Curve Fitting Algorithm Research Articles

Follow-Up Control and Image Recognition of Neck Level for Standard Metal Gauge

An image recognition technique is proposed for determining optimal neck levels for standard metal gauges, in the process of validating pipe provers. A camera-level follow-up control system was designed to achieve automated tracking of fluid levels by a camera, thereby preventing errors from inclined viewing angles. An orange background plate was placed behind the tube to reduce background interference, and highlight scale numbers/lines and concave meniscus. A segmentation algorithm, based on edge detection and K-means clustering, was used to segment indicator tubes and scales in the acquired images. The concave meniscus reconstruction algorithm and curve-fitting algorithm were proposed to better identify the lowest point of the meniscus. A characteristic edge detection model was used to identify centimeter-scale lines corresponding to the meniscus. A binary tree multiclass support vector machine (MCSVM) classifier was then used to identify scale numbers corresponding to scale lines and determine the optimal neck level for standard metal gauges. Experimental results showed that measurement errors were within ±0.1 mm compared to a ground truth acquired manually using Vernier calipers. The recognition time, including follow-up control, was less than 10 s, which is much lower than the switching time required between measuring individual tanks. This automated measurement approach for gauge neck levels can effectively reduce measurement times, decrease manmade errors in liquid level readings, and improve the efficiency of pipe prover validation.

A Self-Adaptive Control for Phase-Controlled Electromagnetic Contactor Using Weighted Moving Average Filter

This article proposes a self-adaptive control strategy for controlling the holding current of a novel phase-controlled contactor. The closing moment of contact can be captured by calculating the drop slope of current and the pulsewidth modulation is then applied to decrease the holding current. The weighted moving average filter is employed to filter the current and voltage signals. A novel approach using a quintic B-spline curve-fitting algorithm is proposed to determine the number of sampling values and their weights. Numerous theoretical analyses of electromagnetic force and magnetic flux density distributions are developed. A cosimulation coupling magnetic field, machinery, and circuit are carried out with the Maxwell and circuit editor software. A prototype is manufactured and the experimental results validate the effectiveness of the proposed self-adaptive control strategy for minimizing the holding current.

A Multi-Layer Perceptron Network for Perfusion Parameter Estimation in DCE-MRI Studies of the Healthy Kidney

Background: Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an imaging technique which helps in visualizing and quantifying perfusion—one of the most important indicators of an organ’s state. This paper focuses on perfusion and filtration in the kidney, whose performance directly influences versatile functions of the body. In clinical practice, kidney function is assessed by measuring glomerular filtration rate (GFR). Estimating GFR based on DCE-MRI data requires the application of an organ-specific pharmacokinetic (PK) model. However, determination of the model parameters, and thus the characterization of GFR, is sensitive to determination of the arterial input function (AIF) and the initial choice of parameter values. Methods: This paper proposes a multi-layer perceptron network for PK model parameter determination, in order to overcome the limitations of the traditional model’s optimization techniques based on non-linear least-squares curve-fitting. As a reference method, we applied the trust-region reflective algorithm to numerically optimize the model. The effectiveness of the proposed approach was tested for 20 data sets, collected for 10 healthy volunteers whose image-derived GFR scores were compared with ground-truth blood test values. Results: The achieved mean difference between the image-derived and ground-truth GFR values was 2.35 mL/min/1.73 m2, which is comparable to the result obtained for the reference estimation method (−5.80 mL/min/1.73 m2). Conclusions: Neural networks are a feasible alternative to the least-squares curve-fitting algorithm, ensuring agreement with ground-truth measurements at a comparable level. The advantages of using a neural network are twofold. Firstly, it can estimate a GFR value without the need to determine the AIF for each individual patient. Secondly, a reliable estimate can be obtained, without the need to manually set up either the initial parameter values or the constraints thereof.

Normative Data for Myocardial Native T1 and Extracellular Volume Fraction in Children.

To establish normative data for myocardial T1, including extracellular volume (ECV) fraction, in healthy children. In this retrospective, single-center study, T1 mapping data were collected from 48 healthy pediatric patients (14 years ± 3 [standard deviation]; range, 9-18 years; 27 of 48 [56%] male) referred for cardiac screening 1.5-T MRI between 2014 and 2017. T1 relaxometry was performed using a 5(number of heartbeats [nHB])3 modified Look-Locker inversion recovery (MOLLI) sequence, where nHB was three to five heartbeats depending on the heart rate, and was repeated 15 minutes following the administration of 0.2 mmol per kilogram of body weight of gadobenate dimeglumine, with 19 patients receiving contrast material. T1 values were calculated using a curve-fitting algorithm on average region-of-interest signal and corrected for imperfect inversion pulse efficiency. Comparisons within patients were performed with paired Student t test, between groups with unpaired Student t test or Mann-Whitney U test, and linear regression was performed to examine for associations with other variables. Average native T1 was 1008 msec ± 31, with a nonsignificant increase in females (1017 msec ± 27 vs 1001 msec ± 33, P = .066). Average ECV was 20.8% ± 2.4, with a nonsignificant increase in values in females (21.7% ± 1.9 vs 20.0% ± 2.6, P = .123). T1 and ECV values were increased in the septum versus the free wall. Normative data are presented for myocardial native T1 and ECV using the MOLLI T1 mapping sequence at 1.5 T.Supplemental material is available for this article.© RSNA, 2020.

Laser Lens Size Measurement Using Swept-Source Optical Coherence Tomography

A high-speed, high-resolution swept-source optical coherence tomography (SS-OCT) is presented for focusing lens imaging and a k-domain uniform algorithm is adopted to find the wave number phase equalization. The radius of curvature of the laser focusing lens was obtained using a curve-fitting algorithm. The experimental results demonstrate that the measuring accuracy of the proposed SS-OCT system is higher than the laser confocal microscope. The SS-OCT system has great potential for surface topography measurement and defect inspection of the focusing lens.

Quantifying Perfusion Properties with DCE-MRI Using a Dictionary Matching Approach

Perfusion properties can be estimated from pharmacokinetic models applied to DCE-MRI data using curve fitting algorithms; however, these suffer from drawbacks including the local minimum problem and substantial computational time. Here, a dictionary matching approach is proposed as an alternative. Curve fitting and dictionary matching were applied to simulated data using the dual-input single-compartment model with known perfusion property values and 5 in vivo DCE-MRI datasets. In simulation at SNR 60 dB, the dictionary estimate had a mean percent error of 0.4–1.0% for arterial fraction, 0.5–1.4% for distribution volume, and 0.0% for mean transit time. The curve fitting estimate had a mean percent error of 1.1–2.1% for arterial fraction, 0.5–1.3% for distribution volume, and 0.2–1.8% for mean transit time. In vivo, dictionary matching and curve fitting showed no statistically significant differences in any of the perfusion property measurements in any of the 10 ROIs between the methods. In vivo, the dictionary method performed over 140-fold faster than curve fitting, obtaining whole volume perfusion maps in just over 10 s. This study establishes the feasibility of using a dictionary matching approach as a new and faster way of estimating perfusion properties from pharmacokinetic models in DCE-MRI.

Technical Note: Rapid multiexponential curve fitting algorithm for voxel-based targeted radionuclide dosimetry.

Dosimetry in nuclear medicine often relies on estimating pharmacokinetics based on sparse temporal data. As analysis methods move toward image-based three-dimensional computation, it becomes important to interpolate and extrapolate these data without requiring manual intervention; that is, in a manner that is highly efficient and reproducible. Iterative least-squares solvers are poorly suited to this task because of the computational overhead and potential to optimize to local minima without applying tight constraints at the outset. This work describes a fully analytical method for solving three-phase exponential time-activity curves based on three measured time points in a manner that may be readily employed by image-based dosimetry tools. The methodology uses a series of conditional statements and a piecewise approach for solving exponential slope directly through measured values in most instances. The proposed algorithm is tested against a purpose-designed iterative fitting technique and linear piecewise method followed by single exponential in a cohort of ten patients receiving 177 Lu-DOTA-Octreotate therapy. Tri-exponential time-integrated values are shown to be comparable to previously published methods with an average difference between organs when computed at the voxel level of 9.8±14.2% and -3.6±10.4% compared to iterative and interpolated methods, respectively. Of the three methods, the proposed tri-exponential algorithm was most consistent when regional time-integrated activity was evaluated at both voxel- and whole-organ levels. For whole-body SPECT imaging, it is possible to compute 3D time-integrated activity maps in <5min processing time. Furthermore, the technique is able to predictably and reproducibly handle artefactual measurements due to noise or spatial misalignment over multiple image times. An efficient, analytical algorithm for solving multiphase exponential pharmacokinetics is reported. The method may be readily incorporated into voxel-dose routines by combining with widely available image registration and radiation transport tools.

