scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

scholarly journals A Closed-Form Solution to Linear Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 13 (18) ◽  
pp. 3571
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian ◽  
Hua Zhang
Keyword(s):  
Objective Function ◽  
Closed Form ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Linear Features ◽  
Registration Method ◽  
Linear Feature ◽  
Feature Based ◽  
Transformation Parameters

Due to the high complexity of geo-spatial entities and the limited field of view of LiDAR equipment, pairwise registration is a necessary step for integrating point clouds from neighbouring LiDAR stations. Considering that accurate extraction of point features is often difficult without the use of man-made reflectors, and the initial approximate values for the unknown transformation parameters must be estimated in advance to ensure the correct operation of those iterative methods, a closed-form solution to linear feature-based registration of point clouds is proposed in this study. Plücker coordinates are used to represent the linear features in three-dimensional space, whereas dual quaternions are employed to represent the spatial transformation. Based on the theory of least squares, an error norm (objective function) is first constructed by assuming that each pair of corresponding linear features is equivalent after registration. Then, by applying the extreme value analysis to the objective function, detailed derivations of the closed-form solution to the proposed linear feature-based registration method are given step by step. Finally, experimental tests are conducted on a real dataset. The derived experimental result demonstrates the feasibility of the proposed solution: By using eigenvalue decomposition to replace the linearization of the objective function, the proposed solution does not require any initial estimates of the unknown transformation parameters, which assures the stability of the registration method.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product

2013 ◽  
Vol 5 (3) ◽  
Author(s):  
Mili Shah
Keyword(s):  
Kronecker Product ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Accurate Method ◽  
Form Solution ◽  
Singular Value ◽  
Error Metrics ◽  
Calibration Problem ◽  
Value Decomposition

This paper constructs a separable closed-form solution to the robot-world/hand-eye calibration problem AX = YB. Qualifications and properties that determine the uniqueness of X and Y as well as error metrics that measure the accuracy of a given X and Y are given. The formulation of the solution involves the Kronecker product and the singular value decomposition. The method is compared with existing solutions on simulated data and real data. It is shown that the Kronecker method that is presented in this paper is a reliable and accurate method for solving the robot-world/hand-eye calibration problem.

scholarly journals A WEIGHTED CLOSED-FORM SOLUTION FOR RGB-D DATA REGISTRATION

2016 ◽  
Vol XLI-B3 ◽  
pp. 403-409 ◽  
Author(s):  
K. M. Vestena ◽  
D. R. Dos Santos ◽  
E. M. Oilveira Jr. ◽  
N. L. Pavan ◽  
K. Khoshelham
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Body Motion ◽  
Random Errors ◽  
Scale Invariant ◽  
Loop Closure ◽  
Dual Number ◽  
Data Registration

Existing 3D indoor mapping of RGB-D data are prominently point-based and feature-based methods. In most cases iterative closest point (ICP) and its variants are generally used for pairwise registration process. Considering that the ICP algorithm requires an relatively accurate initial transformation and high overlap a weighted closed-form solution for RGB-D data registration is proposed. In this solution, we weighted and normalized the 3D points based on the theoretical random errors and the dual-number quaternions are used to represent the 3D rigid body motion. Basically, dual-number quaternions provide a closed-form solution by minimizing a cost function. The most important advantage of the closed-form solution is that it provides the optimal transformation in one-step, it does not need to calculate good initial estimates and expressively decreases the demand for computer resources in contrast to the iterative method. Basically, first our method exploits RGB information. We employed a scale invariant feature transformation (SIFT) for extracting, detecting, and matching features. It is able to detect and describe local features that are invariant to scaling and rotation. To detect and filter outliers, we used random sample consensus (RANSAC) algorithm, jointly with an statistical dispersion called interquartile range (IQR). After, a new RGB-D loop-closure solution is implemented based on the volumetric information between pair of point clouds and the dispersion of the random errors. The loop-closure consists to recognize when the sensor revisits some region. Finally, a globally consistent map is created to minimize the registration errors via a graph-based optimization. The effectiveness of the proposed method is demonstrated with a Kinect dataset. The experimental results show that the proposed method can properly map the indoor environment with an absolute accuracy around 1.5% of the travel of a trajectory.

scholarly journals A FREQUENCY-DRIFT COMPENSATED CLOSED-FORM SOLUTION FOR STEREO RGB-D MAPPING

