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 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.

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.

3D pose estimation of large and complicated workpieces based on binocular stereo vision

2017 ◽  
Vol 56 (24) ◽  
pp. 6822 ◽  
Author(s):  
Zhifeng Luo ◽  
Ke Zhang ◽  
Zhigang Wang ◽  
Jian Zheng ◽  
Yixin Chen
Keyword(s):  
Pose Estimation ◽  
Stereo Vision ◽  
3D Pose Estimation ◽  
Binocular Stereo Vision ◽  
Binocular Stereo

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.

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