Analytical Solution for Sparse Data Interpolation Using Geodesic Distance Affinity Space: Application to the Optical Flow Problem and 3D Reconstruction

2020 ◽  
Vol 65 (12) ◽  
pp. 1469-1475
Author(s):  
V. N. Karnaukhov ◽  
V. I. Kober ◽  
M. G. Mozerov
Keyword(s):  
Analytical Solution ◽  
3D Reconstruction ◽  
Optical Flow ◽  
Flow Problem ◽  
Geodesic Distance ◽  
Sparse Data ◽  
Space Application ◽  
Data Interpolation ◽  
Affinity Space

scholarly journals Sparse Data Interpolation Using the Geodesic Distance Affinity Space

2019 ◽  
Vol 26 (6) ◽  
pp. 943-947
Author(s):  
Mikhail G. Mozerov ◽  
Fei Yang ◽  
Joost van de Weijer
Keyword(s):  
Geodesic Distance ◽  
Sparse Data ◽  
Data Interpolation ◽  
Affinity Space

scholarly journals Intrinsic Optimal Control for Mechanical Systems on Lie Group

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chao Liu ◽  
Shengjing Tang ◽  
Jie Guo
Keyword(s):  
Optimal Control ◽  
Analytical Solution ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Control Method ◽  
Geodesic Distance ◽  
Infinite Horizon ◽  
Mechanical Systems ◽  
Programming Approach

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

3D Reconstruction from Un-Calibrated Images Using Optical Flow Magnitude Based Method

2017 ◽  
Vol 23 (5) ◽  
pp. 3955-3959
Author(s):  
Intan Syaherra Ramli ◽  
Rahmita Wirza O. K Rahmat ◽  
Ng Seng Beng ◽  
Puteri Suhaiza Sulaiman ◽  
Hizmawati Madzin
Keyword(s):  
3D Reconstruction ◽  
Optical Flow ◽  
Calibrated Images

scholarly journals Optical Flow-Based Epipolar Estimation of Spherical Image Pairs for 3D Reconstruction

2017 ◽  
Vol 10 (5) ◽  
pp. 476-485 ◽  
Author(s):  
Sarthak PATHAK ◽  
Alessandro MORO ◽  
Atsushi YAMASHITA ◽  
Hajime ASAMA
Keyword(s):  
3D Reconstruction ◽  
Optical Flow ◽  
Spherical Image ◽  
Image Pairs

3D reconstruction from uncalibrated-camera optical flow and its reliability evaluation

2002 ◽  
Vol 33 (9) ◽  
pp. 1-10 ◽  
Author(s):  
Kenichi Kanatani ◽  
Naoya Ohta ◽  
Yoshiyuki Shimizu
Keyword(s):  
3D Reconstruction ◽  
Optical Flow ◽  
Reliability Evaluation ◽  
Uncalibrated Camera
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