Digital Signal Processing Reference
In-Depth Information
information[2].Cross-correlation technique is to measure the same target displacement
in the movement in the adjacent two images, combined with the frame rate, displace-
ment divided by the reciprocal of the frame rate (i.e. the time interval) to get the
velocity[3]. In order to validate the correctness and reliability of the algorithm, it is
necessary to calibrate and clarify the accuracy of the algorithm.
Calibration of the algorithm by computing the image of the different particle densi-
ty was calculated and analyzed to select the most suitable size of the sub-region[4].
Cross-calibration of the correlation algorithm is to enable the measurement of the
algorithm can be applied to the speed of the image of the particle motion in a variety
of situations, and as much as possible to minimize the error introduced by the algo-
rithm itself. Meanwhile, the cross-correlation algorithm in the calculation, by using
the fast Fourier transform in order to improve computing speed[3], to reduce the
computational complexity and improve the program timeliness.
OpenCV is Intel ® Open Source Computer Vision Library. It consists of a series of
C functions and a small amount of C++ classes, and many common image processing
and computer vision algorithms[5]. Algorithm is the standard functions on the basis of
openCV provided.
2
Calculation Method
2.1
Principle of the Cross-Correlation Algorithm
The algorithm is calculation of the cross-correlation function of two adjacent images
using FFT (Fast Fourier Transform)[6]. The first step is to convert the information of
the two sub-regions from the spatial to the frequency domain, and then do the convo-
lution of two Fourier spectrums, and then Fourier's inverse transformation to restore it
to the spatial domain. The proceeds of a cross-correlation function, the location of its
maximum value is the particle displacement coordinates of the demand area.
2.2
Calculation Steps
Division of the Sub-region
The selection of the sub-region size is very important in the cross-correlation calcula-
tion. The larger region is set, it will has more information in it, more computation
time will needed to calculate, also more noise will be produced to, reducing the corre-
lation of the two sub-region. Instead, the smaller sub-region will contain little
information, the less effective bubble pairs will reduced, or even unable to meet the
necessary conditions for correlation analysis, which will affect the reliability and
correctness of the analysis results. Therefore, the choice of a suitable size of sub-
region will reduce the impact of the noise to be reduced to the lowest level, reduce the
amount of calculation of the correlation analysis, and while at the same time improve
the accuracy and reliability of the results of the analysis. According to the Nyquist
sampling theorem, the sampling frequency is greater than the twice of highest signal
frequency, the signal will be reconstructed without distortion[7]. Therefore, the size
of the sub-region should be chosen at least three times larger than the bubble maxi-
mum displacement in the sub-region.
