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The Visual Computer

, Volume 28, Issue 6–8, pp 553–562 | Cite as

Fast optimization-based elasticity parameter estimation using reduced models

  • Huai-Ping Lee
  • Ming C. Lin
Original Article

Abstract

Elasticity parameters are central to physically-based animation and medical image analysis. We present an accelerated method to automatically estimate these parameters for a deformation simulator using an iterative optimization framework, given the desired (target) output surface/shape. During the optimization, the input model is deformed by the simulator, and the distance between the deformed surface and the target surface is minimized numerically. To accelerate the optimization process, we introduce a dimension reduction technique to allow a trade-off between the computational efficiency and desired accuracy. The reduced model is constructed using statistical training with a set of example deformations. To demonstrate this approach, we apply the computational framework to 2D animations of elastic bodies simulated with a linear finite element method. We also present a 3D elastography example, which is simulated with a reduced-dimension finite element model to improve the performance of the optimizer.

Keywords

Physically-based modeling Finite element method Computer animation 

Notes

Acknowledgements

We thank Mark Foskey, Marc Niethammer, Ron Alterovitz, and Ed Chaney for helpful discussions. We also thank Zijie Xu and Dr. Ron Chen for providing prostate patient CT data. This work was partially supported by Army Research Office, National Science Foundation, and Carolina Development Foundation.

Supplementary material

371_2012_686_MOESM1_ESM.mpg (387 kb)
(MPG 387 kB)

