Journal of Mathematical Imaging and Vision

, Volume 32, Issue 2, pp 127–137

Stable Algebraic Surfaces for 3D Object Representation

Authors

  • Turker Sahin
    • Department of Computer EngineeringGebze Institute of Technology
    • Faculty of Engineering and Natural SciencesSabanci University
Article

DOI: 10.1007/s10851-008-0092-3

Cite this article as:
Sahin, T. & Unel, M. J Math Imaging Vis (2008) 32: 127. doi:10.1007/s10851-008-0092-3

Abstract

Linear fitting techniques by implicit algebraic models usually suffer from global stability problems. Ridge regression regularization can be used to improve the stability of algebraic surface fits. In this paper a Euclidean Invariant 3D ridge regression matrix is developed and applied to a particular linear algebraic surface fitting method. Utilization of such a regularization in fitting process makes it possible to globally stabilize 3D object fits with surfaces of any degree. Robustness to noise and moderate levels of occlusion has also been enhanced significantly. Experimental results are presented to verify the improvements in global stability and robustness of the resulting fits.

Keywords

Algebraic surfaces Implicit polynomials Fitting Stability Ridge regression

Copyright information

© Springer Science+Business Media, LLC 2008