Advertisement

Bayesian Inference for Layer Representation with Mixed Markov Random Field

  • Ru-Xin Gao
  • Tian-Fu Wu
  • Song-Chun Zhu
  • Nong Sang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4679)

Abstract

This paper presents a Bayesian inference algorithm for image layer representation [26], 2.1D sketch [6], with mixed Markov random field. 2.1D sketch is an very important problem in low-middle level vision with a synthesis of two goals: segmentation and 2.5D sketch, in other words, it is to consider 2D segmentation by incorporating occulision/depth explicitly to get the partial order of final segmented regions and contour completion in the same layer. The inference is based on Swendsen-Wang Cut (SWC) algorithm [4] where there are two types of nodes, instead of all nodes being the same type in traditional MRF model, in the graph representation: atomic regions and their open bonds desribed by address variables. These makes the problem a mixed random field. Therefore, two kinds of energies should be simultaneously minimized by maximizing a joint posterior probability: one is for region coloring/layering, the other is for the assignments of address variables. Given an image, its primal sketch is computed firstly, then some atomic regions can be obtained by completing some sketches into a closed contour. At the same time, T-junctions are detected and broken into terminators as the open bonds of atomic regions after being assigned the ownership between them and atomic regions. With this graph representation, the presented inference algorithm is performed and satisfactory results are shown in the experiments.

Keywords

Layer Representation 2.1D Sketch Bayesian Inference Contour Completion Mixed Markov Field Swendsen-Wang Cut MCMC 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Guo, C.E., Zhu, S.C., Wu, Y.N.: Modeling visual patterns by integrating descriptive and generative models. IJCV 53(1), 5–29 (2003)CrossRefGoogle Scholar
  2. 2.
    Guo, C.E., Zhu, S.C., Wu, Y.N.: Primal sketch: integrating texture and structure. In: Proc. Int’l. Conf. on Computer Vision (2003)Google Scholar
  3. 3.
    Barbu, A., Zhu, S.C.: Graph Partition by Swendsen-Wang Cuts. In: Proc. Int’l. Conf. on Computer Vision (2003)Google Scholar
  4. 4.
    Barbu, A., Zhu, S.C.: Generalizing Swendsen-Wang to Sampling Arbitrary Posterior Probabilities. IEEE Trans. on PAMI 27, 1239–1253 (2005)Google Scholar
  5. 5.
    Marr, D.: Vision. Freeman Publisher, San Francisco (1983)Google Scholar
  6. 6.
    Nitzberg, M., Shiota, T., Mumford, D.: Filtering, Segmentation and Depth. LNCS, vol. 662. Springer, Heidelberg (1993)zbMATHGoogle Scholar
  7. 7.
    Eseddoglu, S.: Segment Image With Depth but Without Detecting Junction. Journal of Mathematical Imaging and Vision 18 (2003)Google Scholar
  8. 8.
    Yu, S.X., Lee, T.S., Kanade, T.: A Hierarchical Markov Random Field Model for Figure-Ground Segregation. In: Figueiredo, M., Zerubia, J., Jain, A.K. (eds.) EMMCVPR 2001. LNCS, vol. 2134, pp. 118–133. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Chan, T., Shen, J.: Mathematical Models for Local Nontexture Inpaintings. SIAM Journal of Applied Mathematics 62, 1019–1043 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Bertalmio, M., Sapiro, G., Ballester, C.: Image Inpainting.Computer, Graphics, SIGGRAPH (2000)Google Scholar
  11. 11.
    Joyeux, L., Buisson, O., Besserer, B.: Detection and Removal of Line Scratches in Motion Picture Films. In: Proceedings of CVPR 1999. IEEE Int. Conf. on Computer Vision and Pattern Recognition, FortCollins (1999)Google Scholar
  12. 12.
    Joshi, S., Srivastava, A., Mio, W.: Hierarchical Organization of Shapes for Efficient Retrieval. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 570–591. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Kumar, M.P., Torr, Zisserman, P.H.S.: Obj. Cut. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 3 (2005)Google Scholar
  14. 14.
    Authors from the same group: Compositional boosting for computing hierarchical image structures. In: CVPR 2007 (submitted, 2007)Google Scholar
  15. 15.
    Kimia, B.B., Frankel, I., Popescu, A.M.: Euler spiral for shape completion. International journal of computer vision 54, 159–182 (2003)zbMATHCrossRefGoogle Scholar
  16. 16.
    Mumford, D., Shah, J.: Optimal approximations of piecewise smooth functions ans associated variatioanl problems. Comm. in pure and appl. Math 42, 577–685 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Saund, E.: Perceptual organization of occluding contours generated by opaque surfaces. CVPR 19999, 624–630 (1999)Google Scholar
  18. 18.
    Shum, H.: Prior, Context and Interactive Computer Vision. The Microsoft Research Asia Technical Report (2006)Google Scholar
  19. 19.
    Horn, B.K.P.: The curve of least energy. ACM Transactions on Mathematical Software 9, 441–460 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Ballester, C., Bertalmio, M., Caselles, V.: Filling-In by Joint Interpolation of Vector Fields and Gray Levels. IEEE Transactions on Image Processing 10, 1200–1211 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Kolmogorov, V., Zabih, R.: What Energy Functions Can Be Minimized via Graph Cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 147–159 (2004)CrossRefGoogle Scholar
  22. 22.
    Fridman, A.: Mixed Markov models. Applied mathematics. PNAS 100(14), 8092–8096 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Gilks, W.R., Richardson, S., Spiegelhalter: Markov Chain Monte Carlo In practive. Chapman and Hall, Sydney (1996)Google Scholar
  24. 24.
    Saund, E.: Perceptual organization of occluding contours generated by opaque surfaces. In: Proceedings of the 1999 Conference on Computer Vision and Pattern Recognition, pp. 624–630 (1999)Google Scholar
  25. 25.
    Geiger, D., Kumaran, K., Parida, L.: Visual organization for figure/ground separation. In: Proc. IEEE Conf. on Computer Vision and Pattern Recognition, pp. 155–160 (1996)Google Scholar
  26. 26.
    Adelson, E.A., Wang, J.Y.A.: Representing Moving Images with Layers. IEEE Trans. on Image Processing 3, 625–638 (1994)CrossRefGoogle Scholar
  27. 27.
    Wang, J., Gu, E., Betke, M.: MosaicShape: Stochastic Region Grouping with Shape Prior. Computer Vision and Pattern Recognition 1, 902–908 (2005)Google Scholar
  28. 28.
    Efros, A.A., Freeman, W.T.: Image Quilting for Texture Synthesis and Transfer. In: Proceedings of SIGGRAPH 2001, Los Angeles, California, (August 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ru-Xin Gao
    • 1
    • 2
  • Tian-Fu Wu
    • 2
  • Song-Chun Zhu
    • 2
    • 3
  • Nong Sang
    • 1
  1. 1.IPRAI, Huazhong University of Science and TechnologyChina
  2. 2.Lotus Hill Research InstituteChina
  3. 3.Departments of Statistics and Computer Science, UCLA 

Personalised recommendations