Title :
First order error propagation of the Procrustes method for 3D attitude estimation
Author_Institution :
Intelligent Syst. Lab., Amsterdam Univ., Netherlands
Abstract :
The well-known Procrustes method determines the optimal rigid body motion that registers two point clouds by minimizing the square distances of the residuals. In this paper, we perform the first order error analysis of this method for the 3D case, fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body motion. These results are much more specific than the error bounds which have been established in numerical analysis. We provide an intuitive understanding of the outcome to facilitate direct use in applications.
Keywords :
attitude measurement; error analysis; minimisation; motion estimation; parameter estimation; 3D attitude estimation; Procrustes method; directional noise; error bounds; first order error analysis; first order error propagation; numerical analysis; optimal rigid body motion; parameter estimation; square distance minimization; two point clouds; Clouds; Error analysis; Gaussian noise; Motion analysis; Motion estimation; Noise shaping; Position measurement; Robot vision systems; Shape control; Shape measurement; Index Terms- Rigid body motion analysis; Procrustes method; attitude estimation; error propagation; orthogonal Procrustes problem; perturbation analysis; polar decomposition.; pose estimation; Algorithms; Artificial Intelligence; Computer Simulation; Data Interpretation, Statistical; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Information Storage and Retrieval; Models, Statistical; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted; Subtraction Technique;
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
DOI :
10.1109/TPAMI.2005.29
