Area- and Angle-Preserving Parameterization for Vertebra Surface Mesh
- 1k Downloads
This paper proposes a parameterization method of vertebra models by mapping them onto the parameterized surface of a torus. Our method is based on a modified Self-organizing Deformable Model (mSDM) , which is a deformable model guided by competitive learning and an energy minimization approach. Unlike conventional mapping methods, the mSDM finds the one-to-one mapping between arbitrary surface model and the target surface with the same genus as the model. At the same time, the mSDM can preserve geometrical properties of the original model before and after mapping. Moreover, users are able to control mapping positions of the feature vertices in the model. Using the mSDM, the proposed method maps the vertebra model onto a torus surface through an intermediate surface with the approximated shape of the vertebra. The use of the intermediate surface results in the stable mapping of the vertebra to a torus compared with the direct mapping from the model to the torus.
KeywordsFeature Vertices Intermediate Surface Vertebral Model Target Surface Tor Surface
This work was supported by Foundation of Kyushu University, JSPS KAKENHI Grant Number 26560262, 24390345 and the Ministry of Health, Labour and Welfare(2010241 71A).
- 1.Miyauchi, S., Morooka, K., Miyagi, Y., Fukuda, T., Tsuji, T., Kurazume, R.: Tissue surface model mapping onto arbitrary target surface based on self-organizing deformable model. In: Workshop on Computer Vision at the 4th International Conference on Emerging Security Technologies, pp. 79–82 (2013)Google Scholar
- 3.Morooka, K., Nakamoto, M., Sato, Y.: A survey on statistical modeling and machine learning approaches to computer assisted medical intervention: Intraoperative anatomy modeling and optimization of interventional procedures. Trans. Inf. Syst. E96-D(4), 784–797 (2013)Google Scholar
- 5.Hormann, K., Levy, B., Sheffer, A.: Mesh parameterization:theory and practice. (2007)Google Scholar
- 8.Becker, M., Kirschner, M., Fuhrmann, S., Wesarg, S.: Automatic construction of statistical shape models for vertebrae. In: Medical Image Computing and Computer-Assisted Intervention-MICCAI 2011, pp. 500–507. Springer, Heidelberg (2011)Google Scholar
- 9.Morooka, K. I., Nagahashi, H.: Self-organizing deformable model: a new method for fitting mesh model to given object surface. In: Advances in Visual Computing, pp. 151–158. Springer, Heidelberg (2005)Google Scholar
- 10.Sederberg, T. W., Parry, S. R.: Free-form deformation of solid geometric models. In: ACM Siggraph Computer Graphics, vol. 20, no. 4, pp. 151–160. ACM (1986)Google Scholar
- 11.Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Advances in multiresolution for Geometric Modelling, pp. 157–186. Springer, Heidelberg (2005)Google Scholar