Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithm 676: ODRPACK: software for weighted orthogonal distance regression
ACM Transactions on Mathematical Software (TOMS)
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating 3-D location parameters using dual number quaternions
CVGIP: Image Understanding
Self-calibration of an affine camera from multiple views
International Journal of Computer Vision
Estimating 3-D rigid body transformations: a comparison of four major algorithms
Machine Vision and Applications - Special issue on performance evaluation
Linear fitting with missing data for structure-from-motion
Computer Vision and Image Understanding
Analysis of 3-D Rotation Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Estimation of Rigid Body Rotation from Noisy Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Optimal Estimation of Three-Dimensional Rotation and Reliability Evaluation
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Visual Modeling with a Hand-Held Camera
International Journal of Computer Vision
A Closed-Form Solution to Non-Rigid Shape and Motion Recovery
International Journal of Computer Vision
Simultaneous Registration and Modeling of Deformable Shapes
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Total least squares fitting of point sets in m-D
CGI '05 Proceedings of the Computer Graphics International 2005
Global registration of multiple 3D point sets via optimization-on-a-manifold
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
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Generalized procrustes analysis computes the best set of transformations that relate matched shape data. In shape analysis the transformations are usually chosen as similarities, while in general statistical data analysis other types of transformation groups such as the affine group may be used. Generalized procrustes analysis has a nonlinear and nonconvex formulation. The classical approach alternates the computation of a so-called reference shape and the computation of transformations relating this reference shape to each shape datum in turn.We propose the stratified approach to generalized procrustes analysis. It first uses the affine transformation group to analyze the data and then upgrades the solution to the sought after group, whether Euclidean or similarity. We derive a convex formulation for each of these two steps, and efficient practical algorithms that gracefully handle missing data (incomplete shapes).Extensive experimental results show that our approaches perform well on simulated and real data. In particular our closed-form solution gives very accurate results for generalized procrustes analysis of Euclidean data.