Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
Triangulation of Points, Lines and Conics
Journal of Mathematical Imaging and Vision
Global Optimization through Rotation Space Search
International Journal of Computer Vision
Removing outliers by minimizing the sum of infeasibilities
Image and Vision Computing
A branch-and-bound algorithm for globally optimal camera pose and focal length
Image and Vision Computing
Generalized Convexity in Multiple View Geometry
Journal of Mathematical Imaging and Vision
L-infinity norm minimization in the multiview triangulation
AICI'10 Proceedings of the 2010 international conference on Artificial intelligence and computational intelligence: Part I
Efficient Suboptimal Solutions to the Optimal Triangulation
International Journal of Computer Vision
Approximate and SQP two view triangulation
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
A fast approach to deformable surface 3D tracking
Pattern Recognition
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Stable structure from motion for unordered image collections
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Global Optimization for One-Dimensional Structure and Motion Problems
SIAM Journal on Imaging Sciences
A variant of the trace quotient formulation for dimensionality reduction
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
Robust Estimation for an Inverse Problem Arising in Multiview Geometry
Journal of Mathematical Imaging and Vision
Enhancing point clouds accuracy of small baseline images based on convex optimization
IEA/AIE'12 Proceedings of the 25th international conference on Industrial Engineering and Other Applications of Applied Intelligent Systems: advanced research in applied artificial intelligence
Robust fitting for multiple view geometry
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Covariance propagation and next best view planning for 3d reconstruction
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Fast 3d spine reconstruction of postoperative patients using a multilevel statistical model
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Two-view underwater structure and motion for cameras under flat refractive interfaces
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
A multi-stage linear approach to structure from motion
ECCV'10 Proceedings of the 11th European conference on Trends and Topics in Computer Vision - Volume Part II
Verifying Global Minima for L2 Minimization Problems in Multiple View Geometry
International Journal of Computer Vision
Sampling Minimal Subsets with Large Spans for Robust Estimation
International Journal of Computer Vision
An Adversarial Optimization Approach to Efficient Outlier Removal
Journal of Mathematical Imaging and Vision
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This paper presents a new framework for solving geometric structure and motion problems based on {$L_\infty$}-norm. Instead of using the common sum-of-squares cost-function, that is, the {$L_\two$}-norm, the model-fitting errors are measured using the {$L_\infty$}-norm. Unlike traditional methods based on {$L_\two$}, our framework allows for efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using Second-Order Cone Programming (SOCP) which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance.