Lines and Points in Three Views and the Trifocal Tensor
International Journal of Computer Vision
Minimal Decomposition of Model-Based Invariants
Journal of Mathematical Imaging and Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
When is it Possible to Identify 3D Objects From Single Images Using Class Constraints?
International Journal of Computer Vision
Algebraic Geometry and Computer Vision: Polynomial Systems, Real andComplex Roots
Journal of Mathematical Imaging and Vision
On the Structure and Properties of the Quadrifocal Tensor
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Shape tensors for efficient and learnable indexing
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
A framework for modeling 3D scenes using pose-free equations
ACM Transactions on Graphics (TOG)
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
| Hi-index | 0.00 |
The paper unifies most of the current literature on 3D geometric invariants from point correspondences across multiple 2D views by using the tool of elimination from algebraic geometry. The technique allows one to predict results by counting parameters and reduces many complicated results obtained in the past (reconstructuon from two and three views, epipolar geometry from seven points, trilinearity of three views, the use of a priori 3D information such as bilateral symmetry, shading and color constancy, and more) into a few lines of reasoning each. The tool of Grobner base computation is used in the elimination process. In the process we obtain several results on N view geometry, and obtain a general result on invariant functions of 4 views and its corresponding quadlinear tensor: 4 views admit minimal sets of 16 invariant functions (of quadlinear forms) with 81 distinct coefficients that can be solved linearly from 6 corresponding points across 4 views. This result has non trivial implications to the understanding of N view geometry. We show a new result on single view invariants based on 6 points and show that certain relationships are impossible. One of the appealing features of the elimination approach is that it is simple to apply and does not require any understanding of the underlying 3D from 2D geometry and algebra.