scholarly journals Robust Techniques in Least Squares-Based Motion Estimation Problems

2003 ◽  
pp. 62-70 ◽  
Author(s):  
Raúl Montoliu ◽  
Filiberto Pla
Keyword(s):  
Motion Estimation ◽  
Least Squares ◽  
Robust Techniques ◽  
Estimation Problems

Total least squares 3-D motion estimation

2002 ◽  
Author(s):  
K.I. Diamantaras ◽  
T. Papadimitriou ◽  
M.G. Strintzis ◽  
M. Roumeliotis
Keyword(s):  
Motion Estimation ◽  
Least Squares ◽  
Total Least Squares

Localization of Mobile Robot Based on Least Square Method

2013 ◽  
Vol 347-350 ◽  
pp. 808-811
Author(s):  
Jia Lu Li ◽  
Lin Bing Long ◽  
Bao Feng Zhang
Keyword(s):  
Motion Estimation ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Least Squares ◽  
Least Square Method ◽  
Least Square ◽  
Experimental Results ◽  
Sift Algorithm ◽  
Key Techniques ◽  
Point Detection

Localization is the basis for navigation of mobile robots. This paper focuses on key techniques of localization for mobile robots based on vision. Firstly, the specific measures and steps of the algorithm are analyzed and researched in depth. In the study, SIFT algorithm combined with epipolar geometry constraint is used on the environment feature point detection, matching and tracking. And the method of RANSAC combined with the least squares is used to obtain accurate results of the motion estimation. Then the necessary experiments are carried out to verify the correctness and effectiveness of algorithms. The experimental results verified the accuracy of the improved algorithm.

Linear Least-Squares Computations Using Givens Transformations

1983 ◽  
Vol 37 (4) ◽  
pp. 225-233 ◽  
Author(s):  
J. A. R. Blais
Keyword(s):  
Least Squares ◽  
Error Estimates ◽  
Data Storage ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Direct Method ◽  
Linear Least Squares ◽  
Normal Equations ◽  
Estimation Problems ◽  
A Direct Method

Givens transformations provide a direct method for solving linear least-squares estimation problems without forming the normal equations. This approach has been shown to be particularly advantageous in recursive situations because of characteristics related to data storage requirements, numerical stability and computational efficiency. The following discussion will concentrate on the problem of updating least-squares parameter and error estimates using Givens transformations. Special attention will be given to photogrammetric and geodetic applications.

Experience in using homotopy methods to solve motion estimation problems

1990 ◽  
Author(s):  
Robert J. Holt ◽  
Arun N. Netravali ◽  
Thomas S. Huang
Keyword(s):  
Motion Estimation ◽  
Homotopy Methods ◽  
Estimation Problems

Robust L∞convex optimisation for monocular visual odometry trajectory estimation

Robotica ◽  
2014 ◽  
Vol 34 (3) ◽  
pp. 703-722 ◽  
Author(s):  
Mohammed Boulekchour ◽  
Nabil Aouf ◽  
Mark Richardson
Keyword(s):  
Motion Estimation ◽  
Least Squares ◽  
Uncertain Data ◽  
Image Features ◽  
Absolute Scale ◽  
Convex Optimisation ◽  
Scale Ratio ◽  
Robust Least Squares ◽  
Image Pairs ◽  
Value Decomposition

SUMMARYThe most important applications of many computer vision systems are based on robust features extraction, matching and tracking. Due to their extraction techniques, image features locations accuracy is heavily dependent on the variation in intensity within their neighbourhoods, from which their uncertainties are estimated. In the present work, a robust L∞optimisation solution for monocular motion estimation systems has been presented. The uncertainty estimation techniques based on SIFT derivative approach and its propagation through the eight-point algorithm, singular value decomposition SVD and the triangulation algorithm have proved an improvement to the global motion estimation. Using monocular systems makes the motion estimation challenging due to the absolute scale ambiguity caused by projective effects. For this, we propose robust tools to estimate both the trajectory of a moving object and the unknown absolute scale ratio between consecutive image pairs. Experimental evaluations showed that robust convex optimisation with the L∞norm under uncertain data and the Robust Least Squares clearly outperform classical methods based on Least Squares and Levenberg-Marquardt algorithms.

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