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Static and Dynamic Texture Mixing Using Optimal Transport

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Scale Space and Variational Methods in Computer Vision (SSVM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7893))

Abstract

This paper tackles the problem of mixing static and dynamic texture by combining the statistical properties of an input set of images or videos. We focus on Spot Noise textures that follow a stationary and Gaussian model which can be learned from the given exemplars. From here, we define, using Optimal Transport, the distance between texture models, derive the geodesic path, and define the barycenter between several texture models. These derivations are useful because they allow the user to navigate inside the set of texture models, interpolating a new one at each element of the set. From these new interpolated models, new textures can be synthesized of arbitrary size in space and time. Numerical results obtained from a library of exemplars show the ability of our method to generate new complex and realistic static and dynamic textures.

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References

  1. Popat, K., Picard, R.W.: Novel cluster-based probability model for texture synthesis, classification, and compression. In: Visual Communications and Image Processing, pp. 756–768 (1993)

    Google Scholar 

  2. Efros, A.A., Leung, T.K.: Texture synthesis by non-parametric sampling. In: Proc. of ICCV 1999, p. 1033 (1999)

    Google Scholar 

  3. Wei, L.Y., Lefebvre, S., Kwatra, V., Turk, G.: State of the art in example-based texture synthesis. In: Eurographics 2009, State of the Art Report, EG-STAR. Eurographics Association (2009)

    Google Scholar 

  4. Portilla, J., Simoncelli, E.P.: A parametric texture model based on joint statistics of complex wavelet coefficients. Int. Journal of Computer Vision 40, 49–70 (2000)

    Article  MATH  Google Scholar 

  5. Zhu, S.C., Wu, Y., Mumford, D.: Filters, random fields and maximum entropy (FRAME): Towards a unified theory for texture modeling. International Journal of Computer Vision 27, 107–126 (1998)

    Article  Google Scholar 

  6. Kwatra, V., Schödl, A., Essa, I., Turk, G., Bobick, A.: Graphcut textures: image and video synthesis using graph cuts. ACM Trans. Graph. 22, 277–286 (2003)

    Article  Google Scholar 

  7. Galerne, B., Gousseau, Y., Morel, J.M.: Random phase textures: Theory and synthesis. IEEE Transactions on Image Processing 20, 257–267 (2011)

    Article  MathSciNet  Google Scholar 

  8. van Wijk, J.J.: Spot noise texture synthesis for data visualization. In: Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1991, pp. 309–318. ACM, New York (1991)

    Chapter  Google Scholar 

  9. Wei, L.Y., Levoy, M.: Fast texture synthesis using tree-structured vector quantization. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2000, pp. 479–488. ACM Press/Addison-Wesley Publishing Co., New York (2000)

    Chapter  Google Scholar 

  10. Doretto, G., Chiuso, A., Wu, Y., Soatto, S.: Dynamic textures. International Journal of Computer Vision 51, 91–109 (2003)

    Article  MATH  Google Scholar 

  11. Doretto, G., Jones, E., Soatto, S.: Spatially homogeneous dynamic textures. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004, Part II. LNCS, vol. 3022, pp. 591–602. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Xia, G.S., Ferradans, S., Peyré, G., Aujol, J.F.: Compact representations of stationary dynamic textures. In: Proc. ICIP 2012 (2012)

    Google Scholar 

  13. Bar-Joseph, Z., El-Yaniv, R., Lischinski, D., Werman, M.: Texture mixing and texture movie synthesis using statistical learning. IEEE Tr. on Vis. and Comp. Graph. 7, 120–135 (2001)

    Article  Google Scholar 

  14. Matusik, W., Zwicker, M., Durand, F.: Texture design using a simplicial complex of morphable textures. ACM Transactions on Graphics 24, 787–794 (2005)

    Article  Google Scholar 

  15. Rabin, J., Peyré, G., Delon, J., Bernot, M.: Wasserstein barycenter and its application to texture mixing. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 435–446. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  16. Moisan, L.: Periodic plus smooth image decomposition. Journal of Mathematical Imaging and Vision 39, 161–179 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Villani, C.: Topics in Optimal Transportation. American Mathematical Society (2003)

    Google Scholar 

  18. Dowson, D.C., Landau, B.V.: The fréchet distance between multivariate normal distributions. J. Multivariate Anal. 3, 450–455 (1982)

    Article  MathSciNet  Google Scholar 

  19. Takatsu, A.: Wasserstein geometry of gaussian measures. Osaka J. Math (2011)

    Google Scholar 

  20. Agueh, M., Carlier, G.: Barycenters in the wasserstein space. SIAM J. on Mathematical Analysis 43, 904–924 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Knott, M., Smith, C.S.: On a generalization of cyclic monotonicity and distances among random vectors. Linear Algebra and its Applications 199, 363–371 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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Ferradans, S., Xia, GS., Peyré, G., Aujol, JF. (2013). Static and Dynamic Texture Mixing Using Optimal Transport. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2013. Lecture Notes in Computer Science, vol 7893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38267-3_12

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  • DOI: https://doi.org/10.1007/978-3-642-38267-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38266-6

  • Online ISBN: 978-3-642-38267-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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