Elliptical Fitting Research Articles

Physical properties of trans-Neptunian object (143707) 2003 UY117 derived from stellar occultation and photometric observations

Context. Trans-Neptunian objects (TNOs) are considered to be among the most primitive objects in our Solar System. Knowledge of their primary physical properties is essential for understanding their origin and the evolution of the outer Solar System. In this context, stellar occultations are a powerful and sensitive technique for studying these distant and faint objects. Aims. We aim to obtain the size, shape, absolute magnitude, and geometric albedo for TNO (143707) 2003 UY117. Methods. We predicted a stellar occultation by this TNO for 2020 October 23 UT and ran a specific campaign to investigate this event. We derived the projected profile shape and size from the occultation observations by means of an elliptical fit to the occultation chords. We also performed photometric observations of (143707) 2003 UY117 to obtain the absolute magnitude and the rotational period from the observed rotational light curve. Finally, we combined these results to derive the three-dimensional shape, volume-equivalent diameter, and geometric albedo for this TNO. Results. From the stellar occultation, we obtained a projected ellipse with axes of (282 ± 18) × (184 ± 32) km. The area-equivalent diameter for this ellipse is Deq,A = 228 ± 21 km. From our photometric R band observations, we derived an absolute magnitude of HV = 5.97 ± 0.07 mag using V − R = 0.46 ± 0.07 mag, which was derived from a V band subset of these data. The rotational light curve has a peak-to-valley amplitude of ∆m = 0.36 ± 0.13 mag. We find the most likely rotation period to be P = 12.376 ± 0.0033 hours. By combining the occultation with the rotational light curve results and assuming a triaxial ellipsoid, we derived axes of a × b × c = (332 ± 24) km × (216 ± 24) km × (180−24+28) km for this ellipsoid, and therefore a volume-equivalent diameter of Deq,V = 235 ± 25 km. Finally, the values for the absolute magnitude and for the area-equivalent diameter yield a geometric albedo of pV = 0.139 ± 0.027.

Speed planning and interpolation algorithm of high-speed NURBS curve based on an elliptical arc fitting

Speed planning and interpolation algorithm of high-speed NURBS curve based on an elliptical arc fitting

Study on Effect of Scaling and Anisotropy on Roughness of Natural Fractured Rock Surfaces

In the modified formula for the cubic law, the roughness correction coefficient C serves as a parameter that indicates the characteristics of the roughness of a rock’s surface. In this study, surface data for natural rock samples were acquired through high-precision 3D scanning and combined with publicly accessible CT scan data on rough rock fractures to generate spatial coordinates. The roughness correction coefficient C was calculated and analyzed using both formulaic and numerical methods. The analysis revealed significant effects of scale on the roughness correction coefficient for rock fractures within a size range of 5 to 10 cm (determined based on the actual sample size), with tensile fractures demonstrating greater variations compared to shear fractures. When calculating the roughness correction coefficient on the same fracture surface in different directions, significant directional effects were observed. Furthermore, elliptical fitting demonstrated favorable results. The conclusion drawn was that the roughness correction coefficient for fracture surfaces can be represented effectively using a tensor form, thereby simplifying the expression of directionality. Calculating and analyzing the fractal dimension of a rough surface further confirmed the existence of effects of size on roughness.

Geometrical misalignment-induced nonlinear error in homodyne interferometers

This paper discusses the generation of a novel periodic nonlinear error in homodyne interferometers due to geometric misalignments. These misalignments arise from cumulative assembly errors among the sensor head interior, target mirror, test platform, and detector, leading to dynamic misplacement of the measurement beam on the detector's surface. A physical model was developed to explain this error, focusing on the interference field produced by Gaussian beams under conditions of beam separation and inclined interference. Observations from misaligned setups revealed a strong correlation between the modulation of the interference signal by an envelope curve and the distorted, complex patterns of Lissajous figures, with the movement of the target mirror. Numerical simulations and experimental results demonstrated that segmented elliptical fitting effectively calibrates vortex trajectories and substantially reduces periodic nonlinear errors. However, numerical simulations also uncovered previously undetected picometer-scale second-order nonlinear errors due to the geometric misalignments. This research highlights the physical mechanisms behind new nonlinear errors, emphasizing their importance in advancing homodyne interferometers toward picometer-level accuracy.

