### Citations

1502 | Condensation — conditional density propagation for visual tracking
- Isard, Blake
- 1998
(Show Context)
Citation Context ...cal solution and is usually difficult to implement numerically for a high dimensional state vector. As a matter of fact, Monte-Carlo probabilistic tracking methods as proposed in the literature [17], =-=[23]-=-, [31] are efficient only to track objects of reduced dimension such as points or curves described by several discrete control points. These techniques are not able to cope with high dimensional featu... |

1433 |
Numerical Solution of Stochastic Differential Equations
- KLOEDEN, PLATEN
- 1992
(Show Context)
Citation Context ... (i) t )dB (i) t , (11) are independent Brownian motions. The simulation from the SDE (11) can be done with the Euler scheme or other numerical simulation methods of stochastic differential equations =-=[24]-=-. The Euler scheme has the following form: x (i) t+∆t = x(i) t + f(x (i) t )∆t + σ(x (i) t )(B (i) t+∆t − B(i) t ), (12) April 28, 2008 DRAFT9 where the increments B (i) t+∆t −B(i) t are independent ... |

1322 | Performance of optical flow techniques
- Barron, Fleet, et al.
- 1994
(Show Context)
Citation Context ... difficult and prone to errors. Another major difficulty in motion estimation is the temporal consistency between estimates. This problem is inherent to motion estimation techniques (see for instance =-=[3]-=- for an extended review on motion estimation techniques). As a matter of fact, most of the motion estimation approaches use only a small set of images (usually two consecutive images of a sequence) an... |

1049 | On sequential Monte Carlo sampling methods for Bayesian filtering
- Doucet, Godsill, et al.
- 2000
(Show Context)
Citation Context ...nalytical solution and is usually difficult to implement numerically for a high dimensional state vector. As a matter of fact, Monte-Carlo probabilistic tracking methods as proposed in the literature =-=[17]-=-, [23], [31] are efficient only to track objects of reduced dimension such as points or curves described by several discrete control points. These techniques are not able to cope with high dimensional... |

488 |
Spectral Methods in Fluid Dynamics
- Canuto, Hussaini, et al.
- 1988
(Show Context)
Citation Context ...scribing the model. For instance, it is possible to rely on the global knowledge of the flow in order to construct a reduced representation of it. The flow can then be described by its spectral modes =-=[6]-=- or by spatial basis functions in case of the POD (proper orthogonal decomposition [4]). These methods are widely used for the simulation of fluid flows. For flows exhibiting a repetitive behavior, th... |

312 | The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
- Berkooz, Holmes, et al.
- 1993
(Show Context)
Citation Context ...e flow in order to construct a reduced representation of it. The flow can then be described by its spectral modes [6] or by spatial basis functions in case of the POD (proper orthogonal decomposition =-=[4]-=-). These methods are widely used for the simulation of fluid flows. For flows exhibiting a repetitive behavior, the POD offers a very efficient representation. Such a decomposition is computed from se... |

249 |
A Mathematical Introduction to Fluid Mechanics
- Chorin, Marsden
- 1979
(Show Context)
Citation Context ...otential function ψ is solution of a Poisson equation: ∆ψ(x) = ξ(x), where ∆ denotes the Laplacian operator. Let G be the Green’s function associated to the Laplacian operator in 2D: G(x) = 1 ln(‖x‖) =-=[9]-=- . The solution ψ is then obtained by convolution: 2π ψ(x) = G ∗ ξ(x) = ∫ R2 G(x − u) curl w(u)du . Finally, w(x) = K ∗ξ(x) where K(x) = ∇ ⊥ G(x) = x⊥ 2π‖x‖2 . Note that this relation between the sole... |

194 |
Numerical Study of Slightly Viscous Flow
- Chorin
- 1973
(Show Context)
Citation Context ...luid flows [15], [13] relying on adequate basis functions. The used basis functions stem from Biot-Savart integration of a regularized discretization of the vector field vorticity and divergence maps =-=[7]-=-, [12]. Such a representation enables a reduced-size representation of a fluid motion. The second difficulty is related to the continuous nature of the involved dynamic evolution law. The problem cons... |

150 |
Vortex Methods: Theory and Practice
- Cottet, Koumoutsakos
- 2000
(Show Context)
Citation Context ...flows [15], [13] relying on adequate basis functions. The used basis functions stem from Biot-Savart integration of a regularized discretization of the vector field vorticity and divergence maps [7], =-=[12]-=-. Such a representation enables a reduced-size representation of a fluid motion. The second difficulty is related to the continuous nature of the involved dynamic evolution law. The problem consists t... |

