Abstract. The work proposed and
investigated the method of interpolation sequentially calculating the Fourier
spectrum which allows you to retouch and restore the missing (shaded) parts of
the image. The distortion of the images of the objects can be described in
terms of convolution equations [1.2] with the appropriate instrumental function
(IF). Image restoration is complicated by the need to determine the type of IF
and its parameters. Different objects presented in the image may be distorted by
different IF. Furthermore, objects may overshade each other. A number of studies
considered the possibility of the restoration is partially shaded images [3-5].
We used replacement (retouching) shading objects for an image obtained by linear
interpolation [3-5]. On the reconstructed image the artifacts caused by
retouching are appeared. If the shape of the shading object is different from
rectangle, the difficulty in applying linear interpolation increases.
A number of
studies [6-13] considered the possibility of retouching the missing parts of the
image using wavelets, different types of interpolation (bilinear, spline,
trigonometric, polynomial). Using these techniques for retouching shading
objects to further restoration of the image distorted by IF, is possible.
However, the arbitrary shape of the shading object and the appearance of
additional artifacts caused by such retouching, limit the applicability of these
conclusions can be drawn from this study:
Method of Sequential Computation of the Fourier spectrum (IMSCS) allows you to
retouch missing (shaded) part of the image.
2. Unlike IMSCS,
linear interpolation can be used in any form of a missing parts of the image.
images, which were distorted by IF and retouched with help of IMSCS makes
artifacts less noticed in comparision with the results of the linear
4. Retouching and
IMSCS image restoration can give good results even with a large part of the
missing image (see. Figure 6, 9 and 10).
interpolation, retouching and
restoration of images, Fourier spectrum.
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