Critical Configurations for Projective Reconstruction from Multiple Views

Authors:
Richard Hartley;Fredrik Kahl
Affiliations:
Australian National University, and National ICT Australia, Australia;Australian National University, and Centre for Mathematical Sciences, Lund University, Sweden
Venue:
International Journal of Computer Vision
Year:
2007

Citing 9
Cited 6

The twisted cubic and camera calibration

Computer Vision, Graphics, and Image Processing
Projective Reconstruction and Invariants from Multiple Images

IEEE Transactions on Pattern Analysis and Machine Intelligence
Theory of Reconstruction from Image Motion

Theory of Reconstruction from Image Motion
Ambiguous Configurations for the 1D Structure and Motion Problem

Journal of Mathematical Imaging and Vision
Critical Curves and Surfaces for Euclidean Reconstruction

ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Duality of reconstruction and positioning from projective views

VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
Multiple View Geometry in Computer Vision

Multiple View Geometry in Computer Vision
Ambiguity in Reconstruction From Images of Six Points

ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A critical configuration for reconstruction from rectilinear motion

CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition

Reconstruction of Some Segmented and Dynamic Scenes: Trifocal Tensors in P4 Theoretical Set Up for Critical Loci, and Instability

ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Globally Optimal Least Squares Solutions for Quasiconvex 1D Vision Problems

SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Critical line-set configurations to epipolar geometry determination and application to image line transfer

Pattern Recognition Letters
Degeneracy from twisted cubic under two views

Journal of Computer Science and Technology
Twisted cubic: degeneracy degree and relationship with general degeneracy

ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization

International Journal of Computer Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper investigates a classical problem in computer vision: Given corresponding points in multiple images, when is there a unique projective reconstruction of the 3D geometry of the scene points and the camera positions? A set of points and cameras is said to be critical when there is more than one way of realizing the resulting image points. For two views, it has been known for almost a century that the critical configurations consist of points and camera lying on a ruled quadric surface. We give a classification of all possible critical configurations for any number of points in three images, and show that in most cases, the ambiguity extends to any number of cameras.The underlying framework for deriving the critical sets is projective geometry. Using a generalization of Pascal's Theorem, we prove that any number of cameras and scene points on an elliptic quartic form a critical set. Another important class of critical configurations consists of cameras and points on rational quartics. The theoretical results are accompanied by many examples and illustrations.