Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Canonic representations for the geometries of multiple projective views
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Artificial Intelligence - Special volume on computer vision
Sequential quadratic programming for large-scale nonlinear optimization
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Computing the Moore--Penrose Inverse for the Covariance Matrix in Constrained Nonlinear Estimation
SIAM Journal on Optimization
A Practical Algorithm for General Large Scale Nonlinear Optimization Problems
SIAM Journal on Optimization
CAIP '95 Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns
Autocalibration and the absolute quadric
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Ellipsoid Reconstruction from Three Perspective Views
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Quadric Reconstruction from Dual-Space Geometry
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Multiple textures stitching and blending on 3D objects
EGWR'99 Proceedings of the 10th Eurographics conference on Rendering
3-D retinal curvature estimation
IEEE Transactions on Information Technology in Biomedicine - Special section on body sensor networks
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We propose using SQP (Sequential Quadratic Programming) to directly recover 3D quadratic surface parameters from multiple views. A surface equation is used as a constraint. In addition to the sum of squared reprojection errors defined in the traditional bundle adjustment, a Lagrangian term is added to force recovered points to satisfy the constraint. The minimization is realized by SQP. Our algorithm has three advantages. First, given corresponding features in multiple views, the SQP implementation can directly recover the quadratic surface parameters optimally instead of a collection of isolated 3D points coordinates. Second, the specified constraints are strictly satisfied and the camera parameters and 3D coordinates of points can be determined more accurately than that by unconstrained methods. Third, the recovered quadratic surface model can be represented by a much smaller number of parameters instead of point clouds and triangular patches. Experiments with both synthetic and real images show the power of this approach.