Abstract
Unlike conventional perspectives cameras, omnidirectional cameras allow to capture images with a large field of view. However, the resulting images contain important distortions that need to be taken into account in any image processing task. In this paper, we introduce a novel approach for omnidirectional images motion deblurring. We propose to adapt the Wiener deconvolution technique in order to takes into account the omnidirectional images geometry. We present a reformulation of the motion deblurring problem on the sphere which is considered as the most appropriate space for omnidirectional image processing. For this purpose, we develop a spherical Wiener filter using the necessary mathematical tools for spherical images processing and we model the motion blur using the velocity fields estimated via our omnidirectional optical flow estimation method. Experimental results show that our approach performs well on real and synthetic omnidirectional images.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bascle, B., Blake, A., Zisserman, A.: Motion deblurring and super-resolution from an image sequence. In: Buxton, B., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1065, pp. 571–582. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61123-1_171
Stern, A., Kopeika, N.S.: Analytical method to calculate optical transfer functions for image motion using moments and its implementation in image restoration. In: Proceedings of SPIE 2827, Digital Image Recovery and Synthesis III, 25 October 1996. https://doi.org/10.1117/12.255083
Yitzhaky, Y., Boshusha, G., Levy, Y., Kopeika, N.S.: Restoration of an image degraded by vibrations using only a single frame. Opt. Eng. 39(8) (2000). https://doi.org/10.1117/1.1305319
Zhang, Y., Wen, C., Zhang, Y.: Estimation of motion parameters from blurred images. Pattern Recogn. Lett. 21(5), 425–433 (2000). https://doi.org/10.1016/S0167-8655(00)00014-3. ISSN 0167–8655
Levin, A., Durand, R.F.F., Freeman, W.T.: Image and depth from a conventional camera with a coded aperture. ACM Trans. Graph. 26(3), 70-es (2007). https://doi.org/10.1145/1276377.1276464
Krishnan, D., Fergus, R.: Fast image deconvolution using hyper-Laplacian priors. In: Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference, pp. 1033–1041 (2009). https://doi.org/10.1145/1531326.1531402
Schmidt, U., Rother, C., Nowozin, S., Jancsary, J., Roth, S.: Discriminative non-blind deblurring. In: IEEE Conference on Computer Vision and Pattern Recognition 2013, pp. 604–611 (2013). https://doi.org/10.1109/CVPR.2013.84
Woods, J., Ingle, V.: Kalman filtering in two dimensions: further results. IEEE Trans. Acoust. Speech Signal Process. 29(2), 188–197 (1981). https://doi.org/10.1109/TASSP.1981.1163533
Miller, K.: Least squares methods for ill-posed problems with a prescribed bound. SIAM J. Math. Anal. 1, 52–74 (1970)
Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-posed Problems. John Wiley Sons, Washington, D.C.: V. H. Winston Sons, New York (1977)
Wiener, N.: Extrapolation, interpolation, and smoothing of stationary time series: with engineering applications. MIT Press 113(21), 1043–54 (1949)
Alibouch, B., Radgui, A., Demonceaux, C., Rziza, M., Aboutajdine, D.: A phase-based framework for optical flow estimation on omnidirectional images. SIViP 10(2), 285–292 (2014). https://doi.org/10.1007/s11760-014-0739-z
Surin, I., Fety, L.: Filtrage de Wiener adaptatif appliqué á la restauration d’images. In: 15eme colloque sur le traitement du signal et des images, Juan-Les-Pins, France, 18–21 septembre 1995, September 1995
Bigot-Marchand, S., Kachi, D., Durand, S., Mouaddib, El.M.: Spherical image denoising and its application to omnidirectional imaging. In: International Conference on Computer Vision Theory and Applications, Spain (2007)
Bigot, S., Kachi, D., Durand, S.: Spherical edge detector: application to omnidirectional imaging. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2008. LNCS, vol. 5259, pp. 554–565. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88458-3_50
Bigot-Marchand, S.: Image processing tools for omnidirectional vision. Theses, Université de Picardie Jules Verne, Octobre 2008
Driscoll, J.R., Healy, D.M.: Computing Fourier transforms and convolutions on the 2-Sphere. Adv. Appl. Math. 15(2), 202–250 (1994). https://doi.org/10.1006/aama.1994.1008. ISSN 0196–8858
Texin, C.: Optical flow using phase information for deblurring. Thesis (M. Eng.)-Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Alibouch, B., Rziza, M. (2021). Catadioptric Omnidirectional Images Motion Deblurring. In: Elbiaze, H., Sabir, E., Falcone, F., Sadik, M., Lasaulce, S., Ben Othman, J. (eds) Ubiquitous Networking. UNet 2021. Lecture Notes in Computer Science(), vol 12845. Springer, Cham. https://doi.org/10.1007/978-3-030-86356-2_25
Download citation
DOI: https://doi.org/10.1007/978-3-030-86356-2_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-86355-5
Online ISBN: 978-3-030-86356-2
eBook Packages: Computer ScienceComputer Science (R0)