Motion-induced Errors Research Articles

Three-dimensional deformation monitoring of internal nodes of large-span suspended dome structure using videogrammetry under camera instability

Large-span suspended domes often serve as landmarks for cities or countries. This paper proposes a videogrammetric method for monitoring the 3D deformation of internal key nodes in such structures, even under conditions of camera instability. Utilizing circular targets strategically placed on the measurement area, a dynamic parameter calibration method is developed to estimate the instantaneous position and orientation of cameras relative to the world coordinate system, minimizing camera motion-induced errors. Combined with surface targets on the rigid structure and local coordinate frame transformation, the 3D displacement response of structural internal nodes can be precisely measured using the proposed tracking method. The effectiveness and accuracy of the proposed methods were validated through exhaustive experiments, improving positioning accuracy for the structural internal nodes from 47.24 mm to 1.62 mm after dynamic parameter correction. This methodology offers a low-cost, easily implemented, and non-destructive vision-based solution for the long-term monitoring of large-span suspended domes.

Real-time motion-induced error reduction for phase-shifting profilometry with projection points tracking method

Fringe projection profilometry is a significant method for three-dimensional measurement due to its non-contact and high accuracy. However, the motion-induced error will lead to the loss of measurement accuracy in dynamic scenes due to the disruption of the phase measurement process. In this paper, we introduce a novel motion error model that considers object motion causes the misalignment of the projection points on the camera, and propose the projection points tracking method to reduce the motion-induced error. First, the speckle pattern is added to projection sequences, after which the projection point displacements are determined using the digital image correlation (DIC) method between the adjacent speckle patterns. Finally, the fringe patterns are corrected using the image remapping method to calculate the 3D shape. Quantitative analysis and dynamic measurement experiments verify the feasibility of the proposed method. Different from 3D-DIC, we use one camera-projector system to realize high-accuracy measurement in dynamic scenes.

Parallel camera network: Motion-compensation vision measurement method and system for structural displacement

This study proposes a motion-compensation vision measurement method and system for structural displacement, termed the parallel camera network (PCN). Based on the fixedly connected calibration cameras and measurement cameras, the PCN method effectively address the optical measurement problems of the unstable observation platform. Unlike existing ego-motion compensation methods, the PCN method allows for reference or stationary points that are distant from the camera stations, significantly reducing motion-induced measurement errors of the observation platform. Laboratory tests showed that compensating for platform motion tripled measurement accuracy using the PCN method. In practical applications, the system has been successfully deployed for monitoring subsidence of operational high-speed rail piers and the arch axis during large-span arch bridge construction. The proposed method and system significantly enhance the engineering flexibility of visual measurements.

Field Evaluation of an Autonomous, Low-Power Eddy Covariance CO2 Flux System for the Marine Environment

Abstract Eddy covariance (EC) air–sea CO2 flux measurements have been developed for large research vessels, but have yet to be demonstrated for smaller platforms. Our goal was to design and build a complete EC CO2 flux package suitable for unattended operation on a buoy. Published state-of-the-art techniques that have proven effective on research vessels, such as airstream drying and liquid water rejection, were adapted for a 2-m discus buoy with limited power. Fast-response atmospheric CO2 concentration was measured using both an off-the-shelf (“stock”) gas analyzer (EC155, Campbell Scientific, Inc.) and a prototype gas analyzer (“proto”) with reduced motion-induced error that was designed and built in collaboration with an instrument manufacturer. The system was tested on the University of New Hampshire (UNH) air–sea interaction buoy for 18 days in the Gulf of Maine in October 2020. The data demonstrate the overall robustness of the system. Empirical postprocessing techniques previously used on ship-based measurements to address motion sensitivity of CO2 analyzers were generally not effective for the stock sensor. The proto analyzer markedly outperformed the stock unit and did not require ad hoc motion corrections, yet revealed some remaining artifacts to be addressed in future designs. Additional system refinements to further reduce power demands and increase unattended deployment duration are described.

Motion-Induced Error Reduction for Motorized Digital Fringe Projection System

Motion-Induced Error Reduction for Motorized Digital Fringe Projection System

Rapid -weighted MRI using multishot EPI with retrospective motion and phase correction in the emergency department.

Brain MRI is increasingly used in the emergency department (ED), where -weighted MRI is an essential tool for detecting hemorrhage and stroke. The goal of this study was to develop a rapid -weighted MRI technique capable of correcting motion-induced artifacts, thereby simultaneously improving scan time and motion robustness for ED applications. A 2D gradient-echo (GRE)-based multishot EPI (msEPI) technique was implemented using a navigator echo for estimating motion-induced errors. Bulk rigid head motion and phase errors were retrospectively corrected using an iterative conjugate gradient approach in the reconstruction pipeline. Three volunteers and select patients were imaged at 3 T and/or 1.5 T with an approximately 1-min full-brain protocol using the proposed msEPI technique and compared to an approximately 3-min standard-of-care GRE protocol to examine its performance. Data from volunteers demonstrated that in-plane motion artifacts could be effectively corrected with the proposed msEPI technique, and through-plane motion artifacts could be mitigated. Patient images were qualitatively reviewed by one radiologist without a formal statistical analysis. These results suggested the proposed technique could correct motion-induced artifacts in the clinical setting. In addition, the conspicuity of susceptibility-related lesions using the proposed msEPI technique was comparable, or improved, compared to GRE. A 1-min full-brain -weighted MRI technique was developed using msEPI with a navigator echo to correct motion-induced errors. Preliminary clinical results suggest faster scans and improved motion robustness and lesion conspicuity make msEPI a competitive alternative to traditional -weighted MRI techniques for brain studies in the ED.

A CO2 and H2O Gas Analyzer with Reduced Error due to Platform Motion

Abstract One long-standing technical problem affecting the accuracy of eddy correlation air–sea CO2 flux estimates has been motion contamination of the CO2 mixing-ratio measurement. This sensor-related problem is well known but its source remains unresolved. This report details an attempt to identify and reduce motion-induced error and to improve the infrared gas analyzer (IRGA) design. The key finding is that a large fraction of the motion sensitivity is associated with the detection approach common to most closed- and open-path IRGA employed today for CO2 and H2O measurements. A new prototype sensor was developed to both investigate and remedy the issue. Results in laboratory and deep-water tank tests show marked improvement. The prototype shows a factor of 4–10 reduction in CO2 error under typical at-sea buoy pitch and roll tilts in comparison with an off-the-shelf IRGA system. A similar noise reduction factor of 2–8 is observed in water vapor measurements. The range of platform tilt motion testing also helps to document motion-induced error characteristics of standard analyzers. Study implications are discussed including findings relevant to past field measurements and the promise for improved future flux measurements using similarly modified IRGA on moving ocean observing and aircraft platforms.

On the correction of respiratory motion-induced image reconstruction errors in positron-emission tomography-guided radiation therapy

Free breathing (FB) positron emission tomography (PET) images are routinely used in radiotherapy for lung cancer patients. Respiration-induced artifacts in these images compromise treatment response assessment and obstruct clinical implementation of dose painting and PET-guided radiotherapy. The purpose of this study is to develop a blurry image decomposition (BID) method to correct motion-induced image-reconstruction errors in FB-PETs. Assuming a blurry PET is represented as an average of multi-phase PETs. A four-dimensional computed-tomography image is deformably registered from the end-inhalation (EI) phase to other phases. With the registration-derived deformation maps, PETs at other phases can be deformed from a PET at the EI phase. To reconstruct the EI-PET, the difference between the blurry PET and the average of the deformed EI-PETs is minimized using a maximum-likelihood expectation-maximization algorithm. The developed method was evaluated with computational and physical phantoms as well as PET/CT images acquired from three patients. The BID method increased the signal-to-noise ratio from 1.88±1.05 to 10.5±3.3 and universal-quality index from 0.72±0.11 to 1.0 for the computational phantoms, and reduced the motion-induced error from 69.9% to 10.9% in the maximum of activity concentration and from 317.5% to 8.7% in the full width at half maximum of the physical PET-phantom. The BID-based corrections increased the maximum standardized-uptake values by 17.7±15.4% and reduced tumor volumes by 12.5±10.4% on average for the three patients. The proposed image-decomposition method reduces respiration-induced errors in PET images and holds potential to improve the quality of radiotherapy for thoracic and abdominal cancer patients.

Efficient dynamic 3D shape measurement technique for resisting motion-induced error

The phase-shifting profilometry is usually used to acquire dynamic 3D scenarios owning to these merits of dense 3D points, high speed, and simple devices. However, the object in motion will introduce an unknown phase shift, inducing the motion error in 3D shape. Eliminating the motion error with high efficiency is still a significant challenge. This paper analyzes the model of motion error and proposes a novel fringe projection strategy to resist the motion error. Unlike the traditional methods, typically compensating for the motion error with supplementary computing, the proposed method can directly obtain the accurate phase since the designed fringe projection strategy possesses the function of resisting motion error. Therefore, it is more efficient without the post-processing procedure. Simulations and experiments reveal that the proposed method can significantly improve efficiency with reasonable accuracy.

Quantification of motion-induced measurement error on floating lidar systems

Abstract. Floating lidar systems (FLSs) are widely used for offshore wind site assessment, and their measurements show good agreement when compared to trusted reference sources. However, some influence of motion on mean wind speed data from FLS has to be assumed but could not have been quantified with experimental methods yet because the involved uncertainties are larger than the expected impact of motion. This study describes the motion-induced bias on horizontal mean wind speed estimates from FLS with the help of simulations of the lidar sampling pattern of a continuous-wave (CW) velocity–azimuth display (VAD) scanning wind lidar. Analytic modeling is used to validate the simulations. It is found that the mean bias depends on amplitude and frequency of motion, the angle between motion and wind direction, and wind speed and strength of wind shear. The simulations are used to quantify the measurement deviation that is caused by motion for the example of the Fugro SEAWATCH Wind LiDAR Buoy (SWLB) carrying a ZX 300M profiling wind lidar. The strongest bias of −0.67 % of the measurement values was estimated for a test case with “strong” waves aligned with the inflow wind direction. Under “normal” wave conditions the bias is smaller. The reason for these low errors lies in a fortunate combination of the frequencies of lidar prism rotation and tilt motion.

Motion-Induced Phase Error Compensation Using Three-Stream Neural Networks

Phase-shifting profilometry (PSP) has been widely used in the measurement of dynamic scenes. However, the object motion will cause a periodical motion-induced error in the phase map, and there is still a challenge to eliminate it. In this paper, we propose a method based on three-stream neural networks to reduce the motion-induced error, while a general dataset establishment method for dynamic scenes is presented to complete three-dimensional (3D) shape measurement in a virtual fringe projection system. The numerous automatically generated data with various motion types is employed to optimize models. Three-step phase-shift fringe patterns captured along a time axis are divided into three groups and processed by trained three-stream neural networks to produce an accurate phase map. The actual experiment’s results demonstrate that the proposed method can significantly perform motion-induced error compensation and achieve about 90% improvement compared with the traditional three-step phase-shifting algorithm. Benefiting from the robust learning-based technique and convenient digital simulation, our method does not require empirical parameters or complex data collection, which are promising for high-speed 3D measurement.

Accurate dynamic 3-D shape measurement based on the fringe pattern super-reconstruction technique

Fringe projection profilometry (FPP) has been widely used for three-dimensional (3-D) shape measurement. However, measuring the dynamic objects is always problematic due to the movement of objects during the inter-frame time gap. Many dynamic solutions have been developed, but they are fragile for practical applications. In this paper, we propose a new method for dynamic 3-D measurement with flexible implementation and high measurement accuracy, which utilizes the inverse relationship between camera sampling speed and sampling resolution and image super-reconstruction technique. The camera selects a low sampling resolution to capture fringe patterns, thus improving the sampling speed and alleviating the influence of object’s dynamic motion. However, insufficient resolution will affect the accuracy and details of the reconstructed 3-D shape. Inspired by the successes of computational imaging techniques, the resolution and details lost by the front-end camera can be restored by the back-end image processing. Therefore, we specifically designed a details restoration and super-reconstruction network (DRSRNet) to transform the captured low-resolution fringes into the desired high-quality and high-resolution fringes. The desired 3-D shapes are calculated from these transformed fringes combined with the correspondence system calibration parameters. The provided experiments verify that the proposed method can improve the 3-D profiling speed by 5 times while ensuring the profiling accuracy, and the motion-induced errors can be obviously eliminated compared with FPP using the camera with a high sampling resolution. Furthermore, the proposed method can achieve different 3-D profiling speed increases to flexibly suit different measurement requirements.

