Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Shape Ambiguities in Structure From Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision and Image Understanding
On the Optimization Criteria Used in Two-View Motion Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Minimal Projective Reconstruction Including Missing Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating the Fundamental Matrix via Constrained Least-Squares: A Convex Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Exact Two-Image Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multi-camera Scene Reconstruction via Graph Cuts
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Optimal Structure from Motion: Local Ambiguities and Global Estimates
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
An Invitation to 3-D Vision: From Images to Geometric Models
An Invitation to 3-D Vision: From Images to Geometric Models
Convex Optimization
Globally Convergent Autocalibration Using Interval Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
How Hard is 3-View Triangulation Really?
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Globally Optimal Estimates for Geometric Reconstruction Problems
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
Global optimization of rational functions: a semidefinite programming approach
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Detecting and Handling Unreliable Points for Camera Parameter Estimation
International Journal of Computer Vision
Triangulation of Points, Lines and Conics
Journal of Mathematical Imaging and Vision
Canonical subsets of image features
Computer Vision and Image Understanding
Global Optimization through Rotation Space Search
International Journal of Computer Vision
Compact Fundamental Matrix Computation
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
Computer Vision and Image Understanding
Monocular 3-D tracking of inextensible deformable surfaces under L2-norm
IEEE Transactions on Image Processing
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Optimal non-iterative pose estimation via convex relaxation
Image and Vision Computing
Twisted cubic: degeneracy degree and relationship with general degeneracy
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
Monocular template-based tracking of inextensible deformable surfaces under L2-norm
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
A QCQP approach to triangulation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
| Hi-index | 0.00 |
We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality--or a combination of both--we pursue the goal of achieving global solutions of the statistically optimal cost-function.Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum.