Location Uncertainty Principle: Toward the Definition of Parameter-Free Motion Estimators

  • Shengze Cai
  • Etienne Mémin
  • Pierre Dérian
  • Chao XuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10746)


In this paper, we propose a novel optical flow approach for estimating two-dimensional velocity fields from an image sequence, which depicts the evolution of a passive scalar transported by a fluid flow. The Eulerian fluid flow velocity field is decomposed into two components: a large-scale motion field and a small-scale uncertainty component. We define the small-scale component as a random field. Then the data term of the optical flow formulation is based on a stochastic transport equation, derived from a location uncertainty principle [17]. In addition, a specific regularization term built from the assumption of constant kinetic energy involves the same diffusion tensor as the one appearing in the data transport term. This enables us to devise an optical flow method dedicated to fluid flows in which the regularization parameter has a clear physical interpretation and can be easily estimated. Experimental evaluations are presented on both synthetic and real images. Results indicate very good performance of the proposed parameter-free formulation for turbulent flow motion estimation.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Shengze Cai
    • 1
  • Etienne Mémin
    • 2
  • Pierre Dérian
    • 2
  • Chao Xu
    • 1
    Email author
  1. 1.State Key Laboratory of Industrial Control Technology and the Institute of Cyber-Systems and ControlZhejiang UniversityHangzhouChina
  2. 2.National Institute for Research in Computer Science and Control (Inria)Campus Universitaire de BeaulieuRennesFrance

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