A constrained particle swarm optimization algorithm for hyperelastic and visco-hyperelastic characterization of soft biological tissues

A constrained particle swarm optimization algorithm (C-PSO) is introduced and modified for hyperelastic and visco-hyperelastic characterization of bovine brain tissue at three different strain rates. Using the elasticity compatibility and Drucker’s stability criterion, the constraints of the hyperelastic and visco-hyperelastic models are identified and implemented in the C-PSO algorithm and its performance is compared with the classic curve fitting algorithms including Levenberg-Marquardt and trust region reflective. The accuracy of the C-PSO was found to be superior for visco-hyperelastic characterization, as for some strain rates, the trust region reflective algorithm failed to provide a reasonable approximation.

Research on spectral signal calibration method of ink composition test system based on composite filter

In spectral information acquisition, the removal of stray light, noise, and other signals in the spectral system have always been an important part of the research. In this paper, the removal technology of stray light, noise, and other signals in the development of an ink testing system based on visible spectrum technology is deeply studied. Then, by researching composite digital filtering, curve fitting algorithm, and the fitting equation peak-seeking calibration method, a system for dynamically collecting grating spectral information is designed, which effectively improves the system's detection and extraction accuracy of light source signals. The experimental results show that the composite digital filtering method of moving average filtering and median filtering can not only suppress the accidental pulse interference, but also effectively filter out the observable random noise. For spectral information after filtering, the 6th order Gaussian algorithm was used to fit the acquired signal of the light source, and the R-square value and RMSE value were 0.9867 and 0.0277 respectively, showing better fitting accuracy and reduction degree. Finally, the fitting equation peak-seeking calibration method is adopted based on least square method. The experimental results show that the maximum error is 0.0045 nm and the RMSE value is 0.0029. The system shows better calibration accuracy.

Research on observation method of along the contour of China coastline based on CASEarth Satellite

Facing the rugged complicated coastline in china, three ways including data smoothing algorithm based on Third-Order Bezier Curve, High-order Bezier curve fitting algorithm and curve fitting algorithm based on least squares method are used to generate a smooth contour of coastline by analysing coordinate of coastal city. In the meanwhile, setting a series of leading point that meet the constraints of performance of CASEarth satellite to guide the satellite’s centre of view to move along the contour, and giving best solution among the three methods by the comparison.

Distributed Brillouin frequency shift extraction via a convolutional neural network

Distributed optical fiber Brillouin sensors detect the temperature and strain along a fiber according to the local Brillouin frequency shift (BFS), which is usually calculated by the measured Brillouin spectrum using Lorentzian curve fitting. In addition, cross-correlation, principal component analysis, and machine learning methods have been proposed for the more efficient extraction of BFS. However, existing methods only process the Brillouin spectrum individually, ignoring the correlation in the time domain, indicating that there is still room for improvement. Here, we propose and experimentally demonstrate a BFS extraction convolutional neural network (BFSCNN) to retrieve the distributed BFS directly from the measured two-dimensional data. Simulated ideal Brillouin spectra with various parameters are used to train the BFSCNN. Both the simulation and experimental results show that the extraction accuracy of the BFSCNN is better than that of the traditional curve fitting algorithm with a much shorter processing time. The BFSCNN has good universality and robustness and can effectively improve the performances of existing Brillouin sensors.

Electric Vehicle Sales Catastrophe Averted (?)

The literature indicates catastrophic potential for electric vehicles around the year 2019. Amidst the predicted time, this research revisits the prequel analysis with state-of-the-art deterministic artificial intelligence methodologies to posit the potential for catastrophe in the upcoming year. The methodology has proven effective with motion mechanics, electrodynamics, and even financial analysis of sales date in the prequels, since the model commences with simple regression for mathematical model formulation asserting the certainty equivalence principle, followed by derivative modeling and eventually catastrophe analysis of the derivative models. The prequel analysis paradigms are retained in this sequel utilizing both monthly and cumulative sales data in simple least squares algorithms for predictive curve fitting to establish context and help correctly model the mathematical degree of the data. Extrapolation by forward time-propagation established predictions for models of various mathematical degrees (again merely for context). Next, catastrophe analysis (of the derivative form) revealed stable and unstable equilibrium points and then parametric variation was induced to evaluate the resulting behavior of the derivative models, highlighting the importance of the coefficient of the second order term (the acceleration or change of rate of sales as a forcing function). While the forcing function typically embodies both gasoline prices and vehicle charging proliferation, the relative stability of gas prices together with factors such as vehicle-to-grid elevate charging-station proliferation as the primary forcing function of slow-dynamics in catastrophe analysis. This brief manuscript revisits the prequel research to test the validity of those conclusions and with the benefit of the passage of time, reveal how well the mathematical modeling predicted real behavior. The main finding is the predicted potential catastrophe is less likely to occur and recommendations are made to insure catastrophe is averted.

