Curve Reconstruction Research Articles

Implicit progressive-iterative approximation for curve and surface reconstruction

Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or spurious sheets arising in the reconstruction process make the reconstruction result challenging to be interpreted and damage the final result. In this paper, we propose an implicit curve and surface reconstruction method based on the progressive-iterative approximation, named implicit progressive-iterative approximation (I-PIA). The proposed method elegantly and naturally eliminates the spurious sheets without requiring any explicit minimization procedure, thus significantly reducing the computing cost and providing high-quality reconstruction results. Numerical examples are presented to demonstrate the efficiency and effectiveness of the proposed method.

Re-evaluation and optimisation of dissolution methods for strontium isotope stratigraphy based on chemical leaching of carbonate certificated reference materials

Strontium isotope stratigraphy (SIS) is widely used in geoscience as a chemo-stratigraphic tracer. In past SIS research, diverse sample dissolution methods have been developed and applied to bulk carbonate rocks to extract target Sr isotope signatures of primary carbonates, which are easily contaminated with Sr from extraneous phases. However, the accuracy of the various dissolution methods is debated because all carbonate materials in previous studies were collected directly from the field and did not undergo strict homogeneity examination before sample dissolution. To verify and evaluate the actual bias for carbonate in SIS research, in this study, we analysed a set of artificial carbonate mixed standard samples including carbonate certificate reference materials (CRMs) GBW03105a for limestone and JDo-1 for dolostone in addition to that for clay minerals, GBW03103. These samples were verified to be stable in their Sr concentrations and 87Sr/86Sr ratios and could be used as benchmarks to enable reasonable evaluation on the extraction method for carbonate materials. We conducted a subtle chemical leaching experiment with 12 steps on these samples after preleaching by ammonium acetate.Our results show that the acidic preleach is useful in diminishing the Sr contamination from the extraneous phases. Nevertheless, the Sr contamination from the clay mineral can not be completely removed by the chemical leaching method and it would be more substantial for carbonate samples with lower purity and relatively lower original 87Sr/86Sr. Our work suggests an optimised dissolution scheme for carbonate 87Sr/86Sr analysis: (1) an acidic preleach to dissolve about ~60% of the sample, (2) a further dissolution of ~20% of the sample to prepare for the 87Sr/86Sr analysis, (3) leaving at least 10% of the sample undissolved. A simplified dissolution protocol with advantage of rapid operational and relatively-high reliability was finally proposed for strontium isotope stratigraphy research, particularly for reconstruction of secular Sr isotope evolution curve.

Effects of noises on curve fitting to the I–V characteristics of retarding filed analyzers

Retarding filed analyzers (RFAs) measure the ion velocity distribution in edge plasmas, leading to an estimate of the ion temperature and space potential through curve fitting. This paper describes the bi-directional RFA detector installed on the Experimental Advanced Superconducting Tokamak for edge plasma parameter measurements. The paper also describes a technique to compensate for a known induced noise using a dummy signal line and a method to reconstruct the I–V curve from the scanning voltage signal and the resultant ion current waveform. Fitting to experimental data and numerical simulations show that the I–V curve reconstruction method serves for both smoothing and induction noise compensation purposes.

Asymmetric Probability Distribution Function-Based Distillation Curve Reconstruction and Feature Extraction for Industrial Oil-Refining Processes

A distillation curve is an essential property for petroleum. Its features are beneficial for the modeling and optimization of oil-refining processes. To capture these features with a small number o...

Energy-Efficient Reconstruction Method for Transmission Lines Galloping With Conditional Generative Adversarial Network

Conductor galloping seriously threatens the safe operation of power systems and may lead to various damages such as wire fractures or tower collapses and large-scale grid breakdowns. Real-time galloping data are important in the mechanism and effect analysis of conductor dancing prevention; moreover, they are critical for verifying anti-galloping designs and developing galloping prevention plans. However, owing to the limitations of using sensors on cables, obtaining complete galloping data is an ill-posed and challenging problem. In this study, a novel curve reconstruction method using a conditional generative adversarial network (GAN), CR-CGAN, is proposed for fully synthesizing transmission line galloping curves. We use the modeling capabilities of the recently introduced GAN by imposing additional constraints to achieve full reconstruction of the galloping curves. Moreover, we introduce a novel design in the generator-discriminator pair for improved results and a new refined loss function to enhance details. The generator uses an autoencoder with skip connections, and the inception module is used to capture different scales of spatiotemporal correlation. The discriminator is designed to use global information to determine the reliability and smoothness of the reconstructed curve. The refined loss function is aimed at reducing artifacts introduced by the GAN and ensures better reconstruction quality. A single-degree-of-freedom model is constructed to verify the effectiveness and feasibility of the proposed method. Simulation results demonstrate that the proposed method can accurately reconstruct galloping curves with limited use of sensors, thus meeting the energy efficiency demands of the monitoring system.

Durable shape sensor based on FBG array inscribed in polyimide-coated multicore optical fiber.

The paper presents a novel three-dimensional quasi-continuous shape sensor based on an FBG array inscribed by femtosecond laser pulses into a 7-core optical fiber with a polyimide protective coating. The measured bending sensitivity of individual FBGs ranges from 0.046 nm/m-1 to 0.049 nm/m-1. It is shown that the sensor allows for reconstructing 2- and 3-dimensional shapes with high accuracy. Due to the high value of the core aperture and individual calibration of each FBG we were able to measure the smallest reported bending radii down to 2.6 mm with a record accuracy of ∼1%. Moreover, we investigate the magnitude of the errors of curves reconstruction and errors associated with measurement of curvature radii in the range from 2.6 to 500 mm. The main factors affecting the accuracy of measurements are also discussed. The temperature resistance of both the inscribed FBG structures and of the protective coating, along with the high mechanical strength of the polyimide, makes it possible to use the sensor in harsh environments or in medical and composite material applications.

Approximate symmetries of planar algebraic curves with inexact input

In this paper, we formulate a simple algorithm for an approximate reconstruction of an inexact planar curve which is assumed to be a perturbation of some unknown planar curve with symmetry. The input curve is given by a perturbed polynomial. We use a matrix complex representation of algebraic curves for simple estimation of the potential symmetry. A functionality of the designed reconstruction method is presented on several examples.

3D Highway Curve Reconstruction From Mobile Laser Scanning Point Clouds

The point clouds acquired by a vehicle-borne mobile laser scanning (MLS) system have shown great potential for many applications such as intelligent transportation systems, road infrastructure inventories, and high-definition (HD) maps to support the advanced driver-assistance systems (ADAS) and autonomous vehicles (AVs). This paper presents a novel two-step approach to automated detection and reconstruction of three-dimensional (3D) highway curves from MLS point clouds. However, when dealing with noisy, unstructured, dense point clouds, we often face some challenges, most notably in handling of the outliers introduced during road marking detection and in recognition of curve types during 3D curve reconstruction. Our approach is formed by two main algorithms: a detector based on intensity variance and a robust model fitting estimator. The experimental results obtained using both a virtual scan dataset and a real MLS dataset demonstrated that our approach is very promising in handling of the outliers and reconstruction of 3D road curves. Specifically, a relative accuracy of 0.6% has been achieved in estimation of circle radii based on the virtual scan dataset. A comparative study also showed that our road marking detection approach is more effective and more stable than state-of-the-art approaches.

Arabic Fonts Representation in Cubic Bézier Curve using Different Soft Computing Algorithm

This study presents the comparison between two meta-heuristic algorithms for curve reconstruction of Arabic fonts. The two algorithms namely Sine Cosine Algorithm (SCA) and Whale Optimization Algorithm (WOA) are used for comparison purposes. These algorithms have been applied to optimize the solution of curve fitting problem by using cubic Bezier curve. There are several pre-processing steps involve before curve fitting process has been done. Firstly, extract the boundary. Then, detect the corner of outline fonts and the third step is chord length parameterization. The aim of this study is to find the best curve that fit the data. Sum Square Errors (SSE) has been used to calculate the error given by original image and parametric curve. The finding of this study shows that, WOA gives better curve approximation based on the errors result than SCA. This algorithm significantly improves the shape of the corner of the outline Arabic fonts.

P3553Right ventricular echocardiographic composite parameters in predicting major adverse cardiac events in patients with heart failure with reduced ejection fraction

