Instrumentation & Measurement Magazine 24-4 - 30

Fig. 1. Typical monadic image operations.
picture brighter or darker. Fig. 1 illustrates different possible
operations used for this approach.
Let S(x,y) and d(x,y) be the source and the destination
pixel value at the location (x,y), respectively, and K be the constant.
The approach proposed allows a destination pixel to be
created based on the entire image information. It has a tremendous
application in image processing in which the input is a
set of pixels forming a 2D function that is already discrete. The
output can then be expressed as follows:
11 2
00
Xlm 
NMxejk
1
jk
 
where j and k are column coordinates, 0 jN k M 1
 1 and 0 and   
 1 and 0    .
Particle Image Velocimetry
Basically, Particle Image Velocity (PIV) is a powerful method
used to investigate the characteristics of a flow field [10]. In the
case of this paper, the algorithm consists of a cross correlation
to small corresponding windows sample at the same location
in two successive images. Thanks to Fast Fourier Transform
(FFT) technique, the normalized correlation signal is obtained.
The peak location is determined with sub-pixel accuracy. This
paper uses the Gaussian peak interpolation [11], in which the
peak of such correlation is searched for, giving the displacement
of the particle. The velocity vector corresponds then to
the peak position due to the displacement peak between the
first and the second. Fig. 2 presents the general flow chart of
the main steps when this approach is used. ROI stands for region
of interest.
In the direct case, which is our case for digital images, if the
images' sizes are (2i,2j), the correlation is then:
MN
C x y  FI i j FI i x n y)
i Mj N
m n , ( , ) 

A point-by-point multiplication of FIBm,n
each position (x,y), where IAm,n and IBm,n
FIAm,n and FIBm,n
.
Results
Both PIV and monadic techniques have been used on three
grayscale images at different resolution as presented in Fig. 3.
30
is performed for
are images cut into
Am n(, ) Bm n,, ,
(
(2)
jN k M 1
NM


i
NM



jl km
(1)
Fig. 2. PIV algorithm flow chart, in which ROI stands for region of interest.
These images are from TEM characterization of a carcinoma.
The proposed algorithms have been developed in MATLAB/
Simulink software.
A graph-based segmentation technique like lazy-snapping
enables images to be segmented in pre-processing steps into
foreground and background regions. In the result presented in
Fig. 3, we took the three images of Fig. 3 as input images. Then,
we applied the algorithm to every single pixel in those images.
The functions presented in Fig. 1, applied to pixels in the input
images, are assigned to the corresponding pixels in the output
images, and we use the same functions on every pixel within
the images.
The input pixels were taken in the range 0 through 255,
and these integers have value 0,1,2 and so on. The mapping
of those integers was then presented by a graph. It is important
to notice that in both cases, the mapping is a straight line
and it passes through the origin with a gradient 1. Increasing
the contrast of the image is another way to increase the
brightness of the image. It consists of multiplying all grey
values by a constant, and in this case, the grey values are
multiplied by the value of 2. Graphically, the slope of the line
IEEE Instrumentation & Measurement Magazine
June 2021
Instrumentation & Measurement Magazine 24-4

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