Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Computing occluding and transparent motions
International Journal of Computer Vision
Using collineations to compute motion and structure in an uncalibrated image sequence
International Journal of Computer Vision
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dual Computation of Projective Shape and Camera Positions from Multiple Images
International Journal of Computer Vision
Multi-Frame Estimation of Planar Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Projective Structure from Uncalibrated Images: Structure From Motion and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical Model-Based Motion Estimation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
From Reference Frames to Reference Planes: Multi-View Parallax Geometry and Applications
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Duality, Rigidity and Planar Parallax
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
The Rank 4 Constraint in Multiple (=3) View Geometry
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Automatic Camera Recovery for Closed or Open Image Sequences
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Autocalibration from Planar Scenes
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Dense Shape and Motion from Region Correspondences by Factorization
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Mosaic based representations of video sequences and their applications
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Multi-View Subspace Constraints on Homographies
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
An Analysis of Linear Subspace Approaches for Computer Vision and Pattern Recognition
International Journal of Computer Vision
From lines to epipoles through planes in two views
Pattern Recognition
Homography-based partitioning of curved surface for stereo correspondence establishment
Pattern Recognition Letters
A prism-based single-lens stereovision system: From trinocular to multi-ocular
Image and Vision Computing
Rank Constraints for Homographies over Two Views: Revisiting the Rank Four Constraint
International Journal of Computer Vision
Error Analysis in Homography Estimation by First Order Approximation Tools: A General Technique
Journal of Mathematical Imaging and Vision
Topological maps based on graphs of planar regions
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Rigid motion constraints for tracking planar objects
Proceedings of the 29th DAGM conference on Pattern recognition
Multiple homographies with omnidirectional vision for robot homing
Robotics and Autonomous Systems
Distributed multi-camera visual mapping using topological maps of planar regions
Pattern Recognition
Statistical unbiased background modeling for moving platforms
PIA'11 Proceedings of the 2011 ISPRS conference on Photogrammetric image analysis
Computing homographies from three lines or points in an image pair
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Automatic matching and motion estimation from two views of a multiplane scene
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
Background inpainting for videos with dynamic objects and a free-moving camera
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Live three-dimensional reconstruction system with stereo vision display
Computers and Electrical Engineering
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The image motion of a planar surface between two camera views is captured by a homography (a 2D projective transformation). The homography depends on the intrinsic and extrinsic camera 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 homographies of multiple (\geq 2) planes across multiple views. The paper has three main contributions: 1) We show that the collection of all relative homographies (homologies) of a pair of planes across multiple views, spans a 4-dimensional linear subspace. 2) We show how this constraint can be extended to the case of multiple planes across multiple views. 3) We show that, for some restricted cases of camera motion, linear subspace constraints apply also to the set of homographies of a single plane across multiple views. All the results derived in this paper are true for uncalibrated cameras. The possible utility of these multiview constraints for improving homography estimation and for detecting nonrigid motions are also discussed.