Robust Optimal Pose Estimation
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
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
Outlier Removal by Convex Optimization for L-Infinity Approaches
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
Removing outliers by minimizing the sum of infeasibilities
Image and Vision Computing
Convex optimization for nonrigid stereo reconstruction
IEEE Transactions on Image Processing
Rejecting Mismatches by Correspondence Function
International Journal of Computer Vision
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Sequential L∞ norm minimization for triangulation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
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
Nonrigid stereo reconstruction using linear programming
Proceedings of the 1st international workshop on 3D video processing
Practical methods for convex multi-view reconstruction
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
A fast approach to deformable surface 3D tracking
Pattern Recognition
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
Planar scene modeling from quasiconvex subproblems
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
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
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
An Adversarial Optimization Approach to Efficient Outlier Removal
Journal of Mathematical Imaging and Vision
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Recently, there has been interest in solving geometric vision problems such as triangulation and camera resectioning using L\infty minimization. One key advantage of using the L\infty norm rather than the L2 norm is that the L\infty cost function has a single minimum unlike the commonly used L2 cost function which typically has multiple local minima. However, one drawback of using L\infty minimization is that it is not robust to outliers. By minimizing the L\infty norm instead of the L2 norm, we are, in essence, fitting the outliers and not the good data. Therefore, before one can perform L\infty optimization on a problem, it is first necessary to remove outliers. A popular (but generally unsound) method of removing outliers is to minimize the cost function using standard optimization techniques; then if the residual error is too great, remove the offending measurements and continue. Although this method can fail for simple L2 optimization problems, we show in this paper that for a wide class of L\infty problems it is a valid technique. It is proved that the set of measurements with greatest residual must contain at least one outlier. Thus, if we keep throwing out the measurements with greatest residual, we will eventually remove all outliers in the data. We test this hypothesis on the multiview reconstruction problem and show that even simple strategies for throwing out these maximum residual measurements are effective in removing outliers.