Vector Field Analysis Research Articles

High-numerical-aperture microscopy with a rotating point spread function.

Rotating point spread function (PSF) microscopy via spiral phase engineering can localize point sources over large focal depths in a snapshot mode. The present work gives an approximate vector-field analysis of an improved rotating PSF design that encodes both the 3D location and polarization state of a monochromatic point dipole emitter for high-numerical-aperture microscopy. By examining the angle of rotation and the spatial form of the PSF, one can jointly localize point sources and determine the polarization state of light emitted by them over a 3D field in a single snapshot. Results of numerical simulations of noisy data frames under Poisson shot noise conditions and the errors in the recovery of 3D location and dipole orientation for a single point source are discussed.

Spectral Processing of Tangential Vector Fields

AbstractWe propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier‐type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to the prominent cotan discretization of the Laplace–Beltrami operator. Based on the Fourier representation, we introduce schemes for spectral analysis, filtering and compression of tangential vector fields. Moreover, we introduce a spline‐type editor for modelling of tangential vector fields with interpolation constraints for the field itself and its divergence and curl. Using the spectral representation, we propose a numerical scheme that allows for real‐time modelling of tangential vector fields.

Tracking of Morse sets for 2D bounded time‐dependent vector fields

Morse sets are more numerically stable than the conventional topology. However, the tracking of Morse sets is a missing part for the analysis of time-dependent vector fields. This Letter proposes a novel tracking method of Morse sets for 2D bounded time-dependent vector fields. The critical triangle is defined and detected by a robust combinatorial way. The forward and backward image of a critical triangle can be acquired by the mapping search strategy. Finally, the tracking method of Morse sets is proposed based on their images. Experimental results demonstrate the availability and effectiveness of the proposed method.

Discrete Connection and Covariant Derivative for Vector Field Analysis and Design

In this article, we introduce a discrete definition of connection on simplicial manifolds, involving closed-form continuous expressions within simplices and finite rotations across simplices. The finite-dimensional parameters of this connection are optimally computed by minimizing a quadratic measure of the deviation to the (discontinuous) Levi-Civita connection induced by the embedding of the input triangle mesh, or to any metric connection with arbitrary cone singularities at vertices. From this discrete connection, a covariant derivative is constructed through exact differentiation, leading to explicit expressions for local integrals of first-order derivatives (such as divergence, curl, and the Cauchy-Riemann operator) and for L 2 -based energies (such as the Dirichlet energy). We finally demonstrate the utility, flexibility, and accuracy of our discrete formulations for the design and analysis of vector, n -vector, and n -direction fields.

Simulation analysis and experimental demonstration of velocity vector field of medium flow in double mass vibration mill

To resolve the technical issue that very hard particle is difficult to be refined, the mesoscopic numerical simulation of discrete medium flows based on Particle Flow Code was established. Four combinations of frequency and amplitude were set to simulate the medium flow, and the images of velocity gradation and velocity vector field have been obtained. Results show that the energy in medium flow was transmitted faster, and the effect of impact and shear forces among medium was stronger in the mode with mid-frequency and large amplitude. To verify the simulation results, the diamond ultrafine grinding is done in both normal and new vibration mills with the same basic parameters. Through size detecting in MS 2000 laser particle sizer and recording by high-speed photographic Mikrotron Gmbh, the results are basically consistent with the simulation analysis of velocity vector. Compared with other modes, the kinetic and strain energy of medium flow in the mode of mid-frequency with large amplitude is increased up to 0.3–5 times, and energy-lacking area is reduced by 8–20%; the effect of particle refinement and narrowing distribution is obvious. It becomes a positive technical progress in the field of very hard particle vibration grinding and micronano refinement.

Double compression detection based on local motion vector field analysis in static-background videos

Videos captured by stationary cameras are widely used in video surveillance and video conference. This kind of video often has static or gradually changed background. By analyzing the properties of static-background videos, this work presents a novel approach to detect double MPEG-4 compression based on local motion vector field analysis in static-background videos. For a given suspicious video, the local motion vector field is used to segment background regions in each frame. According to the segmentation of backgrounds and the motion strength of foregrounds, the modified prediction residual sequence is calculated, which retains robust fingerprints of double compression. After post-processing, the detection and GOP estimation results are obtained by applying the temporal periodic analysis method to the final feature sequence. Experimental results have demonstrated better robustness and efficiency of the proposed method in comparison to several state-of-the-art methods. Besides, the proposed method is more robust to various rate control modes.

Net accumulation of suspended sediment and its seasonal variability dominated by shelf circulation in the Yellow and East China Seas

The seasonal transfer and net accumulation of suspended sediment, especially the forming mechanism of the Southwestern Cheju Island Mud (SWCIM) are investigated using multi-year monthly mean suspended sediment flux to establish the linkages between sediment transport and hydrodynamic conditions and to determine the dominant long-term sediment transport process in the Yellow and East China Seas (YECSs). The more accurate suspended sediment flux, and net deposition or erosion driven by shelf circulation in the YECSs are attained using 10-year time series data on surface suspended sediment concentration and more reliable numerically simulated circulation velocity.The calculated net deposition or erosion of suspended sediment with distinct seasonal variability in the YECSs demonstrates that during the wintertime significant deposition occurs not only along the coast, but also offshore areas with water depth of about 100m, such as the SWCIM, which is acknowledged as the only mid-shelf Holocene depocenter in the YECSs. The annual cycle of net deposition or erosion verifies the widely accepted viewpoint, that riverine suspended sediment is stored in the inner shelf, especially adjacent to the estuary in summer and transported to middle or outer shelf in winter in the YECSs. Active sediment-transport process and the forming of the SWCIM mainly influenced by shelf circulation have been reproduced using the vector field analysis on suspended sediment flux. In winter, the Yellow Sea Coastal Current with high suspended sediment concentration flows southeastward along the Changjiang Bank, and interface with the Yellow Sea Warm Current to drive the East China Sea Cold Eddy at the end of the Changjiang Bank, which contributes to the convergency of suspended sediment, eventually generating the SWCIM. The circulation-driven accumulation rates in the YECSs are 0.51mma−1 in the SWCIM area, 0.45mma−1 at the cross-shelf pathway, 0.04mma−1 in the Central Yellow Sea Mud area, 3.62mma−1 in the Changjiang Estuary, and 3.83mma−1 off the Zhejiang Coast, respectively, which agree with the measured ones reasonably well, and further reveal that shelf circulation dominates long term sediment transport. Some uncertainties on the accuracy of suspended sediment flux and influence of tidal residual currents should be resolved in the future study to achieve a more quantitative picture about sediment transport in the YECSs.

Multiscale seamless‐domain method for linear elastic analysis of heterogeneous materials

SummaryA multiscale numerical technique, termed the seamless‐domain method (SDM), is applied to linear elastic problems. The SDM consists of two steps. The first step is a microscopic analysis of the local simulated domain to construct interpolation functions for discretizing governing equations. This allows an SDM solution to represent a structure consisting of heterogeneous microstructure(s) without homogenization. The second step is a macroscopic analysis of a seamless global (entire) domain that has only coarse‐grained points and does not need a mesh or grid. The special functions obtained in the first step are used in interpolating the dependent‐variable distribution in the global domain. Additionally, the SDM can enhance analytical precision and resolution when analyzing both homogeneous and heterogeneous fields. Our previous manuscript gave numerical examples of the application of the method to scalar temperature fields. To investigate the feasibility of the analysis of vector fields, the SDM technique is applied in linear elastic analysis of heterogeneous materials in the present study. The SDM's global models with only a few hundred points gave shear locking‐free and hourglass‐free solutions at the same level of accuracy as solutions obtained from conventional finite element analysis using hundreds of thousands of node points or more. Copyright © 2015 John Wiley & Sons, Ltd.

A semiautomatic method for in vivo three-dimensional quantitative analysis of fascial layers mobility based on 3D ultrasound scans.

Recently, there has been an increasing interest in the role of deep fascia mobility in musculoskeletal dynamics and chronic pain mechanisms; however, no strategies have been presented so far to study in vivo fascial motion in 3D. This paper presents a semiautomatic method, based on ultrasound (US) imaging, enabling a 3D evaluation of fascia mobility. The proposed approach relies on the acquisition of 3D US datasets at rest and during a voluntary muscular contraction and consists of two phases: 3D US dataset analysis and generation of a displacement vector field using a block matching technique (Phase 1) and validation and filtering of the resulting displacement vector field for outliers removal (Phase 2). The accuracy and effectiveness of the proposed method were preliminarily tested on different 3D US datasets, undergoing either simulated (procedural) or real (muscular contraction) deformations. As for the simulated deformation, estimated displacement vectors resulting from Phase 1 presented a mean magnitude percentage error of 8.05 % and a mean angular error of 4.78° which, after Phase 2, were reduced by 69.44 and by 83.05 %, respectively. Tests on real deformations further validated the effectiveness of Phase 2 in the removal of outliers from the displacement vector field. Obtained results preliminarily demonstrate the viability of the proposed algorithm for the analysis of fascia mobility. Such analysis can enable clinicians to better understand the fascia role in musculoskeletal dynamics and disorder. Further experiments are needed to optimize the method in consideration of the anatomical region to be studied.

BIVARIATE QUANTILE INTERPOLATION FOR ENSEMBLE DERIVED PROBABILITY DENSITY ESTIMATES

Probability distribution functions (PDFs) may be estimated from members in an ensemble. For an ensemble of 2D vector fields, this results in a bivariate PDF at each location in the field. Vector field analysis and visualization, e.g., stream line calculation, require an interpolation to be defined over these 2D density estimates. Thus, a nonparametric PDF interpolation must advect features as opposed to cross-fading them, where arbitrary modalities in the distribution can be introduced. This is already achieved for 1D PDF interpolation via inverse cumulative distribution functions (CDFs). However, there is no closed-form extension to bivariate PDF. This paper presents one such direct extension of the 1D closed-form solution for bivariates. We show an example of physically coupled components (velocity) and correlated random variables. Our method does not require a complex implementation or expensive computation as does displacement interpolation Bonneel et al., ACM Trans. Graphics (TOG), 30(6):158, 2011. Additionally, our method does not suffer from ambiguous pair-wise linear interpolants, as does Gaussian Mixture Model Interpolation.

A Chargeless Complex Vector Matter Field in Supersymmetric Scenario

We construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two nochiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms into matter fields by a globalU1gauge symmetry. For the aim of dealing with consistent terms without breaking the globalU1symmetry we imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminates the extra degrees of freedom which is consistent with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca’s type field for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the first steps to extend the analysis of charged massive vector field in a supersymmetric scenario.

Statistical Parametric Mapping (SPM) for alpha-based statistical analyses of multi-muscle EMG time-series

Multi-muscle EMG time-series are highly correlated and time dependent yet traditional statistical analysis of scalars from an EMG time-series fails to account for such dependencies. This paper promotes the use of SPM vector-field analysis for the generalised analysis of EMG time-series. We reanalysed a publicly available dataset of Young versus Adult EMG gait data to contrast scalar and SPM vector-field analysis. Independent scalar analyses of EMG data between 35% and 45% stance phase showed no statistical differences between the Young and Adult groups. SPM vector-field analysis did however identify statistical differences within this time period. As scalar analysis failed to consider the multi-muscle and time dependence of the EMG time-series it exhibited Type II error. SPM vector-field analysis on the other hand accounts for both dependencies whilst tightly controlling for Type I and Type II error making it highly applicable to EMG data analysis. Additionally SPM vector-field analysis is generalizable to linear and non-linear parametric and non-parametric statistical models, allowing its use under constraints that are common to electromyography and kinesiology.

Digital reconstruction of high-quality daily 4D cone-beam CT images using prior knowledge of anatomy and respiratory motion

Conventional in-room cone-beam computed tomography (CBCT) lacks explicit representation of patient respiratory motion and usually has poor image quality and inaccurate CT numbers for target delineation and/or adaptive treatment planning. In-room four-dimensional (4D) CBCT image acquisition is still time consuming and suffers the same issue of poor image quality. To overcome this limitation, we developed a computational framework to digitally synthesize high-quality daily 4D CBCT images using the prior knowledge of motion and appearance learned from the planning 4D CT dataset. A patient-specific respiratory motion model was first constructed from the planning 4D CT images using principal component analysis of displacement vector fields across different respiratory phases. Subsequently, the respiratory motion model as well as the image content of the planning CT was spatially mapped onto the daily CBCT using deformable image registration. The synthesized 4D images possess explicit patient motion while maintaining the geometric accuracy of patient's anatomy at the time of treatment. We validated our model by quantitatively comparing the synthesized 4D CBCT against the 4D CT dataset acquired in the same day from protocol patients undergoing daily in-room CBCT setup and weekly 4D CT for treatment evaluation. Our preliminary results have demonstrated good agreement of contours in different motion phases between the synthesized and acquired scans. Various imaging artifacts were also suppressed and soft-tissue visibility was enhanced.

Development and validation of a fully automated system for detection and diagnosis of mammographic lesions.

We present a comprehensive and fully automated system for computer-aided detection and diagnosis of masses in mammograms. Novel methods for detection include: selection of suspicious focal areas based on analysis of the gradient vector field, rejection of oriented components of breast tissue using multidirectional Gabor filtering, and use of differential features for rejection of false positives (FPs) via clustering of the surrounding fibroglandular tissue. The diagnosis step is based on extraction of contour-independent features for characterization of lesions as benign or malignant from automatically detected circular and annular regions. A new unified 3D free-response receiver operating characteristic framework is introduced for global analysis of two binary categorization problems in cascade. In total, 3,080 suspicious focal areas were extracted from a set of 156 full-field digital mammograms, including 26 malignant tumors, 120 benign lesions, and 18 normal mammograms. The proposed system detected and diagnosed malignant tumors with a sensitivity of 0.96, 0.92, and 0.88 at, respectively, 1.83, 0.46, and 0.45 FPs/image, with two stages of stepwise logistic regression for selection of features, a cascade of Fisher linear discriminant analysis and an artificial neural network with radial basis functions, and leave-one-patient-out cross-validation.

QT-AIM analysis of neutral pterin and its anionic and cationic forms

Abstract Quantum theory of atoms in molecules (QT-AIM) allows detailed insight into the electronic structure of molecules by analysis of the gradient vector field of the electronic density distribution function. First results of a QT-AIM analysis of neutral pterin as well as its anionic and cationic forms in aqueous solution are reported based on density functional theory using B3LYP/6–311+G(2d,p)//6–31G(d) level of theory. Besides reporting QT-AIM results of the atomic partial charges and bond orders of the molecules, their electron density functions, Laplacians and electrostatic potential functions are also shown. The results demonstrate the rather extensive delocalization of both negative and positive extra charges predominantly over the pyrimidine moiety of the pterin ring system and allow a precise quantitation of the effects of addition or elimination of a proton on the bonding structure. Quantum chemical techniques in combination with QT-AIM procedures are thus well-suited to describing the bonding structure as well as the major atomic and bonding features of neutral pterin and its cationic and anionic forms. Moreover, the data demonstrate that the chosen level of theory yields chemically reasonable results while not being computationally too expensive, thus providing a sound basis for further theoretical chemical work on pteridines.

Cubature methods for stochastic (partial) differential equations in weighted spaces

The cubature on Wiener space method, a high-order weak approximation scheme, is established for SPDEs in the case of unbounded characteristics and unbounded test functions. We first describe a recently introduced flexible functional analytic framework, so called weighted spaces, where Feller-like properties hold. A refined analysis of vector fields on weighted spaces then yields optimal convergence rates of cubature methods for stochastic partial differential equations of Da Prato–Zabczyk type. The ubiquitous stability for the local approximation operator within the functional analytic setting is proved for SPDEs, however, in the infinite dimensional case we need a newly introduced technical assumption on weak symmetry of the cubature formula. Computational results for a cubature discretization of a spatially extended stochastic FitzHugh–Nagumo model, an SPDE model from mathematical biology, are shown, illustrating the applicability of our theory.

Clifford algebra-based structure filtering analysis for geophysical vector fields

Abstract. A new Clifford algebra-based vector field filtering method, which combines amplitude similarity and direction difference synchronously, is proposed. Firstly, a modified correlation product is defined by combining the amplitude similarity and direction difference. Then, a structure filtering algorithm is constructed based on the modified correlation product. With custom template and thresholds applied to the modulus and directional fields independently, our approach can reveal not only the modulus similarities but also the classification of the angular distribution. Experiments on exploring the tempo-spatial evolution of the 2002–2003 El Niño from the global wind data field are used to test the algorithm. The results suggest that both the modulus similarity and directional information given by our approach can reveal the different stages and dominate factors of the process of the El Niño evolution. Additional information such as the directional stability of the El Niño can also be extracted. All the above suggest our method can provide a new powerful and applicable tool for geophysical vector field analysis.

Vector field statistical analysis of kinematic and force trajectories

When investigating the dynamics of three-dimensional multi-body biomechanical systems it is often difficult to derive spatiotemporally directed predictions regarding experimentally induced effects. A paradigm of ‘non-directed’ hypothesis testing has emerged in the literature as a result. Non-directed analyses typically consist of ad hoc scalar extraction, an approach which substantially simplifies the original, highly multivariate datasets (many time points, many vector components). This paper describes a commensurately multivariate method as an alternative to scalar extraction. The method, called ‘statistical parametric mapping’ (SPM), uses random field theory to objectively identify field regions which co-vary significantly with the experimental design. We compared SPM to scalar extraction by re-analyzing three publicly available datasets: 3D knee kinematics, a ten-muscle force system, and 3D ground reaction forces. Scalar extraction was found to bias the analyses of all three datasets by failing to consider sufficient portions of the dataset, and/or by failing to consider covariance amongst vector components. SPM overcame both problems by conducting hypothesis testing at the (massively multivariate) vector trajectory level, with random field corrections simultaneously accounting for temporal correlation and vector covariance. While SPM has been widely demonstrated to be effective for analyzing 3D scalar fields, the current results are the first to demonstrate its effectiveness for 1D vector field analysis. It was concluded that SPM offers a generalized, statistically comprehensive solution to scalar extraction's over-simplification of vector trajectories, thereby making it useful for objectively guiding analyses of complex biomechanical systems.

TU‐A‐WAB‐08: Strong Evidence for Physiologic Correlation of 4D‐CT Ventilation Imaging with Respiratory‐Correlated Gallium 68 PET/CT in Humans

Purpose: Four‐dimensional CT (4D‐CT) ventilation imaging has been developed as a complement to nuclear medicine (NM) based methods, but has not yet been validated against a quantitative NM based standard. We are performing the first such study with positron emission tomography using 68 Ga‐labelled nanoparticles (Galli‐PET). Methods: Respiratory correlated Galli‐PET ventilation images are obtained for 10 lung cancer patients using a combined PET/CT scanner with Real‐time Position Management system. We begin by calculating the exhale‐to‐inhale 4D‐CT ventilation image (V) by deformably registering the 4D‐CT maximal inhale phase to the maximal exhale phase, and performing quantitative analysis of the deformation vector fields (DVFs). We then simulate a motion‐blurred or time‐integrated 4D‐CT ventilation image. This facilitates comparison with time‐integrated Galli‐PET, which exhibits better signal than for gated images. We study the correlation of V with gated Galli‐PET at exhale, and between time‐integrated 4D‐CT and Galli‐PET ventilation using four distinct ventilation metrics. Ventilation images were compared using the voxel‐wise spearman correlation (r) within the segmented lung volumes, and dice similarity (d) for the lowest functioning (25th percentile) regions of interest. Results: Averaged over the ten patients and four ventilation metrics in this study, the comparison of V with gated Galli‐PET yielded r = 0.38 and d = 0.40. Time‐integrated images exhibited better agreement for all ventilation metrics, yielding r = 0.53 and d = 0.60 on average. Conclusion: Our results demonstrate moderate correlation between 4D‐CT and NM‐based ventilation images. The comparison between time‐integrated images gives better agreement than for gated images as a Result of the improved Galli‐PET signal. Further validation of 4D‐CT ventilation imaging could facilitate improved access to functional lung imaging and functional lung avoidance in radiotherapy. This work is supported by an NHMRC Australia Fellowship, NHMRC project grant 1034060 and US NCI P01CA116602.

WE‐C‐WAB‐04: Comparison of 4D‐CT Ventilation Imaging with SPECT Ventilation Imaging for Thoracic Cancer Patients

Purpose: A novel lung ventilation imaging technique based on 4D‐CT can be used for functional avoidance to spare high‐functional lung regions, and early prediction or assessment of pulmonary toxicity in radiotherapy. However, there has been minimal validation showing inconsistent results in human subjects. The purpose of this study was to compare 4D‐CT ventilation images with SPECT ventilation images as clinical reference. Methods: In an IRB‐approved clinical trial, 4D‐CT ventilation and SPECT ventilation images were acquired in the supine position for 12 thoracic cancer patients. 4D‐CT ventilation was calculated by deformable image registration of 4D‐CT images, followed by analysis of the resultant displacement vector field to quantify regional volume change (Jacobian), a surrogate for ventilation. SPECT ventilation scans were performed by inhalation of 99mTc‐DTPA aerosols. We evaluated the physiologic accuracy of 4D‐CT ventilation by: (1) comparing 4D‐CT ventilation values in SPECT ventilation defect regions with those in non‐defect regions; (2) quantifying Dice similarity coefficients (DSCs) for the spatial overlap of low‐functional lung regions determined by 4D‐CT ventilation and SPECT ventilation; (3) comparing a ventral‐to‐dorsal gradient of 4D‐CT ventilation with that of SPECT ventilation. Results: Five patients showed severe depositions of SPECT DTPA aerosols in central airways, and hence were excluded from the analysis. The 4D‐CT ventilation value in SPECT ventilation defect regions was found to be significantly lower than that in non‐defect regions (0.14±0.06 vs. 0.19±0.07, p=0.01). The DSC for the spatial overlap of low‐functional lung regions was weak (0.29±0.11). 4D‐CT ventilation demonstrated a ventral‐to‐dorsal gravitational gradient, which was consistent with SPECT ventilation. Conclusion: A 12‐patient study demonstrated reasonable correlations between 4D‐CT ventilation and SPECT ventilation as clinical reference, indicating the potential for 4D‐CT ventilation imaging to achieve high physiologic accuracy. However, poor DSCs suggest the need for further studies to improve 4D‐CT ventilation imaging and/or a validation study design. National Lung Cancer Partnership Young Investigator Research Grant; NIH/NCI 2 R01 CA 093626