Computer Vision: A Modern Approach
Computer Vision: A Modern Approach
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
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
On the Wiberg Algorithm for Matrix Factorization in the Presence of Missing Components
International Journal of Computer Vision
Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Nonconvergence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Structure from Motion using the Extended Kalman Filter
Structure from Motion using the Extended Kalman Filter
General and nested Wiberg minimization
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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Wiberg matrix factorization breaks a matrix Y into low-rank factors U and V by solving for V in closed form given U, linearizing V(U) about U, and iteratively minimizing ||Y−UV(U)||2 with respect to U only. This approach factors the matrix while effectively removing V from the minimization. We generalize the Wiberg approach beyond factorization to minimize an arbitrary function that is nonlinear in each of two sets of variables. In this paper we focus on the case of L2 minimization and maximum likelihood estimation (MLE), presenting an L2 Wiberg bundle adjustment algorithm and a Wiberg MLE algorithm for Poisson matrix factorization. We also show that one Wiberg minimization can be nested inside another, effectively removing two of three sets of variables from a minimization. We demonstrate this idea with a nested Wiberg algorithm for L2 projective bundle adjustment, solving for camera matrices, points, and projective depths.