Journal of Mathematical Imaging and Vision

, Volume 49, Issue 2, pp 296–316 | Cite as

Stochastic Level Set Dynamics to Track Closed Curves Through Image Data

  • C. Avenel
  • E. Mémin
  • P. Pérez


We introduce a stochastic filtering technique for the tracking of closed curves from image sequence. For that purpose, we design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-set representation and the stochastic dynamics is expressed on the level-set function. It takes the form of a stochastic partial differential equation with a Brownian motion of low dimension. The evolution model we propose combines local photometric information, deformations induced by the curve displacement and an uncertainty modeling of the dynamics. Specific choices of noise models and drift terms lead to an evolution law based on mean curvature as in classic level set methods, while other choices yield new evolution laws. The approach we propose is implemented through a particle filter, which includes color measurements characterizing the target and the background photometric probability densities respectively. The merit of this filter is demonstrated on various satellite image sequences depicting the evolution of complex geophysical flows.


Level sets Stochastic curve evolution model Curve tracking Bayesian sequential filter 



We thank the CERSAT/IFREMER laboratory and Meteo-France for having provided us the ice density satellite image and the meteorological infra-red sequence. The authors acknowledge the ANR projects PREVASSEMBLE (ANR-08-COSI-012) and Geo-Fluids (ANR-09-SYSC-005) for their financial support.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.LIP6UPMC—Université Pierre et Marie CurieParis Cedex 05France
  2. 2.INRIARennes CedexFrance
  3. 3.TechnicolorCesson-Sévigné CedexFrance

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