A Markov chain Monte Carlo approach for measurement of jet precession in radio-loud active galactic nuclei

ABSTRACT Jet precession can reveal the presence of binary systems of supermassive black holes. The ability to accurately measure the parameters of jet precession from radio-loud active galactic nuclei is important for constraining the binary supermassive black hole population, which is expected as a result of hierarchical galaxy evolution. The age, morphology, and orientation along the line of sight of a given source often result in uncertainties regarding the jet path. This paper presents a new approach for efficient determination of precession parameters using a two-dimensional Markov chain Monte Carlo curve-fitting algorithm that provides us a full posterior probability distribution on the fitted parameters. Applying the method to Cygnus A, we find evidence for previous suggestions that the source is precessing. Interpreting in the context of binary black holes leads to a constraint of parsec scale and likely sub-parsec orbital separation for the putative supermassive binary.

Comparison of the pore size distributions of concretes with different air-entraining admixture dosages using 2D and 3D imaging approaches

This study aims to more accurately investigate the pore size distribution of air voids in cement-based materials. For this purpose, micro-computed tomography (micro-CT) images were used to describe the inner structure of target materials, without damaging them. Together with the data obtained and the imaging techniques used, the pore structures of the specimens were visualized in 3D, with the pore size distributions being investigated using a volume-based method. The chord-length distribution, another approach to describe heterogeneous pore characteristics, was computed from 3D micro-CT images and compared with the conventional method. A RapidAir 457, an automated air void analyzer, was also used as a reference, with the results obtained being quantitatively and qualitatively compared using several curve fitting algorithms. The correlation between the pore characteristics and the mechanical properties of the specimens was examined, with the results indicating that the pore size distribution described using chord-length distribution is more effective than the conventional volume-based method. The results obtained can be utilized to investigate and predict material properties.

A low-cost autonomous navigation system for a quadrotor in complex outdoor environments

In this article, we design a low-cost navigation system for a quadrotor working in unknown outdoor environments. To reduce the computing burden of the quadrotor, we build a separated system and transfer the computing resources from onboard side to ground station side. Both sides’ communication is guaranteed by 5G wireless networks. We utilize a stereo camera to acquire point clouds and build Octomap for the quadrotor’s navigation. Then, the trajectory is generated in two stages. In the first stage, a modified RRT*-CONNECT algorithm is adopted to generate a set of collision-free waypoints. In the second stage, a curve fitting algorithm is utilized to get a smooth piecewise Bezier trajectory. The advantage of the proposed method is to optimize the path into a safe, smooth, and dynamically feasible trajectory in real time. The modules of the state estimation, dense mapping, and motion planning are integrated into a DJI Matrice 100 quadrotor. Finally, simulation and experiments are both conducted to show the validity and practicality of our method.

A Temperature-Dependent State of Charge Estimation Method Including Hysteresis for Lithium-Ion Batteries in Hybrid Electric Vehicles

Currently, lithium-ion batteries are mainly used as central power components in electric vehicles. Usually, accurate battery cell modeling and state of charge estimation are required in order to effectively use the lithium-ion batteries in electrified vehicles. For an elaborate battery cell modeling on a wide temperature range, we select a temperature-dependent battery cell modeling approach, which relies on one resistance plus second-order resistance-capacitance equivalent circuit model. In order to corporate some temperature effects into the modeling, we derive the sixth-order polynomial functions using the curve fitting algorithm. The functions contribute to the accurate battery cell modeling on the wide temperature range. For a practical usage of the functions in real-time embedded systems, we propose an offset-based lookup table technique. In addition, we propose a novel hysteresis voltage unit model for more accurate parameter estimation of hysteresis voltages. This also leads to more accurate battery cell modeling. Based on the battery cell modeling, we propose a temperature-dependent estimation method for state of charge. This approach exploits the extended Kalman filter, which is suitable for nonlinear characteristics such as the hysteresis effect. Experimental evaluation exhibits that the proposed estimation method outperforms the conventional approaches in the wide temperature range.

