Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
International Journal of Computer Vision
Stratified Self-Calibration with the Modulus Constraint
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Case Against Kruppa's Equations for Camera Self-Calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques
Journal of Global Optimization
Camera Self-Calibration: Theory and Experiments
ECCV '92 Proceedings of the Second European Conference on Computer Vision
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Surviving Dominant Planes in Uncalibrated Structure and Motion Recovery
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
A Comparison of Search Strategies for Geometric Branch and Bound Algorithms
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Effective Tracking through Tree-Search
IEEE Transactions on Pattern Analysis and Machine Intelligence
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Autocalibration and the absolute quadric
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Euclidean Reconstruction from Constant Intrinsic Parameters
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Convex Optimization
Untwisting a Projective Reconstruction
International Journal of Computer Vision
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
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
Algorithms for Feature Selection: An Evaluation
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
Branch-and-Bound Methods for Euclidean Registration Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
A global optimal algorithm for camera calibration with one-dimensional objects
HCII'11 Proceedings of the 14th international conference on Human-computer interaction: design and development approaches - Volume Part I
Maximum likelihood autocalibration
Image and Vision Computing
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Auto-calibration for image mosaicing and stereo vision
Transactions on Computational Science XIX
Self-calibration of stationary non-rotating zooming cameras
Image and Vision Computing
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We present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality. Given a projective reconstruction, we first upgrade it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints. In the second stage, this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic (DIAC). The positive semidefiniteness of the DIAC is explicitly enforced as part of the optimization process, rather than as a post-processing step.For each stage, we construct and minimize tight convex relaxations of the highly non-convex objective functions in a branch and bound optimization framework. We exploit the inherent problem structure to restrict the search space for the DIAC and the plane at infinity to a small, fixed number of branching dimensions, independent of the number of views. Chirality constraints are incorporated into our convex relaxations to automatically select an initial region which is guaranteed to contain the global minimum.Experimental evidence of the accuracy, speed and scalability of our algorithm is presented on synthetic and real data.