Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
Estimation of Relative Camera Positions for Uncalibrated Cameras
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Critical Sets for 3D Reconstruction Using Lines
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Ambiguous Configurations for 3-View Projective Reconstruction
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Dualizing Scene Reconstruction Algorithms
SMILE'98 Proceedings of the European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
Duality of reconstruction and positioning from projective views
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
Ambiguity in Reconstruction From Images of Six Points
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Critical Configurations for Projective Reconstruction from Multiple Views
International Journal of 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
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The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction has recently been reported in the literature. We show that there are critical sets for n-view Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourth-degree curve.