Fast bilateral filtering of aerial images based on decomposition of spatial filters

Mathematical support and software for computers, complexes and networks


Belyaeva O. V.1*, Paschenko O. B.2**, Philippov M. V.2***

1. Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia
2. Russian Aircraft Corporation «MiG», 7, 1st Botkinsky passage, Moscow, 125284, Russia



The paper considers the problem of fast bilateral filtering of aerial photographs, which allows eliminate small-sized noise and interference, while maintaining sharp boundaries of the objects, necessary for the initial frame processing. Hence, the emphasis is increasing the rate of bilateral filtration as an important stage of the frames processing and restoration. To solve the problem, a fast method of bilateral filtering based on decomposition into independent spatial filters, which allow aerial photographs filtering by several processes simultaneously is considered.

To achieve the processing speed of the bilateral filter, a method based on decomposition into recursive Gaussian spatial filters is proposed. Unlike the ordinary bilateral filtration, the presented filter can be parallelized. According to the method, N sets of linear independent filters (components) are computed based on N ranges of pixel intensities on the processed frame. The number of ranges is user-defined (from 2 to 255). The remaining components are computed by bilinear interpolation from the already obtained components. Each component requires computation of two filters, rank and spatial. Hence, the computational complexity of the method will depend on the calculation of the spatial filters in the N components.

The Gauss kernel approximation proposed by Deriche are used in the article for the spatial filters quick computing. This allows increasing the rate by several times, using the pre-calculated filter coefficients that specify the form of the Gaussian function, instead of costly computing the Gaussian distribution of each pixel in the frame. The coefficients are calculated from the infinite impulse response of the Gaussian filter, which can be represented by a recursive sequence with constant coefficients.

Thus, the article reduces the time of bilateral filtration due to bilinear interpolation over N independent spatial filters. The time for calculating the spatial filters is reduced due to the use of the fast Gaussian filtering method by Deriche based on constant coefficients. The article also uses parallel calculation of independent components of the proposed method of bilateral filtration. The steps, proposed in this article allow get real-time results.


aerial photography, bilateral filtering, recursive Gaussian filter, parallelization


  1. Tomasi C., Manduchi R. Bilateral Filtering for Grey and Color Images. Proceedings of the 1998 IEEE International Conference on Computer Vision, Bombay, India, 1998, pp. 839–846.

  2. Buades, A., Coll, B., Morel, J.M. A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation, 2005, vol. 4, pp. 490-530.

  3. Yang, Q., Yang, R., Davis J., Nist´er D. Spatial-depth super resolution for range images. CVPR, IEEE Computer Society Conference on Computer Vision and Pattern, 2007, no.15, pp 1-8.

  4. Wong, W.C.K., Chung, A.C.S., Yu, S.C.H.: Trilateral filtering for biom dical images. In Proceedings of the IEEE International Symposium on Biomedical Imaging, 2004, pp. 820-823.

  5. Oh, B.M., Chen, M., Dorsey, J., Durand, F. Imagebased modeling and photo editing. Proceedings of the 28th annual conference on Computer graphics and interactive techniques Siggraph, 2001, pp. 433-442.

  6. Durand, F., Dorsey, J. Fast bilateral filtering for the display of high-dynamic-range images. Proceedings of the ACM SIGGRAPH conference, 2002, pp.253-263.

  7. Xiao, J., Cheng, H., Sawhney, H., Rao, C., Isnardi, M. Bilateral filtering-based optical flow estimation with occlusion detection. Computer Vision—ECCV 2006, 2006, vol. 21, pp. 211-224.

  8. Knyaz’ V.V., Busurin V.I. Trudy MAI, 2015, no. 81, available at:

  9. Porikli F. Constant time O(1) bilateral filtering. IEEE Conference on Computer Vision and Pattern Recognition, Anchorage, Alaska, USA, 2008, pp. 1–8.

  10. Yang Q., Tan K.-H., Ahuja N. Real-time O(1) bilateral filtering. In Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, (CVPR ’09), June 2009, pp. 557–564.

  11. Deriche R. Recursively implementing the gaussian and its derivatives. In Proceedings of IEEE International Conference on Image Processing, (ICIP ’92), 1992, pp. 263–267.

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