Curve matching and stereo calibration
Image and Vision Computing
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Reconstructing ellipsoids from projections
CVGIP: Graphical Models and Image Processing
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Recognizing algebraic surfaces from their outlines
International Journal of Computer Vision
The Quadric Reference Surface: Theory and Applications
International Journal of Computer Vision
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Q-Warping: Direct Computation of Quadratic Reference Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Active Visual Inference of Surface Shape
Active Visual Inference of Surface Shape
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Prediction Error as a Quality Metric for Motion and Stereo
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Quadric Reconstruction from Dual-Space Geometry
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Complex 3D Shape Recovery Using a Dual-Space Approach
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Using Frontier Points to Recover Shape, Reflectance and Illumunation
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Robust Surface Fitting from Two Views using Restricted Correspondence
Journal of Mathematical Imaging and Vision
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Photographic outlines of 3 dimensional solids are robust and rich in information useful for surface reconstruction. This paper studies algebraic surfaces viewed from 2 cameras with known intrinsic and extrinsic parameters. It has been known for some time that for a degree d=2 (quadric) algebraic surface there is a 1-parameter family of surfaces that reproduce the outlines. When the algebraic surface has degree d2, we prove a new result: that with known camera geometry it is possible to completely reconstruct an algebraic surface from 2 outlines i.e. the coefficients of its defining polynomial can be determined in a known coordinate frame. The proof exploits the existence of frontier points, which are calculable from the outlines. Examples and experiments are presented to demonstrate the theory and possible applications.