Antibody-ligand interactions on a high-capacity staphylococcal protein A resin

Staphylococcal protein-A affinity chromatography has been optimized for antibody purification, achieving a current capacity of up to 90 mg/ml in packed bed. The morphology of the particles, the number of antibodies bound per ligand and the spatial arrangement of the ligands were assessed by in-situ Small-angle X-ray scattering (SAXS) and scanning electron microscopy (SEM) combined with measurement of adsorption isotherms. We employed SAXS measurements to probe the nanoscale structure of the chromatographic resin. From scanning electron microcopy, the morphology and area of the beads were obtained.The adsorption isotherm revealed a bi-Langmuirian behavior where the association constant varied with the critical bulk concentration, indicating multilayer adsorption. Determining the antibody-ligand stoichiometry was crucial for understanding the adsorption mechanism, which was estimated to be 4 at lower concentrations and 4.5 at higher concentrations, suggestive of reversible protein-protein interactions. The same results were reached from the in-situ small angle X-ray scattering measurements. A stoichiometry of 6 cannot be achieved since the two protein A monomers are anchored to the stationary phase and thus sterically hindered.Normalization through ellipsoids facilitated SAXS analysis, enabling the determination of distances between ligands and antibody-ligand complexes. Density fluctuations were examined by subtracting the elliptical fit, providing insights into ligand density distribution. The dense ligand packing of TOYOPEARL® AF-rProtein A HC was confirmed, making further increases in ligand density impractical. Additionally, SAXS analysis revealed structural rearrangements of the antibody-ligand complex with increasing antibody surface load, suggesting reversible association of antibodies.

Horizontal transverse isotropy anisotropic parameter inversion via azimuthal seismic velocity anisotropy and its application to anisotropic 3D in-situ stress estimation

Anisotropic parameter inversion in horizontal transverse isotropy (HTI) media plays an important role in predicting the fracture density and the anisotropic in-situ stress for unconventional reservoirs. The current industry practice is to use the azimuthal PP-wave reflection coefficient to estimate the HTI anisotropic parameters. Based on the linear slip theory, we develop an innovative approach that uses azimuthal P-wave phase velocity to calculate HTI anisotropic parameters, which presents superiority over the conventional azimuthal PP-wave reflection coefficient inversion. Specifically, we first verify that the azimuthal P-wave phase velocity is for the HTI elliptical fitting than the azimuthal PP-wave reflection coefficient using the analytical formulations. Second, we sort the prestack wide-azimuth data into offset vector tile sectors and perform amplitude-variation-with-offset inversion at each azimuth. Third, we apply an elliptical fitting to the obtained azimuthal P-wave phase velocities to estimate the HTI anisotropic parameters, fracture density, and fracture direction. Fourth, based on the HTI mechanical earth model, we formulate a cost-effective 3D in-situ stress estimation method using the obtained elastic parameters and fracture compliance. Finally, field examples from the Zhaotong area, China, demonstrate that the estimated fracture density and anisotropic in-situ stress are more accurate and have higher resolution compared with conventional methods. The dominant stress regime in the study area is a strike-slip faulting regime with a governing orientation of northeast–southwest and presents good alignments with well logs, which demonstrates the reliability and accuracy of our method for predicting fracture density and anisotropic in-situ stress.

Improved Fall Detection Method Based on Local Elliptical Fitting of Human Skeletal Points

Improved Fall Detection Method Based on Local Elliptical Fitting of Human Skeletal Points

The stellar occultation by (319) Leona on 2023 September 13 in preparation for the occultation of Betelgeuse

ABSTRACT On 2023 December 12, the star α Orionis will be occulted by asteroid (319) Leona. This represents an extraordinary and unique opportunity to analyse the brightness distribution of Betelgeuse’s photosphere with extreme angular resolution by studying light curves from different points on Earth and at different wavelengths. Here we present observations of another occultation by asteroid Leona, on 2023 September 13, whose goal was to determine Leona’s projected shape and size in preparation for the December 12th event and its interpretation. The occultation campaign was highly successful with 25 positive detections from 17 different sites and a near miss. The effective diameter in projected area derived from the positive detections was 66 ± 2 km using an elliptical fit to the instantaneous limb. The body is highly elongated, with dimensions of 79.6 ± 2.2 km × 54.8 ± 1.3 km in its long and short axis, respectively, at occultation time. This result, in combination with dense time series photometry of Leona that we recently obtained, together with archival sparse photometry, allowed us to predict the angular size of the asteroid for the Betelgeuse event and to simulate the expected brightness change. Also, an accurate position coming from the occultation is provided, to improve the orbit of Leona.

The two rings of (50000) Quaoar

Context. Quaoar is a classical trans-Neptunian object (TNO) with an area-equivalent diameter of 1100 km and an orbital semi-major axis of 43.3 astronomical units. Based on stellar occultations observed between 2018 and 2021, an inhomogeneous ring (Q1R, i.e., Quaoar’s first ring) has been detected around this body. Aims. A new stellar occultation by Quaoar was observed on August 9, 2022, with the aim of improving Quaoar’s shape models and the physical parameters of Q1R, while searching for additional material around the body. Methods. The occultation provided nine effective chords across Quaoar, pinning down its size, shape, and astrometric position. Large facilities, such as Gemini North and the Canada-France-Hawaii Telescope (CFHT), were used to obtain high acquisition rates and signal-to-noise ratios. The light curves were also used to characterize the Q1R ring (radial profiles and orbital elements). Results. Quaoar’s elliptical fit to the occultation chords yields the limb with an apparent semi-major axis of 579.5 ± 4.0 km, apparent oblateness of 0.12 ± 0.01, and area-equivalent radius of 543 ± 2 km. Quaoar’s limb orientation is consistent with Q1R and Weywot orbiting in Quaoar’s equatorial plane. The orbital radius of Q1R is refined to a value of 4057 ± 6 km. The radial opacity profile of the more opaque ring profile follows a Lorentzian shape that extends over 60 km, with a full width at half maximum (FWHM) of ∼5 km and a peak normal optical depth of 0.4. Besides the secondary events related to the already reported rings, new secondary events detected during the August 2022 occultation in three different data sets are consistent with another ring around Quaoar with a radius of 2520 ± 20 km, assuming the ring is circular and co-planar with Q1R. This new ring has a typical width of 10 km and a normal optical depth of ∼0.004. Just as Q1R, it also lies outside Quaoar’s classical Roche limit.

Accurate C/D ratio estimation with elliptical fitting for OCT image based on joint segmentation and detection network

Proper estimation of the cup-to-disc ratio (C/D ratio) plays a significant role in ophthalmic examinations, and it is urgent to improve the efficiency of C/D ratio automatic measurement. Therefore, we propose a new method for measuring the C/D ratio of OCTs in normal subjects. Firstly, the end-to-end deep convolution network is used to segment and detect the inner limiting membrane (ILM) and the two Bruch's membrane opening (BMO) terminations. Then, we introduce an ellipse fitting technique to post-process the edge of the optic disc. Finally, the proposed method is evaluated on 41 normal subjects using the optic-disc-area scanning mode of three machines: BV1000, Topcon 3D OCT-1, and Nidek ARK-1. In addition, pairwise correlation analyses are carried out to compare the C/D ratio measurement method of BV1000 to existing commercial OCT machines as well as other state-of-the-art methods. The correlation coefficient between the C/D ratio calculated by BV1000 and the C/D ratio calculated by manual annotation is 0.84, which indicates that the proposed method has a strong correlation with the results of manual annotation by ophthalmologists. Moreover, in comparison between BV1000, Topcon and Nidek in practical screening among normal subjects, the proportion of the C/D ratio less than 0.6 calculated by BV1000 accounts for 96.34%, which is the closest to the clinical statistics among the three OCT machines. The above experimental results and analysis show that the proposed method performs well in cup and disc detection and C/D ratio measurement, and compared with the existing commercial OCT equipment, the C/D ratio measurement results are relatively close to reality, which has certain clinical application value.