127 | P.: Dense estimation of fluid flows
- Corpetti, Mémin, et al.
- 2002
(Show Context)
Citation Context ...nt, with null vorticity and null divergence, must be April 28, 2008 DRAFT10 included. This component can be approximated using the Horn and Schunck estimator with a strong regularization coefficient =-=[10]-=-. Let us note that the tracking method we propose is adapted to the solenoidal component of vector fields. In the rest of the paper, the vector field w will then denote the solenoidal part of the flow... |

108 |
Vortex methods for flow simulations
- Leonard
- 1980
(Show Context)
Citation Context ...ion between the solenoidal component w and the scalar vorticity ξ is known as the Biot-Savart integral [9]. 2) Vorticity approximation with vortex particles: The idea of vortex particles methods [7], =-=[25]-=- consists in representing the vorticity distribution of a field by a set of discrete amounts of vorticity. A discretization of the vorticity into a limited number of elements enables to evaluate the v... |

105 |
Variational optic flow computation with a spatio-temporal smoothness constraint”,
- Weickert, Schnorr
- 2001
(Show Context)
Citation Context ...t of images (usually two consecutive images of a sequence) and thus may suffer from a temporal inconsistency from frame to frame. The extension of spatial regularizers to spatio-temporal regularizers =-=[36]-=- or the introduction of April 28, 2008 DRAFT4 simple dynamical constraints in motion segmentation techniques rely mainly on crude dynamic assumptions or that are related to rigid object motion only [... |

74 | Non-gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis
- Farge, Schneider, et al.
- 1999
(Show Context)
Citation Context ...te, the vortex particles allow to construct a reduced representation of the flow without any a priori knowledge on the flow. Note that in the same spirit, a wavelet decomposition can also be proposed =-=[18]-=-. However, one advantage of the vortex particles is that the flow dynamics is described by a set of elements which have a direct physical interpretation. The approximation is indeed based on the vorti... |

53 | Very high accuracy velocity estimation using orientation tensors, parametric motion, and simultaneous segmentation of the motion field
- Farneback
(Show Context)
Citation Context ...] or the introduction of April 28, 2008 DRAFT4 simple dynamical constraints in motion segmentation techniques rely mainly on crude dynamic assumptions or that are related to rigid object motion only =-=[19]-=-. Some recent contributions [20], [29], [30], [34] aim at improving the temporal consistency and the robustness of the estimations over the whole sequence, introducing a physical evolution law in the ... |

46 | Discrete orthogonal decomposition and variational fluid flow estimation
- Yuan, Ruhnau, et al.
- 2005
(Show Context)
Citation Context ...he Helmholtz Decomposition [11], [38]. Let us remark that such a decomposition for a dense motion field can be computed in the Fourier domain [11] or directly specified as a motion estimation problem =-=[37]-=-, [38] from the image sequence. When the null border condition can not be imposed, a transportation component, with null vorticity and null divergence, must be April 28, 2008 DRAFT10 included. This c... |

28 | Dimensional reduction for a bayesian filter,
- Chorin, Krause
- 2004
(Show Context)
Citation Context ...alman filtering techniques, in order to approximate the estimated covariance matrix by a reduced rank one [28], [32]. For the continuous-discrete particle filter, a method has been proposed by Chorin =-=[8]-=-. The idea is to concentrate the sampling effort over unstable directions of the dynamics, defined adaptively along the sequential estimation process. Following Chorin’s paper, we present in this sect... |

28 |
Extraction of singular points from dense motion fields: An analytic approach
- Corpetti, Mémin, et al.
(Show Context)
Citation Context ...eld that vanishes at infinity can be decomposed into a sum of an irrotational component with null vorticity and a solenoidal component with null divergence. This is called the Helmholtz Decomposition =-=[11]-=-, [38]. Let us remark that such a decomposition for a dense motion field can be computed in the Fourier domain [11] or directly specified as a motion estimation problem [37], [38] from the image seque... |

28 |
Hydrodynamics in two dimensions and vortex theory
- Marchioro, Pulvirenti
- 1982
(Show Context)
Citation Context ...ty-velocity formulation of the Navier-Stokes equation belongs to the class of MacKean-Vlasov equations. It has then a rigorous interpretation in terms of stochastic interacting particles systems [5], =-=[26]-=-, [27]. 3) Interacting particles system: The evolution of the q vortex particles is finally described by the following system: q∑ dxl,t = γjKǫj (xl,t − xj,t)dt + √ 2νdBl,t, 1 ≤ l ≤ q, (23) j=1 where B... |

22 | Partial linear Gaussian model for tracking in image sequences using sequential Monte Carlo methods
- Arnaud, Mémin
- 2007
(Show Context)
Citation Context ... the weights is π(xk|x (i) 0:k−1 ,z1:k) = p(xk|x (i) k−1 ,zk) [17]. This optimal function is unfortunately only available for a linear measure equation with Gaussian or mixture of Gaussian likelihood =-=[1]-=-. When such an optimal importance function is not available, the importance function is often simply set to the prediction density [23]: π(xk|x (i) 0:k−1 ,z1:k) = p(xk|x (i) k−1 ). In that case, the r... |

