Coordinates Of Control Points Research Articles

Morphogenesis of free-form surface structures based on geometrically nonlinear isogeometric analysis

Free-form surface structures have taken the forefront in space structure research owing to their free and flexible expressiveness and aesthetic visual effects. Yet, their irregular shapes and large span of the initial structure often lead to the problem of large displacement, necessitating the incorporation of geometric nonlinearity in the analysis. In this paper, we employ structural optimization design principles to investigate the morphogenesis of free-form surface structures while considering their geometric nonlinearity. Particularly, we explore both single-objective and double-objective shape optimization of free-form surface structures by employing structural strain energy and the first natural frequency as optimization indexes and the vertical coordinates of control points as optimization variables. The effectiveness of the proposed method is finally verified by several examples.

Three-dimensional simulation of heat and moisture transfer in woven fabric structures

Fabric structure parameters have a significant impact on the comfort of heat and moisture transfer in garments. Previous numerical simulations required extensive mathematical calculations and mostly investigated one- or two-dimensional models of fiber assembly without considering the weave structure, which is a key parameter, that significantly influences the porosity of the woven structure and consequently its heat and moisture management. While the finite element method supports the simulation of the optimal shape and material properties with better visibility, previous finite element models focused on heat transfer and neglected water vapor transfer in fabrics. In this article, the finite element simulation of heat and moisture transfer in woven fabrics is established based on the testing principle of thermal resistance and moisture resistance tester using COMSOL Multiphysics software. In this simulation, three-dimensional parametric geometrical models of the fabric are created using curve interpolation methods by acquiring the control point coordinates of different weaves (plain, 2/2 balanced twill, and 4/1 unbalanced twill weaves). Heat and moisture transfer properties of fabric models in the horizontal and vertical directions were analyzed, including the heat flux, moisture resistance, water vapor permeability, and water vapor concentration. The article also deals with the effects of weave structure and fabric cover in a range of 72.1–85.1% on the fabric heat flux and water vapor concentration. Comparison between model and experimental results revealed that the three-dimensional simulation can accurately predict the impact of weave pattern and fabric cover on the fabric heat and moisture transfer performance. In addition, this model can be utilized to study the distribution of heat and water vapor within fabrics, providing a theoretical foundation for optimizing heat and moisture comfort in woven fabrics.

Fast Extraction Algorithm of Planar Targets Based on Point Cloud Data for Monitoring the Synchronization of Bridge Jacking Displacements

Transverse synchronization of vertical displacements of all jacking-up points is an important monitoring indicator to replace bearings in assembled multigirder bridges during the jacking phase. Currently, using target paper to identify the 3D coordinates of control points reduces the complexity of monitoring operations and improves the stability of data precision. However, the existing planar target locating methods have low accuracy, inefficiency, and subjectivity, which seriously hinders the construction process of bearing replacement. Accurately obtaining the center coordinates of multiple targets from a point cloud in a short monitoring period remains a challenge. This study proposes a high-precision automated algorithm to extract target center points in low-density point clouds to quickly calculate real target center points. First, we construct a standard point cloud model of the target papers for scanning, including color and geometric features. Then, we extract the measured point cloud of the typical jacking operation phase based on the reflection intensity and size information. Next, we map the intensity values of the measured point cloud into the color channel and register the measured point cloud with its standard point cloud model using the normal vector estimation and colored ICP algorithms. Finally, we extract the center point of the measured targets. Numerical experiments and engineering test results show that the proposed method converges quickly with high precision and good robustness, which saves 91.4% of the time compared with the traditional method. In general, this research can provide effective technical support for 3D laser scanning in monitoring the operation phase of bridge jacking.

Measuring Velocity and Discharge of High Turbidity Rivers Using an Improved Near-Field Remote-Sensing Measurement System

Large-scale particle image velocimetry (LSPIV) is a computer vision-based technique renowned for its precise and efficient measurement of river surface velocity. However, a crucial prerequisite for utilizing LSPIV involves camera calibration. Conventional techniques rely on ground control points, thus restricting their scope of application. This study introduced a near-field remote-sensing measurement system based on LSPIV, capable of accurately measuring river surface velocity sans reliance on ground control points. The system acquires gravity-acceleration data using a triaxial accelerometer and converts this data into a camera pose, thereby facilitating swift camera calibration. This study validates the system through method verification and field measurements. The method verification results indicate that the system’s method for retroactively deriving ground control-point coordinates achieves an accuracy exceeding 90%. Then, field measurements were performed five times to assess the surface velocity of the Datong River. These measured results were analyzed and compared with data collected from the radar wave velocity meter (RWCM) and the LS1206B velocity meter. Finally, a comprehensive sensitivity analysis of each parameter was conducted to identify those significantly impacting the river’s surface velocity. The findings revealed that this system achieved an accuracy exceeding 92% for all river surface velocities measured.

Bandgap structure in elastic metamaterials with curvy Bezier beams

This Letter discusses elastic metamaterials incorporating curved beams in their architecture. Through employing Bezier splines, we reveal a wide versatility of geometrical designs of the unit cells and the consequent programmability of bandgap structures. By analyzing more than ten thousand possible specimens altogether, we highlight the similarity between dynamic properties of metamaterials formed by curves with different geometries defined via three variables only that correspond to the coordinates of control points of the Bezier spline. In particular, we establish the importance of such parameter as effective curve length in defining the probable positions of bandgaps. This study shows, in particular, that the bandgap ratio can reach 71% for metamaterials with proposed curved beams—a noticeable contrast with no bandgaps in their counterpart with straight elements. The employment of the deep learning model enables us to effectively predict passband–stopband structure in such metamaterials with satisfactory accuracy, potentially accelerating the design of metamaterials assembled from versatile unit cells.

3D laser scanning for predicting the alignment of large-span segmental precast assembled concrete cable-stayed bridges

Reasonable alignment control can simplify the bridge construction process, reduce the complexity and cost of construction, and improve construction efficiency. The prefabricated assembling construction method brings challenges to alignment control. This study proposes a method for predicting the alignment of concrete cable-stayed bridge assemblies in unstressed conditions to accelerate the construction process. The method uses the target paper to identify the 3D coordinates of control points and a coarse-to-accurate alignment method to achieve the virtual preassembly of precast concrete sections. The effectiveness of the method is demonstrated by comparing the errors in key parameters between virtual and physical preassembly and the predicted alignment results obtained through 3D coordinate conversion with the designed precast alignment. The method was applied to the construction of a large-span concrete cable-stayed bridge for a high-speed railroad in Guangdong, China, and the construction period was shortened by about 42 days.

Fault-model parameters estimation using a feature-voting technique: Dead Sea fault as a case study

Estimation of fault-model parameters is a challenge faced by researchers. Traditional statistical tools rely on a velocity field derived from precise coordinates of control-points in GNSS networks, changing over-time. This requires dealing with geodetic datum and deformation-monitoring datum, while handling ill-conditioned state models.This paper describes an algorithm for evaluating full fault-model parameters all at once using a feature-voting technique, while relying on precise GNSS vectors computed with scientific GNSS processing software. The algorithm bypasses the datum issues and deals with numerical instabilities using perturbed data replications. Dealing with gross-errors is an embedded attribute of the technique, and noise is an intrinsic feature needed to cope with the ill-conditioned equation-set problem with respect to the low-frequency nature of the data. Thus, the geodetic datum and deformation monitoring datum becomes irrelevant for this algorithm.Simulations of a locked fault-model, based upon a true solved epoch, derive proper parameter values for a preselected fault-model scenario, including simulations with noise. A case study relies on the northern section of the Dead-Sea fault, on 10 northern sites in Israel's continuously operating permanent stations, based on four true-data epochs of computed vectors in order to evaluate Dead-Sea fault model parameters.Similarity is shown between computed fault-model parameters using the presented feature-voting technique and those estimated by traditional processes; with respect to other researchers' work, at the same area over a similar time period, carried out by a traditional statistical least-squares adjustment procedure, including efforts in gross-error filtering and coping mechanisms with the biases caused from both datum issues.The feature-voting based methodology for analyzing fault-model parameters, using precise GNSS vectors and not precise coordinates; enables simultaneous full fault-model parameter computation while avoiding biases originating in deformation-monitoring datum and other error factors.

