Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Stratified Self-Calibration with the Modulus Constraint
IEEE Transactions on Pattern Analysis and Machine Intelligence
Finding the collineation between two projective reconstructions
Computer Vision and Image Understanding
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Incremental Singular Value Decomposition of Uncertain Data with Missing Values
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Uncertainty Modeling for Optimal Structure from Motion
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Euclidean Reconstruction from Uncalibrated Views
Proceedings of the Second Joint European - US Workshop on Applications of Invariance in Computer Vision
Factorization Methods for Projective Structure and Motion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Fast and Accurate Self-Calibration
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Projective Reconstruction from Multiple Views with Minimization of 2D Reprojection Error
International Journal of Computer Vision
Bilinear factorization via augmented lagrange multipliers
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
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In this paper, we propose a new factorization-based algorithm for projective reconstruction from multiple views by minimizing the 2D reprojection error in the images. In our algorithm, the projective reconstruction problem is formulated as a constrained minimization problem, which minimizes the 2D reprojection error in multiple images. To solve this constrained minimization problem, we use the augmented Lagrangian approach to generate a sequence of unconstrained minimization problems, which can be readily solved by standard least-squares technique. Thus we can estimate the projective depths, the projection matrices and the positions of 3D points simultaneously by iteratively solving a sequence of unconstrained minimization problems. The proposed algorithm does not require the projective depths as prior knowledge, unlike bundle adjustment techniques. It converges more robustly and rapidly than the penalty based method. Furthermore, it readily handles the case of partial occlusion, where some points cannot be observed in some images.