21 | Layered estimation of atmospheric mesoscale dynamics from satellite imagery
- Heas, Mémin, et al.
(Show Context)
Citation Context ...se motion estimation methods dedicated to fluid flows, based on a spatial regularization of the vector fields, have been extended to integrate temporal constraints related to the fluid flow evolution =-=[22]-=-, [35], [33]. These constraints are either derived from the vorticity-velocity formulation of the Navier-Stokes equation [22], [35], or from Stokes equation [33]. Recent techniques based on variationa... |

20 | A Low Dimensional Fluid Motion Estimator
- Cuzol, Hellier, et al.
(Show Context)
Citation Context ... to cope with high dimensional features such as dense vector fields. In our work, in order to handle motion fields of reasonable dimension, we rely on an original parametrization of fluid flows [15], =-=[13]-=- relying on adequate basis functions. The used basis functions stem from Biot-Savart integration of a regularized discretization of the vector field vorticity and divergence maps [7], [12]. Such a rep... |

19 | Vortex and source particles for fluid motion estimation
- Cuzol, Memin
- 2005
(Show Context)
Citation Context ...t able to cope with high dimensional features such as dense vector fields. In our work, in order to handle motion fields of reasonable dimension, we rely on an original parametrization of fluid flows =-=[15]-=-, [13] relying on adequate basis functions. The used basis functions stem from Biot-Savart integration of a regularized discretization of the vector field vorticity and divergence maps [7], [12]. Such... |

19 | A variational technique for time consistent tracking of curves and motion
- Papadakis, Mémin
(Show Context)
Citation Context ...T4 simple dynamical constraints in motion segmentation techniques rely mainly on crude dynamic assumptions or that are related to rigid object motion only [19]. Some recent contributions [20], [29], =-=[30]-=-, [34] aim at improving the temporal consistency and the robustness of the estimations over the whole sequence, introducing a physical evolution law in the estimation process. The dense motion estimat... |

18 |
C.: Optical stokes flow estimation: An imaging-based control approach
- Ruhnau, Schnörr
(Show Context)
Citation Context ...timation methods dedicated to fluid flows, based on a spatial regularization of the vector fields, have been extended to integrate temporal constraints related to the fluid flow evolution [22], [35], =-=[33]-=-. These constraints are either derived from the vorticity-velocity formulation of the Navier-Stokes equation [22], [35], or from Stokes equation [33]. Recent techniques based on variational tracking m... |

15 | A stochastic filter for fluid motion tracking
- Cuzol, Mémin
- 2005
(Show Context)
Citation Context ...tems theory. The last section shows tracking results for synthetic and real examples, with applications in experimental fluid mechanics and meteorology. This paper extends a previous conference paper =-=[14]-=-. April 28, 2008 DRAFT6 II. STOCHASTIC FILTERING PROBLEM We present in this section the stochastic filtering problem in continuous time with discrete observations. The particle filter for the discret... |

15 |
L.: Ensemble generation for models of multi-modal systems
- Miller, Ehret
(Show Context)
Citation Context ...sis of stable and unstable directions of a dynamical system. This idea has been used for the Kalman filtering techniques, in order to approximate the estimated covariance matrix by a reduced rank one =-=[28]-=-, [32]. For the continuous-discrete particle filter, a method has been proposed by Chorin [8]. The idea is to concentrate the sampling effort over unstable directions of the dynamics, defined adaptive... |

14 | 3D motion estimation of atmospheric layers from image sequences
- Heas, Mémin
(Show Context)
Citation Context ...8, 2008 DRAFT4 simple dynamical constraints in motion segmentation techniques rely mainly on crude dynamic assumptions or that are related to rigid object motion only [19]. Some recent contributions =-=[20]-=-, [29], [30], [34] aim at improving the temporal consistency and the robustness of the estimations over the whole sequence, introducing a physical evolution law in the estimation process. The dense mo... |

11 |
G.: A fluid motion estimator for schlieren image velocimetry
- Arnaud, Mémin, et al.
- 2006
(Show Context)
Citation Context ...ncertainty term allows to deal with an eventual non validity of the brightness consistency assumption. Let us note that this general brightness consistency model can be adapted to specific situations =-=[2]-=-, [20], [22], [21]. Assuming that Itk (x) and Itk+1 (x′ ) are independent conditionally to xtk likelihood of the vector of observations ztk reads: and consequently: ∀(x,x′ ) ∈ R, the ∏ p(ztk |xtk) = p... |