An accurate and fast method for eyelid detection

A novel method called refine-connect-extend-smooth (R-C-E-S) for detecting eyelids is presented. It consists of four algorithms, Canny edge detector with Prewitt operator, modified refine edge map (MREM), connect edges-extend (CEE) and smooth curve (SC). The method is not based on pre-assumptions that consider eyelids as parabola or lines and it does not use curve fitting algorithm, therefore sever deviation of the detected eyelid curve from the actual eyelid path is avoided. The method is applied to three types of database, CASIA-V1.0, CASIA-V4.0-Lamp and SDUMLA-HMT. The accuracies for detecting the lower eyelid, upper eyelid and free iris are (93.2%, 99.1%, 96.7%) for CASIA-V1.0, while for CASIA-V4.0-Lamp are (97.6%, 98.3%, 97.8%) and for SDUMLA-HMT are (95.1%, 95.3%, 96.92%). The processing times for detecting single eyelid, both eyelids and free iris are (42 ms, 49 ms, 35 ms) for CASIA-V1.0, while for CASIA-V4.0-Lamp are (23 ms, 26 ms, 21 ms) and for SDUMLA-HMT are (35 ms, 40 ms, 31 ms).

Augmented Ship Tracking Under Occlusion Conditions From Maritime Surveillance Videos

Ship tracking provides crucial on-site microscopic kinematic traffic information which benefits maritime traffic flow analysis, ship safety enhancement, traffic control, etc., and thus has attracted considerable research attentions in the maritime surveillance community. Conventional ship tracking methods yield satisfied results by exploring distinct visual ship features in maritime images, which may fail when the target ship is partially or fully sheltered by obstacles (e.g., ships, waves, etc.) in maritime videos. To overcome the difficulty, we propose an augmented ship tracking framework via the kernelized correlation filter (KCF) and curve fitting algorithm. First, the KCF model is introduced to track ships in the consecutive maritime images and obtain raw ship trajectory dataset. Second, the data anomaly detection and rectification procedure are implemented to rectify the contaminated ship positions. For the purpose of performance evaluation, we implement the proposed framework and another three popular ship tracking models on the four typical ship occlusion videos. The experimental results show that our proposed framework successfully tracks ships in maritime video clips with high accuracy (i.e., the average root mean square error (RMSE), root mean square percentage error (RMSPE), mean absolute deviation (MAD) and mean absolute percentage error (MAPE) are less than 10), which significantly outperforms the other popular ship trackers.

Development of Optimal Thresholding Technique for Shape and Size Detection for Through the wall Radar Imaging System

Through-the-wall radar (TWR) images of stationary target behind a wall are subject to strong stationary and non-stationary clutter which obscures the target position and size in the image. Stationary clutters are present due to strong reflection from the wall and non-stationary clutter occurs due to multipath, noise, etc. A lot of work has been reported for mitigating stationary clutter successfully for various real scenarios. However, for mitigating nonstationary clutter various authors have reported their work in this field but any concrete result has not been reported so far. Hence, there is a need for an optimal methodology to mitigate non-stationary clutter in TWR images for achieving a high-quality image representing the target position, shape and its size. Till now it is difficult to achieve shape detection of the target from the TWR system. Therefore, in this paper, a novel optimal thresholding technique is proposed to mitigating non-stationary clutter for further enhancement on shape detection of a target using curve fitting and genetic algorithm. The proposed methodology gives a satisfactory result and can prove to be a powerful technique for minimising clutter.

Feature Line Generation and Regularization From Point Clouds

The shape of the object is mainly described by feature points and lines. Since a feature point can be described by the intersection of two feature lines, feature lines are the key to determine the contour of the object. In this article, a novel method for the generation and regularization of point cloud feature line is presented, which consists of two main steps: extraction of the outline points according to the property of vectors distribution and cluster, feature points are sorted according to the vector deflection angle and distance and they are fitted using the improved cubic b-spline curve fitting algorithm. The performance of the proposed method is evaluated with both large and small point clouds acquired by terrestrial laser scanning devices in real-world scenes. The results show that the proposed method and the analysis of geometrical properties of neighborhoods (AGPN) method achieve very similar performance in the case of planar objects, accurately extracting the outline points of objects. However, in the presence of a curved surface, the proposed method significantly outperforms the existing methods in detecting outline points. The outlines are regularized by the improved cubic b-spline and it is superior to the traditional cubic b-spline curve fitting algorithm.