A ROBUST AND EFFICIENT METHOD FOR TOPOLOGY ADAPTATIONS IN DEFORMABLE MODELS

Jochen Abhau

Abstract

In this paper, we present a novel algorithm for calculating topological adaptations in explicit evolutions of surface meshes in 3D. Our topological adaptation system consists of two main ingredients: A spatial hashing technique is used to detect mesh self-collisions during the evolution. Its expected running time is linear with respect to the number of vertices. A database consisting of possible topology changes is developed in the mathematical framework of homology theory. This database allows for fast and robust topology adaptation during a mesh evolution. The algorithm works without mesh reparametrizations, global mesh smoothness assumptions or vertex sampling density conditions, making it suitable for robust, near real-time application. Furthermore, it can be integrated into existing mesh evolutions easily. Numerical examples from medical imaging are given.

References

  1. Abhau, J., W.Hinterberger, and Scherzer, O. (2007). Segmenting surfaces of arbitrary topology: A two-step approach. In Medical Imaging 2007: Ultrasonic Imaging and Signal Processing. Proceedings of SPIE - Volume 6513.
  2. Bischoff, S. and Kobbelt, L. (2004). Snakes with topology control. In The Visual Computer, Vol 20, pages 197- 206.
  3. Caselles, V., Catte, F., Coll, B., and Dibos, F. (1993). A geometric model for active contours in image processing. Numerische Mathematik, 66:1-31.
  4. Chen, Y. and Medioni, G. (1995). Description of complex objects from multiple range images using an inflating balloon model. Computer Vision and Image Understanding, 61, No 3:325-334.
  5. Delingette, H. (1994). Adaptive and deformable models based on simplex meshes. In IEEE Workshop of NonRigid and Articulated Objects. IEEE Computer Society Press.
  6. Dey, T. K., Edelsbrunner, H., and Guha, S. (1999). Computational topology. In Advances in Discrete and Computational Geometry (Contemporary mathematics 223), pages 109-143. American Mathematical Society.
  7. Hatcher, A. (2002). Algebraic Topology. Cambridge University Press.
  8. Lachaud, J. O. and Montanvert, A. (1999). Deformable meshes with automated topology changes for coarseto-fine three-dimensional surface extraction. Journal of Medical Image Analysis, 3, No 2:187-207.
  9. Lachaud, J. O. and Taton, B. (2003). Deformable model with adaptive mesh and automated topology changes. In Proceedings of 4th International Conference on 3- D Digital Imaging and Modeling (3DIM'2003).
  10. Lachaud, J. O. and Taton, B. (2004). Resolution independent deformable model. In International Conference on Pattern Recognition (ICPR'2004), pages 237-240.
  11. Lachaud, J. O. and Taton, B. (2005). Deformable model with a complexity independent from image resolution. Computer Vision and Image Understanding, 99(3):453-475.
  12. Massey, W. S. (1991). A basic course in algebraic topology. Springer.
  13. McInerney, T. and Terzopoulos, D. (2000). T-snakes: Topology adaptive snakes. Medical Image Analysis, 4(2):73-91.
  14. Moller, T. (1997). A fast triangle-triangle intersection test. Journal of Graphics Tools, 2/2:25-30.
  15. Osher, S. and Sethian, J. A. (1988). Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulations. Journal of Computational Physics, 79:12-49.
  16. PARI (2005). PARI/GP, version 2.1.7. The PARI Group, Bordeaux. available from http://pari.math. u-bordeaux.fr/.
  17. Pons, J. P. and Boissonnat, J. D. (2007). Delaunay deformable models: Topology-adaptive meshes based on the restricted delaunay triangulation.
  18. Taubin, G. (1985). A signal processing approach to fair surface design. In Computer Graphics (SIGGRAPH 95 Proceedings), pages 351-358.
  19. Teschner, M., Heidelberger, B., Mueller, M., Pomeranets, D., and Gross, M. (2003). Optimized spatial hashing for collision detection of deformable objects. In Proceedings of Vision, Modeling, Visualization, pages 47-54.
  20. Teschner, M., Kimmerle, S., Heidelberger, B., Zachmann, G., Raghupathi, L., Fuhrmann, A., Cani, M., Faure, F., Magnenat-Thalmann, N., Strasser, W., and Volino, P. (2005). Collision detection for deformable objects. Computer Graphics Forum, 24:61-81.
  21. Witkin, A., Kass, M., and Terzopoulos, D. (1987). Snakes: Active contour models. International Journal of Computer Vision, 1, No 4:321-331.
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Paper Citation


in Harvard Style

Abhau J. (2008). A ROBUST AND EFFICIENT METHOD FOR TOPOLOGY ADAPTATIONS IN DEFORMABLE MODELS . In Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008) ISBN 978-989-8111-21-0, pages 375-382. DOI: 10.5220/0001085103750382


in Bibtex Style

@conference{visapp08,
author={Jochen Abhau},
title={A ROBUST AND EFFICIENT METHOD FOR TOPOLOGY ADAPTATIONS IN DEFORMABLE MODELS},
booktitle={Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008)},
year={2008},
pages={375-382},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001085103750382},
isbn={978-989-8111-21-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008)
TI - A ROBUST AND EFFICIENT METHOD FOR TOPOLOGY ADAPTATIONS IN DEFORMABLE MODELS
SN - 978-989-8111-21-0
AU - Abhau J.
PY - 2008
SP - 375
EP - 382
DO - 10.5220/0001085103750382