Comparison between Optical Flow and Cross-Correlation Methods for Extraction of Velocity Fields from Particle Images
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1 Comparison between Optical Flow and Cross-Correlation Methods for Extraction of Velocity Fields from Particle Images (Optical Flow vs Cross-Correlation) Tianshu Liu, Ali Merat, M. H. M. Makhmalbaf Claudia Fajardo, Parviz Merati Western Michigan University, Kalamazoo, MI 49008
2 Objective To quantitatively compare the optical flow method and cross-correlation method in extraction of velocity vectors from particle images
3 Cross-Correlation Method in Particle Image Velocimetry (PIV) Images of Discrete Particles t = 0 Velocity Vectors Cross- Correlation t = t
4 Optical Flow Method in Computer Vision Optical flow: the apparent motion of object surfaces in a visual scene caused by the relative motion between an observer (camera) and the scene. Lucas Kanade Method: Local method based on an affine model for the flow field in windows Horn Schunck Method: Global method of minimizing a functional based on residuals from the brightness constancy constraint, and a particular regularization term expressing the expected smoothness of the flow field
5 Physics-Based Optical Flow Method Developed for Extraction of High-Resolution Velocity Field from Images of Continuous Patterns
6 Physics-Based Optical Flow Equation g f ( x,x,g ) g / t u 1 Optical flow has a clear physical meaning: u ( u U 1,u ) where the path-averaged velocity is U 1 1 Diffusion and boundary terms: f ( x1,x,g ) D g B( 1, 1 U 1 1 d X d X 3 3 Normalized image intensity )
7 The Inverse Problem to Solve the Generic Physics-Based Optical Flow Equation Using Variational Method Functional for Minimization: J( u ) g / t g u f dx 1 dx u1 u dx1dx Smooth Constraint
8 Euler-Lagrange Equation g g / t ( gu ) f 0 u Neumann boundary condition: u/n 0 Numerical solution: Finite difference & Jacob iteration
9 Problems in Applying the Optical Flow Method to PIV Images PIV images are spatially non-smooth random intensity fields, which intrinsically are not suitable to the differential method like the optical flow method. It is highly desirable to evaluate Constraints for the optical flow method applied to PIV images
10 Error Analysis and Relevant Parameters Error Estimate x p c 1 u d p p c u p c d 3 p c N 4 m p m x x p p Four Error Parameters Particle displacement Particle diameter d p Particle velocity gradient Particle image density x p N p u p
11 Simulation: Oseen-Vortex Pair in Uniform Flow Optical Flow Correlation (LaVision)
12 Simulation: Oseen-Vortex Pair in Uniform Flow Optical Flow Correlation
13 Simulation: Oseen-Vortex Pair in Uniform Flow Comparison between Velocity Profiles X-velocity component Y-velocity component
14 Simulation: Oseen-Vortex Pair in Uniform Flow RMS Error Distributions Optical Flow Correlation
15 Optical Flow vs Correlation in Parameter Space x p u p N p d p
16 Effect of Illumination Change Non-corrected image Corrected image
17 Effect of Illumination Change Non-corrected images Corrected images
18 Effect of Illumination Change
19 Snapshot Field in Impingement Region of Normal Impinging Jet Optical Flow PIV Image Correlation
20 Impinging Jet: Impingement Region Comparison between Snapshot Velocity Profiles X-velocity component Y-velocity component
21 Snapshot Field in Wall-Jet Region of Normal Impinging Jet PIV Image Optical Flow Correlation 00 data points 30 data points
22 Impinging Jet: Wall-Jet Region Comparison between Snapshot Velocity Profiles X-velocity component Y-velocity component
23 Ensemble-Averaged Fields in Wall-Jet Region of Normal Impinging Jet Optical Flow Correlation Turbulent Kinetic Energy Reynolds Stress
24 Impinging Jet: Wall-Jet Region Comparison between Ensemble-Averaged Profiles Turbulent Kinetic Energy Reynolds Stress
25 Impinging Jet: Wall-Jet Region Comparison between Kinetic Energy Spectra
26 Conclusions (1) The main parameters in optical flow computation for PIV images: Particle displacement Particle velocity gradient Particle density Particle diameter () The optical flow method can obtain improved results with much higher resolution from PIV images when these parameters are suitably selected.
27
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