An integrated design approach for simultaneous shape and topology optimization of shell structures

In this work, a novel design approach is developed to carry out shape and topology optimization of shell structures simultaneously. This approach effectively integrates the IsoGeometric Analysis (IGA) method, the Adaptive Bubble Method (ABM) and the Finite Cell Method (FCM) to make full use of their respective advantages in shell structure optimization. To be specific, the IGA method using Non-Uniform Rational B-Splines (NURBS) elements is adopted to analyze the shell structure and realize shape optimization with merits of exact shell surface representation geometrically and rotation-free shell formulation physically; the ABM is utilized to insert deformable holes adaptively in the parametric domain of the NURBS surface for topology optimization of the shell structure; the FCM is employed to facilitate the optimization process by simplifying significantly the discrimination and the numerical integration processes of trimmed elements involved in fixed-mesh analysis of the holed shell structure. Based on this integrated design approach of IGA/ABM/FCM, shape optimization can be implemented by directly optimizing the control-point coordinates of the NURBS surface in the physical space, while topology optimization could be carried out simultaneously in the parametric domain as easily as for 2D planar structures. Finally, representative examples are investigated to demonstrate the effectiveness and advantages of the proposed design approach.

Automated assessment of facial nerve dysfunction

BACKGROUND: Facial neuropathy at the peripheral level (unilateral muscular weakness of the entire half of the face) is a common neurological disorder. Assessment of the facial nerve dysfunction grade is necessary to track the dynamics of treatment and monitor the effectiveness of rehabilitation. For this purpose, worldwide clinical practice uses grading systems, the most popular of which are the House-Brackmann, Yanagihara, and Nottingham scales. Such methods are non-universal and based on visual diagnosis, which relies solely on the subjective experience of the physician. Consequently, objective measurements and automation are needed to track the dynamics of recovery. With the use of image processing and computer vision techniques, this task became feasible.
 AIM: To develop a method of automated assessment of the facial nerve dysfunction grade by biometric facial analysis to monitor the patients recovery dynamics.
 METHODS: As part of the collaboration with the Herzen Moscow Research Institute of Oncology, a database of target group patients with grades IV (4 people), V (4 people), and VI (11 people) of facial nerve disfunction according to the Haus-Brackmann scale was compiled. A control group consisted of 20 students from the Bauman Moscow State Technical University. During registration, subjects were asked to perform a series of following mimic tests: raising the eyebrows, closing the eyes, smiling, smiling with effort, inflating the cheeks, pouting the lips, and articulating with effort. Control points of the eyebrow, eye, and mouth areas were used to assess the degree of facial asymmetry. The two-dimensional MultiPIE model, implemented in the dlib library and containing 68 control points, was used as a facial model. A program code in Python was written, which calculates asymmetry coefficients based on changes in the coordinates of control points when the patient performs mimic tests.
 RESULTS: A study was conducted to determine statistically significant differences between asymmetry coefficients in the control group and patients. Based on the Mann-Whitney criterion, asymmetry parameters during some mimic tests showed statistically significant differences (p 0.05). Thus, asymmetries in the forehead when raising the eyebrows (0.00 0.05), in the mouth when smiling (0.026 0.05), in the mouth when smiling with effort (0.00 0.05), in the mouth when pouting the lips (0.039 0.05), and in the mouth when articulating with effort (0.004 0.05) were revealed.
 CONCLUSIONS: The results prove the performance of the proposed method and show the need for additional research, particularly the search for differences between groups of patients with different severity and the development of a classification model for machine learning.

3D model of the Turka quarry

The aim of this work is to study the Turka quarry using terrestrial laser scanning, as well as to build a 3D model of the object. Method. The study of the outcrop was carried out with terrestrial laser scanning. The article describes the principles of operation of laser sensors and provides a classification of error sources. It also emphasizes the importance of achieving the maximum accuracy specified by scanner manufacturers. The location of the researched object. The studied quarry is located on the northern outskirts of the city of Turka, Lviv region. From the geological point of view, the object is situated in the Outer Ukrainian Carpathians that belong to the Carpathian mountain system. The inactive quarry is structurally confined to the north-western part of the Krosno nappe of the Ukrainian Carpathians. The characteristic Turka (Krosno) type of cross-section of the Oligocene-Miocene age is exposed in the walls of the quarry. This is a layering of massive packs of gray fine-grained sandstones with argillites and siltstones which are broken with joints. The joints are filled with longitudinal, transverse and differently oriented veins. They are often wedged out. Their thickness ranges from a few mm to 55 mm or more. Slickensides and leaching are observed along the cracks. The research results make it possible to analyze the geological structure without being directly near the object. The paper provides a workflow diagram of the terrestrial scanning workflow. This includes object reconnaissance, establishing and determining the coordinates of reference and control points. It also involves performing terrestrial 3D scanning, photographing an object, creating a cloud of points based on laser scanning data, developing a mash model based on point clouds and digital images. The accuracy of the mash model was defined by comparison of the coordinates of the control points obtained from the mash model and tacheometric survey. The absolute spatial difference does not exceed five centimeters. The scientific novelty and practical significance are in the creation of a virtual model of the Turka quarry. For the first time, terrestrial laser scanning technology was used for the research of this object. As a result, a 3D model was obtained, which can be used for further research in the field of geology, in particular structural geology, sedimentology, mineral reserve calculations and geotourism.

Simulation Analysis of the Geometric Positioning Accuracy for MEO- and HEO-SAR Satellites

Due to the long synthetic aperture time, the large squint angle, and the large imaging width of medium Earth orbit (MEO) and high Earth orbit (HEO) SAR satellites, it is difficult to simulate the geometric positioning accuracy of MEO- and HEO-SAR satellites through the SAR image simulation methods. In this paper, one non-zero Doppler simulation method of geometric positioning accuracy was proposed without simulating SAR images. In order to simulate the geometric positioning accuracy under different errors and imaging observation conditions, the virtual simulation geometric model was constructed by the simulated satellite ephemeris and the coordinates of ground control points (GCPs). On this basis, one geometric accuracy simulation method based on mean value compensation was proposed to simulate the geometric positioning accuracy with GCPs. The experimental results showed that the impact of Doppler center frequency error and velocity error of MEO- and HEO-SAR satellites on geometric positioning accuracy is significant compared with the LEO-SAR satellites, and the maximum error they affect can reach about 1597 m. In addition, the geometric positioning accuracies of MEO- and HEO-SAR satellites with GCPs can be achieved to 1~10 m and 7~29 m, respectively.

The Initial Process of Dam Construction is Seen from a Topographical Perspective (Bench Mark Coordinates and Control Point Coordinates): Case study of D.I. Bajayu Kab Serdang Bedagai

The Initial Process of Dam Construction is Seen from a Topographical Perspective (Bench Mark Coordinates and Control Point Coordinates): Case study of D.I. Bajayu Kab Serdang Bedagai

Effect of Camera Calibration Refreshing on Orthophoto Position Accuracy in UAV Mapping

Unmanned aerial vehicles (UAVs) are autonomous or remote control controlled air vehicles without a pilot. UAVs are aerial platforms capable of carrying non-metric photogrammetric equipment. In this study; the effect of two different calibration values of the camera available on the DJI Phantom 4 Pro equipment to the ortho-photo maps obtained from two different flight heights was investigated. An area within the campus of Gebze Technical University was chosen as a study area. PI 3000 software was used to calibrate the camera and the differences between the calculated parameters and the conventional parameters were determined. Also, the effect of the parameters on position accuracy was investigated. In the photogrammetric stereo model, the rms of Z depends on the picture scale, flight height, base length and the measurement accuracy of image coordinates. Since the measurement accuracy of the image coordinates x, y is also affected by the calibration accuracy, the calibration field independent of the Z value can be used. Geo-referencing and field measurements of the orthophotos produced by the GPS and measurement of the work area from two different heights with UAVs. Office work is the part where orthophotos are produced, georeferenced and analyzed with GPS coordinates of control points. The data obtained in the study reduces the rms value when recalibration is performed at a low flight altitude. However, a similar result could not be obtained for 120 meters flight altitude.

The Initial Process of Dam Construction is Seen from a Topographical Perspective (Bench Mark Coordinates and Control Point Coordinates): Case study of D.I. Bajayu Kab Serdang Bedagai

The research aims to determine the initial process of dam construction is seen from a topographical perspective ( bench mark coordinate and control point coordinates: case study of D.I. Bajayu kab. Serdang Bedagai. The aim and objective of this topographic survey is to collect topographical data from the field in order to produce supporting data in the form of a topographical/situation base map including cross-sectional and longitudinal cross-sectional images along the measurement location. Measurement 20 data of topographi for BM coordinat and CP coordinat, so: measurements are made up to 50 meters from the left and right bank of the river, measurement lengthwise (long section) of ± 8.2 km was carried out from the confluence of the Padang river with the Bah disappeared river to the Bajayu free intake location, measurement benchmark interval for 100 meters straight area and 50 meters turning area,conduct measurements on the linking route/trace from the planned main building to the free intake of D.I Bajayu and the first building for D.I Paya Lombang, measuring 50 meter intervals, the length of the measurement path from the axle of the weir to the Bajayu free intake is 3,600 m following the embankment to the right of the Padang river, the length of the canal trace from the axle of the weir to the building for the first Paya Lombang is 4,600 m following the existing road.

3D model construction and accuracy analysis based on UAV tilt photogrammetry

UAV equipped with tilt photogrammetry platform can obtain multiple angles images and establish 3D model of tilt photogrammetry, which has unique advantages in 3D intelligent construction. The purpose of this paper is to take the playground and library of the Department of Informatics of Wuhan University as the research area, obtain regional UAV images, and evaluate the residual in the spatial direction of the model by using the measured control points and model points collected in the field, so as to evaluate and analyze the accuracy of the 3D model. By analyzing the data, the root mean square error and maximum error of plane coordinates are 0.31 cm and 0.34 cm respectively, the root mean square error and maximum error of elevation are 0.07 cm and 0.11 cm respectively, and the field measured control point coordinates. Through the accuracy evaluation and analysis of the constructed three-dimensional model, it is concluded that the maximum error in X direction is 1.26 cm, the maximum error in Y direction is 1.39 cm, and the maximum error in Z direction is 1.60 cm. The results show that the accuracy of the three-dimensional model in the study area reaches centimeter-level and meets the requirements of relevant production specifications. It can provide reliable data support for construction and urban planning industries.

Adaptive Cloud-to-Cloud (AC2C) Comparison Method for Photogrammetric Point Cloud Error Estimation Considering Theoretical Error Space

The emergence of a photogrammetry-based 3D reconstruction technique enables rapid 3D modeling at a low cost and uncovers many applications in documenting the geometric dimensions of the environment. Although the theoretical accuracy of photogrammetry-based reconstruction has been studied intensively in the literature, the problem remains in evaluating the accuracy of the generated point cloud in practice. Typically, checking the coordinates of ground control points (GCPs) using a total station is considered a promising approach; however, the GCPs have clear and identifiable features and consistent normal vectors or less roughness, which cannot be considered as a typical sample for an accuracy evaluation of the point cloud. Meanwhile, the cloud-to-cloud (C2C) and cloud-to-mesh (C2M) comparison methods usually consider either the closest point or the neighboring points within a fixed searching radius as the “ground truth”, which may not reflect the actual accuracy; therefore, the present paper proposes an adaptive cloud-to-cloud (AC2C) comparison method to search the potential “ground truth” in the theoretical error space. The theoretical error space of each point is estimated according to the position of the corresponding visible cameras and their distances to a target point. A case study is carried out to investigate the feasibility of the proposed AC2C comparison method. The results presented basically the same error distribution range from 0 to 20 mm with the C2C and C2M methods, but with a higher mean value and a much smaller standard deviation. Compared to the existing methods, the proposed method provides new thinking in evaluating the accuracy of SfM-MVS by including the theoretical error constraints.

Regression Modeling of surface piercing propeller performance based on trailing edge geometrical parameters using CFD method

The geometry of the surface piercing propeller has been designed experimentally, and no comprehensive studies are available to identify the influential parameters to attain systematic formulations. This study aims to evaluate the feasibility of presenting systematic relations between the geometric parameters of the blade section and its hydrodynamic characteristics through combined methods of computational fluid dynamics and design of experiments. In this regard, the propeller's parametric geometry is designed based on the cubic B-spline method. Hence, a series of SPPs with different trailing edges is generated according to the coordinates of control points based on the D-optimal response surface methodology. The propeller performance was investigated using URANS numerical simulation method in accordance with the VOF method and sliding mesh technique.ANOVA analyses of the quadratic regression models of hydrodynamic coefficients in terms of edge height (Y) and protrusion length (X), based on a 95% confidence interval, indicate these models have prediction adequacy of more than 90%. The main factor (X) is the only significant factor in both models. Increasing it will reduce the hydrodynamic coefficients. As a result, trailing edge variations can significantly affect torque and thrust coefficients by up to 40%, while efficiency changes are about 7%.

An equivalent parameter geometric shape representation using independent coordinates of cubic Bézier control points

Bézier surface has been commonly applied to represent the complex geometric shape. Generally, all control points are dealt with by the same blending functions, regardless of the effect of independent coordinate. It causes to lack the modeling flexibility. Therefore, this paper proposes an equivalent parameter geometric shape representation method using the independent coordinates of control points. Since the coordinate components of control points are independent, the geometric modeling becomes more flexible. Firstly, a general Bézier curve is described in detail. Related expression is brought out in the form of independent coordinates by introducing two parameters. Then, their geometric meanings are analyzed in detail. Since both parameters are independent to parametric variables u and v, Bézier curve possess the same interval in the discrete parametric space, namely equivalent parameter. Next, a bicubic Bézier subsurface patch representation is discussed, including regular and non-regular subsurface patch. A general surface expression is given out in the form of independent coordinates, as well as the parameter structure and the geometric transformations. Finally, an example of ‘Bézier tree branch’ is constructed by using the proposed method. Results shows that the proposed method is feasible and reasonable.

JOINT BUNDLE ADJUSTMENT OF THERMAL INFRA-RED AND OPTICAL IMAGES BASED ON MULTIMODAL MATCHING

Abstract. Despite the fact that Thermal Infrared (TIR) cameras have been in use for decades, processing of TIR images poses a variety of challenges when compared to optical images, which are captured in the visible part of the electromagnetic spectrum. The estimation of the exterior orientation of TIR cameras by bundle adjustment is a difficult task due to the limited geometric resolution of a TIR camera and the low image quality in terms of contrast and texture compared to optical images. Optical images have a potential to increase TIR external orientation accuracy by incorporating them into a joint bundle adjustment. However, because the modality gap between those two image types is large, classical point matching algorithms typically fail to find matches, making processing both image types in the joint bundle challenging. In order to locate matching points in both modalities, this study suggests using the Edge Histogram Descriptor (EHD) in the frequency domain representation of the images based on phase congruency. To properly allocate edges from the phase congruency, which are then employed in EHD, non-maximum suppression and hysteresis thresholding are used. Considering that both sensors are fixed rigidly to a single platform, the search region for the matching point candidate of the TIR image is determined based on stereo calibration of a thermal/optical stereo setup combined with geometric constraints. The final matching is based on the cosine distance, while RANdom SAmple Consensus (RANSAC) is used in order to eliminate outliers. The findings of this study show that using a joint bundle adjustment with optical images versus a bundle adjustment only with TIR images improves TIR image orientation, which is supported by the increased accuracy of the adjusted Ground Control Point (GCP) coordinates.

Dynamic precision surveying of railway tunnels based on MLS with robust constraints of track control network

The inertial navigation system (INS)/odometer integrated dead reckoning (DR) is usually used for the positioning and orientation of mobile LiDAR system in the precision surveying of railway tunnels. However, due to the accumulation of pose errors and the creaky method of joint surveying of track control points, it is difficult to achieve the millimeter level absolute accuracy of point clouds relative to the track control network under dynamic conditions, especially when there are gross errors of some control points coordinates. This paper puts forward an algorithm to optimize accuracy of INS/odometer integrated DR with robust constraints of track control network. The errors of DR are divided into two types, which affect the relative accuracy and the absolute accuracy respectively; The concept of virtual mileage coordinate system is proposed, in this coordinate system, the influence of gyro bias error on position is modeled as a circular distribution and estimated indirectly by using the high-precision relative spatial relationship of control points; An absolute accuracy optimization method with constraints by sequence match between positions of surveying equipment and track control points is proposed, and the gross errors of control point coordinates are detected and processed based on reduced weight iteration method. The experimental results of North China high speed railway tunnel show that when the distance interval of control points of correction is 120 m, the root mean square (RMS) error of coordinates in X, Y and Z directions are 0.003, 0.003 and 0.005 m respectively. When the distance interval of control points of correction is 420 m, the RMS in X, Y and Z directions are 0.029, 0.030 and 0.010 m respectively. When there are gross errors of some control point coordinates and the distance interval of control points of correction is 120 m, the RMS of coordinates in X, Y and Z directions are 0.005, 0.006 and 0.006 m respectively, and the gross errors of 4 cm in one direction of the three-dimensional control point coordinates can be detected. The experimental results verified the high accuracy of the algorithm and its robustness to the gross errors of control point coordinates.