Coordinate Normalization of Live-Cell Imaging Data Reveals Growth Dynamics of the Arabidopsis Zygote.

Polarization of the zygote defines the body axis during plant development. In Arabidopsis (Arabidopsis thaliana), the zygote becomes polarized and elongates in the longitudinal direction, ultimately forming the apical-basal axis of the mature plant. Despite its importance, the mechanism for this elongation remains poorly understood. Based on live-cell imaging of the zygote, we developed new image analysis methods, referred to as coordinate normalization, that appropriately fix and align positions in an image, preventing fluctuation across a temporal sequence of images. Using these methods, we discovered that the zygote elongates only at its apical tip region, similar to tip-growing cells such as pollen tubes and root hairs. We also investigated the spatiotemporal dynamics of the apical tip contour of the zygote and observed that the zygote tip retains its isotropic, hemispherical apical shape during cell elongation. By looking at the elliptical fitting of the contour over time, we further discovered that the apical cell tip becomes thinner at first and then thickens, with a transient increase in growth speed that is followed by the first cell division. We performed the same series of analyses using root hairs and established that both the hemispherical tip shape and the changes in growth rate associated with changes in tip size are specific to the zygote. In summary, the Arabidopsis zygote undergoes directional elongation as a tip-growing cell, but its tip retains an unusual isotropic shape, and the manner of growth changes with the developmental stage.

Validation of the magnetometer calibration algorithms based on geometric fitting

This paper presents the principle of the proposed elliptical fitting calibration algorithm and compares it to the published ellipsoidal fitting algorithm for correcting the orientation of magnetic measurement, yaw angle. Two algorithms are implemented on a real device which is the magnetometer in an inertial measurement unit (IMU) that is applied to validate the effectiveness of the 2D calibration method. The validation considers the accuracy of the yaw angle with the stepper motor generating the referred angles. It could be noted that the 2D-calibration algorithm can be implemented and be made compatible with the autonomous mobile robot using the data acquired from the magnetometer and IMU for determining the accuracy yaw angle. The result of the comparison to the referred device’s calibrated data assures the potential for subsequent supervising or controlling processes.

The quest for optimal femoral torsion angle measurements: a comparative advanced 3D study defining the femoral neck axis

PurposeThere is high variability in femoral torsion, measured on two-dimensional (2D) computed tomography (CT) scans. The aim of this study was to find a reliable three-dimensional (3D) femoral torsion measurement method, assess the influence of CAM deformity on femoral torsion measurement, and to promote awareness for the used measurement method.Methods3D models of 102 dry femur specimens were divided into a CAM and non-CAM group. Femoral torsion was measured by one 2D-CT method described by Murphy et al. (method 0) and five 3D methods. The 3D methods differed in strategies to define the femoral neck axis. Method 1 is based on an elliptical least-square fit at the middle of the femoral neck. Methods 2 and 3 defined the centre of mass of the entire femoral neck and of the most cylindrical part, respectively. Methods 4 and 5 were based on the intersection of the femoral neck with a 25% and 40% enlarged best fit sphere of the femoral head.Results3D methods resulted in higher femoral torsion measures than the 2D method; the mean torsion for method 0 was 8.12° ± 7.30°, compared to 9.93° ± 8.24° (p < 0.001), 13.21° ± 8.60° (p < 0.001), 8.21° ± 7.64° (p = 1.00), 9.53° ± 7.87° (p < 0.001) and 10.46° ± 7.83° (p < 0.001) for methods 1 to 5 respectively. In the presence of a CAM, torsion measured with method 4 is consistently smaller than measured with method 5.Conclusion2D measurement might underestimate true femoral torsion and there is a difference up to 5°. There is a tendency for a higher mean torsion in hips with a CAM deformity. Methods 4 and 5 are the most robust techniques. However, method 4 might underestimate femoral torsion if a CAM deformity is present. Since method 5 is independent of a CAM deformity, it is the preferred technique to define expected values of torsion.