2019 ◽  
Vol IV-2/W5 ◽  
pp. 293-297
Author(s):  
S. J. Tang ◽  
Q. Zhu ◽  
W. Chen ◽  
W. X. Wang ◽  
Y. Li ◽  
...  
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Frequency Drift ◽  
Pose Tracking ◽  
Camera Pose ◽  
Indoor Scenarios ◽  
Spatially Variant ◽  
Orientation Parameters

<p><strong>Abstract.</strong> In this work, we present a frequency-drift compensated (Fd-C) closed-form solution for stereo RGB-D SLAM. The intrinsic parameters for each sensor are first obtained with a standard camera calibration process and the extrinsic orientation parameters achieved through a coarse-to-fine scheme that solves the initial exterior orientation parameters (EoPs) from control markers and further refines the initial value by an iterative closest point (ICP) variant minimizing the distance between the RGB-D point clouds and the referenced laser point clouds. With the assumption of fix transformation between the frames with the same timestamp, we define one sensor as reference sensor and the other sensor as slave sensor and the slave frames can be mapped to the timeline of the references sensor. Rather than endow the camera pose of the nearest frame to the slave frames, we derive the accurate camera pose for slave frames in a spatially variant way. Therefore, the pose relations between the slave frame and the adjacent reference frame can be derived, which provided opportunity to use the more accuracy observations from multiple frames for better tracking and global optimization. We present the mathematical analysis of the iterative optimizations for pose tracking in multi-RGB-D camera cases. Finally, the experiments in complex indoor scenarios demonstrate the efficiency of the proposed multiple RGB-D slam algorithm.</p>

scholarly journals A WEIGHTED CLOSED-FORM SOLUTION FOR RGB-D DATA REGISTRATION

2016 ◽  
Vol XLI-B3 ◽  
pp. 403-409
Author(s):  
K. M. Vestena ◽  
D. R. Dos Santos ◽  
E. M. Oilveira Jr. ◽  
N. L. Pavan ◽  
K. Khoshelham
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Body Motion ◽  
Random Errors ◽  
Scale Invariant ◽  
Loop Closure ◽  
Dual Number ◽  
Data Registration

Existing 3D indoor mapping of RGB-D data are prominently point-based and feature-based methods. In most cases iterative closest point (ICP) and its variants are generally used for pairwise registration process. Considering that the ICP algorithm requires an relatively accurate initial transformation and high overlap a weighted closed-form solution for RGB-D data registration is proposed. In this solution, we weighted and normalized the 3D points based on the theoretical random errors and the dual-number quaternions are used to represent the 3D rigid body motion. Basically, dual-number quaternions provide a closed-form solution by minimizing a cost function. The most important advantage of the closed-form solution is that it provides the optimal transformation in one-step, it does not need to calculate good initial estimates and expressively decreases the demand for computer resources in contrast to the iterative method. Basically, first our method exploits RGB information. We employed a scale invariant feature transformation (SIFT) for extracting, detecting, and matching features. It is able to detect and describe local features that are invariant to scaling and rotation. To detect and filter outliers, we used random sample consensus (RANSAC) algorithm, jointly with an statistical dispersion called interquartile range (IQR). After, a new RGB-D loop-closure solution is implemented based on the volumetric information between pair of point clouds and the dispersion of the random errors. The loop-closure consists to recognize when the sensor revisits some region. Finally, a globally consistent map is created to minimize the registration errors via a graph-based optimization. The effectiveness of the proposed method is demonstrated with a Kinect dataset. The experimental results show that the proposed method can properly map the indoor environment with an absolute accuracy around 1.5% of the travel of a trajectory.

Circle Pose Estimation Based on Stereo Vision

2012 ◽  
Vol 263-266 ◽  
pp. 2408-2413 ◽  
Author(s):  
Wen Juan Ma ◽  
Shu Sen Sun ◽  
Jin Yu Song ◽  
Wen Shu Li
Keyword(s):  
Pose Estimation ◽  
Stereo Vision ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Form Solution ◽  
Perspective View ◽  
Simple Method ◽  
Binocular Stereo Vision ◽  
Binocular Stereo

This paper presents a simple method of circle pose estimation based on binocular stereo vision. It takes the projective equation of a circle as the basis, and gives the closed form solution of the pose parameters. Since there are two possible sets of pose parameters for a circle from one calibrated perspective view, the stereo vision constraints are incorporated and the accurate pose parameters are determined. Experiments using computer simulated data and real data demonstrate the robustness and accuracy of our method.

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