Journal of Mathematical Imaging and Vision

, Volume 38, Issue 2, pp 139–158

Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations

  • Mustafa Unel
  • Bijoy K. Ghosh
  • Ahmet Y. Yazicioglu

DOI: 10.1007/s10851-010-0209-3

Cite this article as:
Unel, M., Ghosh, B.K. & Yazicioglu, A.Y. J Math Imaging Vis (2010) 38: 139. doi:10.1007/s10851-010-0209-3


Motivated by problems in vision and robotics, in this paper we are interested in describing the dynamics of planar algebraic curves in rigid and affine motion. A new method is presented for modeling the dynamics of such curves in terms of Riccati equations. It is shown that rigid or affine motion of an algebraic curve can be described using the dynamics of line factors obtained from a unique decomposition of the curve, and each individual line dynamics can be described by a Riccati equation. An estimation algorithm is proposed to estimate rigid or affine motion using line parameters. Importance of data normalization is also investigated in the context of motion estimation. Experiments with simulated data and real images demonstrate that the proposed method can provide satisfactory motion estimation results from perturbed data.


Motion estimationAlgebraic curvesAffine motionRiccati equationsData normalization

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Mustafa Unel
    • 1
  • Bijoy K. Ghosh
    • 2
  • Ahmet Y. Yazicioglu
    • 3
  1. 1.Faculty of Engineering and Natural SciencesSabanci UniversityTuzlaTurkey
  2. 2.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  3. 3.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA