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Fast Blended Transformations for Partial Shape Registration

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Abstract

Automatic estimation of skinning transformations is a popular way to deform a single reference shape into a new pose by providing a small number of control parameters. We generalize this approach by efficiently enabling the use of multiple exemplar shapes. Using a small set of representative natural poses, we propose to express an unseen appearance by a low-dimensional linear subspace, specified by a redundant dictionary of weighted vertex positions. Minimizing a nonlinear functional that regulates the example manifold, the suggested approach supports local-rigid deformations of articulated objects, as well as nearly isometric embeddings of smooth shapes. A real-time nonrigid deformation system is demonstrated, and a shape completion and partial registration framework is introduced. These applications can recover a target pose and implicit inverse kinematics from a small number of examples and just a few vertex positions. The resulting reconstruction is more accurate compared to alternative reduced deformable models.

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References

  1. Alexa, M.: Differential coordinates for local mesh morphing and deformation. Vis. Comput. 19(2), 105–114 (2003)

    MATH  Google Scholar 

  2. Alexa, M., Cohen-Or, D., Levin, D.: As-rigid-as-possible shape interpolation. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’00, pp. 157–164. ACM Press/Addison-Wesley Publishing Co., New York, NY, USA (2000). https://doi.org/10.1145/344779.344859

  3. Allen, B., Curless, B., Popović, Z.: The space of human body shapes: reconstruction and parameterization from range scans. ACM Trans. Graph. 22(3), 587–594 (2003). https://doi.org/10.1145/882262.882311

    Article  Google Scholar 

  4. Amberg, B., Romdhani, S., Vetter, T.: Optimal step nonrigid icp algorithms for surface registration. In: IEEE Conference on Computer Vision and Pattern Recognition, 2007. CVPR ’07, pp. 1–8 (2007). https://doi.org/10.1109/CVPR.2007.383165

  5. Anguelov, D., Srinivasan, P., cheung Pang, H., Koller, D., Thrun, S., Davis, J.: The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems vol. 17, pp. 33–40. MIT Press, Cambridge (2005). http://papers.nips.cc/paper/2601-the-correlated-correspondence-algorithm-for-unsupervised-registration-of-nonrigid-surfaces.pdf

  6. Bogo, F., Romero, J., Loper, M., Black, M.J.: Faust: dataset and evaluation for 3d mesh registration. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2014)

  7. Bouaziz, S., Martin, S., Liu, T., Kavan, L., Pauly, M.: Projective dynamics: fusing constraint projections for fast simulation. ACM Trans. Graph. 33(4), 154:1–154:11 (2014). https://doi.org/10.1145/2601097.2601116

    Article  MATH  Google Scholar 

  8. Bouaziz, S., Wang, Y., Pauly, M.: Online modeling for realtime facial animation. ACM Trans. Graph. (TOG) 32(4), 40 (2013)

    Article  MATH  Google Scholar 

  9. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical Geometry of Non-rigid Shapes. Springer, Berlin (2008)

    MATH  Google Scholar 

  10. Brunton, A., Wand, M., Wuhrer, S., Seidel, H.P., Weinkauf, T.: A low-dimensional representation for robust partial isometric correspondences computation. Graph. Models 76(2), 70–85 (2014)

    Article  Google Scholar 

  11. Chao, I., Pinkall, U., Sanan, P., Schröder, P.: A simple geometric model for elastic deformations. In: ACM SIGGRAPH 2010 Papers, SIGGRAPH’10, pp. 38:1–38:6. ACM, New York, NY, USA (2010). https://doi.org/10.1145/1833349.1778775

  12. Der, K.G., Sumner, R.W., Popović, J.: Inverse kinematics for reduced deformable models. ACM Trans. Graph. 25(3), 1174–1179 (2006). https://doi.org/10.1145/1141911.1142011

    Article  Google Scholar 

  13. Dey, T.K., Ranjan, P., Wang, Y.: Eigen deformation of 3d models. Vis. Comput. 28(6–8), 585–595 (2012)

    Article  Google Scholar 

  14. Elad, M.: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  15. Feng, W.W., Kim, B.U., Yu, Y.: Real-time data driven deformation using kernel canonical correlation analysis. In: ACM SIGGRAPH 2008 Papers, SIGGRAPH’08, pp. 91:1–91:9. ACM, New York, NY, USA (2008). https://doi.org/10.1145/1399504.1360690

  16. Fröhlich, S., Botsch, M.: Example-driven deformations based on discrete shells. Comput. Graph. Forum 30(8), 2246–2257 (2011). https://doi.org/10.1111/j.1467-8659.2011.01974.x

    Article  Google Scholar 

  17. Gao, L., Lai, Y.K., Liang, D., Chen, S.Y., Xia, S.: Efficient and flexible deformation representation for data-driven surface modeling. ACM Trans. Graph. (TOG) 35(5), 158 (2016)

    Article  Google Scholar 

  18. Grinspun, E., Hirani, A.N., Desbrun, M., Schröder, P.: Discrete shells. In: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA’03, pp. 62–67. Eurographics Association, Aire-la-Ville, Switzerland, Switzerland (2003)

  19. Jacobson, A., Baran, I., Kavan, L., Popović, J., Sorkine, O.: Fast automatic skinning transformations. ACM Trans. Graph. 31(4), 77:1–77:10 (2012). https://doi.org/10.1145/2185520.2185573

    Article  Google Scholar 

  20. Jacobson, A., Baran, I., Popović, J., Sorkine-Hornung, O.: Bounded biharmonic weights for real-time deformation. Commun. ACM 57(4), 99–106 (2014). https://doi.org/10.1145/2578850

    Article  Google Scholar 

  21. James, D.L., Twigg, C.D.: Skinning mesh animations. In: ACM SIGGRAPH 2005 Papers, SIGGRAPH’05, pp. 399–407. ACM, New York, NY, USA (2005). https://doi.org/10.1145/1186822.1073206

  22. Kaufman, L., Rousseeuw, P.: Clustering by Means of Medoids. North-Holland, Amsterdam (1987)

    Google Scholar 

  23. Kavan, L., Sloan, P.P., O’Sullivan, C.: Fast and efficient skinning of animated meshes. Comput. Graph. Forum 29(2), 327–336 (2010). https://doi.org/10.1111/j.1467-8659.2009.01602.x

    Article  Google Scholar 

  24. Kim, V.G., Lipman, Y., Funkhouser, T.: Blended intrinsic maps. In: ACM SIGGRAPH 2011 Papers, SIGGRAPH’11, pp. 79:1–79:12. ACM, New York, NY, USA (2011). https://doi.org/10.1145/1964921.1964974

  25. Koyama, Y., Takayama, K., Umetani, N., Igarashi, T.: Real-time example-based elastic deformation. In: Proceedings of the 11th ACM SIGGRAPH/Eurographics Conference on Computer Animation, EUROSCA’12, pp. 19–24. Eurographics Association, Aire-la-Ville, Switzerland, Switzerland (2012). https://doi.org/10.2312/SCA/SCA12/019-024

  26. Kry, P.G., James, D.L., Pai, D.K.: Eigenskin: real time large deformation character skinning in hardware. In: Proceedings of the 2002 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA’02, pp. 153–159. ACM, New York, NY, USA (2002). https://doi.org/10.1145/545261.545286

  27. Le, B.H., Deng, Z.: Robust and accurate skeletal rigging from mesh sequences. ACM Trans. Graph. 33(4), 84:1–84:10 (2014). https://doi.org/10.1145/2601097.2601161

    Article  MATH  Google Scholar 

  28. Levi, Z., Gotsman, C.: Smooth rotation enhanced as-rigid-as-possible mesh animation. IEEE Trans. Vis. Comput. Graph. 21(2), 264–277 (2015)

    Article  Google Scholar 

  29. Lewis, J.P., Cordner, M., Fong, N.: Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’00, pp. 165–172. ACM Press/Addison-Wesley Publishing Co., New York, NY, USA (2000). https://doi.org/10.1145/344779.344862

  30. Li, H., Sumner, R.W., Pauly, M.: Global correspondence optimization for non-rigid registration of depth scans. Comput. Graph. Forum 27(5), 1421–1430 (2008). https://doi.org/10.1111/j.1467-8659.2008.01282.x

    Article  Google Scholar 

  31. Lipman, Y., Sorkine, O., Cohen-Or, D., Levin, D., Rossi, C., Seidel, H.P.: Differential coordinates for interactive mesh editing. In: Shape Modeling Applications, 2004. Proceedings, pp. 181–190 (2004). https://doi.org/10.1109/SMI.2004.1314505

  32. Liu, L., Zhang, L., Xu, Y., Gotsman, C., Gortler, S.J.: A local/global approach to mesh parameterization. Comput. Graph. Forum 27(5), 1495–1504 (2008). https://doi.org/10.1111/j.1467-8659.2008.01290.x

    Article  Google Scholar 

  33. Magnenat-thalmann, N., Laperrire, R., Thalmann, D., Montral, U.D.: Joint-dependent local deformations for hand animation and object grasping. In: Proceedings on Graphics interface vol. 88, pp. 26–33 (1988)

