A Closed form Solution for Monocular Re-Projective 3D Pose Estimation of Regular Planar Patterns

2006 ◽  
Author(s):  
T. Hanning ◽  
R. Schoene ◽  
S. Graf
Keyword(s):  
Closed Form ◽  
Pose Estimation ◽  
Closed Form Solution ◽  
Form Solution ◽  
3D Pose Estimation

scholarly journals A Closed-Form Solution for Estimating the Accuracy of Circular Feature’ Pose for Object 2D-3D Pose Estimation System

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Cui Li ◽  
Derong Chen ◽  
Jiulu Gong ◽  
Yangyu Wu
Keyword(s):  
Closed Form ◽  
Covariance Matrix ◽  
Pose Estimation ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Synthetic Image ◽  
Point Selection ◽  
3D Pose Estimation ◽  
Estimation System

Many objects in the real world have circular feature. In general, circular feature’s pose is represented by 5-DoF (degree of freedom) vector ξ = X , Y , Z , α , β T . It is a difficult task to measure the accuracy of circular feature’s pose in each direction and the correlation between each direction. This paper proposes a closed-form solution for estimating the accuracy of pose transformation of circular feature. The covariance matrix of ξ is used to measure the accuracy of the pose. The relationship between the pose of the circular feature of 3D object and the 2D points is analyzed to yield an implicit function, and then Gauss–Newton theorem is employed to compute the partial derivatives of the function with respect to such point, and after that the covariance matrix is computed from both the 2D points and the extraction error. In addition, the method utilizes the covariance matrix of 5-DoF circular feature’s pose variables to optimize the pose estimator. Based on pose covariance, minimize the mean square error (Min-MSE) metric is introduced to guide good 2D imaging point selection, and the total amount of noise introduced into the pose estimator can be reduced. This work provides an accuracy method for object 2D-3D pose estimation using circular feature. At last, the effectiveness of the method for estimating the accuracy is validated based on both random data sets and synthetic images. Various synthetic image sequences are illustrated to show the performance and advantages of the proposed pose optimization method for estimating circular feature’s pose.

scholarly journals HYBRID CAMERA POSE ESTIMATION COMBINING SQUARE FIDUCIALS LOCALIZATION TECHNIQUE AND ORTHOGONAL ITERATION ALGORITHM

2008 ◽  
Vol 08 (01) ◽  
pp. 169-188 ◽  
Author(s):  
JEAN-YVES DIDIER ◽  
FAKHR-EDDINE ABABSA ◽  
MALIK MALLEM
Keyword(s):  
Closed Form ◽  
Pose Estimation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Geometric Constraints ◽  
Hybrid Technique ◽  
Localization Technique ◽  
Camera Pose Estimation ◽  
Camera Pose ◽  
Orthogonal Iteration

Camera pose estimation from video images is a fundamental problem in machine vision and Augmented Reality (AR) systems. Most developed solutions are either linear for both n points and n lines, or iterative depending on nonlinear optimization of some geometric constraints. In this paper, we first survey several existing methods and compare their performances in an AR context. Then, we present a new linear algorithm which is based on square fiducials localization technique to give a closed-form solution to the pose estimation problem, free of any initialization. We also propose an hybrid technique which combines an iterative method, in fact the orthogonal iteration (OI) algorithm, with our own closed form solution. An evaluation of the methods has shown that this hybrid pose estimation technique is accurate and robust. Numerical experiments from real data are given comparing the performances of our hybrid method with several iterative techniques, and demonstrating the efficiency of our approach.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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