functions in Ramachandran space representing sub-ensembles of pPII-, β-strand-, helical-, and turn-like conformations. Our analysis of the amide I' profiles exploits excitonic coupling between the local amide I′ modes in the tetra-peptides. Our results reveal that D and S particularly alter the conformation of their downstream neighbor. In a recent study, these amino acids were shown to have an unusually high preference for type I’/IIβ and asx-turns. A direct comparison of the ensemble obtained for serine in GSAG, GSLG and GSG reveals that A and L cause the asx-turn population to be mitigated in favor of more extended pPII/ β structures. Upon insertion of these ‘turn-forming’ residues, alanine's conformational ensemble is modestly changed (shift from pPII to β), while the position of pPII and particularly of β is shifted to lower ψ-values. DFT calculations indeed show that the forced reduction in ψ for A increases the H-bond distance for serine in the asx-turn conformation. Taken together, our results indicate that Dx and Sx-motifs might act as conformational randomizers in proteins, attenuating intrinsic propensities of neighboring residues.

Towards a Realistic Representation in Surface-Based Pseudoreceptor Modeling: a PDB-Wide Analysis of Binding Pockets.

Surface-based pseudoreceptor methods are expansions of 3D-QSAR techniques placing physico-chemical information onto a 3D surface surrounding a set of aligned compounds that bind into the same binding site of a common protein target. With this mapping pseudoreceptor methods attempt to create models of the target protein binding site around the ligand ensemble. The surface points of the pseudoreceptor model are typically independent descriptors and property mapping onto the surface points is prone to overfitting. In this article, we developed surface descriptors based on 2D Gaussian functions that can model the physico-chemical properties of binding sites of proteins. Binding pocket surfaces of a large set of experimentally determined protein-ligand complex structures are analyzed and 2D Gaussian functions are used to fit the surface properties. The fitted property values differ from the original values on average by 15-25 %, and on average six Gaussian functions are necessary to model each surface property. These descriptors allow for a realistic representation of the binding site and will limit the number of descriptors used throughout the QSAR optimization phase.

A Novel Method for Computing Exponential Function Using CORDIC Algorithm

In this paper, design of Coordinate Rotation Digital Computer (CORDIC) based 2D Gaussian function and an efficient Very Large Scale Integration (VLSI) architecture suitable for Field Programmable Gate Array (FPGA) implementation is presented. The potential application of the proposed 2D Gaussian function includes image enhancement, smoothing, edge detection, filtering etc. The proposed algorithm uses expanded range of CORDIC algorithm since the conventional technique converges within the range of [-1.12, +1.12]. The architectures developed exploits high degrees of pipelining and parallel processing in order to achieve real time performance. The design has been realized using Register Transfer Language (RTL) compliant Verilog code and fits into a single chip with a gate count utilization of 75,151. The algorithm has been tested for Gaussian based image smoothening application and is implemented on XC2V1000-6bg575 Xilinx FPGA device. The architecture developed is capable of processing one pixel per clock cycle and provides results in real time. The experimental results shows that the proposed approach exhibits better performance when compared with the other researcher methods.

Mechanistic Insights into the Twin-Arginine Translocation Cycle of Escherichia Coli by an In Vivo Single-Molecule Approach

The twin-arginine translocation (Tat) system is a unique protein targeting pathway which has been found in bacteria, archea and chloroplasts as well as in plant mitochondria. Its ability to transport fully folded proteins across the cytoplasmic membrane distinguishes it from other translocation pathways. In E. coli the essential components of the system, TatA, TatB, and TatC, have been isolated in complexes of different size, suggesting that a fully active Tat complex forms only transiently. Furthermore, the precise steps in the translocation cycle remain mostly unknown.We perform fluorescence microscopy and single-particle tracking to gain deeper insight into the dynamics of the Tat machinery. To this end, bacteria expressing low levels of GFP-fused Tat subunits are imaged with sensitive laser-illuminated wide-field fluorescence microscopy. Mobile fluorescent spots are observed, and their intensity and location determined by fitting them with a 2D Gaussian function. The trajectories of these spots are then established by linking the Gaussian fits in successive frames.Our data shows that diffusion of TatA-eGFP is heterogeneous, and that its average diffusion coefficient decreases when translocation substrate is over-expressed. Moreover, TatA-eGFP mobility depends on the existence of an electrochemical potential, which is the driving force behind the Tat translocation system. This could suggest that TatA-eGFP complexes undergo a topological transition upon becoming ‘translocation active’.

Identification of Acoustic Wave Orientation for Ultrasound-Based Flow Measurement by Exploiting the Hough Transform

Abstract Ultrasound-based flow measurement relies on the proper knowledge of the angle under which the acoustic waves propagate with respect to the flow direction of the streaming fluid. We present a novel image processing approach for the identification of the wavefronts’ orientation by exploiting a modified Hough transform. The spatially discretized sound pressure amplitude of measurement/simulation data is utilized as a weighting function for the Hough transform. It is shown that the angle and position of a wavefront can be estimated with subpixel accuracy, where the size of a pixel depends on the data's spatial resolution. This is achieved by incorporating a least-squares algorithm, fitting a 2D Gaussian function to the Hough parameter plane and thus improving the accuracy of the detected wavefront properties.

Fast Maximum Likelihood Algorithm for Localization of Fluorescent Molecules

In super-resolution fluorescence microscopy, one key objective is to localize fluorescent molecules as quickly and precisely as possible. The most common approaches involve fitting an image of a molecule to a point spread function, often a Gaussian for simplicity. The separable property of the 2D Gaussian function allows us to separate the tasks of estimating the x and y coordinates. We did this by summing the columns of an image, then we used a maximum likelihood algorithm to estimate the position of the molecule along the x axis. Because we were able to separate the Gaussian, our computational time went from O(L2) to O(L) where L is the width (in pixels) of the pixel array. This algorithm gives us precision close to the Cramer-Rao Lower Bound, and is robust against variations of pixel size, window size, or displacements of the molecule relative to the center of the computational window.

