A new polynomial-time algorithm for linear programming
Combinatorica
A primal-dual interior point algorithm for linear programming
Progress in Mathematical Programming Interior-point and related methods
An interior-point method for fractional programs with convex constraints
Mathematical Programming: Series A and B
An interior-point method for generalized linear-fractional programming
Mathematical Programming: Series A and B
Primal-dual interior-point methods
Primal-dual interior-point methods
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
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
Sparse Structures in L-Infinity Norm Minimization for Structure and Motion Reconstruction
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Smooth Approximation of L_infinity-Norm for Multi-view Geometry
DICTA '09 Proceedings of the 2009 Digital Image Computing: Techniques and Applications
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Practical methods for convex multi-view reconstruction
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Structure-from-motion based hand-eye calibration using L$_8$ minimization
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
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Optimization using the L∞ norm is an increasingly important area in multiview geometry. Previous work has shown that globally optimal solutions can be computed reliably using the formulation of generalized fractional programming, in which algorithms solve a sequence of convex problems independently to approximate the optimal L∞ norm error. We found the sequence of convex problems are highly related and we propose a method to derive a Newton-like step from any given point. In our method, the feasible region of the current involved convex problem is contracted gradually along with the Newton-like steps, and the updated point locates on the boundary of the new feasible region. We propose an effective strategy to make the boundary point become an interior point through one dimension augmentation and relaxation. Results are presented and compared to the state of the art algorithms on simulated and real data for some multiview geometry problems with improved performance on both runtime and Newton-like iterations.