A Study of Non-smooth Convex Flow Decomposition

  • Jing Yuan
  • Christoph Schnörr
  • Gabriele Steidl
  • Florian Becker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)


We present a mathematical and computational feasibility study of the variational convex decomposition of 2D vector fields into coherent structures and additively superposed flow textures. Such decompositions are of interest for the analysis of image sequences in experimental fluid dynamics and for highly non-rigid image flows in computer vision.

Our work extends current research on image decomposition into structural and textural parts in a twofold way. Firstly, based on Gauss’ integral theorem, we decompose flows into three components related to the flow’s divergence, curl, and the boundary flow. To this end, we use proper operator discretizations that yield exact analogs of the basic continuous relations of vector analysis. Secondly, we decompose simultaneously both the divergence and the curl component into respective structural and textural parts. We show that the variational problem to achieve this decomposition together with necessary compatibility constraints can be reliably solved using a single convex second-order conic program.


Particle Image Velocimetry Motion Estimation Compatibility Constraint Image Decomposition Helmholtz Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jing Yuan
    • 1
  • Christoph Schnörr
    • 1
  • Gabriele Steidl
    • 1
  • Florian Becker
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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