Quadratic Surface Reconstruction from Multiple Views Using SQP

Rubin GONG; Gang XU

Quadratic Surface Reconstruction from Multiple Views Using SQP

Rubin GONG, Gang XU

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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.

Publication: IEICE TRANSACTIONS on Information Vol.E87-D No.1 pp.215-223

Publication Date: 2004/01/01

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Type of Manuscript: PAPER

Category: Image Processing, Image Pattern Recognition

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Rubin GONG, Gang XU, "Quadratic Surface Reconstruction from Multiple Views Using SQP" in IEICE TRANSACTIONS on Information, vol. E87-D, no. 1, pp. 215-223, January 2004, doi: .
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/information/10.1587/e87-d_1_215/_p

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@ARTICLE{e87-d_1_215,
author={Rubin GONG, Gang XU, },
journal={IEICE TRANSACTIONS on Information},
title={Quadratic Surface Reconstruction from Multiple Views Using SQP},
year={2004},
volume={E87-D},
number={1},
pages={215-223},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - Quadratic Surface Reconstruction from Multiple Views Using SQP
T2 - IEICE TRANSACTIONS on Information
SP - 215
EP - 223
AU - Rubin GONG
AU - Gang XU
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E87-D
IS - 1
JA - IEICE TRANSACTIONS on Information
Y1 - January 2004
AB - 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.
ER -