Computational geometry: an introduction
Computational geometry: an introduction
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Fitting Parameterized Three-Dimensional Models to Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modeling and rendering architecture from photographs: a hybrid geometry- and image-based approach
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
Constrained Structure and Motion From Multiple Uncalibrated Views of a Piecewise Planar Scene
International Journal of Computer Vision
Scene Modeling Based on Constraint System Decomposition Techniques
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Using Geometric Constraints through Parallelepipeds for Calibration and 3D Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Least-squares 3D reconstruction from one or more views and geometric clues
Computer Vision and Image Understanding
How Hard is 3-View Triangulation Really?
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Multiple View Geometry and the L_"-norm
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Reconstruction with Interval Constraints Propagation
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Adaptive Feature Integration for Segmentation of 3D Data by Unsupervised Density Estimation
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 04
Linear Analysis of Nonlinear Constraints for Interactive Geometric Modeling
Computer Graphics Forum
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This paper proposes a technique for estimating piecewise planar models of objects from their images and geometric constraints. First, assuming a bounded noise in the localization of 2D points, the position of the 3D point is estimated as a polyhedron containing all the possible solutions of the triangulation. Then, given the topological structure of the 3D points cloud, geometric relationships among facets, such as coplanarity, parallelism, orthogonality, and angle equality, are automatically detected. A subset of them that is sufficient to stabilize the 3D model estimation is selected with a flow-network based algorithm. Finally, a feasible instance of the 3D model, i.e. one that satisfies the geometric constraints and whose 3D vertices lie within the associated polyhedral bounds, is computed by solving a Constraint Satisfaction Problem. The process accommodates uncertainty in a non-probabilistic fashion and thus provides rigorous results. Synthetic and real experiments illustrate the approach.