УДК: 004.932.2

Method of prediction based on algorithmic probability in the problem of image restoration in missing regions

Potapov, A.S., Shcherbakov, O.V., Zhdanov, I.N.

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Потапов А.С., Щербаков О.В., Жданов И.Н. Метод предсказания на основе алгоритмической вероятности в задаче восстановления изображений в утерянных областях // Оптический журнал. 2013. Т. 80. № 11. С. 48–53.

Potapov, A. S., Shcherbakov O. V., Zhdanov I. N. Method of prediction based on algorithmic probability in the problem of image restoration in missing regions [in Russian] // Opticheskii Zhurnal. 2013. V. 80. № 11. P. 48–53.

For citation (Journal of Optical Technology):

A. S. Potapov, O. V. Shcherbakov, and I. N. Zhdanov, "Method of prediction based on algorithmic probability in the problem of image restoration in missing regions," Journal of Optical Technology. 80(11), 680-684 (2013). https://doi.org/10.1364/JOT.80.000680

Abstract:

This paper discusses the criterion of algorithmic probability, which offers a general solution to the question of extrapolating symbolic strings. The given criterion extends the theoretical-informational approach based on algorithmic complexity, which is widely used to synthesize image-analysis methods. Methodological recommendations are given concerning the practical application of the algorithmic-probability criterion when processing and analyzing images. As an example, a method is developed for restoring images in missing regions, which can be implemented on a computer by narrowing an algorithmically complete space of models of images to a set of their Fourier transforms.

Keywords:

algorithmic probability, image reconstruction, Fourier transform

References:

1. Q. Luo and T. M. Khoshgoftaar, “Unsupervised multiscale color image segmentation based on MDL principle,” IEEE Trans. Image Process. 15, 2755
(2006).
2. T. Lindeberg and M.-X. Li, “Segmentation and classification of edges using minimum description length approximation and complementary junction
cues,” Comput. Vis. Image Underst. 67, No. 1, 88 (1997).
3. A. Ward and Gh. Hamarneh, “Statistical shape modeling using MDL incorporating shape, appearance, and expert knowledge,” Lect. Notes Comput.
Sci., 4791, 278 (2007).
4. A. Lanterman, “Minimum description length understanding of infrared scenes,” Proc. SPIE 3371, 375 (1998).
5. M. Li, Q. Gao, and P. M. B. Vitanyi, “Recognizing on-line handwritten characters using MDL,” Proceedings of the IEEE Information Theory Workshop, 1993, pp. 24–25

6. Y. G. Leclerq, Q.-T. Luong, and P. Fua , “Self-consistency and MDL: a paradigm for evaluating point-correspondence algorithms, and its application to
detecting changes in surface elevation,” Int. J. Comput. Vis. 51, No. 1, 63 (2003).
7. A.-R. Mansouri and J. Konrad, “Minimum description length region tracking with level sets,” Proc. SPIE 3974, 515 (2000).
8. R. Solomonoff, Does Algorithmic Probability Solve the Problem of Induction? (Oxbridge Research, Cambridge, Mass., 1997).
9. R. Solomonoff, “Algorithmic probability, heuristic programming and AGI,” in Advances in Intelligent Systems Research, E. Baum, M. Hutter,
and E. Kitzelmann, eds. (2010), vol. 10, pp. 151–157.
10. A. S. Potapov, “Choosing image representations based on the minimization of the representation length of their description,” Izv. Vyssh. Uchebn.
Zaved. Prib. 51, No. 7, 3 (2008).
11. P. Arias, V. Caselles, and G. Sapiro, “A variational framework for non-local image inpainting,” in Proceedings of EMMCVPR’09, 2009, pp. 345–358.
12. T. Shibata, A. Iketani, and Sh. Senda, “Fast and structure-preserving inpainting based on probabilistic structure estimation,” in MVA2011
IAPR Conference on Machine Vision Applications, Nara, Japan, 2011, pp. 22–25