Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Projective Reconstruction and Invariants from Multiple Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Canonical representations for the geometries of multiple projective views
Computer Vision and Image Understanding
Computer Vision and Image Understanding
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Estimating the fundamental matrix by transforming image points in projective space
Computer Vision and Image Understanding
Parallax Geometry of Pairs of Points for 3D Scene Analysis
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
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
3D Model Acquisition from Extended Image Sequences
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Euclidean Reconstruction from Uncalibrated Views
Proceedings of the Second Joint European - US Workshop on Applications of Invariance in Computer Vision
Gauge Invariance in Projective 3D Reconstruction
MVIEW '99 Proceedings of the IEEE Workshop on Multi-View Modeling & Analysis of Visual Scenes
In defence of the 8-point algorithm
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Nonlinear Estimation of the Fundamental Matrix with Minimal Parameters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Structure-from-motion using lines: representation, triangulation, and bundle adjustment
Computer Vision and Image Understanding
Structure-from-motion using lines: Representation, triangulation, and bundle adjustment
Computer Vision and Image Understanding
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I address the problem of optimizing projective motion over a minimal set of parameters. Most of the existingworks overparameterize the problem. While this can simplify the estimation process and may ensure well-conditioning of the parameters, this also increases the computational cost since more unknowns than necessary are involvedI propose a method whose key feature is that the number of parameters employed is minimal. The method requires singular value decomposition and minor algebraic manipulations and is therefore straightforward to implement. It can be plugged into most of the optimization algorithms such as Levenberg-Marquardt as well as the corresponding sparse versions. The method relies on the orthonormal camera motion representation that I introduce here. This representation can be locally updated using minimal parameters.I give a detailled description for the implementation of the two-view case within a bundle adjustment framework, which corresponds to the maximum likelihood estimation of the fundamental matrix and scene structure. Extending the algorithm to the multiple-view case is straightforward. Experimental results using simulated and real data show that algorithms based on minimal parameters perform better than the others in terms of the computational cost, i.e. their convergence is faster, while achieving comparable results in terms of convergence to a local optimum. An implementation of the method will be made available.