Stochastic Methods for Image Analysis

  • Agnès DesolneuxEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2237)


These lectures about stochastic methods for image analysis contain three parts. The first part is about visual perception and the non-accidentalness principle. It starts with an introduction to the Gestalt theory, that is a psychophysiological theory of human visual perception. It can be translated into a mathematical framework thanks to a perception principle called the non-accidentalness principle, that roughly says that “we immediately perceive in an image what has a low probability of coming from an accidental arrangement”. The second part of these lectures is about the so-called “a contrario method” for the detection of geometric structures in images. The a contrario method is a generic method, based on the non-accidentalness principle, to detect meaningful geometric structures in images. We first show in details how it works in the case of the detection of straight segments. Then, we show some other detection problems (curves, vanishing points, etc.) The third part of these lectures is about stochastic models of images for the problem of modeling and synthesizing texture images. It gives an overview of some methods of texture synthesis. We also discuss two models of texture images: stationary Gaussian random fields and shot noise random fields.


  1. 1.
    C. Aguerrebere, Y. Gousseau, G. Tartavel, Exemplar-based texture synthesis: the Efros–Leung algorithm. Image Process. Line 3, 223–241 (2013). CrossRefGoogle Scholar
  2. 2.
    A. Almansa, A. Desolneux, S. Vamech, Vanishing point detection without any a priori information. IEEE Trans. Pattern Anal. Mach. Intell. 25(4), 502–507 (2003)CrossRefGoogle Scholar
  3. 3.
    F. Attneave, Some informational aspects of visual perception. Psychol. Rev. 61, 183–193 (1954)CrossRefGoogle Scholar
  4. 4.
    S. Blusseau, A. Carboni, A. Maiche, J.-M. Morel, R. Grompone von Gioi, A psychophysical evaluation of the a contrario detection theory, in Proceedings of the 2014 IEEE International Conference on Image Processing (ICIP) (IEEE, Piscataway, 2014), pp. 1091–1095Google Scholar
  5. 5.
    C. Bordenave, Y. Gousseau, F. Roueff, The dead leaves model: an example of a general tesselation. Adv. Appl. Probab. 38(1), 31–46 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    T. Briand, J. Vacher, B. Galerne, J. Rabin, The Heeger & Bergen pyramid based texture synthesis algorithm. Image Process. Line 4, 276–299 (2014). CrossRefGoogle Scholar
  7. 7.
    F. Cao, Good continuation in digital images, in Proceedings of the International Conference on Computer Vision (ICCV) (2003), pp. 440–447Google Scholar
  8. 8.
    F. Cao, J. Delon, A. Desolneux, P. Musé, F. Sur, A unified framework for detecting groups and application to shape recognition. J. Math. Imaging Vis. 27(2), 91–119 (2007).MathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Ciomaga, P. Monasse, J.-M. Morel, The image curvature microscope: accurate curvature computation at subpixel resolution. Image Process. Line 7, 197–217 (2017). MathSciNetCrossRefGoogle Scholar
  10. 10.
    D. Coupier, A. Desolneux, B. Ycart, Image denoising by statistical area thresholding. J. Math. Imaging Vis. 22(2–3), 183–197 (2005)MathSciNetCrossRefGoogle Scholar
  11. 11.
    A. Desolneux, L. Moisan, J.-M. Morel, Meaningful alignments. Int. J. Comput. Vis. 40(1), 7–23 (2000)CrossRefGoogle Scholar
  12. 12.
    A. Desolneux, L. Moisan, J.-M. Morel, Edge detection by Helmholtz principle. J. Math. Imaging Vis. 14(3), 271–284 (2001)CrossRefGoogle Scholar
  13. 13.
    A. Desolneux, L. Moisan, J.-M. Morel, Maximal meaningful events and applications to image analysis. Ann. Stat. 31(6), 1822–1851 (2003)MathSciNetCrossRefGoogle Scholar
  14. 14.
    A. Desolneux, L. Moisan, J.-M. Morel, From Gestalt Theory to Image Analysis: A Probabilistic Approach (Springer, Berlin, 2008)CrossRefGoogle Scholar
  15. 15.
    A. Desolneux, L. Moisan, S. Ronsin, A compact representation of random phase and Gaussian textures, in 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE, Piscataway, 2012), pp. 1381–1384Google Scholar
  16. 16.
    A.A. Efros, T.K. Leung, Texture synthesis by non-parametric sampling, in Proceedings of the IEEE International Conference on Computer Vision (ICCV 1999), vol. 2 (IEEE, Piscataway, 1999), pp. 1033–1038Google Scholar
  17. 17.
