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
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
Generalized Convexity in Multiple View Geometry
Journal of Mathematical Imaging and Vision
Globally Optimal Algorithms for Stratified Autocalibration
International Journal of Computer Vision
Practical methods for convex multi-view reconstruction
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
3D geometry from uncalibrated images
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
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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Recently, there has been interest in formulating various geometric problems in Computer Vision as L\infty optimization problems. The advantage of this approach is that under L\infty norm, such problems typically have a single minimum, and may be efficiently solved using Second-Order Cone Programming (SOCP). This paper shows that such techniques may be used effectively on the problem of determining the track of a camera given observations of features in the environment. The approach to this problem involves two steps: determination of the orientation of the camera by estimation of relative orientation between pairs of views, followed by determination of the translation of the camera. This paper focusses on the second step, that of determining the motion of the camera. It is shown that it may be solved effectively by using SOCP to reconcile translation estimates obtained for pairs or triples of views. In addition, it is observed that the individual translation estimates are not known with equal certainty in all directions. To account for this anisotropy in uncertainty, we introduce the use of covariances into the L\infty optimization framework.