Skip to main content
SpringerLink
Log in

Character motion in function space

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We address the problem of animated character motion representation and approximation by introducing a novel form of motion expression in a function space. For a given set of motions, our method extracts a set of orthonormal basis (ONB) functions. Each motion is then expressed as a vector in the ONB space or approximated by a subset of the ONB functions. Inspired by the static PCA, our approach works with the time-varying functions. The set of ONB functions is extracted from the input motions by using functional principal component analysis and it has an optimal coverage of the input motions for the given input set. We show the applications of the novel compact representation by providing a motion distance metric, motion synthesis algorithm, and a motion level of detail. Not only we can represent a motion by using the ONB; a new motion can be synthesized by optimizing connectivity of reconstructed motion functions, or by interpolating motion vectors. The quality of the approximation of the reconstructed motion can be set by defining a number of ONB functions, and this property is also used to level of detail. Our representation provides compression of the motion. Although we need to store the generated ONB that are unique for each set of input motions, we show that the compression factor of our representation is higher than for commonly used analytic function methods. Moreover, our approach also provides lower distortion rate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Akhter, I., Simon, T., Khan, S., Matthews, I., Sheikh, Y.: Bilinear spatiotemporal basis models. ACM Trans. Gr. 31(2), 1–12 (2012)

    Article  Google Scholar 

  2. Alon, J., Sclaroff, S., Kollios, G., Pavlovic, V.: Discovering clusters in motion time-series data. In: Proceedings of 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. I-375–I-381 (2003)

  3. Arikan, O.: Compression of motion capture databases. ACM Trans. Gr. 25(3), 890–897 (2006)

    Article  MathSciNet  Google Scholar 

  4. Aristidou, A., Cohen-Or, D., Hodgins, J.K., Chrysanthou, Y., Shamir, A.: Deep motifs and motion signatures. ACM Trans. Gr. 37(6), 1–13 (2018)

    Article  Google Scholar 

  5. Barbič, J., Safonova, A., Pan, J.-Y., Faloutsos, C., Hodgins, J. K., Pollard, N. S.: Segmenting motion capture data into distinct behaviors. In: Proceedings of Graphics Interface 2004, GI ’04, School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, Canadian Human-Computer Communications Society, pp. 185–194 (2004)

  6. Beaudoin, P., Coros, S., van de Panne, M., Poulin, P.: Motion-motif graphs. In: Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’08, Aire-la-Ville, Switzerland, Switzerland, Eurographics Association, pp. 117–126 (2008)

  7. Bernard, J., Wilhelm, N., Krüger, B., May, T., Schreck, T., Kohlhammer, J.: Motionexplorer: exploratory search in human motion capture data based on hierarchical aggregation. IEEE Trans. Vis. Comput. Gr. 19(12), 2257–2266 (2013)

    Article  Google Scholar 

  8. Chao, M.-W., Lin, C.-H., Assa, J., Lee, T.-Y.: Human motion retrieval from hand-drawn sketch. IEEE Trans. Vis. Comput. Gr. 18(5), 729–740 (2012)

    Article  Google Scholar 

  9. Coffey, N., Harrison, A., Donoghue, O., Hayes, K.: Common functional principal components analysis: a new approach to analyzing human movement data. Hum. Mov. Sci. 30(6), 1144–1166 (2011)

    Article  Google Scholar 

  10. Courrieu, P.: Fast computation of moore-penrose inverse matrices. In: CoRR. arXiv:0804.4809 (2008)

  11. Du, H., Hosseini, S., Manns, M., Herrmann, E., Fischer, K.: Scaled functional principal component analysis for human motion synthesis. In: Proceedings of the 9th International Conference on Motion in Games, MIG ’16, New York, NY, USA, ACM, pp. 139–144 (2016)

  12. Forbes, K., Fiume, E.: An efficient search algorithm for motion data using weighted PCA. In: Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’05, New York, NY, USA, ACM, pp. 67–76 (2005)

  13. Gall, J., Rosenhahn, B., Brox, T., Seidel, H.-P.: Optimization and filtering for human motion capture. Int. J. Comput. Vis. 87(1–2), 75–92 (2010)

    Article  Google Scholar 

  14. Heck, R., Gleicher, M.: Parametric motion graphs. In: Proceedings of the 2007 Symposium on Interactive 3D Graphics and Games, I3D ’07, New York, NY, USA, ACM, pp. 129–136 (2007)

  15. Hou, J., Chau, L., Magnenat-Thalmann, N., He, Y.: Human motion capture data tailored transform coding. CoRR, arXiv:1410.4730 (2014)

  16. Ikemoto, L., Arikan, O., Forsyth, D.: Knowing when to put your foot down. In: Proceedings of the 2006 Symposium on Interactive 3D Graphics and Games, I3D ’06, New York, NY, USA, ACM, pp. 49–53 (2006)

  17. Ikemoto, L., Arikan, O., Forsyth, D.: Generalizing motion edits with gaussian processes. ACM Trans. Gr. 28(1), 1:1–1:12 (2009)

    Article  Google Scholar 

  18. Karni, Z., Gotsman, C.: Compression of soft-body animation sequences. Comput. Gr. 28(1), 25–34 (2004)

    Article  Google Scholar 

  19. Keogh, E., Palpanas, T., Zordan, V. B., Gunopulos, D., Cardle, M.: Indexing large human-motion databases. In: Proceedings of the Thirtieth International Conference on Very Large Data Bases - Volume 30, VLDB ’04, VLDB Endowment, pp. 780–791 (2004)

  20. Kovar, L., Gleicher, M.: Automated extraction and parameterization of motions in large data sets. ACM Trans. Gr. 23(3), 559–568 (2004)

    Article  Google Scholar 

  21. Kovar, L., Gleicher, M., Pighin, F.: Motion graphs. ACM Trans. Gr. 21(3), 473–482 (2002a)

    Article  Google Scholar 

  22. Kovar, L., Schreiner, J., Gleicher, M.: Footskate cleanup for motion capture editing. In: Proceedings of the 2002 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’02, New York, NY, USA, ACM, pp. 97–104 (2002b)

  23. Lai, Y.-C., Chenney, S., Fan, S.: Group motion graphs. In: Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’05, New York, NY, USA, ACM, pp. 281–290 (2005)

  24. Lau, M., Bar-Joseph, Z., Kuffner, J.: Modeling spatial and temporal variation in motion data. ACM Trans. Gr. 28(5), 171:1–171:10 (2009)

    Article  Google Scholar 

  25. Lee, J., Shin, S. Y.: A hierarchical approach to interactive motion editing for human-like figures. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’99, New York, NY, USA, ACM Press/Addison-Wesley Publishing Co, pp. 39–48 (1999)

  26. Lee, K., Lee, S., Lee, J.: Interactive character animation by learning multi-objective control. ACM Trans. Gr. 37(6), 1–10 (2018)

    Google Scholar 

  27. Lee, Y., Wampler, K., Bernstein, G., Popović, J., Popović, Z.: Motion fields for interactive character locomotion. ACM Trans. Gr. 29(6), 138:1–138:8 (2010)

    Google Scholar 

  28. Levine, S., Wang, J.M., Haraux, A., Popović, Z., Koltun, V.: Continuous character control with low-dimensional embeddings. ACM Trans. Gr. 31(4), 28:1–28:10 (2012)

    Article  Google Scholar 

  29. Liu, G., McMillan, L.: Segment-based human motion compression. In: Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’06, Aire-la-Ville, Switzerland, Switzerland, Eurographics Association, pp. 127–135 (2006)

  30. Min, J., Chai, J.: Motion graphs++: a compact generative model for semantic motion analysis and synthesis. ACM Trans. Gr. 31(6), 153:1–153:12 (2012)

    Article  Google Scholar 

  31. Mordatch, I., de Lasa, M., Hertzmann, A.: Robust physics-based locomotion using low-dimensional planning. ACM Trans. Gr. 29(4), 71:1–71:8 (2010)

    Article  Google Scholar 

  32. Müller, M., Baak, A., Seidel, H.-P.: Efficient and robust annotation of motion capture data. In Proceedings of the: ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’09, New York, NY, Association for Computing Machinery, USA, pp. 17–26 (2009)

  33. Müller, M., Röder, T.: Motion templates for automatic classification and retrieval of motion capture data. In: Proceedings of the: ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’06, Goslar. DEU, Eurographics Association, pp. 137–146 (2006)

  34. Ormoneit, D., Black, M.J., Hastie, T., Kjellstrom, H.: Representing cyclic human motion using functional analysis. Image Vis. Comput. 23(14), 1264–1276 (2005)

    Article  Google Scholar 

  35. Peng, X.B., Abbeel, P., Levine, S., van de Panne, M.: Deepmimic: example-guided deep reinforcement learning of physics-based character skills. ACM Trans. Gr. 37(4), 1–14 (2018)

    Google Scholar 

  36. Peng, X.B., Berseth, G., Yin, K., Van De Panne, M.: Deeploco: dynamic locomotion skills using hierarchical deep reinforcement learning. ACM Trans. Gr. 36(4), 1–13 (2017)

    Article  Google Scholar 

  37. Ramsay, J., Silverman, B.W.: Functional Data Analysis. Wiley Online Library, New York (2006)

    MATH  Google Scholar 

  38. Reitsma, P.S.A., Pollard, N.S.: Evaluating motion graphs for character animation. ACM Trans. Gr. (2007). https://doi.org/10.1145/1289603.1289609

  39. Safonova, A., Hodgins, J.K.: Construction and optimal search of interpolated motion graphs (2007). https://doi.org/10.1145/1275808.1276510

  40. Shin, H.J., Lee, J.: Motion synthesis and editing in low-dimensional spaces: research articles. Comput. Anim. Virtual Worlds 17(3–4), 219–227 (2006)

    Article  Google Scholar 

  41. Tang, J.K.T., Leung, H., Komura, T., Shum, H.P.H.: Emulating human perception of motion similarity. Comput. Anim. Virtual Worlds 19(3–4), 211–221 (2008)

    Article  Google Scholar 

  42. Tournier, M., Wu, X., Courty, N., Arnaud, E., Revéret, L.: Motion compression using principal geodesics analysis. Comput. Gr. Forum 28(2), 355–364 (2009)

    Article  Google Scholar 

  43. Unuma, M., Anjyo, K., Takeuchi, R.: Fourier principles for emotion-based human figure animation. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’95, ACM, New York, NY, pp. 91–96 (1995)

  44. Vögele, A., Krüger, B., Klein, R.: Efficient unsupervised temporal segmentation of human motion. In: 2014 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2014)

  45. Wang, H., Ho, E. S., Shum, H. P., Zhu, Z.: Spatio-temporal manifold learning for human motions via long-horizon modeling. In: IEEE Transactions on Visualization and Computer Graphics (2019a)

  46. Wang, Z., Chai, J., Xia, S.: Combining recurrent neural networks and adversarial training for human motion synthesis and control. In: IEEE Transactions on Visualization and Computer Graphics (2019b)

  47. Wei, X., Min, J., Chai, J.: Physically valid statistical models for human motion generation. ACM Trans. Graph. 30(3), 19:1–19:10 (2011)

    Article  Google Scholar 

  48. Yao, F., Mueller, H.-G., Wang, J.-L.: Functional linear regression analysis for longitudinal data. Ann. Stat. 33(6), 2873–2903 (2005)

    Article  MathSciNet  Google Scholar 

  49. Yoo, I., Abdul Massih, M., Ziamtsov, I., Hassan, R., Benes, B.: Motion retiming by using bilateral time control surfaces. Comput. Graph. 47(C), 59–67 (2015)

    Article  Google Scholar 

  50. Yoo, I., Fišer, M., Hu, K., Benes, B.: Character motion in function space. In: Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, vol. 1, INSTICC, SciTePress, pp. 110–121 (2019)

  51. Yoo, I., Vanek, J., Nizovtseva, M., Adamo-Villani, N., Benes, B.: Sketching human character animations by composing sequences from large motion database. Vis. Comput. 30(2), 213–227 (2014)

    Article  Google Scholar 

  52. Zhao, L., Safonova, A.: Achieving good connectivity in motion graphs. Gr. Models, 71(4), 139– 152 (Special Issue of ACM SIGGRAPH / Eurographics Symposium on Computer Animation 2008) (2009)

  53. Zhou, F., De La Torre, F.: Generalized time warping for multi-modal alignment of human motion. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1282–1289 (2012)

  54. Zhou, F., De la Torre, F., Hodgins, J.: Hierarchical aligned cluster analysis for temporal clustering of human motion. IEEE Trans. Pattern Anal. Mach. Intell. 35(3), 582–596 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

This research was funded in part by National Science Foundation Grants #10001387, Functional Proceduralization of 3D Geometric Models and #10001364, Multimodal Affective Pedagogical Agents for Different Types of Learners.

Author information

Authors and Affiliations

  1. Purdue University, West Lafayette, USA

    Innfarn Yoo, Marek Fišer, Kaimo Hu & Bedrich Benes

Authors
  1. Innfarn Yoo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marek Fišer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kaimo Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bedrich Benes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bedrich Benes.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yoo, I., Fišer, M., Hu, K. et al. Character motion in function space. Vis Comput 37, 735–748 (2021). https://doi.org/10.1007/s00371-020-01840-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-020-01840-6

Keywords

Search

Navigation