Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
International Journal of Computer Vision
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
Convex Optimization
Quasiconvex Optimization for Robust Geometric Reconstruction
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Multiple View Geometry and the L_"-norm
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Removing Outliers Using The L\infty Norm
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Recovering Camera Motion Using L\infty Minimization
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Optimal Estimation of Perspective Camera Pose
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Practical methods for convex multi-view reconstruction
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Robust Estimation for an Inverse Problem Arising in Multiview Geometry
Journal of Mathematical Imaging and Vision
A novel fast method for L∞ problems in multiview geometry
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
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This paper presents a study on how to numerically solve thefeasibility test problem which is the core of the bisectionalgorithm for minimizing the L ∞ error functions. Weconsider a strategy that minimizes the maximum infeasibility. Theminimization can be performed using several numerical computationmethods, among which the barrier method and the primal-dual methodare examined. In both of the methods, the inequalities aresequentially approximated by log-barrier functions. An initialfeasible solution is found easily by the construction of thefeasibility problem, and Newton-style update computes the optimalsolution iteratively. When we apply the methods to the problem ofestimating the structure and motion, every Newton update requiressolving a very large system of linear equations. We show that thesparse bundle-adjustment technique, previously developed forstructure and motion estimation, can be utilized during the Newtonupdate. In the primal-dual interior-point method, in contrast tothe barrier method, the sparse structure is all destroyed due to anextra constraint introduced for finding an initial solution.However, we show that this problem can be overcome by utilizing thematrix inversion lemma which allows us to exploit the sparsity inthe same manner as in the barrier method. We finally show that thesparsity appears in both of the L ∞ formulations -linear programming and second-order cone programming.