Navier-Stokes formulation for modelling turbulent optical flow

Doshi, Ashish; Borş, Adrian G.

doi:10.5244/c.21.97

Cited by 7 publications

(7 citation statements)

References 13 publications

(23 reference statements)

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“…Several different approaches have been developed for computing the optical fiow of turbulent fiow fields, such as the Navier-Stokes approach of Doshi et al in [11] and the self-similar regularization approach of Heas, et al in [19]. Past work for computing fiuid optical flows can be found, for example in [2,3,21,25], and in each case, the ability to capture the structures of vortices rests on extracting discontinuity information from the flow field.…”

Section: ) Jnmentioning

confidence: 99%

An Optical Flow Approach to Analyzing Species Density Dynamics and Transport

Holloway¹

2012

JCM

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Classical optical fiow techniques were developed for computing virtual motion fields between two images of the same scene, assuming conservation of intensity and a smoothness of the flow field. If these assumptions are dropped, such techniques can be adapted to compute apparent flows between time snapshots of data that do not come from images, even if these fiows are turbulent and divergent, as in the case of flows representing complex spatiotemporal dynamics. While imaging methods have been used to analyze dynamics in experimental applications, they are only beginning to be applied to dynamics computations in settings outside the laboratory, for example in the analysis of species population dynamics from satellite data. In this work we present a variational optical flow approach based on the continuity equation and total variation regularization for computing the flow fields between population densities generated from a two-species predator-prey model for phyto-and Zooplankton interactions. Given the time-varying vector fields produced from the optical flow, computational methods from dynamical systems can be employed to study pseudo-barriers present in the species interaction. This method allows to measure the mixing of the species, as well as the transport of the populations throughout the domain.Mathematics subject classification: 49N45, 49M99, 37M25, 65P99, 68T45.

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Section: ) Jnmentioning

confidence: 99%

An Optical Flow Approach to Analyzing Species Density Dynamics and Transport

Holloway¹

2012

JCM

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“…They create a pyramidal structure to refine the optical flow linearly. In some related works [18][19][20], the NavierStokes (N-S) equation is employed. Wang et al [21] also make use of the N-S equation to refine the fluid motion from dense reconstruction.…”

Section: Related Workmentioning

confidence: 99%

Fluid re-simulation based on physically driven model from video

2015

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Customizing a desired naturalistic fluid simulation result from video to obtain similar artistic effect is significant in practice. But art-directed customizing is challengeable due to the chaotic nature of the physics contained in it, and this still remains to be a difficult task in spite of rapid advancements of computer graphics during the last two decades. This paper focuses on the problem of physically based fluid re-simulation which is foundational to customize desired naturalistic simulation result from video example. In the previous achievements, conventional algorithms primarily recover 3D geometry of fluid surface or obtain the velocity of fluid particles in video. However, to launch new derivative results, just geometry and velocity are not enough, and physically based driven models are promising. We present a novel method that is capable of efficiently recovering physically driven model from an existing video. We advocate a new approach to calculate the velocity and non-normalized surface geometry under the constraints of the appearance and dynamic behavior of the example fluid in multi-scale framework, and use the calculated physical properties quickly to recover the fluid-driven model. In particular, to calculate the surface geometry more accurately, we introduce a scale factor between normalized geometry and non-normalized geometry to acquire a more accurate result. We propose a novel recovery algorithm, in which the particle densities of lattice Boltzmann method can be recovered more accurately from matching fluid advection geometry with the calculated non-normalized geometry. Fluid re-simulations with different types of density can be achieved, including constrained particle density, auto-advection density, and enhanced particle density. We demonstrate our results in several challenging scenarios and provide qualitative evaluation to our method. Some applications based on our approach are also demonstrated in the implementation.

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“…This formulation has become common for analyzing fluid flows, for example in connection with and in comparison to particle image velocimetry (PIV) [5,13], geophysical fluid flows [1,2], and atmospheric motion [4]. While it is possible to incorporate the full Navier-Stokes equations for fluid flows in order to more accurately model the evolution of a fluid system [8], the model (1) is robust and results in more straightforward computational schemes. Under the assumption that the flow being imaged is a "potential flow," i.e.…”

Section: Stream Function Optical Flowmentioning

confidence: 99%

A Stream Function Approach to Optical Flow with Applications to Fluid Transport Dynamics

Luttman

Bollt

Basnayake

et al. 2011

Proc Appl Math and Mech

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Optical flow is one of the classical problems in computer vision, but it has recently also been adapted to applications from other fields, such as fluid mechanics and dynamical systems. If the goal is to analyze the dynamics of system whose evolution is governed by a flow field that is the gradient of a potential function -which describes many flows in fluid dynamics -it is natural to approach the optical flow problem by reconstructing the potential function, also called the stream function, rather than reconstructing the components of the flow directly. This alternate approach allows one to impose scientific priors, via regularization, directly on the flow itself rather than on its components independently. We demonstrate the stream function formulation of optical flow and its application to reconstructing an oceanic fluid flow driven by satellite measurements. It is also shown how these flow fields can be used to analyze mixing and mass transport in the fluid system being imaged. Stream Function Optical FlowOptical flow is an image-based method for computing the apparent flow field governing a system evolution. Recently much work has been done using optical flow to analyze fluids, which requires a different physical model from the classical HornSchunk method [12]. Corpetti et al. [6,7] proposed an alternative based on the continuity equation, resulting in an optical flow energy of the formwhere Ω is the spatial domain, R(u, v) is an appropriate regularization scheme, and α > 0 is the regularization parameter. This formulation has become common for analyzing fluid flows, for example in connection with and in comparison to particle image velocimetry (PIV) [5,13], geophysical fluid flows [1,2], and atmospheric motion [4]. While it is possible to incorporate the full Navier-Stokes equations for fluid flows in order to more accurately model the evolution of a fluid system [8], the model (1) is robust and results in more straightforward computational schemes. Under the assumption that the flow being imaged is a "potential flow," i.e. that the flow field is the gradient of a potential, or stream function, it is natural to instead formulate the optical flow problem in terms of reconstructing the stream function directly. Within a Hamiltonian framework, the evolution equation governing the flow is thus I t = −div (I∇ H ψ), where ∇ H ψ = −ψ y , ψ x is the symplectic gradient. The resulting optical flow energy iswhere R(ψ) is a regularization of the stream function. There are two primary goals of regularizing a variational optimization problem. The first goal is to ensure that the optimization problem is well-posed, i.e. that a solution exists, is unique, and is stable with respect to perturbations in the input data. For optical flow problems, this need not happen in general. In particular, for nearly any physically appropriate regularization, there exist data for which the governing flow field is not unique. The second reason for regularization -and one of the main advantages to computing optical flow via (2) -is to im...

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Navier-Stokes formulation for modelling turbulent optical flow

Cited by 7 publications

References 13 publications

An Optical Flow Approach to Analyzing Species Density Dynamics and Transport

An Optical Flow Approach to Analyzing Species Density Dynamics and Transport

Fluid re-simulation based on physically driven model from video

A Stream Function Approach to Optical Flow with Applications to Fluid Transport Dynamics

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