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
methods.
The following
conclusions can be drawn from this study:
1. Interpolation
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.
3. Restoring
images, which were distorted by IF and retouched with help of IMSCS makes
artifacts less noticed in comparision with the results of the linear
interpolation.
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).
Key words:
interpolation, retouching and
restoration of images, Fourier spectrum.
References
1.
Rafael
C. Gonzalez, Richard E. Woods “Digital Image Processing” Second Edition by
Prentice-Hall, Inc. Upper Saddle River,
New Jersey 07458, 2002.
2. Yu. V. Gulyaev, À.Yu. Zrazhevsky, A.V. Kokoshkin,
V.A. Korotkov, V. A. Cherepenin “Correction of the spacial spectrum
distorted by the optical system using the reference image method. Part 2.
Adaptive reference image method.” Zhurnal radioelectroniki - Journal of Radio
Electronics, N 12 - December 2013. Available at URL: http://jre.cplire.ru/jre/dec13/2/text.html
(In Russian)
3. A. V. Kokoshkin, V. A. Korotkov, E. P.
Novichihin “Effects of partially shaded in reconstructing the image, distorted
by blurring”. Zhurnal radioelectroniki - Journal of Radio Electronics, N 9 - September 2014. Available at URL:
http://jre.cplire.ru/jre/sep14/3/text.html
(In
Russian)
4.
À. Yu. Zrazhevsky, V. A. Korotkov, K. V. Korotkov “Semidarkness
effects on an image formed by lens with a large aperture”. Zhurnal
radioelectroniki - Journal of Radio Electronics, N 9 - September 2014. Available at URL:
http://jre.cplire.ru/jre/sep14/7/text.html
(In
Russian)
5.
À. Yu. Zrazhevsky, A.V. Kokoshkin, V. A. Korotkov, K. V. Korotkov “Recovery of defocusing
partially shaded image”. Zhurnal radioelectroniki - Journal of Radio
Electronics, N 10 - October 2014. Available at URL:
http://jre.cplire.ru/jre/oct14/9/text.html
(In
Russian)
6. Jong-Keuk Lee Ji-Hong Kim
Jin-Seok Seo. Adaptive Recovery of Image Blocks Using Spline Approach. //
IJCSNS International Journal of Computer Science and Network Security, VOL.11
No.2, February 2011.
7.
Jiho
Park, Dong-Chul Park, R.J. Mark, M.A. El-Sharkawi. Block loss recovery in DCT
image encoding using POCS. Conference Paper (PDF
Available) · January 2002 with 25 Reads
DOI:
10.1109/ISCAS.2002.1010686 · Source: DBLPConference: Circuits and Systems, 2002.
ISCAS 2002. IEEE International Symposium on, Volume: 5
8. T. Strohmer,
“Computationally attractive reconstruction of bandlimited images from irregular
samples,” IEEE Trans. on Image Processing, 6 (4), pp 540-548, Apr. 1997.
9.
Chen
Chen , Eric W.
Tramel, James
E. Fowler.
Compressed-Sensing Recovery of Images and Video Using Multihypothesis
Predictiobs.
2011 Conference Record
of the Forty Fifth Asilomar Conference on Signals, Systems and Computers
(ASILOMAR).
10.
Seung
Hwa Hyun ; Sang
Soo Kim ; Byoung
Chul Kim ; Il Kyu
Eom. Efficient
Directional Interpolation for Block Recovery Using Difference Values of Border
Pixels.
Image and Signal
Processing, 2008. CISP '08. Congress on (Volume:3 ).
11. Ching-Tang
Hsieh , Yen-Liang Chen and Chih-Hsu Hsu. Fast Image Restoration Method Based on
the Multi-Resolution Layer. Tamkang Journal of Science and Engineering, Vol.
12, No. 4, pp. 439-448 (2009).
12. Jiho Park,
Dong-Chul Park, Robert J. Marks, Fellow, Mohamed A. El-Sharkawi. Recovery of
image blocks using the method of alternating projections. // IEEE TRANSACTIONS
ON IMAGE PROCESSING, VOL. 14, NO. 4, APRIL 2005.
13. Seung Hwa
Hyuna, Il Kyu Eomb, Yoo Shin Kim. Directional Filtering for Block Recovery
Using Wavelet Features. Proc. SPIE 5960, Visual Communications and Image
Processing 2005, 59600Z (31 July 2006); doi:10.1117/12.631414.
14. Belim S.V.,
Mayor Zilbernagel A.O. "Search algorithm damaged pixels and remove impulse
noise in the images using the method of association rules." // Science and
education. MTSU NE Bauman. 2014. ¹ 12. S. 716-737.
(In Russian)