Rigid Shape Registration Based on Extended Hamiltonian Learning
Abstract
:1. Introduction
2. Geometry of Special Euclidean Groups
3. Extended Hamiltonian Learning on SE(n)
4. 2D/3D Rigid Shape Registration Based on Extended Hamiltonian Learning
Algorithm 1 EHLICP Algorithm 
Input: Initial Data ${\left\{{x}_{i}\right\}}_{i=1}^{{N}_{x}}$; Target Data ${\left\{{y}_{i}\right\}}_{i=1}^{{N}_{y}}$ Output: Rotation ${r}^{k}$; Translation ${t}^{k}$; Registration Error ${V}^{k}$;

5. Numerical Results
5.1. 2D Rigid Shape Registration
5.2. 3D Shape Registration
6. Conclusions and Future Works
Author Contributions
Funding
Conflicts of Interest
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Group  Model  Test  SVD  ID  LGO  EHLICP 

(1)  bird3  bird4  0.5841  0.9996  0.5690  0.4048 
(2)  deer1  deer4  0.5263  2.7598  0.5272  2.8826 
(3)  horse3  horse4  0.5107  1.4278  0.5112  0.3880 
(4)  beetle7  beetle8  0.8749  0.8746  0.5242  0.4730 
(5)  cattle1  cattle20  22.8580  28.3719  22.5155  1.1656 
(6)  hammer4  hammer5  0.4846  0.8037  0.4232  0.3043 
(7)  chicken2  chicken3  0.5484  2.7 843  0.5471  0.5202 
(8)  butterfly1  butterfly2  18.1726  34.3588  6.9691  2.9062 
(9)  horseshoe9  horseshoe17  0.5425  0.5690  0.5873  0.3577 
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Yi, J.; Zhang, S.; Cao, Y.; Zhang, E.; Sun, H. Rigid Shape Registration Based on Extended Hamiltonian Learning. Entropy 2020, 22, 539. https://doi.org/10.3390/e22050539
Yi J, Zhang S, Cao Y, Zhang E, Sun H. Rigid Shape Registration Based on Extended Hamiltonian Learning. Entropy. 2020; 22(5):539. https://doi.org/10.3390/e22050539
Chicago/Turabian StyleYi, Jin, Shiqiang Zhang, Yueqi Cao, Erchuan Zhang, and Huafei Sun. 2020. "Rigid Shape Registration Based on Extended Hamiltonian Learning" Entropy 22, no. 5: 539. https://doi.org/10.3390/e22050539