11 |
Monte-Carlo approximations for 2d Navier–Stokes equations with measure initial data
- Méléard
(Show Context)
Citation Context ...ocity formulation of the Navier-Stokes equation belongs to the class of MacKean-Vlasov equations. It has then a rigorous interpretation in terms of stochastic interacting particles systems [5], [26], =-=[27]-=-. 3) Interacting particles system: The evolution of the q vortex particles is finally described by the following system: q∑ dxl,t = γjKǫj (xl,t − xj,t)dt + √ 2νdBl,t, 1 ≤ l ≤ q, (23) j=1 where Bl,t is... |

10 |
The Monte-Carlo method for filtering with discrete-time observations. Probability Theory and Related
- Protter
- 2001
(Show Context)
Citation Context ...tion of the weights w(i) k w (i) k ∝ w(i) k−1 simplifies as: (i) p(zk|x ). (8) 2) Continuous-discrete time particle filter: The particle filter algorithm can be extended to a general continuous model =-=[16]-=-. Indeed, the importance distribution can be fixed to the transition density p(xtk |xt (i) ) between two observation times tk−1 and tk (as for the bootstrap particle k−1 filter [23]). For a general co... |

9 |
Some stochastic particle methods for nonlinear parabolic PDEs
- Bossy
- 2005
(Show Context)
Citation Context ...rticity-velocity formulation of the Navier-Stokes equation belongs to the class of MacKean-Vlasov equations. It has then a rigorous interpretation in terms of stochastic interacting particles systems =-=[5]-=-, [26], [27]. 3) Interacting particles system: The evolution of the q vortex particles is finally described by the following system: q∑ dxl,t = γjKǫj (xl,t − xj,t)dt + √ 2νdBl,t, 1 ≤ l ≤ q, (23) j=1 w... |

9 |
C.: Variational estimation of experimental fluid flows with physics-based spatio-temporal regularization
- Ruhnau, Stahl, et al.
(Show Context)
Citation Context ...ion estimation methods dedicated to fluid flows, based on a spatial regularization of the vector fields, have been extended to integrate temporal constraints related to the fluid flow evolution [22], =-=[35]-=-, [33]. These constraints are either derived from the vorticity-velocity formulation of the Navier-Stokes equation [22], [35], or from Stokes equation [33]. Recent techniques based on variational trac... |

6 | C.: On-line variational estimation of dynamical fluid flows with physics-based spatio-temporal regularization
- Ruhnau, Stahl, et al.
- 2006
(Show Context)
Citation Context ...mple dynamical constraints in motion segmentation techniques rely mainly on crude dynamic assumptions or that are related to rigid object motion only [19]. Some recent contributions [20], [29], [30], =-=[34]-=- aim at improving the temporal consistency and the robustness of the estimations over the whole sequence, introducing a physical evolution law in the estimation process. The dense motion estimation me... |

5 | 2007-b) Time-consistent estimator of 2d/3d motion of atmospheric layers from pressure image
- Héas, Papadakis, et al.
(Show Context)
Citation Context ...llows to deal with an eventual non validity of the brightness consistency assumption. Let us note that this general brightness consistency model can be adapted to specific situations [2], [20], [22], =-=[21]-=-. Assuming that Itk (x) and Itk+1 (x′ ) are independent conditionally to xtk likelihood of the vector of observations ztk reads: and consequently: ∀(x,x′ ) ∈ R, the ∏ p(ztk |xtk) = p(Itk (x)|xtk), (29... |

5 |
A variational method for joint tracking of curve and motion
- Papadakis, Mémin
- 2007
(Show Context)
Citation Context ...8 DRAFT4 simple dynamical constraints in motion segmentation techniques rely mainly on crude dynamic assumptions or that are related to rigid object motion only [19]. Some recent contributions [20], =-=[29]-=-, [30], [34] aim at improving the temporal consistency and the robustness of the estimations over the whole sequence, introducing a physical evolution law in the estimation process. The dense motion e... |

4 |
Data fusion for visual tracking
- Pérez, Vermaak, et al.
(Show Context)
Citation Context ...lution and is usually difficult to implement numerically for a high dimensional state vector. As a matter of fact, Monte-Carlo probabilistic tracking methods as proposed in the literature [17], [23], =-=[31]-=- are efficient only to track objects of reduced dimension such as points or curves described by several discrete control points. These techniques are not able to cope with high dimensional features su... |

3 |
A singular evolutive extended Kalman filter for data assimilation in oceanography
- Roubaud
- 1998
(Show Context)
Citation Context ... stable and unstable directions of a dynamical system. This idea has been used for the Kalman filtering techniques, in order to approximate the estimated covariance matrix by a reduced rank one [28], =-=[32]-=-. For the continuous-discrete particle filter, a method has been proposed by Chorin [8]. The idea is to concentrate the sampling effort over unstable directions of the dynamics, defined adaptively alo... |