A new energy-based method for 3D motion estimation of incompressible PIV flows

Álvarez, Luis; Castaño, C. A.; García, Miguel Ángel; Krissian, Karl; Mazorra, Luis; Salgado, Agustín; Sánchez, Javier

doi:10.1016/j.cviu.2009.01.005

Cited by 20 publications

(16 citation statements)

References 19 publications

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“…Optical flow-based methods have been promising in the area of fluid flow estimation in PIV [46–51]. For example, in [47], incompressibility of the flow is added as a constraint in the optical flow minimization problem. In [48], the vorticity transport equation, which describes the evolution of the fluid's vorticity over time, is used in physically consistent spatio-temporal regularization to estimate fluid motion.…”

Section: Introductionmentioning

confidence: 99%

An Optical Flow-Based Approach for Minimally Divergent Velocimetry Data Interpolation

Kanberoglu

Das

Nair

et al. 2019

International Journal of Biomedical Imaging

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Three-dimensional (3D) biomedical image sets are often acquired with in-plane pixel spacings that are far less than the out-of-plane spacings between images. The resultant anisotropy, which can be detrimental in many applications, can be decreased using image interpolation. Optical flow and/or other registration-based interpolators have proven useful in such interpolation roles in the past. When acquired images are comprised of signals that describe the flow velocity of fluids, additional information is available to guide the interpolation process. In this paper, we present an optical-flow based framework for image interpolation that also minimizes resultant divergence in the interpolated data.

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Section: Introductionmentioning

confidence: 99%

An Optical Flow-Based Approach for Minimally Divergent Velocimetry Data Interpolation

Kanberoglu

Das

Nair

et al. 2019

International Journal of Biomedical Imaging

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show abstract

“…Optical flow-based methods have been promising in the area of fluid flow estimation in PIV [46][47][48][49][50][51]. For example, in [47], incompressibility of the flow is added as a constraint in the optical flow minimization problem. In [48], the vorticity transport equation, which describes the evolution of the fluid's vorticity over time, is used in physically consistent spatio-temporal regularization to estimate fluid motion.…”

Section: Introductionmentioning

confidence: 99%

An optical flow-based approach for the interpolation of minimally divergent velocimetry data

Kanberoglu

Nair

2017

2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017)

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“…Heitz et al [14] point out potential research directions for variational PIV and advocate the use of correct physical constraints, focusing mainly on 2D problems. Alvarez et al [2] were, to our knowledge, the first to present a variational model of 3D-PIV that accounts for the physical properties of incompressible fluids. However, their method is applicable only as refinement after an initial flow estimation with another (not physically grounded) model.…”

Section: Related Workmentioning

confidence: 99%

“…Regularizers which penalize divergence have been tried for both 2D and 3D problems [2,13,14]. Here, we propose an energy whose optimality conditions correspond to the stationary Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Volumetric Flow Estimation for Incompressible Fluids Using the Stationary Stokes Equations

Lasinger

Vogel

Schindler

2017

2017 IEEE International Conference on Computer Vision (ICCV)

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In experimental fluid dynamics, the flow in a volume of fluid is observed by injecting high-contrast tracer particles and tracking them in multi-view video. Fluid dynamics researchers have developed variants of space-carving to reconstruct the 3D particle distribution at a given time-step, and then use relatively simple local matching to recover the motion over time. On the contrary, estimating the optical flow between two consecutive images is a long-standing standard problem in computer vision, but only little work exists about volumetric 3D flow. Here, we propose a variational method for 3D fluid flow estimation from multi-view data. We start from a 3D version of the standard variational flow model, and investigate different regularization schemes that ensure divergence-free flow fields, to account for the physics of incompressible fluids. Moreover, we propose a semi-dense formulation, to cope with the computational demands of large volumetric datasets. Flow is estimated and regularized at a lower spatial resolution, while the data term is evaluated at full resolution to preserve the discriminative power and geometric precision of the local particle distribution. Extensive experiments reveal that a simple sum of squared differences (SSD) is the most suitable data term for our application. For regularization, an energy whose Euler-Lagrange equations correspond to the stationary Stokes equations leads to the best results. This strictly enforces a divergence-free flow and additionally penalizes the squared gradient of the flow.

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A new energy-based method for 3D motion estimation of incompressible PIV flows

Cited by 20 publications

References 19 publications

An Optical Flow-Based Approach for Minimally Divergent Velocimetry Data Interpolation

An Optical Flow-Based Approach for Minimally Divergent Velocimetry Data Interpolation

An optical flow-based approach for the interpolation of minimally divergent velocimetry data

Volumetric Flow Estimation for Incompressible Fluids Using the Stationary Stokes Equations

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