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Continuous Global Optimization in Multiview 3D Reconstruction

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4679))

Abstract

In this work, we introduce a robust energy model for multiview 3D reconstruction that fuses silhouette- and stereo-based image information. It allows to cope with significant amounts of noise without manual pre-segmentation of the input images. Moreover, we suggest a method that can globally optimize this energy up to the visibility constraint. While similar global optimization has been presented in the discrete context in form of the maxflow-mincut framework, we suggest the use of a continuous counterpart. In contrast to graph cut methods, discretizations of the continuous optimization technique are consistent and independent of the choice of the grid connectivity. Our experiments demonstrate that this leads to visible improvements. Moreover, memory requirements are reduced, allowing for global reconstructions at higher resolutions.

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References

  1. Appleton, B., Talbot, H.: Globally optimal geodesic active contours. J. Math. Imaging Vis. 23(1), 67–86 (2005)

    Article  MathSciNet  Google Scholar 

  2. Appleton, B., Talbot, H.: Globally minimal surfaces by continuous maximal flows. IEEE Trans. Pattern Anal. Mach. Intell. 28(1), 106–118 (2006)

    Article  Google Scholar 

  3. Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(11), 1222–1239 (2001)

    Article  Google Scholar 

  4. Bresson, X., Esedoglu, S., Vandergheynst, P., Thiran, J.P., Osher, S.: Global minimizers of the active contour/snake model. Technical Report CAM-05-04, Department of Mathematics, University of California at Los Angeles, CA (January 2005)

    Google Scholar 

  5. Caselles, V., Catté, F., Coll, T., Dibos, F.: A geometric model for active contours in image processing. Numerische Mathematik 66, 1–31 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  6. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Proc. Fifth International Conference on Computer Vision, pp. 694–699. IEEE Computer Society Press, Cambridge, MA (1995)

    Chapter  Google Scholar 

  7. Chambolle, A.: Total variation minimization and a class of binary MRF models. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 136–152. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Chan, T., Esedoglu, S., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM Journal on Applied Mathematics 66(5), 1632–1648 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Duan, Y., Yang, L., Qin, H., Samaras, D.: Shape reconstruction from 3D and 2D data using PDE-based deformable surfaces. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 238–251. Springer, Heidelberg (2004)

    Google Scholar 

  10. Esteban, C.H., Schmitt, F.: Silhouette and stereo fusion for 3D object modeling. Computer Vision and Image Understanding 96(3), 367–392 (2004)

    Article  Google Scholar 

  11. Faugeras, O., Keriven, R.: Variational principles, surface evolution, PDE’s, level set methods, and the stereo problem. IEEE Transactions on Image Processing 7(3), 336–344 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hu, T.C.: Integer Programming and Network Flows. Addison-Wesley, Reading, MA (1969)

    MATH  Google Scholar 

  13. Kass, M., Witkin, A.: Analyzing oriented patterns. Computer Vision, Graphics and Image Processing 37, 362–385 (1987)

    Article  Google Scholar 

  14. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1, 321–331 (1988)

    Article  Google Scholar 

  15. Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. In: Proc. Fifth International Conference on Computer Vision, pp. 810–815. IEEE Computer Society Press, Cambridge, MA (1995)

    Chapter  Google Scholar 

  16. Kolev, K., Brox, T., Cremers, D.: Robust variational segmentation of 3D objects from multiple views. In: Franke, K., Müller, K.-R., Nickolay, B., Schäfer, R. (eds.) Pattern Recognition. LNCS, vol. 4174, pp. 688–697. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Kutulakos, K.N., Seitz, S.M.: A theory of shape by space carving. International Journal of Computer Vision 38(3), 199–218 (2000)

    Article  MATH  Google Scholar 

  18. Laurentini, A.: The visual hull concept for visual-based image understanding. IEEE Transactions on Pattern Analysis and Machine Intelligence 16(2), 150–162 (1994)

    Article  Google Scholar 

  19. Lempitsky, V., Boykov, Y., Ivanov, D.: Oriented visibility for multiview reconstruction. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 226–238. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Martin, W.N., Aggarwal, J.K.: Volumetric descriptions of objects from multiple views. IEEE Transactions on Pattern Analysis and Machine Intelligence 5(2), 150–158 (1983)

    Article  Google Scholar 

  21. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–685 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  22. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  23. Sinha, S., Pollefeys, M.: Multi-view reconstruction using photo-consistency and exact silhouette constraints: A maximum-flow formulation. In: Proc. International Conference on Computer Vision, pp. 349–356. IEEE Computer Society, Washington, DC (2005)

    Google Scholar 

  24. Snow, D., Viola, P., Zabih, R.: Exact voxel occupancy with graph cuts. In: Proc. International Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 345–353 (2000)

    Google Scholar 

  25. Strang, G.: Maximal flow through a domain. Mathematical Programming 26, 123–243 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  26. Tran, S., Davis, L.: 3D surface reconstruction using graph cuts with surface constraints. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952, pp. 219–231. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  27. Vogiatzis, G., Torr, P., Cippola, R.: Multi-view stereo via volumetric graph-cuts. In: Proc. International Conference on Computer Vision and Pattern Recognition, pp. 391–399 (2005)

    Google Scholar 

  28. Yezzi, A., Soatto, S.: Stereoscopic segmentation. International Journal of Computer Vision 53(1), 31–43 (2003)

    Article  MathSciNet  Google Scholar 

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Alan L. Yuille Song-Chun Zhu Daniel Cremers Yongtian Wang

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Kolev, K., Klodt, M., Brox, T., Esedoglu, S., Cremers, D. (2007). Continuous Global Optimization in Multiview 3D Reconstruction. In: Yuille, A.L., Zhu, SC., Cremers, D., Wang, Y. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2007. Lecture Notes in Computer Science, vol 4679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74198-5_34

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  • DOI: https://doi.org/10.1007/978-3-540-74198-5_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74195-4

  • Online ISBN: 978-3-540-74198-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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