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Erschienen in: Experiments in Fluids 3/2010

01.03.2010 | Review Article

Variational fluid flow measurements from image sequences: synopsis and perspectives

verfasst von: Dominique Heitz, Etienne Mémin, Christoph Schnörr

Erschienen in: Experiments in Fluids | Ausgabe 3/2010

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Abstract

Variational approaches to image motion segmentation has been an active field of study in image processing and computer vision for two decades. We present a short overview over basic estimation schemes and report in more detail recent modifications and applications to fluid flow estimation. Key properties of these approaches are illustrated by numerical examples. We outline promising research directions and point out the potential of variational techniques in combination with correlation-based PIV methods, for improving the consistency of fluid flow estimation and simulation.

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Fußnoten
4
P(s) = Id for a constant model; \(P(s)=\left[\begin{array}{cccccc}1 & x & y & 0& 0& 0 \\ 0&0&0&1&x&y \end{array}\right]\) for an affine model and \(P(s)=\left[\begin{array}{cccccccc}1 & x & y &0 &0 & 0 &x^2 & xy \\ 0&0&0&1&x&y &xy &y^2\end{array} \right]\) for a quadratic model.
 
5
This corresponds to the total least squares solution. Given a (m × p) homogeneous linear system \(M \user2{x} =0\), a total least squares solution minimizes \(\|M\user2{x}\|^2\) subject to the constraint \(\|\user2{x}\|=1\) in order to avoid the trivial solution.
 
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Metadaten
Titel
Variational fluid flow measurements from image sequences: synopsis and perspectives
verfasst von
Dominique Heitz
Etienne Mémin
Christoph Schnörr
Publikationsdatum
01.03.2010
Verlag
Springer-Verlag
Erschienen in
Experiments in Fluids / Ausgabe 3/2010
Print ISSN: 0723-4864
Elektronische ISSN: 1432-1114
DOI
https://doi.org/10.1007/s00348-009-0778-3

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