scholarly journals Robust affine registration method using line/surface normals and correntropy criterion

2022 ◽  
Author(s):  
Abdurrahman Yilmaz ◽  
Hakan Temeltas
Keyword(s):  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Least Square ◽  
3D Registration ◽  
Point Sets ◽  
Registration Method ◽  
Affine Registration ◽  
Surface Normal ◽  
Application Procedure

AbstractThe problem of matching point clouds is an efficient way of registration, which is significant for many research fields including computer vision, machine learning, and robotics. There may be linear or non-linear transformation between point clouds, but determining the affine relation is more challenging among linear cases. Various methods have been presented to overcome this problem in the literature and one of them is the affine variant of the iterative closest point (ICP) algorithm. However, traditional affine ICP variants are highly sensitive to effects such as noises, deformations, and outliers; the least-square metric is substituted with the correntropy criterion to increase the robustness of ICPs to such effects. Correntropy-based robust affine ICPs available in the literature use point-to-point metric to estimate transformation between point clouds. Conversely, in this study, a line/surface normal that examines point-to-curve or point-to-plane distances is employed together with the correntropy criterion for affine point cloud registration problems. First, the maximum correntropy criterion measure is built for line/surface normal conditions. Then, the closed-form solution that maximizes the similarity between point sets is achieved for 2D registration and extended for 3D registration. Finally, the application procedure of the developed robust affine ICP method is given and its registration performance is examined through extensive experiments on 2D and 3D point sets. The results achieved highlight that our method can align point clouds more robustly and precisely than the state-of-the-art methods in the literature, while the registration time of the process remains at reasonable levels.

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 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 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.

scholarly journals Obtaining the Correspondence Between Bayesian and Neural Networks

1998 ◽  
Vol 12 (07) ◽  
pp. 901-920 ◽  
Author(s):  
A. Stassopoulou ◽  
M. Petrou
Keyword(s):  
Neural Network ◽  
Bayesian Network ◽  
Full Range ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Least Square ◽  
Novel Method ◽  
Probability Matrices ◽  
Desertification Assessment

We present in this paper a novel method for eliciting the conditional probability matrices needed for a Bayesian network with the help of a neural network. We demonstrate how we can obtain a correspondence between the two networks by deriving a closed-form solution so that the outputs of the two networks are similar in the least square error sense, not only when determining the discriminant function, but for the full range of their outputs. For this purpose we take into consideration the probability density functions of the independent variables of the problem when we compute the least square error approximation. Our methodoloy is demonstrated with the help of some real data concerning the problem of risk of desertification assessment for some burned forests in Attica, Greece where the parameters of the Bayesian network constructed for this task are successfully estimated given a neural network trained with a set of data.

Affine ICP for Fine Localization of Smart-AGVs in Smart Factories

2019 ◽  
Author(s):  
Abdurrahman Yılmaz ◽  
Hakan Temeltaş
Keyword(s):  
Least Square ◽  
Automated Guided Vehicles ◽  
Translation Vector ◽  
Point Sets ◽  
Registration Method ◽  
Point Set Registration ◽  
Localization Algorithms ◽  
Load Carrying ◽  
Smart Factories ◽  
Fine Localization

Abstract With the emergence of the concept of Industry 4.0, smart factories have started to be planned in which the production paradigm will change. Automated Guided Vehicles, abbreviated as AGV, that will perform load carrying and similar tasks in smart factories, Smart-AGVs, will try to reach their destinations on their own route instead of predetermined routes like in today’s factories. Moreover, since they will not reach their targets in a single way, they have to dock a target with their fine localization algorithms. In this paper, an affine Iterative Closest Point, abbreviated as ICP, based fine localization method is proposed, and applied on Smart-AGV docking problem in smart factories. ICP is a point set registration method but it is also used for localization applications due to its high precision. Affine ICP is an ICP variant which finds affine transformation between two point sets. In general, the objective function of ICP is constructed based on least square metric. In this study, we use affine ICP with correntropy metric. Correntropy is a similarity measure between two random variables, and affine ICP with correntropy tries to maximize the similarity between two point sets. Affine ICP has never been utilized in fine localization problem. We make an update on affine ICP by means of polar decomposition to reach transformation between two point sets in terms of rotation matrix and translation vector. The performance of the algorithm proposed is validated in simulation and the efficiency of it is demonstrated on MATLAB by comparing with the docking performance of the traditional ICP.

scholarly journals Multiple-Antenna Emitters Identification Based on a Memoryless Power Amplifier Model

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5233 ◽  
Author(s):  
Jun Lu ◽  
Xiaodong Xu
Keyword(s):  
Power Amplifier ◽  
Mimo System ◽  
Closed Form Solution ◽  
Form Solution ◽  
Least Square ◽  
Misclassification Rate ◽  
Multiple Antenna ◽  
Amplifier Model ◽  
Value Decomposition ◽  
Linear Least Square

Power amplifier (PA) nonlinearity is typically unique at the radio frequency (RF) front-end for particular emitters. It can play a crucial role in the application of specific emitter identification (SEI). In this paper, under the Multi-Input Multi-Output (MIMO) multipath communication scenario, two data-aided approaches are proposed to identify multi-antenna emitters using PA nonlinearity. Built upon a memoryless polynomial model, the first approach formulates a linear least square (LLS) problem and presents the closed-form solution of nonlinear coefficients in a MIMO system by means of singular value decomposition (SVD) operation. Another alternative approach estimates nonlinear coefficients of each individual PA through nonlinear least square (NLS) solved by the regularized Gauss–Newton iterative scheme. Moreover, there are some practical discussions of our proposed approaches about the mismatch of the order of PA model and the rank-deficient condition. Finally, the average misclassification rate is derived based on the minimum error probability (MEP) criterion, and the proposed approaches are validated to be effective through extensively numerical simulations.

An Initial Registration Method of Point Clouds Based on Random Sampling

2014 ◽  
Vol 513-517 ◽  
pp. 3680-3683 ◽  
Author(s):  
Xiao Xu Leng ◽  
Jun Xiao ◽  
Deng Yu Li
Keyword(s):  
Random Sampling ◽  
Point Cloud ◽  
Critical Role ◽  
Point Clouds ◽  
Least Square ◽  
Target Point ◽  
Registration Method ◽  
Source Point ◽  
Base Points ◽  
The Matrix

As the first step in 3D point cloud process, registration plays an critical role in determining the quality of subsequent results. In this paper, an initial registration algorithm of point clouds based on random sampling is proposed. In the proposed algorithm, the base points set is first extracted randomly in the target point cloud, next an optimal corresponding points set is got from the source point cloud, then a transform matrix is estimated based on the two sets with least square methods, finally the matrix is applied on the source point cloud. Experimental results show that this algorithm has ideal precision as well as good robustness.

Collision-Free Multi-Robot Navigation Using Autonomous Object Selection

2013 ◽  
Vol 313-314 ◽  
pp. 918-922
Author(s):  
Kong Woo Lee ◽  
Jae D. Jeon ◽  
Doo Jin Kim ◽  
Beom Hee Lee
Keyword(s):  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Threshold Function ◽  
Selection Algorithm ◽  
Sift Algorithm ◽  
Object Selection ◽  
Depth Maps ◽  
Surface Segmentation ◽  
Multi Robot

For successful SLAM, landmarks for pose estimation should be continuously observed. Firstly, we proposed the object selection algorithm from 2D images and 3D depth maps without human’s supervision. We used the SIFT algorithm to obtain descriptors of point features inside the object, and the surface segmentation algorithm to obtain separated objects from point clouds of 3D depth maps. Automatically selected objects were tested by the threshold function using repeatability, distinctiveness and saliency whether the objects were suitable or not for reusing and sharing between the robots. Secondly, we suggested the closed-form solution to estimate the 3D pose of robots from the information of selected objects. Furthermore, we provided the effective way to accomplish the tasks using multi-robot by compensating the accumulated navigating errors and re-planning the collision-free motion of the robots using the extended collision map algorithm.

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