    B. Galerne, Y. Gousseau, J.-M. Morel, Random phase textures: theory and synthesis. IEEE Trans. Image Process. 20(1), 257–267 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    B. Galerne, Y. Gousseau, J.-M. Morel, Micro-texture synthesis by phase randomization. Image Process. Line 1, 213–237 (2011). CrossRefGoogle Scholar
  19. 19.
    L.A. Gatys, A.S. Ecker, M. Bethge, Texture synthesis using convolutional neural networks, in Proceedings of the Conference on Neural Information Processing Systems, 2015 (2015), pp. 262–270Google Scholar
  20. 20.
    R. Grompone von Gioi, G. Randall, Unsupervised smooth contour detection. Image Process. Line 6, 233–267 (2016). MathSciNetCrossRefGoogle Scholar
  21. 21.
    R. Grompone von Gioi, J. Jakubowicz, J.-M. Morel, G. Randall, A fast line segment detector with a false detection control. IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732 (2010)CrossRefGoogle Scholar
  22. 22.
    R. Grompone von Gioi, J. Jakubowicz, J.-M. Morel, G. Randall, LSD: a line segment detector. Image Process. Line 2, 35–55 (2012). CrossRefGoogle Scholar
  23. 23.
    P.E. Hart, How the Hough transform was invented. IEEE Signal Process. Mag. 26(6), 18–22 (2009)CrossRefGoogle Scholar
  24. 24.
    D.J. Heeger, J.R. Bergen, Pyramid-based texture analysis/synthesis, in Proceedings of the Conference SIGGRAPH ’95 (IEEE, Piscataway, 1995), pp. 229–238Google Scholar
  25. 25.
    G. Kanizsa, Grammatica del Vedere/La Grammaire du Voir (Bologna/Éditions Diderot, Arts et Sciences, IL Mulino, 1980/1997)Google Scholar
  26. 26.
    E. Levina, P.J. Bickel, Texture synthesis and nonparametric resampling of random fields. Ann. Stat. 35(4), 1751–1773 (2006)MathSciNetCrossRefGoogle Scholar
  27. 27.
    D. Lowe, Perceptual Organization and Visual Recognition (Kluwer Academic Publishers, Dordecht, 1985)CrossRefGoogle Scholar
  28. 28.
    W. Metzger, Gesetze des Sehens (Kramer, Frankfurt, 1953).Google Scholar
  29. 29.
    L. Moisan, Periodic plus smooth image decomposition. J. Math. Imaging Vis. 39(2), 161–179 (2011)MathSciNetCrossRefGoogle Scholar
  30. 30.
    L. Moisan, B. Stival, A probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix. Int. J. Comput. Vis. 57(3), 201–218 (2004)CrossRefGoogle Scholar
  31. 31.
    P. Musé, F. Sur, F. Cao, Y. Gousseau, Unsupervised thresholds for shape matching, in Proceedings 2003 International Conference on Image Processing (ICIP 2003), vol. 2 (IEEE, Piscataway, 2003), pp. 647–650Google Scholar
  32. 32.
    A.V. Oppenheim, J.S. Lim, The importance of phase in signals. IEEE Proc. 69, 529–541 (1981)CrossRefGoogle Scholar
  33. 33.
    J. Portilla, E.P. Simoncelli, A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. Comput. Vis. 40(1), 49–71 (2000)CrossRefGoogle Scholar
  34. 34.
    L. Raad, A. Desolneux and J.-M. Morel, A conditional multiscale locally Gaussian texture synthesis algorithm. J. Math. Imaging Vis. 56(2), 260–279 (2016)MathSciNetCrossRefGoogle Scholar
  35. 35.
    J. Rabin, J. Delon, Y. Gousseau, A statistical approach to the matching of local features. SIAM J. Imag. Sci. 2(3), 931–958 (2009)MathSciNetCrossRefGoogle Scholar
  36. 36.
    N. Sabater, A. Almansa, J.-M. Morel, Meaningful matches in stereovision. IEEE Trans. Pattern Anal. Mach. Intell. 34(5), 930–942 (2012)CrossRefGoogle Scholar
  37. 37.
    L. Santalo, Integral Geometry and Geometric Probability, 2nd edn. (Cambridge University Press, Cambridge, 2004)CrossRefGoogle Scholar
  38. 38.
    A. Srivastava, X. Liu, U. Grenander, Universal analytical forms for modeling image probabilities. IEEE Trans. Pattern Anal. Mach. Intell. 24(9), 1200–1214 (2002)CrossRefGoogle Scholar
  39. 39.
    G.Tartavel, Y. Gousseau, G. Peyré, Variational texture synthesis with sparsity and spectrum constraints. J. Math. Imaging Vis. 52(1), 124–144 (2015)MathSciNetCrossRefGoogle Scholar
  40. 40.
    J.J. van Wijk, Spot noise texture synthesis for data visualization, in Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’91 (ACM, New York, 1991), pp. 309–318CrossRefGoogle Scholar
  41. 41.
    T. Veit, F. Cao, P. Bouthemy, An a contrario decision framework for region-based motion detection. Int. J. Comput. Vis. 68(2), 163–178 (2006)CrossRefGoogle Scholar
  42. 42.
    M. Wertheimer, Unterzuchungen zur lehre der gestalt. Psychol. Forsch. 4(1), 301–350 (1923)CrossRefGoogle Scholar
  43. 43.
    S.C. Zhu, Embedding gestalt laws in markov random fields. IEEE Trans. Pattern Anal. Mach. Intell. 21(11), 1170–1187 (1999)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CNRSCMLA and ENS Paris-SaclayParisFrance

Personalised recommendations