Ellipse Parameters Research Articles

A note on evaluating model tidal currents against observations

The root-mean-square magnitude of the vector difference between modeled and observed tidal ellipses is a comprehensive metric to evaluate the representation of tidal currents in ocean models. A practical expression for this difference is given in terms of the harmonic constants that are routinely used to specify current ellipses for a given tidal constituent. The resulting metric is sensitive to differences in all four current ellipse parameters, including phase.

Characterization of Color Images with Multiscale Monogenic Maxima.

Can we build a feature-based analysis that fully characterizes images? The literature answers with edge-based reconstruction methods inspired by Marr's paradigm but limited to the greyscale case. This paper studies the color case. A new sparse representation is carried out with the monogenic concept and the Mallat-Zhong wavelet maxima method. Our monogenic maxima provide efficient contour shape and color characterization, as a sparse set of local features including amplitude, phase, orientation and ellipse parameters. This rich description takes the wavelet maxima representation further towards the wide topic of keypoint analysis. We propose a reconstruction process that retrieves the image from its monogenic maxima. While known works all rely on constrained optimization, implying an iterative use of the filterbank, we propose to interpolate the data in the feature domain by exploiting the visual knowledge from the feature-set. This direct retrieval is accurate enough so that no iteration is required. The main question is finally answered with comparative experiments. It is shown that a reasonably small amount of features is sufficiently informative for visually appealing image retrieval. The features appear numerically stable to rotation, and can be intuitively simplified to perform image regularization.

Results from a triple chord stellar occultation and far-infrared photometry of the trans-Neptunian object (229762) 2007 UK126

A stellar occultation by a trans-Neptunian object (TNO) provides an opportunity to probe its size and shape. Very few occultations by TNOs have been sampled simultaneously from multiple locations, while a robust estimation of shadow size has been possible for only two objects. We present the first observation of an occultation by the TNO 2007 UK126 on 15 November 2014, measured by three observers, one nearly on and two almost symmetrical to the shadow's centerline. This is the first multi-chord dataset obtained for a so-called detached object, a TNO subgroup with perihelion distances so large that the giant planets have likely not perturbed their orbits. We revisit Herschel/PACS far-infrared data, applying a new reduction method to improve the accuracy of the measured fluxes. Combining both datasets allows us to comprehensively characterize 2007 UK126. We use error-in-variable regression to solve the non-linear problem of propagating timing errors into uncertainties of the ellipse parameters. Based on the shadow's size and a previously reported rotation period, we expect a shape of a Maclaurin spheroid and derive a geometrically plausible size range. To refine our size estimate of 2007 UK126, we model its thermal emission using a thermophysical model code. We conduct a parametric study to predict far-infrared fluxes and compare them to the Herschel/PACS measurements. The favorable geometry of our occultation chords, combined with minimal dead-time imaging, and precise GPS time measurements, allow for an accurate estimation of the shadow size (best-fitting ellipse with axes 645.80 $\pm$ 5.68 km $\times$ 597.81 $\pm$ 12.74 km) and the visual geometric albedo (15.0 $\pm$ 1.6 %). By combining our analyses of the occultation and the far-infrared data, we can constrain the effective diameter of 2007 UK126 to 599 - 629 km. We conclude that subsolar surface temperatures are $\approx$ 50 - 55 K.

A robust interpolation procedure for producing tidal current ellipse inputs for regional and coastal ocean numerical models

Regional and/or coastal ocean models can use tidal current harmonic forcing, together with tidal harmonic forcing along open boundaries in order to successfully simulate tides and tidal currents. These inputs can be freely generated using online open-access data, but the data produced are not always at the resolution required for regional or coastal models. Subsequent interpolation procedures can produce tidal current forcing data errors for parts of the world’s coastal ocean where tidal ellipse inclinations and phases move across the invisible mathematical “boundaries” between 359° and 0° degrees (or 179° and 0°). In nature, such “boundaries” are in fact smooth transitions, but if these mathematical “boundaries” are not treated correctly during interpolation, they can produce inaccurate input data and hamper the accurate simulation of tidal currents in regional and coastal ocean models. These avoidable errors arise due to procedural shortcomings involving vector embodiment problems (i.e., how a vector is represented mathematically, for example as velocities or as coordinates). Automated solutions for producing correct tidal ellipse parameter input data are possible if a series of steps are followed correctly, including the use of Cartesian coordinates during interpolation. This note comprises the first published description of scenarios where tidal ellipse parameter interpolation errors can arise, and of a procedure to successfully avoid these errors when generating tidal inputs for regional and/or coastal ocean numerical models. We explain how a straightforward sequence of data production, format conversion, interpolation, and format reconversion steps may be used to check for the potential occurrence and avoidance of tidal ellipse interpolation and phase errors. This sequence is demonstrated via a case study of the M2 tidal constituent in the seas around Korea but is designed to be universally applicable. We also recommend employing tidal ellipse parameter calculation methods that avoid the use of Foreman’s (1978) “northern semi-major axis convention” since, as revealed in our analysis, this commonly used conversion can result in inclination interpolation errors even when Cartesian coordinate-based “vector embodiment” solutions are employed.

Conversion relationships between several parameter groups of completely polarized electromagnetic waves

It is known that polarization as the third characteristic of electromagnetic waves plays substantial roles which are comparable with the wave amplitude and phase, in describing the tempo and spatial properties of electromagnetic waves. Various parameter groups for characterizing the polarization state of electromagnetic waves with different initial states and boundary conditions have been proposed. However, a full-scale set of conversion relationships between these parameter groups with specific initial phases is not yet available. In this work, the initial phases as additional parameters for the orthogonal linear polarization and the polarization ellipse parameter groups and the digitized elliptical angle ' as a complementary parameter to the polarization ellipse parameter group are taken into account respectively. Consequently, a full-scale set of conversion relationships between these parameter groups has been rigorously derived out. The validity of these conversion relationships are confirmed by the numerical calculations in terms of mathematical completeness and one-to-one correspondence. These conversion relationships make the tedious computation of the wave polarization much simpler and straightforward, benefiting practical implementation of the polarization theory of electromagnetic waves.

Ellipse fitting via low-rank generalized multidimensional scaling matrix recovery

This paper develops a novel ellipse fitting algorithm by recovering a low-rank generalized multidimensional scaling (GMDS) matrix. The main contributions of this paper are: i) Based on the derived Givens transform-like ellipse equation, we construct a GMDS matrix characterized by three unknown auxiliary parameters (UAPs), which are functions of several ellipse parameters; ii) Since the GMDS matrix will have low rank when the UAPs are correctly determined, its recovery and the estimation of UAPs are formulated as a rank minimization problem. We then apply the alternating direction method of multipliers as the solver; iii) By utilizing the fact that the noise subspace of the GMDS matrix is orthogonal to the corresponding manifold, we determine the remaining ellipse parameters by solving a specially designed least squares problem. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed algorithm.

Imaging and structural feature decomposition of a complex target using multi-aspect polarimetric scattering

Based on the Huynen parametric decomposition of target scattering matrix, the polarimetric ellipse parameters are transformed and applied to decomposition of scattering mechanisms of a complex target in VHR POL-SAR images (very high resolution, polarimetric synthetic aperture radar). Making use of multi-aspect (or circle-aspect) and wideband VHR POL-SAR images, scattering mechanisms of a volumetric target and its structural components are recognized over image pixels. Utilizing the layover features, the target height profile is also estimated from two-dimensional image. As example, polarimetric scattering data of some vehicles on ground, including multi-aspect simulated data and experimental measurements, are applied to validations of scattering mechanism decompositions and target structural feature recognition.

Fast ellipse detection based on three point algorithm with edge angle information

In this paper, we introduce a fast ellipse detection method that uses the geometric properties of three points on an ellipse. Many conventional ellipse detection methods carry out detection using five points, but a random selection of such points among candidate edges requires much redundant processing. To search for an ellipse with the minimum number of points, this study used the normal and differential equations of an ellipse, which requires three points based on their locations and edge angles. First, to reduce the number of candidate edges, the edges were divided into 8 groups depending on the edge angle, and then a new geometric constraint called the quadrant condition was introduced to reduce noisy candidate edges. Clustering was employed to find prominent candidates in the space of a few ellipse parameters. Experiments using many real images showed that the proposed method satisfies both reliability and computing speed for ellipse detection.

Tide, Wind, and River Forcing of the Surface Currents in the Fraser River Plume

ABSTRACTA long-term record of surface currents from a high-frequency radar system, along with near-surface hydrographic transects, moored current meter records, and satellite imagery, are analyzed to determine the relative importance of river discharge, wind, and tides in driving the surface flow in the Fraser River plume. The observations show a great deal of oceanographic and instrumental variability. However, averaged quantities yielded robust results. The effect of river flow, which determines buoyancy and inertia near the river mouth, was found by taking a long-term average. The resulting flow field was dominated by a jet with two asymmetric gyres; the anticyclonic gyre to the north had flow speeds consistent with geostrophy. The mean flow speed near the river mouth was 14.3 cm s–1, while the flow further afield was 5 cm s–1 or less. Wind stress and surface currents were highly coherent in the subtidal frequency band. Northwesterly winds drive a surface flow to the southeast at speeds of nearly 30 cm s–1. Southeasterly winds drive a surface flow to the northwest at speeds reaching 20 cm s–1; however, there is more spatial variability in speed and direction relative to the northwesterly wind case. A harmonic analysis was used to extract the tidally driven flows. Ellipse parameters for the major tidal constituents varied considerably in both alignment and aspect ratio over the radar domain, in direct contrast to a barotropic model which predicted rectilinear flow along the Strait of Georgia. This is a result of water filling and draining the shallow mud flats north of the Fraser's main channel. The M2 velocities at the surface were also weaker than their barotropic counterparts. However, the shallow water constituent MK3 was enhanced at the surface and nearly as strong as the mean flow, implying that non-linear interactions are important to surface dynamics.

Balance of Isotropic and Directed Forces Determines Cell Shape

The shape of a cell membrane is largely defined by the underlying actin cytoskeleton and membrane mechanics. The actin cytoskeleton asserts contractile forces on the membrane that can be divided in isotropic and directed forces. We present a theory which is an extension of the Young-Laplace equation. It models cell edges as parts of one uniform ellipse, which changes from cell to cell. The ellipse parameters are characterized by the ratio of isotropic to directed contractility of the cell. We demonstrate the capabilities of this model using fibroblasts seeded on an elastic micro-pillar array. In this way adhesion forces exerted by the cell at single adhesion sites are measured. We show that isotropic and directed forces balance the line tension in cortical actin. Furthermore, for cells with homogeneous contractile forces and a single orientation of stress-fibers any part of the cell edge follows a universal ellipse, enabling us to calculate the magnitude of isotropic and directed contractility in a single cell. We show that in 3T3 fibroblasts the directed contractility is about three times as strong as the isotropic contractility. If myosin motors are inhibited, however, directed contractility decreases, effectively disabling forces generated by stress-fibers, and the elliptical cell cortex turns into a circular shape predicted for an isotropic contractile cytoskeleton. Our analysis shows that a simple two-parameter model explains polarity, shape of the cell cortex and cellular forces as experimentally observed. Potentially this model can be used to predict stresses and forces on the extracellular matrix and tissue.

The Impact of the Severity of Knee Osteoarthritis on the Postural Stability

Knee osteoarthritis is one of the most widespread orthopedic diseases among elderly people. Biomechanical effects of this disorder are widely studied. In case of very intense knee osteoarthritis, typical measurements such as gait analysis are no longer possible. On the other hand stance tests can be performed even in these very severe cases. In our research, the biomechanical effects of knee osteoarthritis on postural stability in respect to the degree of abrasion were studied. The participants were divided into two groups according to the degree of osteoarthritis on Kellgren-Lawrence scale (KL3 and KL4+). The load distribution was measured during 30seconds long bipedal stance. Load distribution between the affected and non-affected leg was determined. From measured parameters the coordinates of the center of pressure (COP) and the axes’ length and area of the 95% confidence ellipse of COP are also calculated. It was found that the confidence ellipse parameters are significantly increasing in respect to the severity of osteoarthritis which means the deterioration of osteoarthritis causes worsening the balancing capability. It could be established, the affected leg is less loaded compared to the healthy leg in both groups.

The influence of the droplet clouds microstructure on the polarization characteristics of a double scattering lidar signal

The results of calculation of the ratio of polarization degrees of the double scattering lidar return from droplet clouds with different microstructure at sensing by circularly and linearly polarized radiation are given in this report. The influence of the droplet size on ellipse parameters of linearly polarized radiation are discussed.

Empirical Stochastic Modeling of Multipath Polarizations in Indoor Propagation Scenarios

In this contribution, a stochastic modeling approach is proposed for characterizing the polarization status of multipath components (MPCs) in propagation channels. The $2 \times 2$ polarization matrix of each MPC is represented by the geometrical parameters of two ellipses, i.e., the ovality, tilt angle, and size of each ellipse, as well as the rotating direction of electric field intensity along the ellipse. The statistics of these parameters including correlation behaviors among them extracted from measurement data constitute the stochastic polarization model for the propagation scenario of interest. Analytical expressions are presented for the transformation from the ellipse parameters to the $2 \times 2$ polarization matrix, and vice versa. Comparing with conventional polarization models addressing merely the cross-polarization ratios, the new model provides a more complete description for the per-path polarizations in terms of the power imbalance, tilting, and polarization spread. Furthermore, based on multiple-input multiple-output channel measurement data collected with 100-MHz bandwidth and at the center frequency of 5.25 GHz, stochastic polarization models of the proposed structure are extracted for five indoor scenarios. These models are complementary to the existing geometry-based stochastic channel models for generating realistic polarization matrices for MPCs.

Reliable pose estimation of underwater dock using single camera: a scene invariant approach

It is well known that docking of Autonomous Underwater Vehicle (AUV) provides scope to perform long duration deep-sea exploration. A large amount of literature is available on vision-based docking which exploit mechanical design, colored markers to estimate the pose of a docking station. In this work, we propose a method to estimate the relative pose of a circular-shaped docking station (arranged with LED lights on periphery) up to five degrees of freedom (5-DOF, neglecting roll effect). Generally, extraction of light markers from underwater images is based on fixed/adaptive choice of threshold, followed by mass moment-based computation of individual markers as well as center of the dock. Novelty of our work is the proposed highly effective scene invariant histogram-based adaptive thresholding scheme (HATS) which reliably extracts positions of light sources seen in active marker images. As the perspective projection of a circle features a family of ellipses, we then fit an appropriate ellipse for the markers and subsequently use the ellipse parameters to estimate the pose of a circular docking station with the help of a well-known method in Safaee-Rad et al. (IEEE Trans Robot Autom 8(5):624---640, 1992). We analyze the effectiveness of HATS as well as proposed approach through simulations and experimentation. We also compare performance of targeted curvature-based pose estimation with a non-iterative efficient perspective-n-point (EPnP) method. The paper ends with a few interesting remarks on vantages with ellipse fitting for markers and utility of proposed method in case of non-detection of all the light markers.

Elliptical Monogenic Wavelets for the Analysis and Processing of Color Images

This paper studies and gives new algorithms for image processing based on monogenic wavelets. Existing greyscale monogenic filterbanks are reviewed and we reveal a lack of discussion about the synthesis part. The monogenic synthesis is therefore defined from the idea of wavelet modulation, and an innovative filterbank is constructed by using the Radon transform. The color extension is then investigated. First, the elliptical Fourier atom model is proposed to generalize the analytic signal representation for vector-valued signals. Then, a color Riesz-transform is defined so as to construct color elliptical monogenic wavelets. Our Radon-based monogenic filterbank can be easily extended to color according to this definition. The proposed wavelet representation provides efficient analysis of local features in terms of shape and color, thanks to the concepts of amplitude, phase, orientation, and ellipse parameters. The synthesis from local features is deeply studied. We conclude the paper by defining the color local frequency, proposing an estimation algorithm.

Controlling the Twin Wire Arc Spray Process Using Artificial Neural Networks (ANN)

One approach for controlling the twin wire arc spray process is to use optical properties of the particle beam as input parameters for a process control. The idea is that changes in the process like eroded contact nozzles or variations of current, voltage, and/or atomizing gas pressure may be detected through observation of the particle beam. It can be assumed that if these properties deviate significantly from those obtained from a beam recorded for an optimal coating process, the spray particle and thus the coating properties change significantly. The goal is to detect these deviations and compensate the occurring errors by adjusting appropriate process parameters for the wire arc spray unit. One method for monitoring optical properties is to apply the diagnostic system particle flux imaging (PFI): PFI fits an ellipse to an image of a particle beam thereby defining easy to analyze characteristical parameters by relating optical beam properties to ellipse parameters. Using artificial neural networks (ANN), mathematical relations between ellipse and process parameters can be defined. It will be shown that in the case of a process disturbance through the use of an ANN-based control new process parameters can be computed to compensate particle beam deviations.

Semidiurnal Baroclinic Tides on the Central Oregon Inner Shelf

AbstractSemidiurnal velocity and density oscillations are examined over the mid- and inner continental shelf near Heceta Bank on the Oregon coast. Measurements from two long-term observation networks with sites on and off the submarine bank reveal that both baroclinic velocities and displacements are dominated by the first mode, with larger velocities on the midshelf and northern parts of the bank. Midshelf sites have current ellipses that are near the theoretical value for single, progressive internal tidal waves compared to more linearly polarized currents over the inner shelf. Baroclinic current variability is not correlated to the spring–neap cycle and is uncorrelated between mooring locations. An idealized model of two internal waves propagating from different directions reproduces some of the observed variability in semidiurnal ellipse parameters. At times, the phasing between moorings along a cross-shelf transect are consistent with onshelf wave propagation, a characteristic also present in the output of a three-dimensional regional circulation model. Regional wind-driven upwelling/downwelling influences stratification at all shelf moorings. At locations north of the bank, stronger baroclinic velocities were found during periods of higher background stratification.

Measurement of needle susceptibility artifacts in magnetic resonance images

Abstract The success of minimally invasive procedures under MR-guidance can be increased by the knowledge of the current needle pose. We hypothesize that a one-toone mapping exists between the needle orientation with respect to the static magnetic field and the cross-sectional shape of the needle’s susceptibility artifact. For this purpose, we derived a mathematical model, which describes the cross sectional geometry of the needle artifact. It is approximated by two ellipses. Certain parameters of these ellipses can be utilized for mapping the geometry of the needle artifact onto the needle orientation. The relation between the two ellipse parameters α (inclination of the semi-major axis) and b (length of the semi-minor axis) and the needle’s azimuth angle can be approximated by linear regression in a certain angle interval. A combination of these two ellipse parameters is suitable for estimating the needle’s azimuth angle within a range between 0° and 60°.

Robust Ellipse Fitting via Half-Quadratic and Semidefinite Relaxation Optimization.

Ellipse fitting is widely applied in the fields of computer vision and automatic manufacture. However, the introduced edge point errors (especially outliers) from image edge detection will cause severe performance degradation of the subsequent ellipse fitting procedure. To alleviate the influence of outliers, we develop a robust ellipse fitting method in this paper. The main contributions of this paper are as follows. First, to be robust against the outliers, we introduce the maximum correntropy criterion into the constrained least-square (CLS) ellipse fitting method, and apply the half-quadratic optimization algorithm to solve the nonlinear and nonconvex problem in an alternate manner. Second, to ensure that the obtained solution is related to an ellipse, we introduce a special quadratic equality constraint into the aforementioned CLS model, which results in the nonconvex quadratically constrained quadratic programming problem. Finally, we derive the semidefinite relaxation version of the aforementioned problem in terms of the trace operator and thus determine the ellipse parameters using semidefinite programming. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.

Geometric design and simulation of tooth profile using elliptical segments as its line of action

A mathematical model of gear tooth profiles using the ellipse curve, whose curvature is convenient to control by changing the mathematical parameters as its line of action, was built based on the meshing theory. The equation of undercutting condition was derived from the model. A special epicycloidal tooth profile was also presented. An example gear drive with variation of the ellipse parameters was taken to illustrate the proposed method. The contact ratio of the gear drive designed by the proposed method was analyzed. A comparison of the property of the gear drive designed with the involute gear drive was also carried out. The results confirm that the proposed gear drive has higher contact ratio in comparison with the involute gear drive.