Implementation of EPID transit dosimetry based on a through-air dosimetry algorithm

A method to perform transit dosimetry with an electronic portal imaging device (EPID) by extending the commercial implementation of a published through-air portal dose image (PDI) prediction algorithm Van Esch et al. [Radiother. Oncol. 71, 223-234 (2004)] is proposed and validated. A detailed characterization of the attenuation, scattering, and EPID response behind objects in the beam path is used to convert through-air PDIs into transit PDIs. The EPID detector response beyond a range of water equivalent thicknesses (0-35 cm) and field sizes (3×3 to 22.2×29.6 cm(2)) was analyzed. A constant air gap between the phantom exit surface and the EPID was utilized. A model was constructed that accounts for the beam's attenuation along the central axis, the presence of phantom scattered radiation, the detector's energy dependent response, and the difference in EPID off-axis pixel response relative to the central pixel. The efficacy of the algorithm was verified by comparing predicted and measured PDIs for IMRT fields delivered through phantoms of increasing complexity. The expression that converts a through-air PDI to a transit PDI is dependent on the object's thickness, the irradiated field size, and the EPID pixel position. Monte Carlo derived narrow-beam linear attenuation coefficients are used to model the decrease in primary fluence incident upon the EPID due to the object's presence in the beam. This term is multiplied by a factor that accounts for the broad beam scatter geometry of the linac-phantom-EPID system and the detector's response to the incident beam quality. A 2D Gaussian function that models the nonuniformity of pixel response across the EPID detector plane is developed. For algorithmic verification, 49 IMRT fields were repeatedly delivered to homogeneous slab phantoms in 5 cm increments. Over the entire set of measurements, the average area passing a 3%∕3mm gamma criteria slowly decreased from 98% for no material in the beam to 96.7% for 35 cm of material in the beam. The same 49 fields were delivered to a heterogeneous slab phantom and on average, 97.1% of the pixels passed the gamma criteria. Finally, a total of 33 IMRT fields were delivered to the anthropomorphic phantom and on average, 98.1% of the pixels passed. The likelihood of good matches was independent of anatomical site. A prediction of the transit PDI behind a phantom or patient can be created for the purposes of treatment verification via an extension of the Van Esch through-air PDI algorithm. The results of the verification measurements through phantoms indicate that further investigation through patients during their treatments is warranted.

Dynamic control of 3D chemical profiles with a single 2D microfluidic platform

Dynamic control of three-dimensional (3D) chemical patterns with both high precision and high speed is important in a range of applications from chemical synthesis, flow cytometry, and multi-scale biological manipulation approaches. A central challenge in controlling 3D chemical patterns is the inability to create rapidly tunable 3D profiles with simple and direct approaches that avoid complicated microfabrication. Here, we present the ability to rapidly and precisely create 3D chemical patterns using a single two-dimensional (2D) microfluidic platform. We are not only able to create these 3D patterns, but can rapidly switch from one mode to another (e.g. from a focused to a defocused pattern in less than 1 second) via simple changes in inlet pressures. A feedback control scheme with a pressure modulation mechanism controls the pressure changes. In addition to experiments, we conducted computational simulations for guiding the optimum design of the channels as well as revealing the sensitivity of the patterns to the channel dimensions; these simulations have high experimental correlations. We also show that microvortices play an important role in creating these tunable 3D patterns in this microfluidic platform. We quantitatively determine the degrees of the focused patterns in 2D cross-sections using a focus index with a 2D Gaussian function. Our integrated approach combining feedback control with simple microfluidics will be useful for researchers in diverse disciplines including chemistry, engineering, physics, and biology.

Intrinsic Properties of immunoglobulin IgG1 Isotype-Switched B Cell Receptors Promote Microclustering and the Initiation of Signaling

Memory B cells express high-affinity, immunoglobulin GB cell receptors (IgG BCRs) that enhance B cell responses, giving rise to the rapid production of high-affinity, IgG antibodies. Despite the central role of IgG BCRs in memory responses, the mechanisms by which the IgG BCRs function to enhance B cell responses are not fully understood. Using high-resolution live-cell imaging, we showed that IgG1 BCRs dramatically enhanced the earliest BCR-intrinsic events that followed within seconds of B cells' encounter with membrane bound antigen, including BCR oligomerization and BCR microcluster growth, leading to Syk kinase recruitment and calcium responses. The enhancement of these early events was dependent on a membrane proximal region of the IgG1 cytoplasmic tail not previously appreciated to play a role in IgG1 BCR signaling. Thus, intrinsic properties of the IgG1 BCR enhance early antigen-driven events that ultimately translate into heightened signaling.

Adapting the ITK Registration Framework to Fit Parametric Image Models

The image registration framework in the Insight Tookit offers a powerful body of code for finding the optimal spatial transform that registers one image with another. However, ITK currently lacks a way to fit parametric models of image pixel values to an input image. Such a capability is necessary in certain applications such as sub-resolution localization of molecules in fluorescence microscopy. This document describes new classes that enable the use of the registration framework to provide this capability. We describe a new base class, itk::ParametricImageSource, that defines an interface for parametric image sources. An adapter class itk::ImageToParametricImageSourceMetric that enables itk::ParametricImageSources to be hooked into the registration framework is also described. An example adapter class that enables the existing itk::GaussianImageSource to be used for image fitting is presented, and we demonstrate use of the classes by fitting a 2D Gaussian function to an image generated by the itk::GaussianImageSource class.