Amplification Of Error Research Articles

Fast 3D Reconstruction of UAV Images Based on Neural Radiance Field

Traditional methods for 3D reconstruction of unmanned aerial vehicle (UAV) images often rely on classical multi-view 3D reconstruction techniques. This classical approach involves a sequential process encompassing feature extraction, matching, depth fusion, point cloud integration, and mesh creation. However, these steps, particularly those that feature extraction and matching, are intricate and time-consuming. Furthermore, as the number of steps increases, a corresponding amplification of cumulative error occurs, leading to its continual augmentation. Additionally, these methods typically utilize explicit representation, which can result in issues such as model discontinuity and missing data during the reconstruction process. To effectively address the challenges associated with heightened temporal expenditures, the absence of key elements, and the fragmented models inherent in three-dimensional reconstruction using Unmanned Aerial Vehicle (UAV) imagery, an alternative approach is introduced—the neural radiance field. This novel method leverages neural networks to intricately fit spatial information within the scene, thereby streamlining the reconstruction steps and rectifying model deficiencies. The neural radiance field method employs a fully connected neural network to meticulously model object surfaces and directly generate the 3D object model. This methodology simplifies the intricacies found in conventional 3D reconstruction processes. Implicitly encapsulating scene characteristics, the neural radiance field allows for iterative refinement of neural network parameters via the utilization of volume rendering techniques. Experimental results substantiate the efficacy of this approach, demonstrating its ability to complete scene reconstruction within a mere 5 min timeframe, thereby reducing reconstruction time by 90% while markedly enhancing reconstruction quality.

The spatial accuracy of ring-mounted halcyon linac versus C-arm TrueBeam linac for single-isocenter/multi-target SBRT treatment.

Stereotactic body radiotherapy (SBRT) treatment of oligometastatic lesions via single-isocenter/multi-target (SIMT) plan is more efficient than using multi-isocenter/multitarget SBRT. This study quantifies the spatial positioning accuracy of 2 commercially available LINAC systems for SIMT treatment pertaining to the potential amplification of error as a function of the target's distance-to-isocenter. We compare the Ring-Gantry Halcyon LINAC equipped with the fast iterative conebeam-CT (iCBCT) for image-guided SIMT treatment, and the SBRT-dedicated C-Arm TrueBeam with standard pretreatment CBCT imaging. For both systems, Sun Nuclear's MultiMet Winston-Lutz Cube phantom with 6 metallic BBs distributed at different planes up to 7 cm away from the isocenter was used. The phantom was aligned and imaged via CBCT, and then couch corrections were applied. To treat all 6 BBs, an Eclipse 10-field 3D-conformal Field-in-Field (2×2 cm2 MLC field to each BB) plan for varying gantry, collimator, and couch (TrueBeam only) positions was developed for both machines with 6MV-FFF beam. The plan was delivered through ARIA once a week. The EPID images were analyzed via Sun Nuclear's software for spatial positioning accuracy. On TrueBeam, the treatment plan was delivered twice: once with 3DoF translational corrections and once with PerfectPitch 6DoF couch corrections. The average 3D spatial positioning accuracy was 0.55 ± 0.30 mm, 0.54 ± 0.24 mm, and 0.56 ± 0.28 mm at isocenter, and 0.59 ± 0.30 mm, 0.69 ± 0.30 mm, and 0.70 ± 0.35 mm at 7 cm distance-to-isocenter for Halcyon, TrueBeam 3DoF, and TrueBeam 6DoF, respectively. This suggests there are no clinically significant deviations of spatial uncertainty between the platforms with the distance-to-isocenter. On both platforms, our weekly independent measurements demonstrated the reproducibility for less than 1.0 mm positional accuracy of off-axis targets up to 7 cm from the isocenter. Due to this, no additional PTV-margin is suggested for lesions within 7 cm of isocenter. This study confirms that Halcyon can deliver similar positional accuracy to SBRT-dedicated TrueBeam to off-axis targets up to 7 cm from isocenter. These results further benchmark the spatial uncertainty of our extensively used SBRT-dedicated TrueBeam LINAC for SIMT SBRT treatments.

Simulation and measurement of systematic errors of stitching interferometry for high precision X-ray mirrors with large radius of curvature.

To accurately measure the surface figure of curved mirrors with large radius of curvature (RoC) using stitching interferometry methods, three types of measurement errors are systematically studied, including retrace error, defocusing error within a single subaperture, and stitching angle error among different subapertures. It was found that part of the retrace error caused by the mismatch between the reference wavefront and reflected wavefront has little effect, while the overall retrace error, including the influence of the imperfect optical elements, will cause an error of 1-2 nm RMS within a single subaperture. Defocusing error will enlarge the error due to amplification of optical path error caused by the deviation of the position of the CCD. Because the error is mainly in the edge area, a slope threshold, which controls the maximum surface slope of each subaperture, can be optimized to reduce the effect of the defocus on stitching measurement error. Constant angle error among neighboring subapertures has the biggest accumulation effect on the final stitched figure. For the spherical mirror with RoC of 100 m of 80mm×40mm, the error of the one-dimensional residual profile is 4.67 nm PV, assuming a constant angle error of 2×10-7rad. For the elliptical mirror with RoC of 60-140 m, it is more than 15 nm peak-to-valley (PV). It is because the profile difference caused by constant angle error is closer to a circle, which can be mostly removed after subtraction of a best-fit sphere. Based on the above error analysis, the developed algorithm-based stitching method was used to measure an elliptical cylindrical mirror of 74mm×40mm with RoC of 60-140 m, and the result was compared with a slope measurement instrument from the Beijing Synchrotron Radiation Facility. After removing the best fitting ellipse profile, the one-dimensional difference between the two results is only 0.77 nm RMS, which demonstrated good measurement accuracy.

The choice levels modulate outcome processing during outcome independent of behavior selection: Evidence from event-related potentials

Having a choice is a basic demand to influence human behavior. However, how various choice levels modulate outcome processing when the outcome is independent of the choices remains unclear. In this event-related potential (ERP) study, thirty-seven participants were instructed to perform a one-person choice task in which they were required to choose one card from 1 (no-choice level), 2 (medium-choice level), and 8 cards (high-choice level) to win a reward, with a 50% chance. Behavioral results indicated that pleasure and perceived control rating scores were linearly promoted with increased choice levels. ERP results revealed that having choices (medium- and high-choice level) elicited greater original-RewP and PCA-RewP amplitudes than having no choice (no-choice level), suggesting the amplification of the reward prediction error by quickly detecting whether there is a choice or not. Moreover, ERP results revealed that the original-P300 amplitudes were linearly enhanced with increased choice levels, suggesting the increased attentional allocation based on the motivational and emotional significance, due to advanced processing of the value of choice levels. Therefore, these results suggest that choice levels can modulate outcome processing, even when the outcome is independent of the choices, and provide further evidence to support the intrinsic value of having choices.

The impact of error covariance matrix structure of GRACE’s gravity solution on the mass flux estimates of Greenland ice sheet

The error variance-covariance matrices of the monthly GRACE gravity field models are usually well-structured (e.g., order-leading) to contain the error information of the monthly gravity field models, and they are important information to further improve the accuracy of the estimated mass transportation by a post-processing scheme. Intensive studies have been performed to understand the impact of different approximations of the full error variance-covariance matrix on the mass estimates obtained with the conventional GRACE-post processing methods (e.g., the de-striping method). In this study, based on the variants of the mascon approach which treat monthly GRACE solutions as input, we consider four different structures to the error variance-covariance matrix, (i) full matrix, (ii) block diagonal matrix, (iii) diagonal matrix, and (iv) identity matrix, and examine their impact on the mass transport estimates in Greenland. Using both synthetic and real data, we analyze the results at four temporal scales: (i) the long-term decadal scale, (ii) the inter-annual scale, (iii) the seasonal scale, and (iv) the monthly scale. Based on the synthetic study, we find that for the recovery of the long-term trend, the application of the diagonal structure obtains the best estimates. This is caused by the amplification of the model error in the mascon approach when considering the full and block diagonal structures of error variance-covariance matrix, not due to any imperfection of them. Therefore, we emphasize that one should be aware of mascon model deficiency in the mascon approach. Furthermore, the best inter-annual, seasonal and monthly mass estimates are derived by considering the block diagonal and full structures. This is caused by the behavior of the bias and the unique parameterization error in the case of different structures. A similar finding is also presented in the real data case. Finally, our analysis denotes the necessity of releasing the block diagonal structure together with the official monthly gravity field model for the GRACE Follow-On mission, instead of releasing only the diagonal structure as done for the GRACE mission.

An atmospheric dynamics perspective on the amplification and propagation of forecast error in numerical weather prediction models: A case study

Despite huge progress made, state‐of‐the‐art numerical weather prediction systems occasionally experience severe forecast busts for the large‐scale extratropical circulation. This study investigates one of the most severe forecast busts for Europe in the European Centre for Medium‐Range Weather Forecasts integrated forecasting system (IFS) in recent years. The forecast bust occurred in March 2016 and was associated with a misforecast of the onset of a blocking regime. We investigate the evolution of the forecast error in the IFS ensemble by employing a potential vorticity perspective combined with Lagrangian diagnostics. We show that the error grows rapidly from an initially small perturbation in the detailed structure of an upper‐level trough near Newfoundland. This trough triggers strong diabatic warm conveyor belt activity in the North Atlantic region. The misrepresentation of this warm conveyor belt activity in the ensemble forecast amplifies the initial condition error and communicates it downstream into Europe. Specifically, the ensemble underestimates poleward warm conveyor belt ascent and associated warm conveyor belt outflow into high latitudes. Instead, all ensemble members forecast too strong warm conveyor belt outflow further to the south, which ultimately results in a wrong forecast of the upper‐level Rossby wave pattern over Europe. This case study shows that warm conveyor belts and the associated latent heat release in slantwise ascending air can trigger a nonlinear feedback mechanism that amplifies forecast error strongly and communicates it into regions far downstream. It corroborates the fact that multiscale interactions and moist‐and dry‐dynamical processes ranging from microphysical to synoptic scales need to be represented accurately in numerical weather prediction, in order to predict the extratropical large‐scale circulation correctly.

SWATH Tandem Mass Spectrometry Workflow for Quantification of Mass Isotopologue Distribution of Intracellular Metabolites and Fragments Labeled with Isotopic 13C Carbon.

Accurate quantification of mass isotopologue distribution (MID) of metabolites is a prerequisite for 13C-metabolic flux analysis. Currently used mass spectrometric (MS) techniques based on multiple reaction monitoring (MRM) place limitations on the number of MIDs that can be analyzed in a single run. Moreover, the deconvolution step results in amplification of error. Here, we demonstrate that SWATH MS/MS, a data independent acquisition (DIA) technique allows quantification of a large number of precursor and product MIDs in a single run. SWATH sequentially fragments all precursor ions in stacked mass isolation windows. Co-fragmentation of all precursor isotopologues in a single SWATH window yields higher sensitivity enabling quantification of MIDs of fragments with low abundance and lower systematic and random errors. We quantify the MIDs of 53 precursor and product ions corresponding to 19 intracellular metabolites from a dynamic 13C-labeling of a model cyanobacterium, Synechococcus sp. PCC 7002. The use of product MIDs resulted in an improved precision of many measured fluxes compared to when only precursor MIDs were used for flux analysis. The approach is truly untargeted and allows additional metabolites to be quantified from the same data.

Neuromotor Noise Is Malleable by Amplifying Perceived Errors.

Variability in motor performance results from the interplay of error correction and neuromotor noise. This study examined whether visual amplification of error, previously shown to improve performance, affects not only error correction, but also neuromotor noise, typically regarded as inaccessible to intervention. Seven groups of healthy individuals, with six participants in each group, practiced a virtual throwing task for three days until reaching a performance plateau. Over three more days of practice, six of the groups received different magnitudes of visual error amplification; three of these groups also had noise added. An additional control group was not subjected to any manipulations for all six practice days. The results showed that the control group did not improve further after the first three practice days, but the error amplification groups continued to decrease their error under the manipulations. Analysis of the temporal structure of participants’ corrective actions based on stochastic learning models revealed that these performance gains were attained by reducing neuromotor noise and, to a considerably lesser degree, by increasing the size of corrective actions. Based on these results, error amplification presents a promising intervention to improve motor function by decreasing neuromotor noise after performance has reached an asymptote. These results are relevant for patients with neurological disorders and the elderly. More fundamentally, these results suggest that neuromotor noise may be accessible to practice interventions.

Correction of a Technical Error in the Golf Swing: Error Amplification Versus Direct Instruction

ABSTRACTPerformance errors drive motor learning for many tasks. The authors' aim was to determine which of two strategies, method of amplification of error (MAE) or direct instruction (DI), would be more beneficial for error correction during a full golfing swing with a driver. Thirty-four golfers were randomly assigned to one of three training conditions (MAE, DI, and control). Participants were tested in a practice session in which each golfer performed 7 pretraining trials, 6 training-intervention trials, and 7 posttraining trials; and a retention test after 1 week. An optoeletronic motion capture system was used to measure the kinematic parameters of each golfer's performance. Results showed that MAE is an effective strategy for correcting the technical errors leading to a rapid improvement in performance. These findings could have practical implications for sport psychology and physical education because, while practice is obviously necessary for improving learning, the efficacy of the learning process is essential in enhancing learners' motivation and sport enjoyment.

The effects of two different correction strategies on the snatch technique in weightlifting

ABSTRACTImproving motor skills represents one of the major issues in motor control and motor learning literature. The aim of this study was to investigate which of two strategies, method of amplification of error (MAE) or direct instruction (DI), would be more beneficial for error correction of the snatch technique. Thirty well-trained male weightlifters were randomly assigned to one of three training conditions (MAE, DI and Control). The experiment took place in only one practice session in which each lifter performed 3 pretraining trials, 8 training intervention trials, and 3 post-training trials, and a retention test session after 1 week. An optoelectronic motion capture system was used to measure the kinematic parameters of the weightlifting performance. After the training intervention, data showed that the MAE group revealed a greater improvement in several kinematic parameters when compared to the DI and Control groups, and the benefits derived from its application were still present 1 week later in the retention test. Nevertheless, the findings of the present study should be interpreted with caution due to the relatively small sample size; further research will also be necessary to evaluate the effects of MAE with different ability levels and other sport skills. The present findings could have practical implications for sport psychology and physical education because while practice is obviously necessary for improving learning, the efficacy of the learning process is essential in enhancing learners’ motivation and sport enjoyment.

Global error analysis and inertial manifold reduction

Four types of global error for initial value problems are considered in a common framework. They include classical forward error analysis and shadowing error analysis together with extensions of both to include rescaling of time. To determine the amplification of the local error that bounds the global error we present a linear analysis similar in spirit to condition number estimation for linear systems of equations. We combine these ideas with techniques for dimension reduction of differential equations via a boundary value formulation of numerical inertial manifold reduction. These global error concepts are exercised to illustrate their utility on the Lorenz equations and inertial manifold reductions of the Kuramoto–Sivashinsky equation.

Gate Capacitance Measurement Using a Self-Differential Charge-Based Capacitance Measurement Method

In this letter, we propose a self-differential charge-based capacitance measurement(SDCBCM) method. It is specifically applied to measure MOSFET gate capacitance with high accuracy. SDCBCM has two main advantages. First, it employs a newly proposed self-differential method to derive the capacitance-voltage ( $C$ – $V$ ) curve of gate capacitance, thus avoiding the amplification of systematic error during the differentiation. Second, it can operate at a very high frequency (500 MHz or more), which for the first time allows the gate capacitance of actual operating frequency to be measured and reduces random error to a very low level. Compared with the previous work, the accuracy of our method is increased by tens of times.

Simultaneous Online Measurement of H2O and CO2 in the Humid CO2 Adsorption/Desorption Process.

A dew point meter (DP) and an infrared (IR) CO2 analyzer were assembled in a humid CO2 adsorption/desorption system in series for simultaneous online measurements of H2O and CO2, respectively. The humidifier, by using surface-flushing on a saturated brine solution was self-made for the generation of humid air flow. It was found that by this method it became relatively easy to obtain a low H2O content in air flow and that its fluctuation could be reduced compared to the bubbling method. Water calibration for the DP-IR detector is necessary to be conducted for minimizing the measurement error of H2O. It demonstrated that the relative error (RA) for simultaneous online measurements H2O and CO2 in the desorption process is lower than 0.1%. The high RA in the adsorption of H2O is attributed to H2O adsorption on the transfer pipe and amplification of the measurement error. The high accuracy of simultaneous online measurements of H2O and CO2 is promising for investigating their co-adsorption/desorption behaviors, especially for direct CO2 capture from ambient air.

High acceleration motion control based on a time-domain identification method and the disturbance observer

High acceleration motion tends to excite flexible modes of the motion stage to magnify disturbances, causing challenges for control engineers. Among existing control algorithms, the disturbance observer (DOB) is recognized as an effective tool for improving servo performance by suppressing disturbances. Besides external disturbances, the internal interference caused by model mismatches is an important factor which can degrade the servo performances of the DOB-based controllers. Therefore, a more accurate relay-based model identification method is proposed to deal with model mismatches. This method uses the position signal as the input of the relay module. Simulations show that the proposed identification method achieves higher identification accuracy by preventing the amplification of the quantization error during velocity detection. High acceleration point-to-point motions are conducted on a linear-driving stage with a DOB-based controller and experimental results demonstrate that improved servo performance with a maximum tracking error of 2.0μm at a maximum acceleration of 9.1g (1g=9.806m/s2).

Amplification and suppression of round-off error in Runge–Kutta methods

A simple nonstiff linear initial-value problem is used to demonstrate the amplification of round-off error in the course of using a second-order Runge–Kutta method. This amplification is understood in terms of an appropriate expression for the global error. An implicit method is then used to show how the roundoff error may actually be suppressed. This article describes a phenomenon not usually considered in general purpose textbooks on numerical analysis, and is therefore potentially interesting and useful to students of the subject.

Robust 2D phase correction for echo planar imaging under a tight field‐of‐view

Nyquist ghost artifacts are a serious issue in echo planar imaging. These artifacts primarily originate from phase difference between even and odd echo images and can be removed or reduced using phase correction methods. The commonly used 1D phase correction can only correct phase difference along readout axis. 2D correction is, therefore, necessary when phase difference presents along both readout and phase encoding axes. However, existing 2D methods have several unaddressed issues that affect their practicality. These issues include uncharacterized noise behavior, image artifact due to unoptimized phase estimation, Gibbs ringing artifact when directly applying to partial k(y) data, and most seriously a new image artifact under tight field-of-view (i.e., field-of-view slightly smaller than object size). All these issues are addressed in this article. Specifically, theoretical analysis of noise amplification and effect of phase estimation error is provided, and tradeoff between noise and ghost is studied. A new 2D phase correction method with improved polynomial fitting, joint homodyne processing and phase correction, compatibility with tight field-of-view is then proposed. Various results show that the proposed method can robustly generate images free of Nyquist ghosts and other image artifacts even in oblique scans or when cross-term eddy current terms are significant.

Optimization and performance criteria of a Stokes polarimeter based on two variable retarders

In this paper we present the analysis, optimization and implementation of several Stokes polarimeter configurations based on a set-up including two variable retarders. The polarimeter analysis is based on the Mueller-Stokes formalism, and as a consequence, it is suitable to deal with depolarized light. Complete Stokes polarimeters are optimized by minimizing the amplification of simulated errors into the final solution. Different indicators useful to achieve this aim, as the condition number or the equally weighted variance, are compared in this paper. Moreover, some of the optimized polarimeters are experimentally implemented and it is studied the influence of small deviations from the theoretical ones on the amplification of the Stokes component error. In addition, the benefit of using incomplete polarimeters, when detecting specific ranges of states of polarization, is discussed.

Analysis, optimization and implementation of a variable retardance based polarimeter

We present a comprehensive analysis, optimization and implementation of a Stokes polarimeter based on two liquid crystals acting as variable retarders. For the optimization process, the Conditional Number or the Equally Weighted Variance indicators are applied and compared as a function of different number of polarization analyzers. Moreover, some of the optimized polarimeter configurations are experimentally implemented and the influence of small experimental deviations from the optimized configuration values on the amplification of the Stokes component error is also studied. Some experimental results obtained by using the implemented polarimeters, when measuring different incidence states of polarization, are provided.

Error analysis of marker‐based object localization using a single‐plane XRII

The role of imaging and image guidance is increasing in surgery and therapy, including treatment planning and follow-up. Fluoroscopy is used for two-dimensional (2D) guidance or localization; however, many procedures would benefit from three-dimensional (3D) guidance or localization. Three-dimensional computed tomography (CT) using a C-arm mounted x-ray image intensifier (XRII) can provide high-quality 3D images; however, patient dose and the required acquisition time restrict the number of 3D images that can be obtained. C-arm based 3D CT is therefore limited in applications for x-ray based image guidance or dynamic evaluations. 2D-3D model-based registration, using a single-plane 2D digital radiographic system, does allow for rapid 3D localization. It is our goal to investigate-over a clinically practical range-the impact of x-ray exposure on the resulting range of 3D localization precision. In this paper it is assumed that the tracked instrument incorporates a rigidly attached 3D object with a known configuration of markers. A 2D image is obtained by a digital fluoroscopic x-ray system and corrected for XRII distortions (+/- 0.035 mm) and mechanical C-arm shift (+/- 0.080 mm). A least-square projection-Procrustes analysis is then used to calculate the 3D position using the measured 2D marker locations. The effect of x-ray exposure on the precision of 2D marker localization and on 3D object localization was investigated using numerical simulations and x-ray experiments. The results show a nearly linear relationship between 2D marker localization precision and the 3D localization precision. However, a significant amplification of error, nonuniformly distributed among the three major axes, occurs, and that is demonstrated. To obtain a 3D localization error of less than +/- 1.0 mm for an object with 20 mm marker spacing, the 2D localization precision must be better than +/- 0.07 mm. This requirement was met for all investigated nominal x-ray exposures at 28 cm FOV, and for all but the lowest two at 40 cm FOV. However, even for those two nominal exposures, the expected 3D localization error is less than +/- 1.2 mm. The tracking precision was +/- 0.65 mm for the out-of-plane translations, +/- 0.05 mm for in-plane translations, and +/- 0.05 degrees for the rotations. The root mean square (RMS) difference between the true and projection-Procrustes calculated location was 1.07 mm. It is believed these results show the potential of this technique for dynamic evaluations or real-time image guidance using a single x-ray source and XRII detector.

Edward Norton Lorenz

Edward Norton Lorenz