Distortion Coefficients Research Articles

A High-Quality and Convenient Camera Calibration Method Using a Single Image

Existing camera calibration methods using a single image have exhibited some limitations. These limitations include relying on large datasets, using inconveniently prepared calibration objects instead of commonly used planar patterns such as checkerboards, and requiring further improvement in accuracy. To address these issues, a high-quality and convenient camera calibration method is proposed, which only requires a single image of the commonly used planar checkerboard pattern. In the proposed method, a nonlinear objective function is derived by leveraging the linear distribution characteristics exhibited among corners. An algorithm based on enumeration theory is designed to minimize this function. It calibrates the first two radial distortion coefficients and principal points. The focal length and extrinsic parameters are linearly calibrated from the constraints provided by the linear projection model and the unit orthogonality of the rotation matrix. Additionally, a guideline is explored through theoretical analysis and numerical simulation to ensure calibration quality. The quality of the proposed method is evaluated by both simulated and real experiments, demonstrating its comparability with the well-known multi-image-based method and its superiority over advanced single-image-based methods.

Distortion Control in Intakes Subject to Strong Crosswinds Using Steady Vortex Generator Jets

Flow separation over the intake lip often occurs in gas turbine engines at off-design conditions such as crosswinds. The distortion transferred to the fan face detrimentally impacts the engine performance. The current study explores the efficacy of steady vortex generator jets (VGJ) to alleviate this flow distortion using high-fidelity implicit large-eddy simulations on a quasi-3D intake. The study reveals that VGJs, strategically placed on the windward side of the intake, induce coherent structures that include cylindrical jet shear layers, horseshoe vortices, and counter-rotating vortex pairs similar to transverse jets in crossflow. Parametric studies are carried out to identify the optimal VGJ location and blowing ratios. Superior flow control is achieved when the VGJs are placed on the windward side closer to the leading edge, reducing the distortion coefficient by ≈17% compared to the uncontrolled case. In contrast, when the VGJs are placed farther from the leading edge, the flow relaminarizes and the coherent structures decay rapidly due to severe acceleration over the intake lip. Consistent with experiments, our computations at higher blowing ratios (VR1.5 and VR2) show an improved pressure recovery decreasing the distortion coefficient by ≈40% due to deeper jet penetration and enhanced mixing.

Experimental Study of an Industrial Data Transmission Network in the Automatic Control System of a Wind Turbine

This article explores and optimizes network technologies for wind energy systems, focusing on the RS-485 interface to ensure reliable data transmission in extreme conditions. The study aims to address the impact of various distortions on data quality and wind turbine management. A system was proposed with two wind turbines, each equipped with a Raspberry Pi 4, connected to sensors measuring temperature, vibration, and wind speed. The research examined how data transmission rates affect signal shape, calculating the distortion coefficient. At 460,800 baud, the signal was almost completely distorted, with significant amplitude loss. The distortion coefficients were 1.84 for logic ‘1’ and 1.92 for logic ‘0’. The optimal speed to minimize distortions was found to be 19,200 baud, providing the most stable signal. Additionally, temperature significantly impacted transmission quality, highlighting the need to consider climatic conditions in system design. The findings and methods can help improve existing data transmission systems and enhance wind turbine performance.

Conversion of a piston–cylinder dimensional dataset to the effective area of a mechanical pressure generator

Recent developments in diameter metrology at NIST have improved the dimensional characterization of piston-cylinder assemblies (PCAs) to unprecedented precision. For the newest generation of PCAs, the standard uncertainty in the measurement of the outer diameter is 12 nm, while uncertainty in the measurement of the inner diameter is 14 nm. With a high-accuracy dimensional dataset in hand, the task of determining the pressure generated by a specific PCA is reduced to converting the diameter (and straightness and roundness) to an effective area (and distortion coefficient). The details on how this was performed for the artifact PCA2062 are described. PCA2062 was dimensioned in 2017 and 2020; the area repeated within . The calculation produced estimates of fall rate and rotation decay that agreed with experimental observations within 12 %. The fall rate is proportional to the square of the gap width; therefore, the agreement between calculation and measurement validates the dimensional estimate of the gap width within (36 ± 42) nm, where the 42 nm standard uncertainty is governed by the present state of flow theory. The piston gage model is buttressed by three comparison tests against a laser barometer, which support a view that PCA2062 is linear and reproducible within 0.2 μPa Pa-1. Finally, an estimate of uncertainty in the effective area of a dimensioned artifact is provided: as expected, the diameter measurement is the main culprit, but there are open questions regarding the flow model that preclude an accurate evaluation of the distortion coefficient. For the 530 kPa operating range of PCA2062, distortion is not a significant problem, but the effect would be dominant in assemblies operating at 1 MPa and above.

Design and aerodynamic performance study of subsonic Y-shaped inlet

Abstract A Y-shaped inlet with a quadrate import was designed by the super-ellipse method in this paper, and according to the variation pattern of the cross-section of the inlet, the variation pattern of the short and long axis of the super-ellipse was deduced. For many different flight situations, the numerical simulations of the Y-shaped inlet were made. The result shows (1) If 0.2≤Ma≤0.8, the total pressure recovery coefficient exceeds 0.96, and the total pressure distortion coefficient is close to 0.1, meeting the criterion of the design; (2) When Ma=0.8, for many different attack angle α=-4°∼22°, the total pressure recovery coefficient is close to 0.97, reaching the level of practical application, and it has little impact on total pressure recovery coefficient and the distortion coefficient. (3) These results demonstrate high total pressure recovery and low distortion coefficients across various flight conditions, indicating its potential for practical applications and future inlet designs.

An equivalent model of horizontal vibratory finishing process: Model construction and analysis based on similarity theory

The manufacturing cost of parts and experimental equipment seriously limits the development of experimental research on mass finishing. To tackle this issue, an equivalent model construction method was proposed based on similarity theory. First, the similarity criterion of relevant physical quantities in horizontal vibratory finishing was determined, and the calculation formula of the distortion coefficient was derived to correct the prediction results. Second, the effects of vibration parameters on the characteristics and similarities of particle velocity and normal force were analyzed by DEM simulation. Finally, the validity of the equivalent model was proved by PIV and force tests. The results show that the equivalent model can be used to reflect the variation of the actual model and anticipate the particle velocity and normal force. And the prediction accuracy can reach 99.56 % and 97.46 %, respectively. The research results provide a new efficient and low-cost method for researching the mass finishing process.

Boosting the Sodium‐Ion Storage Performance of Prussian Blue Analogs by Crystalline Regulation

AbstractIn the development of practical sodium‐ion batteries, electrochemical performance and cost efficiency of the electrode materials are vital considerations. Prussian blue analogs (PBAs) have emerged as promising cathode materials due to their affordability, high theoretical capacity, and cycling stability. However, low crystallinity can negatively impact their performance. This study introduces a straightforward “chelating agent‐assisted” method for producing highly crystalline PBAs. The resulting cathode boasts excellent characteristics, including a high capacity of 150 mAh g−1, an initial Coulombic efficiency of 87.2 %, a long cycling lifespan of 1000 cycles, and superior rate performance. Furthermore, the study shows that the low structure distortion and high sodium diffusion coefficient can be attributed to the suppression of structural defects, as evidenced by in situ synchrotron powder diffraction. We believe these findings have the potential to enable the widespread use of PBAs in sodium‐ion batteries for an affordable and large‐scale energy storage system.

Research on the Measurement System and Remote Calibration Technology of a Dual Linear Array Camera

Abstract In order to accurately measure the flight trajectory of the projectile in a long-distance target range, it is important to establish a vertical target measurement system with a two-line array camera at several positions along the range. In the present work, a calibration system using dual theodolites is proposed to calibrate the vertical target measurement system of a dual linear array camera at different positions along a long target range. The present study investigates the principle of intersection measurement in the vertical target measurement system with a double linear array camera and presents the projectile’s target coordinate measurement formula. The calibration method of the measurement system is developed based on an analysis of the parameters in the projectile coordinate measurement formula. The calibration method only requires calibration of the camera’s distortion coefficient, the optical axis angle, and the principal point, ensuring a simplified and expedited calibration process. After calibration, the vertical target measurement system with a 3 m × 3 m measurement area is simulated and analyzed, yielding an error distribution diagram and identifying the factors that influence the measurement accuracy of the projectile’s target coordinates.

Nonlinear control of three level NPC inverter used in PV/grid system: comparison of topologies and control methods

With the passage of time, the importance of using renewable energy systems to overcome energy consumption and improve the quality of the grid has emerged through the use of nonlinear control techniques and reliance on advanced types of inverters such as multi-level inverters. This research is focused on comparing two grid-connected converter topologies in a photovoltaic (PV) generation system connected to a three-phase grid that serves a non-linear load. Additionally, the study explores two different control techniques applied to this converter, evaluating their effects on the total harmonic distortion coefficient. A comparison has been made between the traditional inverter and the three-level inverter type neutral point clamped (NPC) inverter, with the use of integral backstepping (IBS) technique which was also compared with the proportional integral (PI) controller. The simulation results in MATLAB/Simulink are presented illustrating the performances and the strong effectiveness of the three-level NPC inverter controlled by the proposed technique (IBS).

Influencing factors of industrial transformation in resource-based cities: Comprehensive measurement method based on resource price distortion

The rational allocation of industrial factors in resource-based cities is a necessary condition for promoting high-quality economic development. To systematically measure the mismatch of industrial factors, this study integrates the production function model and accounting framework of Aoki (2012). The capital, labor, and energy factors are integrated into the overall measurement framework, and the factor mismatch calculation model is innovatively constructed at the city level. To effectively reflect the factor mismatch of different cities, the relative distortion coefficient of factor price is introduced to establish the relationship between the distortion of factor-use cost and effectiveness of resource allocation. The degree and direction of factor mismatch are effectively measured. This study takes China's resource-based cities as the research object. To avoid the impact of the COVID-19 pandemic, data on 114 resource-based cities in China from 2003 to 2018 are selected, and 164 non-resource-based cities are used as the control group to evaluate the factors affecting the transformation of such cities. Regarding the diversity of resource-based cities in China, this study compares the characteristics of factor misallocation in these cities for different growth stages, geographical regions, and dominant resources. Finally, this study finds that on average, the cities' degree of energy misallocation is the most serious, and the degree of labor misallocation ranks second. The degree of capital misallocation ranks the lowest, but the misallocation of various factors is very different in different situations. Therefore, different types of cities should make detailed policy adjustments in various transformation directions according to the calculation results.

Exploring the effects of weighting against homoplasy in genealogies of palaeontological phylogenetic matrices.

Although simulations have shown that implied weighting (IW) outperforms equal weighting (EW) in phylogenetic parsimony analyses, weighting against homoplasy lacks extensive usage in palaeontology. Iterative modifications of several phylogenetic matrices in the last decades resulted in extensive genealogies of datasets that allow the evaluation of differences in the stability of results for alternative character weighting methods directly on empirical data. Each generation was compared against the most recent generation in each genealogy because it is assumed that it is the most comprehensive (higher sampling), revised (fewer misscorings) and complete (lower amount of missing data) matrix of the genealogy. The analyses were conducted on six different genealogies under EW and IW and extended implied weighting (EIW) with a range of concavity constant values (k) between 3 and 30. Pairwise comparisons between trees were conducted using Robinson-Foulds distances normalized by the total number of groups, distortion coefficient, subtree pruning and regrafting moves, and the proportional sum of group dissimilarities. The results consistently show that IW and EIW produce results more similar to those of the last dataset than EW in the vast majority of genealogies and for all comparative measures. This is significant because almost all of these matrices were originally analysed only under EW. Implied weighting and EIW do not outperform each other unambiguously. Euclidean distances based on a principal components analysis of the comparative measures show that different ranges of k-values retrieve the most similar results to the last generation in different genealogies. There is a significant positive linear correlation between the optimal k-values and the number of terminals of the last generations. This could be employed to inform about the range of k-values to be used in phylogenetic analyses based on matrix size but with the caveat that this emergent relationship still relies on a low sample size of genealogies.

A Straightforward Camera Calibration Method Based on a Single Low-cost Cubical Target

Abstract. Calibrating optical sensors with common targets facilitates the efficient and convenient acquisition of the sensor's internal parameters. In this paper, we present a new method of camera calibration utilizing a low-cost foamy cube, in a form of dice, which is based on the fact that arrangement of pip and cubical die surfaces is mutually orthogonal. Initially, each face and pips are identified through the color information on the die’s surfaces. Subsequently, the centers of pips are corrected using a circular projection model, and radial distortion coefficients are estimated based on centers’ one-to-one correspondences. After that, the tangent information between pairs of pips on orthogonal dice faces are utilized to compute vanishing points, leading to estimation of intrinsic parameters. Experimental results demonstrate that our method has similar effects compared to well-known checkerboard calibration method, reaching an average relative error of 2.43%, simplifying the calibration process in practical applications and showcasing good practicality and robustness.

Investigation on similitude method for dynamic response of high-speed train body considering thickness distortion

Small-scale model test is an economical and efficient method to study the collision process analysis and crashworthiness design of full-scale high-speed trains. For high-speed trains, the vehicle body thickness of scaled train models is too small to be processed, resulting in thickness distortion. Although the distorted model can predict dynamic responses of the full-scale model, there are some errors in predicting the dynamic response parameters. This article proposes a new similitude distortion method to improve the prediction accuracy of the high-speed train body distorted model. First, the complete similitude relationship for train collisions was derived using dimensional analysis. According to the Buckingham π theory, the theoretical expression between prediction coefficient and distortion coefficient was obtained when the high-speed train thickness distortion occurred. Then, based on a full-scale high-speed train body prototype, the benchmark model and distorted model were established. Numerical simulation was used to explore the relationship between prediction coefficient and distortion coefficient. Finally, the distorted similar model was established using the similitude distortion method. The accuracy and feasibility of this approach were verified by comparing and analysing the dynamic response curves obtained by numerical simulations between the distorted similar model and prototype. The errors of the maximum displacement and deceleration were 2.70% and 8.26%. The results show that the similitude distortion method is reliable to relate dynamic responses of scaled models to the prototype when the vehicle body thickness distorts.

Characteristics and evolution of ground vortex under heaving ground conditions: Insights from large eddy simulation (LES) analysis

When an aircraft engine operates near the ground, the ambient vortices generated by the freestream velocity boundary layer and engine suction will gather and lift, forming ground vortices which may result in intake distortion, consequently affecting the engine operation stability. To develop a shipborne test platform, this study conducted large eddy simulation calculations using the ANSYS Fluent and based on the assumption of incompressible flow. The 3-D unsteady Navier-Stokes (N-S) equations were solved using the WALE sub-grid model. The analysis focused on the characteristics and evolution of ground vortices under heaving ground conditions within 1 s. The results indicate that the ground vortex exhibits strong unsteady characteristics. During the descending phase of the platform, the quantity of vortex formed beneath the intake duct would decrease while the trailing vortex becomes more pronounced. However, the structure of the inlet vortex remains relatively unchanged at each time step. The intensity of the vortex and pressure distortion coefficient exhibit significant fluctuations over time, and their temporal variations approximately follow a sinusoidal function, which is also the heaving motion of the platform. Generally, when the velocity of the platform reaches its maximum downward vertical value, the average vortex intensity of the ground vortex tends to be minimal while the pressure distortion coefficient approaches its maximum value. Conversely, when the velocity of the platform reaches its maximum upward vertical value, the opposite trend can be observed.

Lower semicontinuity of distortion coefficients for homeomorphisms of bounded (1, \sigma )-weighted (q, p)-distortion on Carnot groups

In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.

Prostate diffusion-weighted imaging (DWI) in MR-guided radiotherapy: Reproducibility assessment on 1.5 T MR-Linac and 1.5 T MR-simulator

PurposeDiffusion-weighted imaging (DWI) holds promise for image-guided radiotherapy (MRgRT) in prostate cancer. However, challenges persist due to image distortion, artifacts, and apparent diffusion coefficient (ADC) reproducibility issues. This study aimed to assess DWI image quality and ADC reproducibility on both a 1.5 T MR-simulator and a 1.5 T MR-Linac, employing measurements from both an ACR MRI phantom and prostate cancer patients undergoing MRgRT. MethodsDW-MRI scans were conducted on 19 patients (mean age = 69 ± 8 years, with 23 MR-visible intra-prostatic lesions) and an ACR MRI phantom using a 1.5 T MR-simulator (b-values = 0, 800, 1400s/mm2) and a 1.5 T MR-Linac (b-values = 50, 500, 800 s/mm2). ADC homogeneity in the phantom was evaluated via 1D profile flatness (FL) in three directions. Image quality was assessed through qualitative 5-point Likert scale ratings and quantitative ADC and signal-to-noise ratio (SNR) measurements. Intra-observer reproducibility of image quality scores was evaluated using ICC(1, 2). Geometric distortion was measured by comparing landmark sizes on the ACR phantom against the ground truth. Mean ADC and reproducibility were assessed using Bland-Altman plots. ResultsBoth MR-simulator and MR-Linac demonstrated high ADC homogeneity (FL > 87.5% - MR-simulator: 97.23 ± 0.62%, MR-Linac: 94.75 ± 0.62%, p < 0.05) in the phantom. Image quality scores revealed acceptable ratings (≥3) for capsule demarcation, image artifacts, and geometric distortion in patients. However, intra-prostatic lesions were barely discernible in b800 images for both MR-simulator (average score = 2.37 ± 1.33) and MR-Linac (average score = 2.16 ± 1.28). While MR-Linac DWI scans exhibited significantly more severe geometric distortion than MR-simulator scans (p < 0.01), most phantom measurements fell within the image in-plane resolution of 3 mm. Significant differences were noted in MR-simulator ADC (CTV: 1.20 ± 0.14 × 10−3 mm2/s (MR-simulator) vs 1.06 ± 0.10 × 10–3 mm2/s (MR-Linac); GTV: 1.05 ± 0.21 × 10−3 mm2/s vs 0.91 ± 0.16 × 10 mm2/s, all p < 0.05), with a small non-zero bias observed in the Bland-Altman analysis (CTV: 12.3%; GTV: 14.5%). ConclusionThe significantly larger MR-simulator ADC and the small non-zero bias hint at potential systematic differences in ADC values acquired from an MR-simulator and an MR-Linac, both at 1.5 T. Although acceptable ADC homogeneity was noted, caution is warranted in interpreting MR-Linac DWI images due to occasional severe artifacts. Further studies are essential to validate DWI and ADC as reliable imaging markers in prostate cancer MRgRT.

An Algorithm for a Space-Vector Pulse Width Modulation with a Hybrid Switching Sequence for a Three-Level Neutral Point Clamped Voltage Source Inverter

This paper proposes a new algorithm for a space-vector pulse width modulation (SVPWM) with a hybrid switching sequence (SS) designed to control a three-level (3L) neutral point clamped (NPC) voltage source inverter (VSI). Based on the advantages of five-stage and seven-stage SS, we designed a hybrid SS to improve four key parameters in the system: inverter output current quality, neutral point (NP) and common-mode (CM) voltage levels, and switching losses of power switches. The proposed algorithm flexibly regulates meeting the four criteria depending on the system operating conditions by changing the regulation coefficient. The paper obtained an approximate dependence to determine the optimal regulation coefficient for any values of the inverter modulation coefficient when operating jointly with an active-inductive load. The effectiveness of the proposed algorithm is confirmed by computer simulation in the MatLab+Simulink environment, as well as the results of experimental studies. The paper presents the experimental dependences of static state spaces, including the distortion coefficient of higher current harmonics at the inverter output, the maximum error of the NP voltage, the number of switching pairs of power switches, and the pulse duty factor of CM voltage, depending on the inverter modulation coefficient and the regulation coefficient of the hybrid SS. The results showed that in the algorithm for a SVPWM with a hybrid SS, the number of switchings of power switches is reduced by an average of 13.5 % while maintaining the NP voltage balance and the quality of the curve at the inverter output at an acceptable level, close to a seven-stage SS (the deviations do not exceed 0.5 % and 0.2 %, respectively). The average CM voltage coefficient decreased by no more than 4.5 %. The indicators improve the energy saving, the weight-size parameters, and the operational reliability of the 3L NPC VSI. The application area of the algorithm is much wider and includes the control of power switches of active front ends, grid converters for electricity storage systems, active power filters, and power conditioners. DOI: https://doi.org/10.52783/pst.237

Enhancing Single-Plane Fluoroscopy: A Self-Calibrating Bundle Adjustment for Distortion Modeling.

Single-plane fluoroscopy systems with image intensifiers remain commonly employed in a clinical setting. The imagery they capture is vulnerable to several types of geometric distortions introduced by the system's components and their assembly as well as interactions with the local and global magnetic fields. In this study, the application of a self-calibrating bundle adjustment is investigated as a method to correct geometric distortions in single-plane fluoroscopic imaging systems. The resulting calibrated imagery is then applied in the quantitative analysis of diaphragmatic motion and potential diagnostic applications to hemidiaphragm paralysis. The calibrated imagery is further explored and discussed in its potential impact on areas of surgical navigation. This work was accomplished through the application of a controlled experiment with three separate Philips Easy Diagnost R/F Systems. A highly redundant (~2500 to 3500 degrees-of-freedom) and geometrically strong network of 18 to 22 images of a low-cost target field was collected. The target field comprised 121 pre-surveyed tantalum beads embedded on a 25.4 mm × 25.4 mm acrylic base plate. The modeling process resulted in the estimation of five to eight distortion coefficients, depending on the system. The addition of these terms resulted in 83-85% improvement in terms of image point precision (model fit) and 85-95% improvement in 3D object reconstruction accuracy after calibration. This study demonstrates significant potential in enhancing the accuracy and reliability of fluoroscopic imaging, thereby improving the overall quality and effectiveness of medical diagnostics and treatments.

Effect of Ti4+ and Pb2+ on negative thermal expansion and polarization behaviors of KSr2Nb5O15: First-principles investigation

The utilization of both negative and positive thermal expansion coefficients presents a potential means of mitigating internal stress in high-temperature materials, hence offering a novel approach to enhance the impact strength of those materials. The investigation of the thermal expansion coefficient and polarization characteristics of KSr2Nb5O15 doped with Ti4+ and Pb2+ was conducted by the utilization of first-principles calculations. The introduction of Ti4+ and Pb2+ into the KSr2Nb5O15 lattice resulted in an increase in lattice distortion. This effect was particularly pronounced when Ti4+ and Pb2+ were co-doped, leading to the largest lattice distortion observed in KSr2Nb5O15. Furthermore, the negative thermal expansion coefficient of KSr2Nb5O15 was also found to be the highest under these co-doping conditions, with a value of −0.560×10−5 K−1 compared to the original value of −0.011×10−5 K−1. Conversely, when Ti4+ was doped individually, the lattice distortion and negative thermal expansion coefficient of KSr2Nb5O15 were found to be the smallest. Furthermore, the inclusion of Ti4+ and Pb2+ leads to an enhancement in the dielectric constant. This effect is particularly pronounced when Ti4+ and Pb2+ are simultaneously incorporated into the KSr2Nb5O15 lattice. Consequently, the dielectric constant of the material exhibits a substantial improvement. The greatest polarization intensity is achieved when KSr2Nb5O15 is co-doped with Ti4+ and Pb2+, resulting in a polarization intensity of 38.61 μC/cm2. The dense ceramics comprising of KSr2Nb5O15, with the addition of Ti4+ and Pb2+ dopants, were synthesized using the solid-state reaction method. Subsequently, the thermal expansion coefficients and dielectric characteristics of these ceramics were evaluated. The experimental results are not in good agreement with the calculated results, but qualitatively, the trend predicted by the theory is confirmed by experiment. This study establishes the groundwork for the synthesis of KSr2Nb5O15 materials exhibiting pronounced negative thermal expansion characteristics.

Lower Semicontinuity of Distortion Coefficients for Homeomorphisms of Bounded (1, σ)-Weighted (q, p)-Distortion on Carnot Groups

Lower Semicontinuity of Distortion Coefficients for Homeomorphisms of Bounded (1, σ)-Weighted (q, p)-Distortion on Carnot Groups