Multi-Frame Estimation of Planar Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiview Constraints on Homographies
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Plane+Parallax, Tensors and Factorization
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Reconstruction of a Scene with Multiple Linearly Moving Objects
International Journal of Computer Vision
Motion Layer Extraction in the Presence of Occlusion Using Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracking based motion segmentation under relaxed statistical assumptions
Computer Vision and Image Understanding
A 3D Shape Constraint on Video
IEEE Transactions on Pattern Analysis and Machine Intelligence
Object Level Grouping for Video Shots
International Journal of Computer Vision
An Analysis of Linear Subspace Approaches for Computer Vision and Pattern Recognition
International Journal of Computer Vision
Rank Constraints for Homographies over Two Views: Revisiting the Rank Four Constraint
International Journal of Computer Vision
A Probabilistic Method for Point Matching in the Presence of Noise and Degeneracy
Journal of Mathematical Imaging and Vision
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique
Journal of Mathematical Imaging and Vision
Tracking based motion segmentation under relaxed statistical assumptions
Computer Vision and Image Understanding
Rigid motion constraints for tracking planar objects
Proceedings of the 29th DAGM conference on Pattern recognition
Motion layer extraction in the presence of occlusion using graph cut
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Computing homographies from three lines or points in an image pair
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
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The motion of a planar surface between two camera views induces a homography. The homography depends on the camera intrinsic and extrinsic parameters, as well as on the 3D plane parameters. While camera parameters vary across different views, the plane geometry remains the same. Based on this fact, we derive linear subspace constraints on the relative motion of multiple (\math) planes across multiple views.The paper has three main contributions: (i) We show that the collection of all "relative homographies" of a pair of planes (homologies) across multiple views, spans a 4-dimensional linear subspace. (ii) We show how this constraint can be extended to the case of multiple planes across multiple views. (iii) We suggest two potential application areas which can benefit from these constraints: (a) The accuracy of homography estimation can be improved by enforcing the multi-view subspace constraints. (b) Violations of these multi-view constraints can be used as a cue for moving object detection. All the results derived in this paper are true for uncalibrated cameras.