  34. Martin, S., Thomaszewski, B., Grinspun, E., Gross, M.: Example-based elastic materials. ACM Trans. Graph. 30(4), 72:1–72:8 (2011). https://doi.org/10.1145/2010324.1964967

    Article  Google Scholar 

  35. McAdams, A., Selle, A., Tamstorf, R., Teran, J., Sifakis, E.: Computing the singular value decomposition of 3\(\times \) 3 matrices with minimal branching and elementary floating point operations. Technical Report, University of Wisconsin-Madison (2011)

  36. Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2(1), 15–36 (1993). https://doi.org/10.1080/10586458.1993.10504266

    Article  MathSciNet  MATH  Google Scholar 

  37. Rodolà, E., Cosmo, L., Bronstein, M.M., Torsello, A., Cremers, D.: Partial functional correspondence. In: Computer Graphics Forum. Wiley Online Library (2016)

  38. Schumacher, C., Thomaszewski, B., Coros, S., Martin, S., Sumner, R., Gross, M.: Efficient simulation of example-based materials. In: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 1–8. Eurographics Association (2012)

  39. Sloan, P.P.J., Rose III, C.F., Cohen, M.F.: Shape by example. In: Proceedings of the 2001 Symposium on Interactive 3D Graphics, I3D’01, pp. 135–143. ACM, New York, NY, USA (2001). https://doi.org/10.1145/364338.364382

  40. Sorkine, O., Alexa, M.: As-rigid-as-possible surface modeling. In: Proceedings of EUROGRAPHICS/ACM SIGGRAPH Symposium on Geometry Processing, pp. 109–116 (2007)

  41. Sumner, R.W., Popović, J.: Deformation transfer for triangle meshes. ACM Trans. Graph. 23(3), 399–405 (2004). https://doi.org/10.1145/1015706.1015736

    Article  Google Scholar 

  42. Sumner, R.W., Zwicker, M., Gotsman, C., Popović, J.: Mesh-based inverse kinematics. In: ACM SIGGRAPH 2005 Papers, SIGGRAPH’05, pp. 488–495. ACM, New York, NY, USA (2005). https://doi.org/10.1145/1186822.1073218

  43. van Kaick, O., Zhang, H., Hamarneh, G.: Bilateral maps for partial matching. In: Computer Graphics Forum, vol. 32, pp. 189–200. Wiley Online Library (2013)

  44. Von-Tycowicz, C., Schulz, C., Seidel, H.P., Hildebrandt, K.: Real-time nonlinear shape interpolation. ACM Trans. Graph. 34(3), 34:1–34:10 (2015). https://doi.org/10.1145/2729972

    Article  MATH  Google Scholar 

  45. Wang, R.Y., Pulli, K., Popović, J.: Real-time enveloping with rotational regression. ACM Trans. Graph. (2007). https://doi.org/10.1145/1276377.1276468

  46. Wang, Y., Jacobson, A., Barbič, J., Kavan, L.: Linear subspace design for real-time shape deformation. ACM Trans. Graph. (TOG) 34(4), 57 (2015)

    Google Scholar 

  47. Winkler, T., Drieseberg, J., Alexa, M., Hormann, K.: Multi-scale geometry interpolation. Comput. Graph. Forum 29(2), 309–318 (2010). https://doi.org/10.1111/j.1467-8659.2009.01600.x

    Article  Google Scholar 

  48. Xu, D., Zhang, H., Wang, Q., Bao, H.: Poisson shape interpolation. Graph. Models 68(3), 268–281 (2006)

    Article  MATH  Google Scholar 

  49. Zhang, H., Sheffer, A., Cohen-Or, D., Zhou, Q., Van Kaick, O., Tagliasacchi, A.: Deformation-driven shape correspondence. Comput. Graph. Forum 27(5), 1431–1439 (2008). https://doi.org/10.1111/j.1467-8659.2008.01283.x

    Article  Google Scholar 

  50. Zhang, W., Zheng, J., Thalmann, N.M.: Real-time subspace integration for example-based elastic material. In: Computer Graphics Forum, vol. 34, pp. 395–404. Wiley Online Library (2015)

  51. Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67(2), 301–320 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Funding was provided by European Research Council (Grant No. 267414).

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Authors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Alon Shtern, Matan Sela & Ron Kimmel

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  1. Alon Shtern
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  2. Matan Sela
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Correspondence to Alon Shtern.

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Alon Shtern and Matan Sela have contributed equally to this work.

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Shtern, A., Sela, M. & Kimmel, R. Fast Blended Transformations for Partial Shape Registration. J Math Imaging Vis 60, 913–928 (2018). https://doi.org/10.1007/s10851-017-0782-9

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