Development of An Algorithm for Slippage-Induced Motion Artifacts Reduction in Video-Nystagmography

Objectives: The slippage of the video-nystagmography devices causes motion artifacts in the trajectory of the pupil and thus results in distortion in the nystagmus waveform. In this study, the moving average was proposed to reduce slippage-induced motion artifacts from the real-world data obtained in the field.Methods: The dataset consists of an infrared video of positional tests performed on eight patients with a lateral semicircular canal benign paroxysmal positional vertigo. The trajectories of the pupil were obtained from the video with binarization, morphological operation, and elliptical fitting algorithm. The acquired data was observed and the section where the slippage occurred was labeled by an otolaryngologist. The moving average with windows of various lengths was calculated and subtracted from the original signal and evaluated to find the most adequate parameter to reduce the motion artifact.Results: The period of nystagmus in the given data was found to be ranged from 0.01 to 4 seconds. The slippages that appeared in the data can be categorized into fast and slow slippages. The length, distance, and speed of trajectories in the slippage ranges were also measured to find the characteristics of the motion artifact in video-nystagmography data. The shape of the nystagmus waveform was preserved, and the motion artifacts were reduced in both types of slippages when the length of the window in moving average was set to 1 second.Conclusions: The algorithm developed in this study is expected to minimize errors caused by slippage when developing a diagnostic algorithm that can assist clinicians.

Shapes and Centroids of 39 Strong Lensing Galaxy Clusters from the Sloan Giant Arcs Survey

AbstractStrong lensing galaxy clusters provide a powerful observational test of Cold Dark Matter (CDM) structure predictions derived from simulation. Specifically, the shape and relative alignments of the dark matter halo, stars, and hot intracluster gas tells us the extent to which theoretical structure predictions hold for clusters in various dynamical states. We measure the position angles, ellipticities, and locations/centroids of the brightest cluster galaxy (BCG), intracluster light (ICL), the hot intracluster medium (ICM), and the core lensing mass for a sample of strong lensing galaxy clusters from the SDSS Giant Arcs Survey (SGAS). We use iterative elliptical isophote fitting methods and GALFIT modeling on HST WFC3/IR imaging data to extract ICL and BCG information and use CIAO’s Sherpa modeling on Chandra ACIS-I X-ray data to make measurements of the ICM. Using this multicomponent approach, we attempt to constrain the physical state of these strong lensing clusters and evaluate the different observable components in terms of their ability to trace out the gravitational potential of the cluster.

Velocity distribution of elliptical galaxies in the framework of Non-local Gravity model

We investigate the velocity distribution of elliptical galaxies in the framework of Non-local Gravity. According to this approach, it is possible to recover the fundamental plane of elliptical galaxies without the dark matter hypothesis. Specifically, we compare theoretical predictions for circular velocity in Non-local Gravity context with the corresponding values coming from a large sample of observed elliptical galaxies. We adopt the surface brightness, effective radius and velocity dispersion as structural parameters for the fundamental plane. As final result, it is possible to show that non-local gravity effects can reproduce the stellar dynamics in elliptical galaxies and fit consistently observational data.

Yield surface derivation for a structural adhesive based on multiaxial experiments

Yield surface determination is an essential part of a material characterization, enabling the qualification of a suitable yield criterion. In the case of two-component, fiber-reinforced structural adhesives the manufacturing quality of the specimens is directly linked to the determination accuracy of the yield surface. Therefore, this work was based on specimens that have been optimized in a previous study utilizing a structural, epoxy-based adhesive designed for the manufacture of wind turbine rotor blades. This allowed for a precise identification of a yield locus in combined tension–torsion and compression–torsion experiments. A practical elasto-plastic shear stress correction was developed to account for the transition between elastic and plastic states. In addition, a scaling method of an elliptical yield locus fitting function is proposed to calculate equivalent stresses and strains. The obtained results are discussed regarding influences of viscoelasticity and are compared to existing yield criteria.

