Abstract
This paper integrates Statistical reasoning and Grassmann-Cayley algebra for making 2D and 3D geometric reasoning practical. The multi-linearity of the forms allows rigorous error propagation and Statistical testing of geometric relations. This is achieved by representing all objects in homogeneous coordinates and expressing all relations using Standard matrix calculus.1
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Carlsson. The double algebra: An efFective tool for Computing invariants in Computer vision. In J. Mundy, Zisserman A., and D. Forsyth, editors, Applications of Invariance in Computer Vision, number 825 in LNCS. Springer, 1994.
O. Faugeras and B. Mourrain. On the Geometry and Algebra of the Point and Line Correspondencies between N Images. Technical Report 2665, INRIA, 1995.
O. Faugeras and T. Papadopoulo. Grassmann-cayley algebra for modeling systems of cameras and the algebraic equations of the manifold of trifocal tensors. In Trans, of the ROYAL SOCIETY A, 365, pages 1123–1152, 1998.
R.I. Hartley. In defence ofthe 8-point algorithm. In ICCV1995, pages 1064-1070. IEEE CS Press, 1995.
S. Heuel, F. Lang, and W. Förstner. Topological and geometrical reasoning in 3d grouping for reconstructing polyhedral surfaces. In Proceedings of the XIXth ISPRS Congress, volume XXXIII, Amsterdam, 2000. ISPRS.
K. Kanatani. Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier Science, 1996.
K.-R. Koch. Parameterschätzung und Hypothesentests in linearen Modellen. Dümmler, Bonn, 1980.
F. Lang. Geometrische und Semantische Rekonstruktion von gebäuden durch Ableitung von 3D Gebäudeecken. PhD thesis, University of Bonn, 1999.
R.C. Rao. Linear Statistical Inference and Its Applications. J. Wiley, NY, 1973.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Förstner, W., Brunn, A., Heuel, S. (2000). Statistically Testing Uncertain Geometrie Relations. In: Sommer, G., Krüger, N., Perwass, C. (eds) Mustererkennung 2000. Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59802-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-59802-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67886-1
Online ISBN: 978-3-642-59802-9
eBook Packages: Springer Book Archive