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Variational Dense Motion Estimation Using the Helmholtz Decomposition [chapter]

Timo Kohlberger, Étienne Mémin, Christoph Schnörr
2003 Lecture Notes in Computer Science  
We present a novel variational approach to dense motion estimation of highly non-rigid structures in image sequences.  ...  Our representation of the motion vector field is based on the extended Helmholtz Decomposition into its principal constituents: The laminar flow and two potential functions related to the solenoidal and  ...  Dense motion estimation, on the other hand, allows to recover these potential functions more accurately. However, such an estimation as proposed in [5] is not "direct".  ... 
doi:10.1007/3-540-44935-3_30 fatcat:ujx5hjxq5vb2dis4islsvlbmai

Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition [chapter]

Alessandro Becciu, Remco Duits, Bart J. Janssen, Luc M. J. Florack, Hans C. van Assen
2012 Lecture Notes in Computer Science  
We present a method to reconstruct dense cardiac motion from sparse features in tagging MRI, decomposed into solenoidal and irrotational parts using multi-scale Helmholtz decomposition.  ...  Reconstruction is based on energy minimization using covariant derivatives exploiting prior knowledge about the motion field. The method is tested on cardiac motion images.  ...  Our aim is a dense reconstruction of v and its unique Helmholtz decomposition from the sparse evidence represented by (3).  ... 
doi:10.1007/978-3-642-28326-0_27 fatcat:drohyyktp5fy7kxr2f7mhl47om

Vector field analysis for multi-object behavior modeling

Nandita M. Nayak, Yingying Zhu, Amit K. Roy-Chowdhury
2013 Image and Vision Computing  
To recognize the regions of interest, we utilize the Helmholtz decomposition to compute the divergence potential.  ...  Streaklines are used to capture these motion patterns via integration of the flow field.  ...  The Helmholtz decomposition was used to identify regions of useful motion which were analyzed further.  ... 
doi:10.1016/j.imavis.2012.08.011 fatcat:abljsz4uzncozber54ch2adcum

A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

Remco Duits, Bart Janssen, Alessandro Becciu, Hans van Assen
2012 Quarterly of Applied Mathematics  
1 2 REMCO DUITS, BART JANSSEN, ALESSANDRO BECCIU, AND HANS VAN ASSEN single algorithm and show the practical benefit of this approach by an experiment on real cardiac images.  ...  Westenberg of Leiden University Medical Center for providing us the cardiac MR-dataset that we used as input in Section 15 of this article. A.1. Proof of Lemma 8.3.  ...  This follows from the fact that both f 0 and f 1 and their Wronskian are positive (due to 0 ≤ Q(x) ≤ Q(1)), so for example suppose x ≤ y then  ... 
doi:10.1090/s0033-569x-2012-01313-0 fatcat:vxmlmsitqffrphavn4afc45nwm

Dense Estimation of Layer Motions in the Atmosphere

P. Heas, E. Memin, N. Papadakis
2006 18th International Conference on Pattern Recognition (ICPR'06)  
Because of the sparse 3-dimensional nature of observations, classical correlation-based techniques are not suited for the dense estimation of layer motion.  ...  In this paper, we address the problem of estimating dense motion fields related to a stratified atmosphere which is observed through satellite imagery.  ...  Dense estimator for layer motion Introduction of layers To construct a relevant dense estimator for layer motion, we propose to cancel out the influence of undesirable cloud layers by introducing a spatial  ... 
doi:10.1109/icpr.2006.428 dblp:conf/icpr/HeasMP06 fatcat:jy3kd2ywifempeh346a3fxrgfi

Vortex and Source Particles for Fluid Motion Estimation [chapter]

Anne Cuzol, Etienne Mémin
2005 Lecture Notes in Computer Science  
In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields.  ...  This decomposition consists in representing the velocity field as a sum of a divergence free component and a curl free component.  ...  This is called the Helmholtz Decomposition.  ... 
doi:10.1007/11408031_22 fatcat:rtq6u3wyjrejjjh6bc5lryn3wy

A Low Dimensional Fluid Motion Estimator

Anne Cuzol, Pierre Hellier, Etienne Mémin
2007 International Journal of Computer Vision  
Acknowledgements The authors would also like to thank the CEMAGREF for the synthetic 2D turbulence data.  ...  MRI images of the MS patient are courtesy of Beatrice Carsin-Nicole (Radiology) and Gilles Edan (Neurology), Pontchaillou Hospital, Rennes, France.  ...  This is called the Helmholtz decomposition: ¨ ¥ ¤ § ¦ ¦ F © .  ... 
doi:10.1007/s11263-007-0037-0 fatcat:lvvkxftb3nb7pj5t7cfff5pffq

Transition from balanced to unbalanced motion in the eastern tropical Pacific

Saulo M. Soares, Sarah T. Gille, Teresa K. Chereskin, Eric Firing, Jules Hummon, Cesar B. Rocha
2022 Journal of Physical Oceanography  
responsible for its regional and seasonal variations.  ...  The divergent motions, most-likely predominantly IGWs, account for most of the energy at wave-lengths less than 100 km.  ...  (d)-(f) error of the 1D Helmholtz decomposition for annual-mean spectra; the error is defined as the difference between the 1D spectral decomposition and the spectra from a 2D Helmholtz decomposition using  ... 
doi:10.1175/jpo-d-21-0139.1 fatcat:ptyhxml4cngchjtl3lqhd6ji2a

Navier-Stokes formulation for modelling turbulent optical flow

A. Doshi, A. G. Bors
2007 Procedings of the British Machine Vision Conference 2007  
Together with supplemental equations, such as the conservation of mass, and well formulated boundary conditions, the Navier-Stokes equations can be used to model complex fluid motion estimated from image  ...  Moreover, we use a robust statistics mechanism in order to eliminate the outliers from the estimation process.  ...  Corpetti et. al. used the vorticity-stream formulation to recover dense motion of water vapours [5] .  ... 
doi:10.5244/c.21.97 dblp:conf/bmvc/DoshiB07 fatcat:ueaox5y6grdu7dxx6xmomybqze

Layered Estimation of Atmospheric Mesoscale Dynamics From Satellite Imagery

Patrick Heas, Etienne Memin, Nicolas Papadakis, AndrÉ Szantai
2007 IEEE Transactions on Geoscience and Remote Sensing  
Relying on a physically sound vertical decomposition of the atmosphere into layers, we propose a dense-motion estimator dedicated to the extraction of multilayer horizontal wind fields.  ...  Due to the great deal of spatial and temporal distortions of cloud patterns and because of the sparse 3-D nature of cloud observations, standard dense-motion field-estimation techniques used in computer  ...  ACKNOWLEDGMENT The authors would like to thank the EUMETSAT consortium for providing and carefully preprocessing the data.  ... 
doi:10.1109/tgrs.2007.906156 fatcat:mhsfir5kefh4nclgvzjvqnprlu

Repetition Estimation

Tom F. H. Runia, Cees G. M. Snoek, Arnold W. M. Smeulders
2019 International Journal of Computer Vision  
Our method is able to spatially segment repetitive motion directly from the temporal filter responses densely computed over the motion maps.  ...  Starting from motion in 3D we derive three periodic motion types by decomposition of the motion field into its fundamental components.  ...  Spatially dense estimation of the local spectral power enables us to localize regions likely containing repetitive motion.  ... 
doi:10.1007/s11263-019-01194-0 fatcat:7yuqjdgv35dipipomth5abbv2e

Fractional Operators Applied to Geophysical Electromagnetics [article]

Chester J. Weiss, Bart G. van Bloemen Waanders, Harbir Antil
2019 arXiv   pre-print
We outline a practical algorithm for solving the Helmholtz equation using spectral methods coupled with finite element discretization.  ...  Here we apply these concepts to the scalar Helmholtz equation and its use in electromagnetic interrogation of Earth's interior through the magnetotelluric method.  ...  We address these issues through the use of linear decomposition, a Dunford type integral formulation and the very weak form for finite element discretizations.  ... 
arXiv:1902.05096v1 fatcat:wl5fm2q5irheffs3yuyf2mik5a

Dense Motion Analysis in Fluid Imagery [chapter]

T. Corpetti, É. Mémin, P. Pérez
2002 Lecture Notes in Computer Science  
First we describe a dedicated dense motion estimator. The approach relies on constraints issuing from fluid motion properties and allows us to recover dense motion fields of good quality.  ...  Analyzing fluid motion is essential in number of domains and can rarely be handled using generic computer vision techniques. In this particular application context, we address two distinct problems.  ...  Both are derived from dense motion field Helmholtz components w ir = ∇φ and w ⊥ so = ∇ψ, using (12) .  ... 
doi:10.1007/3-540-47969-4_45 fatcat:rqh7zi2b7zebta3olas2kwrnei

Variational Assimilation of Fluid Motion from Image Sequence

Nicolas Papadakis, Étienne Mémin
2008 SIAM Journal of Imaging Sciences  
In this paper, a variational technique derived from optimal control theory is used in order to realize a dynamically consistent motion estimation of a whole fluid image sequence.  ...  By combining physical conservation laws and image observations, a physically grounded temporal consistency is imposed and the quality of the motion estimation is significantly improved.  ...  The authors would like to thank the Cemagref laboratory and the Laboratoire de Météorologie Dynamique for providing the image sequences presented in this paper.  ... 
doi:10.1137/080713896 fatcat:x4mvd33ofnd3noqahzrqxje3cy

Variational fluid flow measurements from image sequences: synopsis and perspectives

Dominique Heitz, Etienne Mémin, Christoph Schnörr
2009 Experiments in Fluids  
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  ...  Variational approaches to image motion segmentation has been an active field of study in image processing and computer vision for two decades.  ...  For fluid flow image analysis, an estimator of this kind, relying on the Helmholtz decomposition, has been proposed in Cuzol & Mémin (2005 .  ... 
doi:10.1007/s00348-009-0778-3 fatcat:p2voujunsrdwxasipwp6ve5syq
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