Abstract Background Echocardiography assessment of right ventricle still play an indispensable role in diagnosis, decision-making for further therapy and risk assessment of patients with heart failure with reduced ejection fraction (HFrEF). Aims Our objective was to compare the predictive value of five composite echo parameters of right ventricle (RV) in decompensated patients with HFrEF. Methods and results A total of 191 NYHA III-IV patients admitted for decompensation of advanced HFrEF (EF=25.53±6,87%) were prospectively enrolled. During the follow-up period mean period of 340±84 days, 111 (58.1%) patients met the primary composite endpoint (MACE) of cardiac death, rehospitalization due to repeated decompensation, malignant rhythm disorders, heart attack or stroke. The average time of MACE occurrence was 110.5±98.7 days. Among group of patients with MACE, during the follow-up, there were 34 (30.6%) cardiac related deaths. Re-hospitalization due to cardiovascular causes had 77 patients (69.4%). The study was performed at our hospital between June 2016 and January 2018. Patients were assessed for the following combined echo parameters: (i) relationship of right and left ventricle basal diameter (RVb/LVb x0,1); (ii) relationship of tricuspid annular plane systolic excursion and right ventricle systolic pressure (TAPSE/RVSP mm/mmHg); (iii) relationship of tricuspid annular systolic velocity and right ventricle systolic pressure (TAs'x100/ RVSP cm/s/mmHg); (iv) product of tricuspid annular systolic velocity and pulmonic valve acceleration time (TAs'x PVAcT (cm/s2 x 1000)); (v) product of systolic and diastolic velocity of tricuspid annulus (TAs xTAe). The last three parameters were result of this study and were not mentioned in earlier researches. In this study, univariat analysis of combined RV echo parameters, TAPSE/RVSP, TAs'x100 /RVSP as well as TAs'xPVAcT have been shown to be highly significant predictors of MACE, p=0.001. The TAs'xTAe' product has been also distinguished as a significant predictor of MACE, p=0.04, as well as the ratio RVb/LVb x 0.1, p=0.007. Multivariate analysis of these five combined RV echo parameters shows that significant independent predictor of MACE turned out to be TAs'x100/RVSP (p<0.001, HR = 0.668 (0.531–0.840)). Obtained by reconstruction of the ROC curve (Area = 0.70 (95% CI 0.59–0.75); p<0.001, we have got cut off value of TAs'x100/RVSP = 1.92 (cm/s/mmHg). Kaplan-Meier curves were constructed by comparing the time to the occurrence of MACE. Patients with TAs'x100/RVSP ≤1.92 (cm/s/mmHg) have a significantly worse prognosis (Log Rank p<0.001). Conclusion New variable TAs'x100/RVSP, derived from this research, proved to be the most powerful combined RV echo parameter, independent predictor of one year MACE, with a better predictive value compared to the already described combined parameters in the literature.

Teoretyczne rekonstrukcje środowiskowej krzywej Kuznetsa

Celem artykulu jest przegląd ekonomicznych modeli środowiskowej krzywej Kuznetsa, ktore uwzgledniają zjawiska konstytutywne dla wspolczesnej gospodarki. Dokonując przeglądu modeli, odpowiadamy na pytanie, w jaki sposob zmiana poziomu rozwoju gospodarczego mierzonego wartością PKB per capita moze wplywac na degradacje albo poprawe jakości środowiska oraz jakie inne czynniki – związane pośrednio z poziomem rozwoju gospodarczego – mogą miec istotny wplyw na omawianą relacje? W artykule podjeto probe wielowymiarowej charakterystyki tego zjawiska, zestawiając roznorodne modele, co umozliwia zdefiniowanie szerszego zakresu badan tej relacji i moze sie przyczynic do lepszego zrozumienia jej strukturalnych wlasności. Z przeprowadzonych studiow literatury wiemy, ze istotne dla wyniku badan hipotezy środowiskowej krzywej Kuznetsa i ich interpretacji są dokladne charakterystyki: procesu degradacji środowiska (rozroznienie pomiedzy czynnikami natychmiastowej degradacji środowiska a zanieczyszczeniami kumulującymi sie w czasie) oraz kilku czynnikow związanych z dochodem – PKB per capita (dochodowej elastyczności popytu na jakośc środowiska, nierowności spolecznych, wzrostu populacji, a takze liberalizacji handlu).

Reconstruction of one-punctured elliptic curves in positive characteristic by their geometric fundamental groups

Our main question is whether the isomorphism class as a scheme of a curve X over an algebraic closure of a finite field can be reconstructed by the etale fundamental group of X. Tamagawa answered this question affirmatively when the genus of X is 0. In this paper, we will discuss the genus 1 case, and prove a similar result when the genus of X is 1, the cardinality of cusps is 1, and the characteristic of X is not equal to 2.

A Novel Adaptive GA-based B-spline Curve Interpolation Method

Background: Curve interpolation is very important in engineering such as computer aided design, image analysis and NC machining. Many patents on curve interpolation have been invented. Objective: Since different knot vector configuration and data point parameterization can generate different shapes of an interpolated B-spline curve, the goal of this paper is to propose a novel adaptive genetic algorithm (GA) based interpolation method of B-spline curve. Method: Relying on geometric features owned by the data points and the idea of genetic algorithm which liberalizes the knots of B-spline curve and the data point parameters, a new interpolation method of B-spline curve is proposed. In addition, the constraint of a tangent vector is also added to ensure that the obtained B-spline curve can approximately satisfy the tangential constraint while ensuring strict interpolation. Results: Compared with the traditional method, this method realizes the adaptive knot vector selection and data point parameterization. Therefore, the interpolation result was better than the traditional method to some extent, and the obtained curve was more natural. Conclusion: The proposed method is effective for the curve reconstruction of any scanned data point set under tangent constraints. Meanwhile, this paper put forward a kind of tangent calculation method of discrete data points, where users can also set the tangent of each data point in order to get more perfect interpolation results.

Galaxy rotation curves using a non-parametric regression method: core, cuspy and fuzzy scalar field dark matter models

ABSTRACT We present a non-parametric reconstruction of the rotation curves (RCs) for 88 spiral galaxies using the LOESS (locally weighted scatterplot smoothing) + SIMEX (simulation and extrapolation) technique. In order to compare methods, we also use a parametric approach, assuming core and cuspy dark matter (DM) profiles: pseudo-isothermal (PISO), Navarro−Frenk–White (NFW), Burkert, Spano, the soliton, and two fuzzy soliton + NFW. As a result of these two approaches, a comparison of the RCs obtained is carried out by computing the distance between the central curves and the distance between the 1σ error bands. Furthermore, we perform a model selection according to two statistical criteria, the Bayesian information criterion and the value of $\chi ^2_{\rm red}$. We work with two groups. The first is a comparison between PISO, NFW, Spano and Burkert, showing that Spano is the most favoured model satisfying our selection criteria. For the second group, we select the soliton, NFW and fuzzy models, resulting in soliton as the best model. Moreover, according to the statistical tools and non-parametric reconstruction, we are able to classify galaxies as core or cuspy. Finally, using a Markov chain Monte Carlo method, for each of the DM models we compute the characteristic surface density, μDM = ρsrs, and the mass within 300 pc. We find that there is a common mass for spiral galaxies of the order of 107 M⊙, which is in agreement with results for dSph Milky Way satellites, independent of the model. This result is also consistent with our finding that there is a constant characteristic volume density of haloes. Finally, we also find that μDM is not constant, which is in tension with the literature.

Visible photoluminescence of color centers in lithium fluoride detectors for low-energy proton beam Bragg curve imaging and dose mapping

In the last few years, the visible photoluminescence (PL) of radiation-induced laser-active F2 and F3+ aggregate color centers (CCs) in lithium fluoride, LiF, has been successfully used for advanced diagnostics of low-energy proton beams. A systematic study of the optical properties of LiF crystals and thin films exposed in different irradiation geometries to a proton beam of nominal energy 7 MeV is under way. The ionization induces the stable formation of primary and aggregate CCs in the crystalline lattice, among which the F2 and F3+ defects possess broad emission bands in the red and green spectral ranges, respectively, when optically pumped at wavelengths close to 450 nm. Their PL intensity has been found to be linearly proportional to the dose absorbed by the host material over at least three orders of magnitude, so that LiF solid-state dosimeters based on spectrally-integrated PL reading can be envisaged. A simple defect formation model that takes into account the energy released in the material, crystals and films, together with the saturation of CC concentration at high doses, allows obtaining both the full Bragg curve reconstruction with its dose distribution with depth and the accumulated bi-dimensional transversal dose-mapping from the visible fluorescence images latently stored in LiF crystals and thin films, respectively. Results obtained by using a fluorescence microscope are presented and discussed with the aim of highlighting some quantitative aspects of the PL behavior of CCs both in LiF crystals and films, which are relevant for low-energy proton-beam Bragg curve imaging and dose mapping in a wide interval of doses up to the ones at which strong CC saturation occurs.

Application of Density Curve Reconstruction Technology in Seismic Inversion

Density curve is one of the indispensable data for impedance inversion. However, the limitation of density logging often results in the loss of density curve. The common solution is to use empirical formulas, such as Gardner formula, to reconstruct the density curve, but the effect is often not ideal. In order to solve this problem, the authors propose to reconstruct the missing density log curve by means of multiple linear regression, and then carry out geostatistical inversion by using the curves with high correlation between natural potential, gamma, resistivity and density curve. Finally, by comparing the inversion results of the two parameters, the inversion results of the former have a significant improvement in the coincidence rate of the posterior wells and the horizontal distribution of sandstone, which proves that the method has a significant application effect in reservoir prediction and lithologic sensitivity.

