- 13 - 
In applications where the degrading function G of the system 
is unknown, image enhancement may be achieved by emphasizing 
high frequencies in the image. This can be implemented either 
by the amplification of high frequencies (contrast enhancement) 
or by suppressing low frequencies (high pass filtering). 
Many realisations of high pass filter techniques have been 
published. With figure 13 - 15 two examples are discussed. Using 
a general high pass filter according to figure 13 the amplitu- 
des of high frequencies are not changed whereas the amplitudes 
below a special frequency fg are decreased. In this method the 
original image is transformed into the Fourier domain, multiplied 
with the filter g and the result of the multiplication is trans- 
formed back to the image domain /22/. Figure 14 shows the re- 
sult of such a process, where in the output image negative va- 
lues have been displayed as dark, zero-values as grey and posi- 
tive values as white. The advantage of this method is the possi- 
bility of a free manipulation of the filter, the disadvantage 
is given by the high amount of computing time for the two trans- 
formations. 
Another realization uses the twodimensional differentiation of 
an image, where this differentiation corresponds to a high pass 
filter-process /23/. The differentiation can be computed in the 
image domain by convolution according to equ. 12 
B5 42 = 
1 
2,1,3 2 (IB T 
11-13 7 Prim, al * | 
By, 5,31 By,i,3+41 1) 
ij — 1 ... n (12) 
The result of this process is shown in figure 15 (original photos 
figures 10a and 14a). 
In the case of contrast enhancement low frequencies remain un- 
changed and high frequencies are emphasized /24/. In one possible 
implementation contrast enhancement is achieved by subtracting 
€ 44 - 
à 
hi 
the second derivative B," from the original image B,,equ. 13 
{13) 
= constant 
The second derivative of an image can be computed by applying 
the Laplacian operator V 2 to each picture element,equ. 14. 
2 
BU" . = B n ER ; à 
1,1, V 1,1,j B1,i-1,j + * B),i,j-1 
4 BL (14) 
1,i,j 
B4 irl,j 
* B, djti 
The principle process of a contrast enhancement and the result 
of an application to a real image is shown in figure 16. 
An other possibility to achieve contrast enhancement is the 
so-called "a-process" /20/. In this case the original image 
1s transformed into the Fourier domain and the amplitudes in 
the frequency domain are stored as magnitude and Phase equ. 15 
Y uv j = V. (15) 
u,v spatial 
Lo iu, vi 
1,u,v 
frequencies 
u,v = O ...Ÿ(n-1)|2 
By a non-linear manipulation of the magnitude of the complex 
amplitude according to equ. 16a or 16b a contrast enhancement is 
realized.