A Parametric Space Approach to the Computation of Multi-scale Geometric Features
Anthousis Andreadis, Georgios Papaioannou, Pavlos Mavridis
2015
Abstract
In this paper we present a novel generic method for the fast and accurate computation of geometric features at multiple scales. The presented method works on arbitrarily complex models and operates in the parametric space. The majority of the existing methods compute local features directly on the geometric representation of the model. Our approach decouples the computational complexity from the underlying geometry and in contrast to other parametric space methods, it is not restricted to a specific feature or parameterization of the surface. We show that the method performs accurately and at interactive rates, even for large feature areas of support, rendering the method suitable for animated shapes.
References
- Bertrand, J., Diquet, C., and Puiseux, V. (1848). Démonstration d'un théorème de Gauss. Journal de Mathématiques, 13:80-90.
- Campagna, S., Kobbelt, L., and Seidel, H.-P. (1998). Directed edges—a scalable representation for triangle meshes. J. Graph. Tools, 3(4):1-11.
- Connolly, M. L. (1986). Measurement of protein surface shape by solid angles. J. Mol. Graph., 4(1):3-6.
- De Floriani, L. and Hui, A. (2005). Data structures for simplicial complexes: An analysis and a comparison. In Proc. of the Third Eurographics Symp. on Geometry Processing, SGP 7805. Eurographics Association.
- Floater, M. and Hormann, K. (2005). Surface parameterization: a tutorial and survey. In Advances in Multiresolution for Geometric Modelling, Mathematics and Visualization, pages 157-186. Springer.
- Griffin, W., Wang, Y., Berrios, D., and Olano, M. (2011). GPU curvature estimation on deformable meshes. In Symp. on Interactive 3D Graphics and Games, I3D 7811, pages 159-166. ACM.
- Gu, X., Gortler, S. J., and Hoppe, H. (2002). Geometry images. In Proc. of the 29th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 7802, pages 355-361. ACM.
- Hormann, K., Polthier, K., and Sheffer, A. (2008). Mesh parameterization: Theory and practice. In ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia 7808, pages 12:1-12:87. ACM.
- Hua, J., Lai, Z., Dong, M., Gu, X., and Qin, H. (2008). Geodesic distance-weighted shape vector image diffusion. IEEE Trans. Vis. Comput. Graph., 14(6):1643- 1650.
- Huang, Q.-X., Flöry, S., Gelfand, N., Hofer, M., and Pottmann, H. (2006). Reassembling fractured objects by geometric matching. ACM Trans. Graph., 25(3):569-578.
- Hulin, D. and Troyanov, M. (2003). Mean curvature and asymptotic volume of small balls. The American Mathematical Monthly, 110(10):947-950.
- