Recognition by Linear Combinations of Models
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Model-based invariants for 3-D vision
International Journal of Computer Vision
Trilinearity in visual recognition by alignment
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Linear and Incremental Acquisition of Invariant Shape Models From Image Sequences
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algebraic Functions For Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Invariants of 6 Points from 3 Uncalibrated Images
ECCV '94 Proceedings of the Third European Conference-Volume II on Computer Vision - Volume II
Trilinearity of three perspective views and its associated tensor
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
The study of 3D-from-2D using elimination
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
Dual Computation of Projective Shape and Camera Positions from Multiple Images
International Journal of Computer Vision
Minimal Decomposition of Model-Based Invariants
Journal of Mathematical Imaging and Vision
Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane
International Journal of Computer Vision
Plane+Parallax, Tensors and Factorization
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
| Hi-index | 0.00 |
Multi-point geometry: The geometry of 1 point in N images under perspective projection has been thoroughly investigated, identifying bilinear, trilinear, and quadrilinear relations between the projections of 1 point in 2, 3 and 4 frames respectively. The dual problem-the geometry of N points in 1 image-has been studied mostly in the context of object recognition, often assuming weak perspective or affine projection. We provide here a complete description of this problem. We employ a formalism in which multiframe and multi-point geometries appear in symmetry. Points and projections are interchangeable. We then derive bilinear equations for 6 points (dual to 3-frame geometry), trilinear equations for 7 points (dual to 3-frame geometry), and quadrilinear equations for 8 points (dual to the epipolar geometry). We show that the quadrilinear equations are dependent on the the bilinear and trilinear equations, and we show that adding more points will not generate any new equation. The new equations are used to design new algorithms for the reconstruction of shape from many frames, and for learning invariant relations for indexing into a database.