Abstract
We present a new approach to 3D scene modeling based on geometrical constraints. Contrary to most of the existing methods, we obtain 3D scene models that respect the given constraints exactly. Our tool can describe a large variety of linear and non-linear constraints in a flexible way.
Our approach is based on a dictionary of so-called r-methods, based on theorems in geometry, which can solve a subset of geometrical constraints in a very efficient way. Two fast and complete graph-based algorithms are proposed to find a reduced parameterization of a scene, and to decompose the equation system in a sequence of r-methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Avis, D., Fukuda, K.: Reverse Search Enumeration. Discrete Applied Mathematics 6, 21–46 (1996)
Bondyfalat, D., Mourrain, B., Papadopoulo, T.: An application of automatic theorem proving in computer vision. In: Automated Deduction in Geometry, pp. 207–231 (1998)
Debevec, P.E., Taylor, C.J., Malik, J.: Modeling and rendering architecture from photographs: a hybrid geometry-and image-based approach. In: SIGGRAPH 1996, New York (August 1996)
Sutherland, I.: Sketchpad: A Man-Machine Graphical Communication System. PhD thesis, Department of Electrical Engineering, MIT (1963)
Trombettoni, G.: A Polynomial Time Local Propagation Algorithm for General Dataflow Constraint Problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 432–446. Springer, Heidelberg (1998)
Wilczkowiak, M., Sturm, P., Boyer, E.: The analysis of ambiguous solutions in linear systems and its application to computer vision. In: Proceedings of the 14th British Machine Vision Conference, Norwich, England (September 2003) (to appear)
Wilczkowiak, M., Trombettoni, G., Jermann, C., Sturm, P., Boyer, E.: Scene reconstruction based on constraint decomposition techniques. In: Proceedings of the 9th International Conference on Computer Vision (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Trombettoni, G., Wilczkowiak, M. (2003). Scene Reconstruction Based on Constraints: Details on the Equation System Decomposition. In: Rossi, F. (eds) Principles and Practice of Constraint Programming – CP 2003. CP 2003. Lecture Notes in Computer Science, vol 2833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45193-8_86
Download citation
DOI: https://doi.org/10.1007/978-3-540-45193-8_86
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20202-8
Online ISBN: 978-3-540-45193-8
eBook Packages: Springer Book Archive