Image Processing Reference
In-Depth Information
This phenomena can be used to detect angle of rotation. To detect an angle of image rotation
the Radon transform of its fragment could be performed with successive analysis of Radon
projections with Fourier transform. Radon transform can be defined as follows: Let function
f(x, y) , is defined in D . We will consider some straight line L on a plane ху , crossing area D .
Then, integrating function f (x, y) along line L , we receive a projection or linear integral of
function f . Integration along all possible lines L on a plane allows to define Radon transform:
*

f
Rf
f (x,y )ds ,
L
where ds - an increment of length along L .
For minimization of edge effects impact of analyzed area on high-frequency part of an
image it is advisable to apply Radon transform over circular fragment with smoothed
borders. Selection of a fragment from the image and smoothing of its borders were done [4]
by normalized two-dimensional Gaussian window
t
2
2
exp
 
2
ht
()
2

ln 2
2BT

shown in figure 3.
Refinement to an angle which 90º degrees multiple is possible to make due to
uncompensated banding traces, which are consequences of non-uniformity of image
brightness component obtained from CCD or CMOS matrixes [2] and traces of compression
artifacts. A consequence of the given phenomenon will be unequal level of maxima of a
Fourier spectrum obtained from result of Radon transform that allows to select only 2 or (in
some cases) 4 angles. Examples of columns spectrograms for a matrix of Radon transformed
image fragment 1024x1024 pixel size are represented in figure 4.
Fig. 3. Two-dimensional normalized Gaussian window used to select an image fragment
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