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Synthesis of the rotational blur kernel in a digital image using measurements of a triaxial gyroscope
N.N. Vasilyuk 1

1 Electrooptika, LLC, 107076, Moscow, Russia, Stromynka, d.18, k.1

 PDF, 1184 kB

DOI: 10.18287/2412-6179-CO-1081

Pages: 763-773.

Full text of article: Russian language.

Abstract:
A method for calculating of a blur kernel arising from the rotation of a digital camera is proposed. The rotation is measured with a three-axis gyroscope attached to the camera. Differential equations of a continuous trajectory of the rotational blur starting from a selected pixel are obtained. These equations are presented both in the form of an explicit system of differential equations for the blur curve in the focal plane and in the form of a matrix equation for the increment of the camera attitude. An expression is given for the integral of the energy illumination from a point light source along the continuous blur trajectory. The integral takes into account the point spread function and the aperture functions of individual photosensitive cells of the photodetector array. The calculation of the integral values for all photosensitive cells illuminated with the point source gives a discrete kernel of rotational blur starting at the selected pixel. Algorithms for the numerical integration of the blur equations are described. The analysis of the blur equations are carried out, characteristic features of the kernels are highlighted and their non-homogeneity is shown, with the kernels of rotational blur revealed not to coincide with each other for different pixels. An example of the synthesis of the blur kernels for given rotation parameters of the digital camera is given.

Keywords:
blur kernel, blur correction, rotational blur, gyroscope, matched filter.

Citation:
Vasilyuk NN. Synthesis of the rotational blur kernel in a digital image using measurements of a triaxial gyroscope. Computer Optics 2022; 46(5): 763-773. DOI: 10.18287/2412-6179-CO-1081.

References:
  1. Pashkov VS. Influence of the image “blurring” on accuracy estimates of its coordinates [In Russian]. In Book: Mechanics, control and informatics. collection of works. IKI RAN Publisher; 2009: 225-230.
  2. Titkov BV, Komrakov DN, Krasnov AS, Konishev AS. Compensation of the images linear velocity blur [In Russian]. Proc A F Mozhaisky Military Space Academy 2012; 636: 50-53.
  3. Kokoshkin AV, Korotkov VA, Korotkov KV, Novichikhin EP. Blind reconstruction of images distorted by blur and defocus with unknown shape and parameters of the instrumentation function [In Russian]. Journal of Radio Electronics 2014; 9: 4.
  4. Breykina KV, Umnyashkin SV. Image quality estimation for blur compensation using Lucy–Richardson method [In Russian]. Proc Univ Electronics 2020; 25(2): 167-174. DOI: 10.24151/1561-5405-2020-25-2-167-174.
  5. Tselousov AV. Motion blur compensation for digitail images restoration using generative adversarial network [In Russian]. Proc DSPA 2018; 8(3): 213-217.
  6. Fursov VA. Image restoration with fir filters constructed by direct identification of the inverse tract [In Russian]. Computer Optics 1996; 16: 103-108.
  7. Vasilyuk NN. Electronic correction of blurred images in the scanning optoelectronic system [In Russian]. Electromagnetic Waves and Electronic Systems 2009; 14(12): 41-48.
  8. Vasilyuk NN. Differential equation of the blur trajectory for the scanning optoelectronic system [In Russian]. Electromagnetic Waves and Electronic Systems 2009; 14(12): 49-51.
  9. Smirnov PV, Tashlinsky AG. Algorithm for compensating for the blurring effect of a moving object in a sequence of frames [In Russian]. Radioelectronic Technique 2013; 1: 141-145.
  10. Karnaukhov VN, Mozerov MG. Reconstruction of multispectral images by the gradient reconstruction method and estimation of blur parameters based on the multipurpose matching model [In Russian]. Information Processes 2016; 16(2): 162-169.
  11. 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.
  12. Smirnov PV, Tashlinsky AG, Смирнов ПВ. Algorithm for the selection of a moving object in the sequence of images with compensation for the "blur" effect [In Russian]. Radioelectronic Technique 2015; 1(7): 121-130.
  13. Smirnov PV, Voronov ID. Using disparity field estimates to compensate for the blur effect of fast-moving objects [In Russian]. Radioelectronic Technique 2017; 1(10): 106-110.
  14. Akimenko TA, Larkin EV, Luchansky OA. Estimation of the image blur in the vision system of a mobile wheeled robot [In Russian]. Bulletin of the Ryazan State Radio Engineering University 2008; 23: 84-87.
  15. Oktyabrsky VV, Ostrovsky AS, Salaman RS. Compensation technique for an unevenly distributed blur of aerial photographs of multi-matrix digital aerial cameras for planned-perspective shooting in conditions of insufficient illumination of the terrain [In Russian]. Proc A F Mozhaisky Military Space Academy 2021; 677: 107-117.
  16. Ruzavin AV. Compensation of image motion blurring on the basis indications of the camcorder's inertial sensors [In Russian]. Proceedings of the Saint-Petersburg State University of Aerospace Instrumentation Research Conference 2018: 241-244.
  17. Bessonov RV, Belinskaya EV, Brysin NN, Voronkov SV, Kurkina AN, Forsh AA. Star trackers in astroinertial systems of flying vehicles [In Russian]. Current Problems in Remote Sensing of the Earth from Space 2018; 15(6): 9-20. DOI: 10.21046/2070-7401-2018-15-6-9-20.
  18. Shah CA, Schickler W. Automated blur detection and removal in airborne imaging systems using IMU data. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (2012 XXII ISPRS Congress) 2012; XXXIX-B1: 321-323. DOI:10.5194/isprsarchives-XXXIX-B1-321-2012.
  19. Joshi N, Kang SB, Zitnick CL, Szeliski R. Image deblurring using inertial measurement sensors. ACM Trans Graph 2010; 29(4): 30. DOI: 10.1145/1778765.1778767.
  20. Zhang Y, Hirakawa K. Combining inertial measurements with blind image deblurring using distance transform. IEEE Trans Comput Imaging 2016; 2(3): 281-293. DOI: 10.1109/TCI.2016.2561701.
  21. Bae H, Fowlkes CC, Chou PH. Accurate motion deblurring using camera motion tracking and scene depth. 2013 IEEE Workshop on Applications of Computer Vision 2013: 148-153. DOI: 10.1109/WACV.2013.6475012.
  22. Hu Z, Yuan L, Lin S, Yang MH. Image deblurring using smartphone inertial sensors. 2016 IEEE Conf on Computer Vision and Pattern Recognition 2016: 1855-1864. DOI: 10.1109/CVPR.2016.205.
  23. Yang C, Feng H, Xu Z, Chen Y, Li Q. Image deblurring utilizing inertial sensors and a short-long-short exposure strategy. IEEE Trans Image Process 2020; 29: 4614-4626. DOI: 10.1109/TIP.2020.2973499.
  24. Sörös G, Münger S, Beltrame C, Humair L. Multiframe visual-inertial blur estimation and removal for unmodified smartphones. J WSCG 2015; 23(2): 101-109.
  25. Gebgart AY, Kolosov MP. Design features of the lens objectives of celestial-orientation apparatus for spacecraft. J Opt Tech 2015; 82(6): 357-360. DOI 10.1364/JOT.82.000357.
  26. Baranov PS, Mantsvetov AA. Optimization of the ratio of the lens scattering circle radius to the pixel size to improve the accuracy of estimating the coordinates of images of small objects [In Russian]. Proc Higher Educational Institutions of Russia. Radio Electronics 2016; 2: 49-53.
  27. Prokhorov ME, Zakharov AI, Touchin MS. Optimum characteristics of the star tracker optical system and matrix photosensor [In Russian]. In Book: Avanesov GA, ed. Modern problems of orientation and navigation of spacecraft: Proceedings of the all-russian scientific and technical conference. Moscow: IKI RAN Publisher; 2013: 80-90.

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