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 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.

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.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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.

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.

scholarly journals A Block-Based Regularized Approach for Image Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Chen ◽  
Xiaotong Huang ◽  
Jing Tian
Keyword(s):  
Cost Function ◽  
Regularization Parameter ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Image Interpolation ◽  
Adaptive Strategy ◽  
Form Solution ◽  
Interpolation Techniques ◽  
Block Based ◽  
Value Decomposition

This paper presents a new efficient algorithm for image interpolation based on regularization theory. To render ahigh-resolution(HR) image from alow-resolution(LR) image, classical interpolation techniques estimate the missing pixels from the surrounding pixels based on a pixel-by-pixel basis. In contrast, the proposed approach formulates the interpolation problem into the optimization of a cost function. The proposed cost function consists of a data fidelity term and regularization functional. The closed-form solution to the optimization problem is derived using the framework of constrained least squares minimization, by incorporating Kronecker product andsingular value decomposition(SVD) to reduce the computational cost of the algorithm. The effect of regularization on the interpolation results is analyzed, and an adaptive strategy is proposed for selecting the regularization parameter. Experimental results show that the proposed approach is able to reconstruct high-fidelity HR images, while suppressing artifacts such as edge distortion and blurring, to produce superior interpolation results to that of conventional image interpolation techniques.

Local singular value decomposition for signal enhancement of seismic data

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. V59-V65 ◽  
Author(s):  
Maïza Bekara ◽  
Mirko Van der Baan
Keyword(s):  
Singular Value Decomposition ◽  
Noise Suppression ◽  
Signal To Noise Ratio ◽  
Real Data ◽  
Global Scale ◽  
Signal Enhancement ◽  
Singular Value ◽  
Median Filtering ◽  
Seismic Sections ◽  
Value Decomposition

Singular value decomposition (SVD) is a coherency-based technique that provides both signal enhancement and noise suppression. It has been implemented in a variety of seismic applications — mostly on a global scale. In this paper, we use SVD to improve the signal-to-noise ratio of unstacked and stacked seismic sections, but apply it locally to cope with coherent events that vary with both time and offset. The local SVD technique is compared with [Formula: see text] deconvolution and median filtering on a set of synthetic and real-data sections. Local SVD is better than [Formula: see text] deconvolution and median filtering in removing background noise, but it performs less well in enhancing weak events or events with conflicting dips. Combining [Formula: see text] deconvolution or median filtering with local SVD overcomes the main weaknesses associated with each individual method and leads to the best results.

Sign in / Sign up

Export Citation Format

Share Document