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An algorithm for the restoration of blurred image obtained with a rotating camera tilted to the horizon

A.V. Kozak 1, O.B. Steinberg 1, B.Y. Steinberg 1

Southern Federal University, Rostov-on-Don, Russia

 PDF, 1371 kB

DOI: 10.18287/2412-6179-CO-598

Pages: 229-235.

Full text of article: Russian language.

This work is a continuation of the authors’ previous  publications, in which the restoration of images obtained with a horizontally rotating camera was considered. In this paper, a mathematical model is constructed for reconstructing blurred images obtained with a camera rotating in the horizontal plane and having its optical axis tilted at an angle to the horizon. The method of image restoration involves constructing a strip of spherical panorama from the original images. Results of numerical experiments that confirm the good quality of the presented image recovery method and the high performance of the developed algorithm are presented.

optical devices, image processing, machine vision, blurred image, computation errors, convolution.

Kozak AV, Steinberg OB, Steinberg BY. An algorithm for the restoration of blurred image obtained with a rotating camera tilted to the horizon. Computer Optics 2020; 44(2): 229-235. DOI: 10.18287/2412-6179-CO-598.

The work was done with the financial support of the Southern Federal University.


  1. Kozak AV, Steinberg BY, Steinberg OB. Fast and accurate restoration of blurred image obtained by rotating the camera. Proceedings of the 12th Central and Eastern European Software Engineering Conference in Russia CEESECR'16 2016: 11. DOI: 10.1145/3022211.3022222.
  2. Kozak AV, Steinberg BY, Steinberg OB. Fast recovery of a blurred image obtained with a horizontally rotating camera. Computer Optics 2018; 42(6): 1046-1053. DOI: 10.18287/2412-6179-2018-42-6-1046-1053.
  3. Kozak AV, Steinberg BY, Steinberg OB. The discrete convolution equation with the characteristic function of a segment and its application. In Book: Transactions of Scientific School of I.B. Simonenko. Issue 2. Rostov-on-Don: Publishing House of the Southern Federal University; 2015: 157-167.
  4. Kozak AV, Steinberg BY, Steinberg OB. Estimation of errors in solving the convolution equation for reconstructing blurred images [In Russian]. Abstracts of the International Conference «Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VI». Rostov-on-Don: 2016.
  5. Kozak AV, Steinberg BY, Steinberg OB. Development of studies on the fast reconstruction of a blurred image [In Russian]. Abstracts of the International Conference «Modern Methods, Problems and Applications Of Operator Theory and Harmonic Analysis VII». Rostov-on-Don: 2017: 28-29.
  6. Graham SL, Snir M, Patterson CA. Getting up to speed: The future of supercomputing. Washington: National Academies Press, 2005. ISBN: 978-0-309-09502-0.
  7. Lucy LB. An iterative technique for the rectification of observed distributions. Astron J 1974; 79: 745. DOI: 10.1086/111605.
  8. Richardson WH. Bayesian-based iterative method of image restoration. J Opt Soc Am 1972; 62(1): 55-59. DOI: 10.1364/JOSA.62.000055.
  9. Whyte O, Sivic J, Zisserman A, Ponce J. Non-uniform deblurring for shaken images. Int J Comput Vis 2012; 98(2): 168-186. DOI: 10.1007/s11263-011-0502-7.
  10. Kornilova AV, Kirilenko IA. MEMS-sensors in Computer Vision: we underestimate them [In Russian]. Software Engineering Conference Russia CEE-SECR '17. Source: <http://2017.secr.ru/program/submitted-presentations/memssensors-in-computer-vision>.
  11. Fursov VA. Constructing a quadratic-exponential FIR-filter with an extended frequency response midrange. Computer Optics 2018; 42(2): 297-305. DOI: 10.18287/2412-6179-2018-42-2-297-305.
  12. Fursov VA, Goshin YeV, Medvedev KS. Technology of enhancing image detalization with nonlinear correction of highly gradient fragments. Computer Optics 2019; 43(3): 484-491. DOI: 10.18287/2412-6179-2019-43-3-484-491.
  13. Dronnikova SA, Gurov IP. Image quality enhancement by processing of video frames with different exposure time. Scientific and Technical Journal of Information Technologies, Mechanics and Optics 2017; 17(3): 424-430. DOI: 10.17586/2226-1494-2017-17-3-424-430.
  14. Gurov IP, Smirnov DS. Improving the quality of images by the method of Van Zittert [In Russian]. Sci Tech J Inf Technol Mech Opt 2002; 6: 178-182.
  15. Gruzman IS, Kirichuk ВС, Kosykh VP, Peretyagin GI, Spektor AA. Digital processing of images in information systems [In Russian]. Novosibirsk: Publishing house of NSTU; 2000.
  16. Tsyganova, YV, Kulikova, MV. On modern array algorithms for optimal discrete filtering. Bulletin of the South Ural State University, Series “Mathematical Modelling, Programming and Computer Software” 2018; 11(4): 5-30. DOI: 10.14529/mmp180401.
  17. Cho S, Lee S. Fast motion deblurring. ACM Transactions on Graphics 2009; 28(5): 145. DOI: 10.1145/1618452.1618491.
  18. Smith Ch. Types of panoramic photography. Source: <https://www.picturecorrect.com/tips/types-of-panoramic-photography/>.
  19. PROPHOTOS. Panoramic shooting. Part 1 [In Russian]. Source: <https://prophotos.ru/lessons/17978-snimaem-panoramy-chast-1>.
  20. Alekseev V. Panoramic shooting: the basics of technology. [In Russian]. Source: <https://rosphoto.com/ublogs/panoramnaya-siemka-5411>.
  21. Adarve JD, Mahony R. Spherepix: a data structure for spherical image processing. Source: <https://www.researchgate.net/publication/311893485_Spherepix_a_Data_Structure_for_Spherical_Image_Processing>.

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