References

  1. 1.
    Balay, S., Gropp, W.D., McInnes, L.C., Smith, B.F.: Efficient management of parallelism in object-oriented numerical software libraries. In: Modern Software Tools Scientific Computing, pp. 163–202 (1997) CrossRefGoogle Scholar
  2. 2.
    Balocco, S., Camara, O., Frangi, A.F.: Towards regional elastography of intracranial aneurysms. In: Medical Image Computing and Computer-Assisted Intervention, vol. 11, pp. 131–138 (2008) Google Scholar
  3. 3.
    Barbič, J., da Silva, M., Popović, J.: Deformable object animation using reduced optimal control. ACM Trans. Graph. 28(3), 1 (2009). Proceedings of ACM SIGGRAPH 2009 CrossRefGoogle Scholar
  4. 4.
    Becker, M., Teschner, M.: Robust and efficient estimation of elasticity parameters using the linear finite element method. In: Proc. of Simulation and Visualization, pp. 15–28 (2007) Google Scholar
  5. 5.
    Bergou, M., Mathur, S., Wardetzky, M., Grinspun, E.: TRACKS: toward directable thin shells. In: ACM SIGGRAPH 2007 Papers, p. 50 (2007) CrossRefGoogle Scholar
  6. 6.
    Bhat, K.S., Twigg, C.D., Hodgins, J.K., Khosla, P.K., Popovic, Z., Seitz, S.M.: Estimating cloth simulation parameters from video. In: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 37–51 (2003) Google Scholar
  7. 7.
    Bickel, B., Bächer, M., Otaduy, M.A., Lee, H.R., Pfister, H., Gross, M., Matusik, W.: Design and fabrication of materials with desired deformation behavior. In: ACM SIGGRAPH 2010 Papers, pp. 1–10 (2010) CrossRefGoogle Scholar
  8. 8.
    Bickel, B., Bächer, M., Otaduy, M.A., Matusik, W., Pfister, H., Gross, M.: Capture and modeling of non-linear heterogeneous soft tissue. In: ACM SIGGRAPH 2009 Papers, pp. 1–9 (2009) CrossRefGoogle Scholar
  9. 9.
    Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models—their training and application. Comput. Vis. Image Underst. 61(1), 38–59 (1995) CrossRefGoogle Scholar
  10. 10.
    Fu, D., Levinson, S., Gracewski, S., Parker, K.: Non-invasive quantitative reconstruction of tissue elasticity using an iterative forward approach. Phys. Med. Biol. 45(6), 1495–1510 (2000) CrossRefGoogle Scholar
  11. 11.
    Hensel, J.M., Menard, C., Chung, P.W.M., Milosevic, M.F., Kirilova, A., Moseley, J.L., Haider, M.A., Brock, K.K.: Development of multiorgan finite element-based prostate deformation model enabling registration of endorectal coil magnetic resonance imaging for radiotherapy planning. Int. J. Radiat. Oncol. Biol. Phys. 68(5), 1522–1528 (2007) CrossRefGoogle Scholar
  12. 12.
    Igarashi, T., Moscovich, T., Hughes, J.F.: As-rigid-as-possible shape manipulation. ACM Trans. Graph. 24(3), 1134–1141 (2005) CrossRefGoogle Scholar
  13. 13.
    Kallel, F., Bertrand, M.: Tissue elasticity reconstruction using linear perturbation method. IEEE Trans. Med. Imaging 15(3), 299–313 (1996) CrossRefGoogle Scholar
  14. 14.
    Kaus, M.R., Brock, K.K., Pekar, V., Dawson, L.A., Nichol, A.M., Jaffray, D.A.: Assessment of a model-based deformable image registration approach for radiation therapy planning. Int. J. Radiat. Oncol. Biol. Phys. 68(2), 572–580 (2007) CrossRefGoogle Scholar
  15. 15.
    Krysl, P., Lall, S., Marsden, J.E.: Dimensional model reduction in non-linear finite element dynamics of solids and structures. Int. J. Numer. Methods Eng. 51(4), 479–504 (2001) MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Lee, H., Foskey, M., Niethammer, M., Lin, M.: Physically-based deformable image registration with material property and boundary condition estimation. In: Proceedings of the 2010 IEEE International Conference on Biomedical Imaging: from Nano to Macro, pp. 532–535 (2010) CrossRefGoogle Scholar
  17. 17.
    Martin, S., Thomaszewski, B., Grinspun, E., Gross, M.: Example-based elastic materials. In: Proceedings of SIGGRAPH 2011, vol. 30, pp. 72:1–72:8 (2011) Google Scholar
  18. 18.
    McNamara, A., Treuille, A., Popović, Z., Stam, J.: Fluid control using the adjoint method. ACM Trans. Graph. 23(3), 449–456 (2004) CrossRefGoogle Scholar
  19. 19.
    Müller, M., Gross, M.: Interactive virtual materials. In: Proceedings of Graphics Interface 2004, GI’04, pp. 239–246 (2004) Google Scholar
  20. 20.
    Muthupillai, R., Ehman, R.L.: Magnetic resonance elastography. Nat. Med. 2(5), 601–603 (1996) CrossRefGoogle Scholar
  21. 21.
    Nealen, A., Muller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. Comput. Graph. Forum 25, 809–836 (2006) CrossRefGoogle Scholar
