Integer and combinatorial optimization
Integer and combinatorial optimization
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
A paraperspective factorization method for shape and motion recovery
ECCV '94 Proceedings of the third European conference on Computer Vision (Vol. II)
Rigidity Checking of 3D Point Correspondences Under Perspective Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Unified Approach to Moving Object Detection in 2D and 3D Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer vision
Multiple view geometry in computer vision
A Global Solution to Sparse Correspondence Problems
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
Multi-camera Scene Reconstruction via Graph Cuts
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A Non-Iterative Greedy Algorithm for Multi-frame Point Correspondence
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Rank Conditions on the Multiple-View Matrix
International Journal of Computer Vision
Contour Point Tracking by Enforcement of Rigidity Constraints
3DIM '05 Proceedings of the Fifth International Conference on 3-D Digital Imaging and Modeling
3D Reconstruction by Fitting Low-Rank Matrices with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Optimal Point Correspondence through the Use of Rank Constraints
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Wide-baseline multiple-view correspondences
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
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Establishing the correct correspondence between features in an image set remains a challenging problem amongst computer vision researchers. In fact, the combinatorial nature of feature matching effectively hinders the solution of large scale problems, which have direct applications in important areas such as 3D reconstruction and tracking. The solution is obtained by imposing a geometric constraint - rigidity - that selects the matching solution resulting in a rank-4 observation matrix. Since this is a global criterion, issues usually associated to local matching algorithms (such as the aperture problem) do not present an obstacle in this case. The use of a geometric constraint of this type assumes that all feature points are visible in every image, so as to obtain a complete observation matrix. The rank of the observation matrix is a function of the matching solutions associated to each image and as such a simultaneous solution for all frames has to be found. For each frame, correspondence is modeled through a permutation matrix, which also allows for the rejection of wrong candidates. Although each image is matched individually, an iterative algorithm is used to integrate correspondence information associated to all remaining images. Each individual matching process results in a linear problem: the reduced computational complexity allows the solution of large problems in an acceptable time interval. Although the algorithm has intrinsically been designed for calibrated systems, some instances of the uncalibrated case can also be solved provided a convenient bootstrap is available.