Advertisement

Part-Aware Distance Fields for Easy Inbetweening in Arbitrary Dimensions

Conference paper
  • 451 Downloads
Part of the Association for Women in Mathematics Series book series (AWMS, volume 1)

Abstract

The motivation for this work is to explore a possible computer graphics application for a part aware distance field developed recently. Computing in-between shapes is chosen as a toy application. Rather than presenting a highly competitive scheme which continuously morphs one shape into another, our aim is to investigate whether in-betweens may be defined as ordinary averages once a proper shape representation (e.g. a part aware field) is established. The constructions are independent of the dimension of the space in which the shape is embedded as well as the number of shapes to be averaged.

Keywords

Shape Boundary Symmetric Positive Definite Matrix Euclidean Distance Function Flat Mode Homogeneous Dirichlet Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I thank M. Genctav for providing a faster code for the ω-field computation. The work is funded by TUBITAK 112E208.

References

  1. 1.
    Bloomenthal, J., Wyvill, B. (eds.): Introduction to Implicit Surfaces. Morgan Kaufmann Publishers, San Francisco (1997)zbMATHGoogle Scholar
  2. 2.
    Bunch, J.R., Nielsen, C.P., Sorensen, D.C.: Rank-one modification of the symmetric eigenproblem. Numerische Mathematik 31(1), 31–48 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Cohen-Or, D., Levin, D., Solomovici, A.: Contour blending using warp-guided distance field interpolation. In: IEEE Visualization, San Francisco, pp. 165–172 (1996)Google Scholar
  4. 4.
    Hofmann, D., Richards, W.: Parts of recognition. Cognition 18, 65–96 (1984)CrossRefGoogle Scholar
  5. 5.
    Klassen, E., Srivastava, A., Mio, W., Joshi, S.H.: Analysis of planar shapes using geodesic paths on shape spaces. IEEE Trans. Pattern Anal. Mach. Intell. 26(3), 372–383 (2004)CrossRefGoogle Scholar
  6. 6.
    Kovacs, I., Julesz, B.: Perceptual sensitivity maps within globally defined visual shapes. Nature 370(6491), 644-646 (1994)CrossRefGoogle Scholar
  7. 7.
    Liu, R., Zhang, H., Shamir, A., Cohen-Or, D.: A part-aware surface metric for shape analysis. Comput. Graph. Forum 28(2), 397–406 (2009)CrossRefGoogle Scholar
  8. 8.
    Pasko, A., Adzhiev, V.: Function-based shape modeling: mathematical framework and specialized language. In: Automated Deduction in Geometry, vol. 2930, pp. 132–160. Springer, Berlin/New York (2004)Google Scholar
  9. 9.
    Reuter, M.: Hierarchical shape segmentation and registration via topological features of Laplace-Beltrami eigenfunctions. Int. J. Comput. Vision 89(2),287–308 (2010)CrossRefGoogle Scholar
  10. 10.
    Tari, S.: Hierarchical shape decomposition via level sets. In: ISMM, Groningen pp. 215–225 (2009)Google Scholar
  11. 11.
    Tari, S.: Fluctuating distance fields, parts, three-partite skeletons. In: Innovations for Shape Analysis, pp. 439–466. Springer, Berlin/New York (2013)Google Scholar
  12. 12.
    Tari, S., Genctav, M.: From a non-local Ambrosio-Tortorelli phase field to a randomized part hierarchy tree. J. Math. Imaging Vis. 49, 69–86 (2013)CrossRefGoogle Scholar
  13. 13.
    Tari, S., Shah, J., Pien, H.: Extraction of shape skeletons from grayscale images. Comput. Vis. Image Underst. 66(2), 133–146 (1997)CrossRefGoogle Scholar
  14. 14.
    Tari, S., Burgeth, B., Tari, I.: Components of the shape revisited. In: Cognitive Shape Processing, American Association Artificial Intelligence Spring Symposium, Stanford (2010)Google Scholar
  15. 15.
    van Kaick, O., Xu, K., Zhang, H., Wang, Y., Sun, S., Shamir, A., Cohen-Or, D.: Co-hierarchical analysis of shape structures. ACM Trans. Graph. 32(4), 1–10 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland & The Association for Women in Mathematics 2015

Authors and Affiliations

  1. 1.Department of Computer EngineeringMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations