Self-calibration Model Research Articles

Self-Calibration Model of Terrestrial Three-Dimensional Laser Scanners Considering Random Errors and Robust Estimation Solution

Self-Calibration Model of Terrestrial Three-Dimensional Laser Scanners Considering Random Errors and Robust Estimation Solution

AN ITERATIVE APPROACH FOR SELF-CALIBRATING BUNDLE ADJUSTMENT

Abstract. Obtaining accurate image interior and exterior orientations is the key to improve 3D measurement accuracy besides reliable and accurate image matching. A majority of cameras used for those tasks are non-metric cameras. Non-metric cameras commonly suffer various distortions. Generally, there are two ways to remove these distortions: 1) conducting prior camera calibration in a controlled environment; 2) applying self-calibrating bundle adjustment in the application environment. Both approaches have their advantages and disadvantages but one thing is common that there is no universal calibration model available so far which can remove all sorts of distortions on images and systemic errors of image orientations. Instead of developing additional calibration models for camera calibration and self-calibrating adjustment, this paper presents a novel approach which applies self-calibrating bundle adjustment in an iterative fashion: after performing a conventional self-calibrating bundle adjustment, the image coordinates of tie points are re-calculated using the newly obtained self-calibration model coefficients, and the self-calibrating bundle adjustment is applied again in the hope that the remaining distortions and systematic errors will be reduced further within next a few iterations. Using a “virtual image” concept this iterative approach does not require to resample images or/and re-measure tie points during iterations, only costs a few additional iterations computational resource. Several trails under various application environments are conducted using this proposed iterative approach and the results indicate that not only the distortions can be reduced further but also image orientations become much stable after a few iterations.

WAVELETS FOR SELF-CALIBRATED BUNDLE BLOCK ADJUSTMENT

Abstract. This paper entails a methodological novelty and builds upon prior research on a wavelets-based model for digital camera self-calibration. We introduce a new kernel function based on the compactly supported orthogonal third-order asymmetric Daubechies wavelet to correct systematic image distortion errors. Tests are done by using aerial images taken with a high-resolution metric digital aerial mapping camera. The quality of experimental results is evaluated by using reliable and high precision ground check points in the calibration field. For example, a four-fold block with this wavelet self-calibration model has the external accuracy of about 0.28 GSD (=ground sampling distance) in the horizontal direction, and about 0.43 GSD in the vertical direction, respectively, where 1GSD ≈ 4.6cm. The posterior standard deviations σ̂0 of unit weight are reduced from 0.37 pixel to 0.27 pixel. The residual vector lengths are also significantly reduced after our wavelet additional parameters are used. Experimental results support the proposal and demonstrate the applicability of this new model.

Self-Calibration of the Stereo Vision System of the Chang'e-4 Lunar Rover Based on the Points and Lines Combined Adjustment

The stereo vision system is the special engineering measurement instrument of the Chang'e-4 lunar rover. It is composed of the Navigation Camera (NavCam) and the Mast Mechanism (MasMec). An improved self-calibration method for the stereo vision system of the Chang'e-4 lunar rover is proposed. The method consists of two parts: the NavCam's self-calibration and the MasMec's self-calibration. A combined adjustment based on the points and lines is proposed. The baseline constraint of the NavCam is considered. The self-calibration model of the MasMec is established based on the product-of-exponentials formula. Finally, the premission laboratory calibration and the on-site calibration are carried out. The laboratory calibration shows that the proposed approach has high accuracy. The checkpoint with a distance of about 2.7 m to the left NavCam has a point error of about 4 mm. Finally, the proposed approach is applied in the on-site calibration.

Chemical-shift encoding-based water-fat separation with multifrequency fat spectrum modeling in spin-lock MRI.

Chemical exchange saturation transfer is used commonly to generate MRI contrast based on the chemical exchange effect. The spin-lock techniques can also be used to probe the chemical exchange and other molecular motion processes in tissues. The presence of fat can cause errors in spin-lock MRI. Signals from fat are typically suppressed based on spectral selectivity or T1 nulling approaches in spin-lock imaging. However, these methods cannot be used to suppress fat signals from multiple fat peaks. To address this problem, we report chemical-shift encoding-based water-fat separation approaches with multifrequency fat spectrum modeling. Both the conventional spin-lock and the adiabatic continuous-wave constant-amplitude spin lock (ACCSL) with multi-echo acquisitions are investigated for chemical-shift encoding-based water-fat separation in spin-lock imaging. A comparison is made of reconstructions based on 3 models: a single-peak fat spectrum model, a standard precalibrated proton density 6-peak fat spectrum model, and the self-calibrated relaxation-dependent 3-peak fat spectrum model. Comparisons were performed using Bloch simulations, phantom, and in vivo experiments at 3 T. Conventional spin-lock acquisitions cannot be used for reliable water-fat separation with a multipeak fat spectrum model. Water-fat separation based on ACCSL acquisitions achieves superior performance compared with the use of conventional spin-lock acquisitions. The best result is achieved from ACCSL acquisition with self-calibrated relaxation-dependent multipeak fat spectrum modeling. The ACCSL acquisition can be used for chemical-shift encoding-based water-fat separation with multipeak fat spectrum modeling. This approach has the potential to improve quantitative analysis using spin-lock MRI for assessing the biochemical properties of tissues.

Self-calibration for the 2D stage based on weighted least squares

As one of the core components of ultra-precision machining and inspection equipment, the 2D stage plays a major role in sophisticated technology. Self-calibration is considered an excellent method to separate stage system errors because of its low cost and high efficiency. In this paper, the self-calibration model is represented using an overdetermined equations system. A weight matrix was used to solve the system through least squares with unequal accuracy. The error propagation ratios increase with a decrease in the number of positions or increase in the number of points, however, all the ratios are less than one. Self-calibration based on weighted least squares can suppress the noise, which was proved through simulation. Experiments were conducted to confirm that self-calibration separated the stage system errors successfully. The effectiveness and repeatability of the method were confirmed by the fact that the standard deviation among the plates returning to the initial position was of tens of nanometers. Two methods of self-calibration, namely self-calibration based on least squares and optimization self-calibration, were verified against each other. The differences between the stage system errors separated in the two methods were only a few nanometers.

Geometric Calibration for the Aerial Line Scanning Camera GFXJ

The Gao Fen Xiang Ji (GFXJ) is the first Chinese self–developed airborne three–line array charge-coupled devices (CCD) camera and is designed to meet 8 cm ground sample distance (GSD), 0.5 m planimetry accuracy, and 0.28 m elevation accuracy for ground three-dimensional (3D) points at a flight height of 2000 m. These values also meet the 1:1000 scale mapping requirements in China. However, the original direct geopositioning accuracy of the GFXJ is approximately 4 m in the planimetry direction and 6 m in the elevation direction. To meet the ground 3D point accuracy requirements and improve the direct geopositioning accuracy of the GFXJ, this paper carries out a deep investigation on the GFXJ geometric calibration. This geometric calibration includes two main parts: the Global Navigation Satellite System (GNSS) lever arms and inertial measurement unit (IMU) boresight misalignment calibration, and the camera lens and CCD line distortion calibration. First, a brief introduction is given on the imaging properties of the GFXJ camera. Then, the GNSS lever arms and IMU boresight misalignment calibration models are built for the GFXJ camera. Next, a piecewise self-calibration model based on the CCD viewing angle is established for the GFXJ lens and CCD line distortion calibration. Subsequently, an iterative two-step calibration scheme is proposed for the geometric calibration. Finally, experiments were implemented using multiple flight blocks obtained in the Songshan remote sensing comprehensive field and the Hegang area of Heilongjiang Province. Through calibration experiments, geometric calibration values were obtained for the GNSS lever arms and IMU boresight misalignment. Reliable CAM files were independently generated for the forward, nadir, and backward line arrays. The experiments showed that the proposed GNSS lever arms and IMU boresight misalignment calibration models and the piecewise self-calibration model had good applicability and effectiveness for the GFXJ camera. The proposed two-step calibration scheme can significantly enhance the geometric positioning accuracy of the GFXJ camera. The original direct geopositioning accuracy of the GFXJ is approximately 4 m in the planimetry direction and 6 m in the elevation direction. Using the GNSS lever arms and the IMU boresight misalignment calibration values and the CAM files, the positioning accuracy of the GFXJ camera can fulfill the 3D point accuracy requirements and the 1:1000 mapping accuracy requirements at a 2000 m flight height after aerial triangulation with only several ground control points. The planimetry accuracy is approximately 0.2 m, and the elevation accuracy is less than 0.28 m. In addition, the calibration models and calibration scheme established in this paper can provide a reference for calibration studies on other airborne linear array CCD cameras.

Photogrammetric Solution for Analysis of Out-Of-Plane Movements of a Masonry Structure in a Large-Scale Laboratory Experiment

This paper proposes a photogrammetric procedure able to determine out-of-plane movements experienced by a masonry structure subjected to a quasi-static cyclic test. The method tracks the movement of circular targets by means of a coarse-to-fine strategy. These targets were captured by means of a photogrammetric network, made up of four cameras optimized following the precepts of a zero-, first-, and second-order design. The centroid of each circular target was accurately detected for each image using the Hough transform, a sub-pixel edge detector based on the partial area effect, and a non-linear square optimization strategy. The three-dimensional (3D) coordinates of these targets were then computed through a photogrammetric bundle adjustment considering a self-calibration model of the camera. To validate the photogrammetric method, measurements were carried out in parallel to an ongoing test on a full-scale two-story unreinforced masonry structure (5.4 × 5.2 × 5.4-m) monitored with more than 200 contact sensors. The results provided by the contact sensors during one of the load phases were compared with those obtained by the proposed approach. According to this accuracy assessment, the method was able to determine the out-of-plane displacement during the quasi-static cyclic test with a sub-pixel accuracy of 0.58.

Self-calibrated ballistic model for sprinkler irrigation with a field experiments data base

Simulation models of sprinkler irrigation are a valuable tool to improve the irrigation water management at plot scale. Ballistic theory has been commonly used to simulate drop dynamics in sprinkler irrigation models. A number of experiments on sprinkler irrigation performed in previous studies in the Ebro Valley Spain were analyzed and integrated in a data base. The evaluations were performed on six sprinkler types with different nozzle sizes, operating pressures under different meteorological conditions and spacings. The data base includes 40 isolated and 167 solid-set experiments that were processed with a self-calibrated model to calibrate and validate the ballistic parameters. The ballistic model used in this research was improved with respect to a previous model, moreover some novelties were added. These modifications were done in the phases of: the numerical solution, a wind drift and evaporation losses model, simulations considering slope in the terrain, drop generation (using regular and random methods), the size of the terrain cells where the drops are simulated and considering two drop size distributions, upper limit lognormal and Weibull. The results indicated larger and significant differences of Christiansen´s Uniformity Coefficient measured and simulated when considering a constant wind velocity (9%) and no differences when the wind velocity is defined for intervals equal to or less than 30 min (6%). Regarding the effect of the slope in the terrain, differences between both uniformity coefficients are relevant (11%) when the wind velocity is larger than 4 m s−1. Both drop size distributions were similar in accuracy however, the upper limit lognormal was more suitable to simulate a sprinkler especially designed to operate under low pressure. The predictive ability of the model once calibrated and validated was satisfactory (99% and 75%, respectively). The new model improves the accuracy with respect to previous research and minimizes the computing time for the calibration and validation processes using the cluster Trueno-CSIC.

Continuous self‐calibration of platform inertial navigation system based on attitude quaternion model

This study focuses on the continuous self-calibration of platform inertial navigation system. Since the estimate accuracy of inertial platform error coefficients would be reduced by the large misalignment angle, the inertial platform gimbal angle is used to establish the continuous self-calibration model. And furthermore, to avoid a large number of triangle operations and the phenomenon of gimbal lock in traditional Euler angle represented gimbal angle continuous self-calibration model, an attitude quaternion continuous self-calibration model is proposed. In this model, the attitude quaternion is used to replace the Euler angle to describe the rotation of the inertial platform. Then, a quaternion unscented Kalman filter based on singular value decomposition (SVD-QUKF) is proposed to calibrate the error coefficients of the inertial platform in the attitude quaternion continuous self-calibration model. Finally, the simulation and experiment results prove that the proposed quaternion continuous self-calibration model and the SVD-QUKF can calibrate all the error coefficients of inertial platform with the relative error <1%, and the calibration precision and the computing speed are better than the traditional method.

