Biomedical Engineering Reference
In-Depth Information
The background of a digital image for micro-PIV measurement can be determined by averaging
a number of N particle images. Because the particles of the flow field are stochastically distributed and
therefore removed by integration, the background image remains:
L X
N
1
I
ð
i
;
j
Þ¼
I k ð
i
;
j
Þ:
(8.23)
k ¼
1
The background can be removed by subtracting I
ð
i
;
j
Þ
from the measured particle image:
(8.24)
In many cases, the tracing particles are not dense enough for an accurate evaluation of the velocity
field. One method for increasing the number of particles in the image is overlapping of several
recorded images:
I
ð
i
;
j
Þ¼
I
ð
i
;
j
Þ
I
ð
i
;
j
Þ:
N
k
(8.25)
Noise may lead to a wrong correlation peak in the matrix R ( m , n ). Thus, integration over several
correlation matrices can form a sharp correlation peak for subsequent subpixel refinement:
I 0 ð
i
;
j
Þ¼
max
½
I k ð
i
;
j
Þ
1 :
¼
N X
N
1
R
ð
m
;
n
Þ¼
R k ð
m
;
n
Þ:
(8.26)
k
¼
1
8.2.2 Measurement of concentration field
The intensity of a fluorescent dye solution is proportional to the concentration of the dye molecules.
Thus, the concentration field can be measured indirectly as the intensity field of a fluorescent dye. This
measurement is easily achieved with a CCD camera attached to a fluorescence microscope. The
following example demonstrates the use of image processing functions for evaluating the digital image
of concentration field of a fluorescent dye. The functions are available in the Image Processing
Toolbox of MATLAB (MathWorks, Inc.).
Example 8.1 ( Measurement of concentration field based on a digital image ). Fig. 8.11 shows
a digital image of a fluorescent dye stored in the Windows bitmap format. The evaluation of this image
with MATLAB is described in the following steps. For more details on digital image processing with
MATLAB, the reader is referred to the topic by Gonzalez et al. [2] .
The following command reads a bitmap image stored in the file 'FieldExample.bmp' and converts
it to a two-dimensional array of intensity values I :
I ¼ imread( ' FieldExample ' , ' bmp ' );
The information about the image file can be obtained by using
imfinfo FieldExample.bmp
The image can be displayed in the default 256 gray levels with the following command:
imshow(I);
As shown in Fig. 8.11 (a), there is a high level of noise, especially in areas with high intensity. To
reduce the level of noise, spatial filtering can be applied to each point of the intensity array. Spatial
filtering is implemented in the following steps:
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