comparison between optical flow and cross-correlation
TRANSCRIPT
(Optical Flow vs Cross-Correlation)
Tianshu Liu, Ali Merat, M. H. M. Makhmalbaf
Claudia Fajardo, Parviz Merati
Western Michigan University, Kalamazoo, MI 49008
Comparison between Optical Flow and
Cross-Correlation Methods for Extraction
of Velocity Fields from Particle Images
Objective
To quantitatively compare the optical flow
method and cross-correlation method in
extraction of velocity vectors from particle
images
Cross-Correlation Method in Particle Image Velocimetry (PIV)
Images of Discrete Particles
Cross-
Correlation
Velocity Vectors t = 0
t = t
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
Physics-Based Optical Flow Method Developed for Extraction of High-Resolution
Velocity Field from Images of Continuous Patterns
Physics-Based Optical Flow Equation
1221 )u,u( Uu
Optical flow has a clear physical meaning:
),(BgD)g,x,x(f 2122
21
Diffusion and boundary terms:
)g,x,x(fgt/g 21 u
2
1
2
1
3
312
12
Xd
Xd
U
U
where the path-averaged velocity is
Normalized image
intensity
The Inverse Problem to Solve the Generic
Physics-Based Optical Flow Equation
Using Variational Method
Functional for Minimization:
21
2
2
2
1
212
dxdxuu
dxdxfgt/g)(J uu
Smooth Constraint
Euler-Lagrange Equation
Neumann boundary condition:
0n u/
Numerical solution:
Finite difference & Jacob iteration
0f)g(t/gg 2 uu
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
Error Analysis and Relevant Parameters
2
p
2
pm
mp
4
2p
32
p22
p
2p1
pN
c
d
cc
dc
x
xu
u
x
Error Estimate
Particle displacement
Particle diameter
Particle velocity gradient
Particle image density
Four Error Parameters
px
pd
pu
pN
Simulation:
Oseen-Vortex Pair in Uniform Flow
Optical Flow Correlation (LaVision)
Simulation:
Oseen-Vortex Pair in Uniform Flow
Optical Flow Correlation
Simulation:
Oseen-Vortex Pair in Uniform Flow
X-velocity component Y-velocity component
Comparison between Velocity Profiles
Simulation:
Oseen-Vortex Pair in Uniform Flow
Optical Flow Correlation
RMS Error Distributions
Optical Flow vs Correlation in Parameter Space
px
pd
pu
pN
Effect of Illumination Change
Non-corrected image Corrected image
Effect of Illumination Change
Corrected images
Non-corrected images
Effect of Illumination Change
Snapshot Field in Impingement Region
of Normal Impinging Jet
Optical Flow
Correlation
PIV Image
Impinging Jet: Impingement Region
Comparison between Snapshot Velocity Profiles
Y-velocity component X-velocity component
Snapshot Field in Wall-Jet Region
of Normal Impinging Jet PIV Image
Optical Flow
Correlation 200 data points
30 data points
Impinging Jet: Wall-Jet Region
Comparison between Snapshot Velocity Profiles
Y-velocity component X-velocity component
Ensemble-Averaged Fields in Wall-Jet Region
of Normal Impinging Jet
Optical Flow Correlation
Turbulent Kinetic Energy
Reynolds Stress
Impinging Jet: Wall-Jet Region
Comparison between Ensemble-Averaged Profiles
Reynolds Stress Turbulent Kinetic Energy
Impinging Jet: Wall-Jet Region
Comparison between Kinetic Energy Spectra
Conclusions
(1) The main parameters in optical flow
computation for PIV images:
(2) The optical flow method can obtain improved
results with much higher resolution from PIV
images when these parameters are suitably selected.
Particle displacement
Particle velocity gradient
Particle density
Particle diameter
