A new closed-form solution for absolute orientation

1994 ◽  
Author(s):  
Zhengyan Wang ◽  
Jepson
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Absolute Orientation

scholarly journals An Efficient Closed Form Solution to the Absolute Orientation Problem for Camera with Unknown Focal Length

Sensors ◽  
2021 ◽  
Vol 21 (19) ◽  
pp. 6480
Author(s):  
Kai Guo ◽  
Hu Ye ◽  
Zinian Zhao ◽  
Junhao Gu
Keyword(s):  
Closed Form ◽  
Focal Length ◽  
Closed Form Solution ◽  
Geometric Approach ◽  
Polynomial Equation ◽  
Form Solution ◽  
Camera Model ◽  
Absolute Orientation ◽  
Camera Position ◽  
The Absolute

In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D–3D point correspondences and the camera position. The problem can be decomposed into two simple sub-problems and can be solved with angle constraints. A polynomial equation of one variable is solved to determine the focal length, and then a geometric approach is used to determine the absolute orientation. The geometric derivations are easy to understand and significantly improve performance. Rewriting the camera model with the known camera position leads to a simpler and more efficient closed form solution, and this gives a single solution, without the multi-solution phenomena of perspective-three-point (P3P) solvers. Experimental results demonstrated that our proposed method has a better performance in terms of numerical stability, noise sensitivity, and computational speed, with synthetic data and real images.

scholarly journals Closed-form solution of absolute orientation using orthonormal matrices

1988 ◽  
Vol 5 (7) ◽  
pp. 1127 ◽  
Author(s):  
Berthold K. P. Horn ◽  
Hugh M. Hilden ◽  
Shahriar Negahdaripour
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Absolute Orientation

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

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.

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