Reconstruction of Late Pleistocene and Holocene Sea Level Curve for the East Coast of India

ABSTRACT Holocene sea level curve has been generated for the East Coast of India. About seventy five 14C dates which are available from published works on coastal plains and offshore regions of the East Coast were considered and were subsequently calibrated into calendar years for analysis and plotting thereof. From the 100m depth, a moderate rate of sea level rising at the rate of about 0.88m/100 years is observed during 14,800 to 10,800 YBP. In between 10,800 to 9,200 YBP, a steep rise (Sea Level Rise - SR1) is noticed at the rate of 2.06m/100 years. Following a brief sluggish phase (for nearly about 1,100 years) of slow rising around 0.82m/100 years, another steep rate of rising of about 2.22m/100 years (SR2) is observed during 8,100 to 7,200 YBP. After that period to the Recent, there were 5 minor fluctuations with regression phases dominating over transgression phases in terms of duration and magnitude. It is also observed that the magnitude of all five high stands in between 7,200 to the recent has a decreasing trend from +4m to 0m. It obviously indicates that the most of the present day coastal plains were once under the sea as evidenced by the presence of many inland leftover paleo delta signatures in the East Coast of India.

Reconstructing oedometric compression curves for selecting design parameters

The mineral structure of soft clays is extremely fragile. Sampling operations and laboratory handling cause unavoidable disturbance. Undisturbed sampling is a theoretical concept because the stress release imposes disturbance. Consolidation tests on disturbed samples provide one-dimensional (1D)-compression curves very different from field response, which leads to inaccurate settlement estimates. Among the approaches for curve reconstruction, Schmertmann’s method is probably the most commonly adopted in engineering practice. However, it presents difficulties in determining preconsolidation stress. The paper primarily addresses Schmertmann’s and Nagaraj et al.’s propositions and discusses their advantages and shortcomings. A new approach for reconstructing the 1D-compression curve is proposed with the main objective being its independence of the interpretation of the experimental results. The validity was examined by comparing the reconstructed curves with those obtained by other methods. Experimental results on high- and low-quality specimens have been analyzed as well. The results revealed that the reconstructed curves for the cases analyzed are almost unique and independent of specimen quality. The proposed method allows both graphical and analytical implementation and the reconstructed curves are unaffected by experimental curve interpretation.

Reconstruction of high-speed cam curve based on high-order differential interpolation and shape adjustment

Mathematical defects of general cam curves such as high-order discontinuity and overlarge peak values often bring excessive transmission errors and vibrations to high-speed cam-follower systems. A comprehensive method is proposed in this study to develop high-speed cam curves with preferable mathematical characteristics. A high-order differential interpolation curve is first constructed by using nodal basis functions to accurately match with the multi-order derivatives on multiple nodes. A flexible cam curve is then reconstructed by adding variable shape factors on critical nodes for further shape adjustments. Numerical cases indicate that the proposed method can not only help construct a faithful cam curve satisfying all the given constraints for displacement, velocity, acceleration and jerk, but also effectively reconstruct a high-order continuous cam curve with lower peak values for high-speed precision cam mechanisms. The proposed method has been demonstrated to be effective and applicable in user-oriented reverse design, modification, and optimization of high-speed cam curves.

A simple method for determining ligament stiffness during total knee arthroplasty in vivo

A key requirement in both native knee joints and total knee arthroplasty is a stable capsular ligament complex. However, knee stability is highly individual and ranges from clinically loose to tight. So far, hardly any in vivo data on the intrinsic mechanical of the knee are available. This study investigated if stiffness of the native ligament complex may be determined in vivo using a standard knee balancer. Measurements were obtained with a commercially available knee balancer, which was initially calibrated in vitro. 5 patients underwent reconstruction of the force-displacement curves of the ligament complex. Stiffness of the medial and lateral compartments were calculated to measure the stability of the capsular ligament complex. All force-displacement curves consisted of a non-linear section at the beginning and of a linear section from about 80 N onwards. The medial compartment showed values of 28.4 ± 1.2 N/mm for minimum stiffness and of 39.9 ± 1.1 N/mm for maximum stiffness; the respective values for the lateral compartment were 19.9 ± 0.9 N/mm and 46.6 ± 0.8 N/mm. A commercially available knee balancer may be calibrated for measuring stiffness of knee ligament complex in vivo, which may contribute to a better understanding of the intrinsic mechanical behaviour of knee joints.