Deep learning-based method for non-uniform motion-induced error reduction in dynamic microscopic 3D shape measurement.

The non-uniform motion-induced error reduction in dynamic fringe projection profilometry is complex and challenging. Recently, deep learning (DL) has been successfully applied to many complex optical problems with strong nonlinearity and exhibits excellent performance. Inspired by this, a deep learning-based method is developed for non-uniform motion-induced error reduction by taking advantage of the powerful ability of nonlinear fitting. First, a specially designed dataset of motion-induced error reduction is generated for network training by incorporating complex nonlinearity. Then, the corresponding DL-based architecture is proposed and it contains two parts: in the first part, a fringe compensation module is developed as network pre-processing to reduce the phase error caused by fringe discontinuity; in the second part, a deep neural network is employed to extract the high-level features of error distribution and establish a pixel-wise hidden nonlinear mapping between the phase with motion-induced error and the ideal one. Both simulations and real experiments demonstrate the feasibility of the proposed method in dynamic macroscopic measurement.

Quasi-pixelwise motion compensation for 4-step phase-shifting profilometry based on a phase error estimation.

Phase-shifting profilometry (PSP) is widely used in 3D shape measurement due to its high accuracy. However, in dynamic scenarios, the motion of objects will introduce phase-shifting errors and result in measurement errors. In this paper, a novel compensation method based on 4-step phase-shifting profilometry is proposed to reduce motion-induced errors when objects undergo uniform or uniformly accelerated motion. We utilize the periodic characteristic of fringe patterns to estimate the phase errors from only four phase-shifting patterns and realize a pixel-wise error compensation. This method can also be applied to non-rigid deforming objects and help restore high-quality texture. Both simulation and experiments demonstrate that the proposed method can effectively improve the measurement accuracy and reduce surface ripples introduced by motion for a standard monocular structured-light system.

Suppressing motion-induced phase error by using equal-step phase-shifting algorithms in fringe projection profilometry.

Phase-shifting fringe projection profilometry is a widely used and important technique for three-dimensional surface measurement, where N-step fixed-step phase-shifting algorithms are commonly used. With a pressing need to apply this technique for dynamic object/scene measurement, the motion-induced error poses a challenge in achieving high measurement accuracy. A few correction methods have been developed by involving physical markers or complicated algorithms. In this paper, the equal-step phase-shifting algorithms are proposed as a simpler yet more effective solution. By approximating the phase variations as unknown but linear phase shifts, the equal-step algorithms are naturally immune to object motion. In particular, two classical algorithms, including the four-step Carré algorithm and the five-step Stoilov algorithm, are adopted. Furthermore, a novel three-step gradient-based equal-step phase-shifting (GEPS) algorithm is proposed. These equal-step algorithms are studied through comprehensive simulations and experiments, showing that, (i) the equal-step algorithms are all effective in greatly suppressing the motion-induced errors in both ideal and noisy situations; and (ii) among the three algorithms, the Stoilov algorithm is more robust to handle the object motion and the harmonics simultaneously, while the GEPS requires a least number of frames. This study will urge the use of the equal-step algorithms for phase extraction in dynamic profilometry for immediate motion-error suppression by merely implementing a single phase-calculation equation.

Motion-induced error reduction for phase-shifting profilometry with phase probability equalization

Phase-shifting algorithms have been widely used for three-dimensional (3D) shape measurement. However, when measuring moving objects, the object motion may distort the linear phase and lead to the phase error. This paper presents an effective phase probability equalization (PPE) method for motion-induced error reduction, which directly equalizes the distorted phase to estimate the linear phase. In general, adequate sampling pixels are needed to compute the accurate phase probability (PP). This paper further presents an improved shifted-phase probability equalization (SPE) method, which combines the original phase and its π-shifted phase to double the sampling pixels. Both simulations and experiments have been conducted to measure objects moving in z-direction, and their results validate that the proposed PPE and SPE methods could effectively compensate the motion-induced error.

Gyro-stellar inertial attitude estimation for satellite with high motion rate

AbstractFor a common micro-satellite, orbiting in a circular sun-synchronous orbit (SSO) at an altitude between 500 and 600km, the satellite attitude during off-nadir imaging and staring-imaging operations can be up to ±45 degree on roll and pitch angles. During these off-nadir pointing for both multi-trip operation and staring imaging operations, the spacecraft body is commonly subject to high-rate motion. This posts challenges for a spacecraft attitude determination subsystem called Gyro Stellar Inertial Attitude Estimate (GS IAE), which employs gyros and star sensors to maintain the required attitude knowledge, since star trackers will severely degrade attitude estimation accuracies when the spacecraft is subject to high-rate motion. This paper analyses the star motion-induced errors for a typical star tracker, models the star motion-induced errors to assess the performance impact on the attitude estimation accuracy, and investigates the adaptive extended Kalman filter design in the GS IAE while evaluating its effectiveness.

Two-frequency phase-shifting method vs. Gray-coded-based method in dynamic fringe projection profilometry: A comparative review

Two-frequency phase-shifting phase unwrapping and Gray-coded-based phase unwrapping are two typical temporal phase unwrapping methods to recover discontinuous or spatially isolated surfaces in fringe projection profilometry (FPP). But in dynamic measurement, environmental noise, required number of patterns and inter-frame motion affect the performance of these two methods on measuring anti-noise ability, efficiency and robustness in varying degrees. So, it is a challenge to quantitatively compare these methods’ abilities and determine the optimum one with appropriate system parameters and under a certain condition. In this paper, a detailed comparative study is conducted for the two-frequency phase-shifting method including hierarchical, number-theoretical and heterodyne approaches and the Gray-coded-based method including traditional Gray code approach, complementary Gray code approach and Gray code approach with tripartite phase unwrapping (Tri-PU). First, the principles of six approaches are reviewed; then, their anti-noise ability was quantitatively compared based on the proposed noise model; next, theoretical comparison of measuring efficiency, comparative review of improved methods and recommendation on usage are given to boost their efficiency; finally, motion-induced error model in phase unwrapping was presented to determine the appropriate system parameters in dynamic measurement. Theoretical analysis, numerical simulation and experimental results are consistent and demonstrate that (i) Gray-coded-based method has better anti-noise ability than two-frequency phase-shifting method; (ii) two-frequency phase-shifting method is more efficient than traditional Gray-coded-based method when the number of encoding fringe periods exceeds 8; (iii) hierarchical approach and Gray-coded approach with Tri-PU have best performance to resist motion-induced error in their respective types of methods. Comparative results can give a helpful guidance to choose the “best” approach in different application scenes and quantitatively determine the projected fringe periods and imaging or projecting speed in dynamic measurement for FPP.

Accurate 3D Reconstruction of Dynamic Objects by Spatial-Temporal Multiplexing and Motion-Induced Error Elimination.

Three-dimensional (3D) reconstruction of dynamic objects has broad applications, including object recognition and robotic manipulation. However, achieving high-accuracy reconstruction and robustness to motion simultaneously is a challenging task. In this paper, we present a novel method for 3D reconstruction of dynamic objectS, whose main features are as follows. Firstly, a structured-light multiplexing method is developed that only requires 3 patterns to achieve high-accuracy encoding. Fewer projected patterns require shorter image acquisition time, thus, the object motion is reduced in each reconstruction cycle. The three patterns, i.e. spatial-temporally encoded patterns, are generated by embedding a specifically designed spatial-coded texture map into the temporal-encoded three-step phase-shifting fringes. A temporal codeword and three spatial codewords are extracted from the composite patterns using a proposed extraction algorithm. The two types of codewords are utilized separately in stereo matching: the temporal codeword ensures the high accuracy, while the spatial codewords are responsible for removing phase ambiguity. Secondly, we aim to eliminate the reconstruction error induced by motion between frames abbreviated as motion induced error (MiE). Instead of assuming the object to be static when acquiring the 3 images, we derive the motion of projection pixels among frames. Using the extracted spatial codewords, correspondences between different frames are found, i.e. pixels with the same codewords are traceable in the image sequences. Therefore, we can obtain the phase map at each image-acquisition moment without being affected by the object motion. Then the object surfaces corresponding to all the images can be recovered. Experimental results validate the high reconstruction accuracy and precision of the proposed method for dynamic objects with different motion speeds. Comparative experiments show that the presented method demonstrates superior performance with various types of motion, including translation in different directions and deformation.

Efficient Dynamic 3d Shape Measurement Technique for Resisting Motion-Induced Error

Efficient Dynamic 3d Shape Measurement Technique for Resisting Motion-Induced Error