1 Imaging Techniques for Flow and Motion Measurement Lecture 10 Lichuan Gui University of Mississippi 2011 Direct Correlation & MQD Method

2 Direct Correlation (w/o FFT) Method 1: g 2 (i,j) limited in the window frame oM N j i g 1 (i,j) m n g 2 (i+m,j+n) A

3 Direct Correlation (w/o FFT) Method 2: g 2 (i,j) not limited in the window frame oM N j i g 1 (i,j) m n g 2 (i+m,j+n) A

4 Particle Image Pattern Tracking Tracking ensemble of particle images 1 st recording 2 nd recording tracked image pattern Image pattern at (m,n)

5 Minimum-quadratic-difference (MQD) method M  N dimensional vectors Quadratic difference of the vectors Double exposureSingle exposures Minimum-quadratic-difference (MQD) method Particle Image Pattern Tracking

6 Modified MQD tracking function Particle Image Pattern Tracking - D * (m,n) and D(m,n) identical for determining particle image displacement - 3-point Gaussian fit directly applied to D * (m,n) Normalized MQD tracking functions

7 Correlation-based tracking method Correlation-based tracking function Particle Image Pattern Tracking

8 Modified correlation-based tracking function zero

9 oM N j i g 1 (i,j) m n A g 2 (i+m,j+n)     tr (m,n)/D * (m,n) 22 22   Tracking radius Particle Image Pattern Tracking Tracking area & tracking radius

10 Acceleration with FFT Particle Image Pattern Tracking No periodical, no FFT: Zero padding: Periodical, with FFT: g 1 (i,j) g 2 (i,j)

11 for [ ‑   m < , ‑   n <  ] 0 Acceleration with FFT Particle Image Pattern Tracking

12 Computation time Particle Image Pattern Tracking Correlation tracking with FFT Test computer: IBM 6×86 P166+ [pixel]

Imaging techniques for fluid flow and insect motion experiments 13 Evaluation error Particle Image Pattern Tracking Image pattern tracking methods - periodical error distribution on particle image displacement (1 pixel period) - MQD has higher accuracy for ideal PIV images, but more sensitive to noises Correlation algorithm - error dependent on particle image displacement, high accuracy at very small displacement Evaluation error for ideal PIV recordings by using different algorithms with a 64x64-pixel interrogation window

14 –Programming Compute correlation-based tracking function at the center of image01.bmp with 32x32-pixel window –Practice with EDPIV Evaluation settings: - Exposure type: Double - Flow direction: E - interrogation grid: 31x31 pixels - iteration number: 0, 1 - Search radius: 20 pixels Functions used in “Evaluation” window - create a regular evaluation grid - select a test point at the center - start an evaluation - view image samples and evaluation function - determine discrete and sub-pixel displacement Homework