Attitude quaternion continuous self-calibration model of hybrid inertial navigation system

Attitude quaternion continuous self-calibration model of hybrid inertial navigation system

DESCENT TRAJECTORY RECOVERY OF CHANG’E-4 LANDER BASED ON DESCENT IMAGES

Abstract. Chang’e-4 lander, carrying Yutu-2 rover, was successfully landed on the far side of lunar surface in Von Kármán crater inside the South Pole-Aitken basin on January 3rd, 2019. The descent images, captured by the descent camera mounted on the lander, captured the sequential descent images and recorded the scene changes during the entry, descent and landing (EDL) process. This paper proposed a bundle adjustment based geometric processing method for descent and landing trajectory recovery using descent images. A frame camera based self-calibration model was introduced for high precision estimation of interior and exterior parameters of descent images simultaneously in a least squares manners. Evenly distributed GCPs were selected from the landing area in a digital orthophoto map generated from LROC NAC images and SLDEM2015. The experimental results demonstrated the effectiveness of the proposed method in Chang’e-4 descent trajectory recovery.

Terrestrial Laser Scanner Autonomous Self-Calibration With No Prior Knowledge of Point-Clouds

To improve the positional accuracy of point-clouds, a self-calibration model of a terrestrial laser scanner (TLS) was used to calibrate mounting angle errors as systematic errors. The model was based on the TLS scanning mechanism, and parameters of the model were determined by using measured TLS point-clouds. To automatically solve parameters of the self-calibration model, a background target-based autonomous method was proposed to find the feature points used as input for the model. The autonomous self-calibration method presented here involved three steps: determination of initial feature points using a keypoint quality algorithm with no prior knowledge, filtering the initial feature points to find coarse feature points using a $K$ -means algorithm, optimization of coarse feature points to find fine feature points based on measurement precision. In comparison with the auxiliary target-based method, experimental results showed that the background target-based autonomous method is a valid self-calibration method for TLS, with comparable measurement precision and a simplified self-calibration procedure.

Optimal-arrangement-based four-scanning-heads error separation technique for self-calibration of angle encoders

Conventional methods for the calibration of angle encoders typically only consider the graduation error of the encoder’s circular scale. However, the radial motion of the circular scale during its rotation, due to its eccentricity and the axis of rotation radial error motion, can also introduce noticeable errors to the angle measurement in most practical applications. Based on the analysis of the influence of radial motion, an optimal-arrangement-based four-scanning-heads error separation technique for in situ self-calibration of angle encoders is presented. This Fourier-based technique uses the basic self-calibration model to measure the first-order Fourier component of the encoder error which includes the contribution of eccentricity. Meanwhile, the separation technique is utilized to separate the residual Fourier components of the graduation error from the measurement deviation due to radial error motion. The effect of the scanning heads’ angular position errors on the calibration results is discussed. Optimal arrangements of the four heads are achieved to avoid the suppression of the Fourier components, and reduce the propagation of errors. Numerical results and experimental comparisons demonstrate the effectiveness of the proposed method. Moreover, this technique can also be used for measuring the spindle radial error motion for some users.

System Self-Calibration Model for Non-Vertical Four-Prism Airborne LiDAR

ABSTRACTSystem errors in light detection and ranging (LiDAR) systems cannot be ignored due to their influence on geo-referencing accuracy. Previous calibration methods are based on the vertical LiDAR system and do not simultaneously consider the bore-sight angles, lever-arm errors, angles, range, trajectory position, and angle correction parameters for each strip. This study proposes a system self-calibration model based on a high-precision positioning model for the non-vertical four-prism airborne LiDAR system. Furthermore, an automatic system calibration process is presented using this model that identifies 12 parameters for overlapping LiDAR data. Also, each strip of trajectory data has three position corrections and three angle corrections. The feasibility and applicability of the method is demonstrated via qualitative and quantitative analyses using real data from plain and hilly areas. The experimental results prove that the proposed method is stable and reliable. Specifically, the proposed method can compensate for system bias, correct original flight data, and provide seamless data. This model can be applied to actual flight engineering datasets, has no terrain limitations, no specific requirements for the trajectory configuration, no specific hypotheses, and no need for control information.

Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology

In this contribution, we present a highly accurate approach for thickness measurements of multi-layered automotive paints using terahertz time domain spectroscopy in reflection geometry. The proposed method combines the benefits of a model-based material parameters extraction method to calibrate the paint coatings, a generalized Rouard's method to simulate the terahertz radiation behavior within arbitrary thin films, and the robustness of a powerful evolutionary optimization algorithm to increase the sensitivity of the minimum thickness measurement limit. Within the framework of this work, a self-calibration model is introduced, which takes into consideration the real industrial challenges such as the effect of wet-on-wet spray in the painting process.

Portable visual metrology without traditional self-calibration measurement model

To improve the 3D measurement accuracy of portable visual metrology using generic digital SLRs, deficiencies related to the traditional self-calibration model are analyzed, and a novel calibration method of generic digital SLRs is proposed. The collinear equations are established using the orientation angles of the targets, which are determined using a non-parameterized calibration platform. After calibration, the camera maps the orientation angles of incoming scene rays to the corresponding pixels on the image plane, becoming a goniometer. Additionally, the implementation and error analysis of the non-parameterized calibration model are investigated. The image points matching method, external station orientation method and bundle adjustment algorithm, which are based on orientation angles of image points, are studied. Finally, the calibration and 3D measurement accuracy are verified, along with the variation in the measurement accuracy with different calibration rotation intervals and LED intervals of the straight line target. The experimental results show that our calibration method is efficient to improve the 3D measurement accuracy of generic digital SLRs.

Automatic Processing of Chinese GF-1 Wide Field of View Images

Abstract. The wide field of view (WFV) imaging instrument carried on the Chinese GF-1 satellite includes four cameras. Each camera has 200km swath-width that can acquire earth image at the same time and the observation can be repeated within only 4 days. This enables the applications of remote sensing imagery to advance from non-scheduled land-observation to periodically land-monitoring in the areas that use the images in such resolutions. This paper introduces an automatic data analysing and processing technique for the wide-swath images acquired by GF-1 satellite. Firstly, the images are validated by a self-adaptive Gaussian mixture model based cloud detection method to confirm whether they are qualified and suitable to be involved into the automatic processing workflow. Then the ground control points (GCPs) are quickly and automatically matched from the public geo-information products such as the rectified panchromatic images of Landsat-8. Before the geometric correction, the cloud detection results are also used to eliminate the invalid GCPs distributed in the cloud covered areas, which obviously reduces the ratio of blunders of GCPs. The geometric correction module not only rectifies the rational function models (RFMs), but also provides the self-calibration model and parameters for the non-linear distortion, and it is iteratively processed to detect blunders. The maximum geometric distortion in WFV image decreases from about 10-15 pixels to 1-2 pixels when compensated by self-calibration model. The processing experiments involve hundreds of WFV images of GF-1 satellite acquired from June to September 2013, which covers the whole mainland of China. All the processing work can be finished by one operator within 2 days on a desktop computer made up by a second-generation Intel Core-i7 CPU and a 4-solid-State-Disk array. The digital ortho maps (DOM) are automatically generated with 3 arc second Shuttle Radar Topography Mission (SRTM). The geometric accuracies of the generated DOM are 20m for camera-2 and 3, and 30m accuracy for camera-1 and 4. These products are now widely used in the fields of land and resource investigation, environment protection, and agricultural research.

A SEVA soft sensor method based on self-calibration model and uncertainty description algorithm

Soft sensors are widely used to estimate process variables that are difficult to measure online. However, due to poor quality of input data and deterioration of prediction model as time passes, soft sensors make poor performance. We have been constructing a principal component analysis (PCA) model before performing a prediction. Furthermore, the just-in-time (JIT) learning model has been improved and served as prediction model for self validating (SEVA) soft sensors. The proposed soft sensor not only carries out internal quality assessment but also generates multiple types of output data, including the prediction values (PV), input sensor status (ISS), validated measurement (VM), output sensor status (OSS) and the uncertainty values (UV) which represent the credibility of soft sensors' output. The effectiveness of the proposed SEVA soft sensors is demonstrated through a case study of a wastewater treatment process.

Bayesian-Monte Carlo Model for Collision Avoidance System Design of Cognitive Connected Vehicle

Cognitive connected vehicles will require a number of essential features that integrate intelligent technology and human factors, including collision avoidance advice and adaptive longitudinal control. This paper describes a self-calibrating adaptive model for aiding the design of a warning system for preventing rear and side swipe collisions. The cognitive vehicle is expected to have the capability of information on location and distance between vehicles obtained on-line. The location and distance information is used in association with a Monte Carlo simulation and Bayesian decision model to identify pre-crash condition. Here, the case of human control is covered and the system provides advice for avoiding rear or side swipe accidents while minimizing false alarms. The model structure and algorithm are presented and illustrative examples of distracted driving are provided.