THE APPLICATION OF COMPUTER VISION FOR THE ESTIMATION OF SHRINKAGE AND DEFORMATION OF THIN MANGO SLICES DURING AIR DRYING PROCESS

Computer vision has been currently a new trend in developing new tools for automatic real-time quality control process in food drying. During drying process, the size and shape of mango slides are critically changed. These changes usually determine the sensorial value of products, as well as which drying conditions would be needed to obtain the highest quality of dried products. In this study, we report on the development of a computer vision tool, requiring a normal digital camera installed, to evaluate the changes in size and shape of mango slides during the drying process. The technique is expected to replace the observation with human eyes to evaluate the changes of food products during the drying process, which might not be able to provide reliable and consistent judgements all the time. Image of drying mango slide is taken by a digital camera, then the feature extraction is implemented. The area of mango slice is determined by the area ratio via the pixel number counting and the comparison to an original sample with predefined reference size. The shrinkage deformation is evaluated by elliptical fitting to develop the automated utility. The utility is built on MATLAB platform. The variations in size and shape of the mango slices during a convective drying process with different processing conditions are examined and acquired by the built software which achieves real-time performance on the personal laptop.

Fully automatic detection and measurement of abdominal aortic aneurysm using artificial intelligence

Abstract Background Abdominal aortic aneurysm (AAA) is a life-threatening disease, and the decision to treat relies on the exact detection and size of AAA, which is time-consuming and prone to high inter-reader variability. Artificial intelligence (AI) has revealed new insights into the management of AAA, but it needs large amounts of contrast-enhanced CT data. Moreover, there has been few studies about the fully automatic detection and measurement of AAA. Purpose The aim of this study is to evaluate the accuracy of AI for the detection and measurement of AAA using small amounts of non-contrast CT. Methods We retrospectively collected 145 non-contrast CT scans of suspected AAA. The first step was to manually segment the 30 non-contrast CT scans to create training data for the AI, and the second step was to improve accuracy using 9 of non-contrast CT scans. Image processing is used to identify the AAA area and automatically measure the size. The AAA region was identified from the amount of change in the minor-axis, and the maximum minor-axis diameter was calculated using elliptical fitting. To evaluate the diagnostic utility of AI for the detection of AAA, the sensitivity and positive predictive value were calculated referred for the diagnostic report. The reproducibility in the size of AAA was assessed using intraclass correlation coefficients (ICCs) between the diagnostic report and AI. Results Among 145 of non-contrast CT scans, 111 had AAA. The sensitivity and positive predictive value of AI for the detection of AAA were 94.6% and 53.8%, respectively (Picture 1). The size of AAA calculated by the AI (42.5±8.8 mm) showed a strong correlation with the those of diagnostic reports (44.6±8.4 mm; ICCs = 0.97) (Picture 2). Conclusions AI represents a useful tool in the fully automatic detection and measurement of AAA using small amounts of non-contrast CT. Funding Acknowledgement Type of funding sources: None. Picture 1Picture 2

AutoProf – I. An automated non-parametric light profile pipeline for modern galaxy surveys

ABSTRACT We present an automated non-parametric light profile extraction pipeline called autoprof. All steps for extracting surface brightness (SB) profiles are included in autoprof, allowing streamlined analyses of galaxy images. autoprof improves upon previous non-parametric ellipse fitting implementations with fit-stabilization procedures adapted from machine learning techniques. Additional advanced analysis methods are included in the flexible pipeline for the extraction of alternative brightness profiles (along radial or axial slices), smooth axisymmetric models, and the implementation of decision trees for arbitrarily complex pipelines. Detailed comparisons with widely used photometry algorithms (photutils, xvista, and galfit) are also presented. These comparisons rely on a large collection of late-type galaxy images from the PROBES catalogue. The direct comparison of SB profiles shows that autoprof can reliably extract fainter isophotes than other methods on the same images, typically by &amp;gt;2 mag arcsec−2. Contrasting non-parametric elliptical isophote fitting with simple parametric models also shows that two-component fits (e.g. Sérsic plus exponential) are insufficient to describe late-type galaxies with high fidelity. It is established that elliptical isophote fitting, and in particular autoprof, is ideally suited for a broad range of automated isophotal analysis tasks. autoprof is freely available to the community at: https://github.com/ConnorStoneAstro/AutoProf.