The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
International Journal of Computer Vision
Means and Averaging in the Group of Rotations
SIAM Journal on Matrix Analysis and Applications
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Simultaneous Multiple 3D Motion Estimation via Mode Finding on Lie Groups
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Pursuing Informative Projection on Grassmann Manifold
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold
International Journal of Computer Vision
Nonlinear Optimization
Pedestrian Detection via Classification on Riemannian Manifolds
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Comparative Analysis of RANSAC Techniques Leading to Adaptive Real-Time Random Sample Consensus
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
Reconstruction from Projections Using Grassmann Tensors
International Journal of Computer Vision
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
Multi-class classification on Riemannian manifolds for video surveillance
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Statistics of shape via principal geodesic analysis on lie groups
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Subspace estimation using projection based m-estimators over grassmann manifolds
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Generalized projection based M-estimator: Theory and applications
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Averaging complex subspaces via a Karcher mean approach
Signal Processing
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Most geometric computer vision problems involve orthogonality constraints. An important subclass of these problems is subspace estimation, which can be equivalently formulated into an optimization problem on Grassmann manifolds. In this paper, we propose to use the conjugate gradient algorithm on Grassmann manifolds for robust subspace estimation in conjunction with the recently introduced generalized projection based M-Estimator (gpbM). The gpbM method is an elemental subset-based robust estimation algorithm that can process heteroscedastic data without any user intervention. We show that by optimizing the orthogonal parameter matrix on Grassmann manifolds, the performance of the gpbM algorithm improves significantly. Results on synthetic and real data are presented.