Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
IEEE Transactions on Pattern Analysis and Machine Intelligence
The SVD and reduced rank signal processing
Signal Processing - Theme issue on singular value decomposition
A theory of self-calibration of a moving camera
International Journal of Computer Vision
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Jacobi's method is more accurage than QR
SIAM Journal on Matrix Analysis and Applications
Computational framework for determining stereo correspondence from a set of linear spatial filters
Image and Vision Computing - Special issue: 2nd European Conference on Computer Vision
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
A Second-Order Perturbation Expansion for the SVD
SIAM Journal on Matrix Analysis and Applications
Machine Learning - Special issue on applications in molecular biology
Artificial Intelligence - Special volume on computer vision
Relative Affine Structure: Canonical Model for 3D From 2D Geometry and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Paraperspective Factorization Method for Shape and Motion Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
Kruppa's Equations Derived from the Fundamental Matrix
IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-Calibration of a Moving Camera from PointCorrespondences and Fundamental Matrices
International Journal of Computer Vision
A Sequential Factorization Method for Recovering Shape and Motion From Image Streams
IEEE Transactions on Pattern Analysis and Machine Intelligence
Characterizing the uncertainty of the fundamental matrix
Computer Vision and Image Understanding
On the determination of Epipoles using cross-ratios
Computer Vision and Image Understanding
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
SVD and Signaling Processing III: Algorithms, Architectures, and Applications
SVD and Signaling Processing III: Algorithms, Architectures, and Applications
Analysis of 3-D Rotation Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Relative Camera Positions for Uncalibrated Cameras
ECCV '92 Proceedings of the Second European Conference on Computer Vision
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Cylindrical rectification to minimize epipolar distortion
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Noise estimation and filtering using block-based singular value decomposition
IEEE Transactions on Image Processing
Combined techniques of singular value decomposition and vector quantization for image coding
IEEE Transactions on Image Processing
On Computing Metric Upgrades of Projective Reconstructions Under the Rectangular Pixel Assumption
SMILE '00 Revised Papers from Second European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
Point Cloud Glue: constraining simulations using the procrustes transform
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Efficient hyperelastic regularization for registration
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
3D active shape models using gradient descent optimization of description length
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Aligning shapes by minimising the description length
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Adaptive anisotropic remeshing for cloth simulation
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Computer Vision and Image Understanding
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The Singular Value Decomposition (SVD) of a matrix is a linear algebra tool that has been successfully applied to a wide variety of domains. The present paper is concerned with the problem of estimating the Jacobian of the SVD components of a matrix with respect to the matrix itself. An exact analytic technique is developed that facilitates the estimation of the Jacobian using calculations based on simple linear algebra. Knowledge of the Jacobian of the SVD is very useful in certain applications involving multivariate regression or the computation of the uncertainty related to estimates obtained through the SVD. The usefulness and generality of the proposed technique is demonstrated by applying it to the estimation of the uncertainty for three different vision problems, namely self-calibration, epipole computation and rigid motion estimation.