  22. 22.
    Nocedal, J., Wright, S.: Numerical Optimization. Springer, Berlin (1999) zbMATHCrossRefGoogle Scholar
  23. 23.
    Ophir, J., Alam, S., Garra, B., Kallel, F., Konofagou, E., Krouskop, T., Varghese, T.: Elastography: ultrasonic estimation and imaging of the elastic properties of tissues. Proc. Inst. Mech. Eng., H J. Eng. Med. 213(3), 203–233 (1999) CrossRefGoogle Scholar
  24. 24.
    Pai, D.K., Doel, K.v.d., James, D.L., Lang, J., Lloyd, J.E., Richmond, J.L., Yau, S.H.: Scanning physical interaction behavior of 3D objects. In: Proceedings of SIGGRAPH 2001, SIGGRAPH ’01, pp. 87–96 (2001). Google Scholar
  25. 25.
    Pizer, S.M., Fletcher, P.T., Joshi, S., Thall, A., Chen, J.Z., Fridman, Y., Fritsch, D.S., Gash, A.G., Glotzer, J.M., Jiroutek, M.R., Lu, C., Muller, K.E., Tracton, G., Yushkevich, P., Chaney, E.L.: Deformable M-Reps for 3D medical image segmentation. Int. J. Comput. Vis. 55(2–3), 85–106 (2003) CrossRefGoogle Scholar
  26. 26.
    Press, W.H.: Numerical Recipes. Cambridge University Press, Cambridge (2007) zbMATHGoogle Scholar
  27. 27.
    Rivaz, H., Boctor, E., Foroughi, P., Zellars, R., Fichtinger, G., Hager, G.: Ultrasound elastography: a dynamic programming approach. IEEE Trans. Med. Imaging 27(10), 1373–1377 (2008) CrossRefGoogle Scholar
  28. 28.
    Schnur, D.S., Zabaras, N.: An inverse method for determining elastic material properties and a material interface. Int. J. Numer. Methods Eng. 33(10), 2039–2057 (1992) zbMATHCrossRefGoogle Scholar
  29. 29.
    Shewchuk, J.R.: Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In: Applied Computational Geometry Towards Geometric Engineering, vol. 1148, pp. 203–222. Springer, Berlin (1996) CrossRefGoogle Scholar
  30. 30.
    Si, H.: TetGen: a quality tetrahedral mesh generator and three-dimensional Delaunay triangulator (2009). URL http://tetgen.berlios.de/
  31. 31.
    Skovoroda, A., Emelianov, S.: Tissue elasticity reconstruction based on ultrasonic displacement and strain images. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42(4), 141 (1995) CrossRefGoogle Scholar
  32. 32.
    Syllebranque, C., Boivin, S.: Estimation of mechanical parameters of deformable solids from videos. Vis. Comput. 24(11), 963–972 (2008) CrossRefGoogle Scholar
  33. 33.
    Taylor, Z.A., Crozier, S., Ourselin, S.: Real-time surgical simulation using reduced order finite element analysis. Med. Image Comput. Comput. Assist. Interv. 13(Pt 2), 388–395 (2010) Google Scholar
  34. 34.
    Teschner, M., Heidelberger, B., Manocha, D., Govindaraju, N., Zachmann, G., Kimmerle, S., Mezger, J., Fuhrmann, A.: Collision handling in dynamic simulation environments: the evolution of graphics: where to nex? In: Eurographics 2005 Tutorial (2005) Google Scholar
  35. 35.
    Treuille, A., McNamara, A., Popović, Z., Stam, J.: Keyframe control of smoke simulations. In: ACM SIGGRAPH 2003 Papers, pp. 716–723 (2003) CrossRefGoogle Scholar
  36. 36.
    Washington, C.W., Miga, M.I.: Modality independent elastography (MIE): a new approach to elasticity imaging. IEEE Trans. Med. Image 23(9), 1117–1128 (2004) CrossRefGoogle Scholar
  37. 37.
    Weng, Y., Xu, W., Wu, Y., Zhou, K., Guo, B.: 2D shape deformation using nonlinear least squares optimization. Vis. Comput. 22(9–11), 653–660 (2006) CrossRefGoogle Scholar
  38. 38.
    Yang, W., Feng, J., Jin, X.: Shape deformation with tunable stiffness. Vis. Comput. 24(7–9), 495–503 (2008) CrossRefGoogle Scholar
  39. 39.
    Yoo, T.S., Ackerman, M.J., Lorensen, W.E., Schroeder, W., Chalana, V., Aylward, S., Metaxas, D., Whitaker, R.: Engineering and algorithm design for an image processing API: a technical report on ITK—the insight toolkit (2002) Google Scholar
  40. 40.
    Yushkevich, P.A., Piven, J., Hazlett, H.C., Smith, R.G., Ho, S., Gee, J.C., Gerig, G.: User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. NeuroImage 31(3), 1116–1128 (2006) CrossRefGoogle Scholar
  41. 41.
    Zhu, Y., Hall, T., Jiang, J.: A finite-element approach for Young’s modulus reconstruction. IEEE Trans. Med. Imaging 22(7), 890–901 (2003) CrossRefGoogle Scholar
  42. 42.
    Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method, 6th edn. Butterworth-Heinemann, Oxford (2005) zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.University of North CarolinaChapel HillUSA

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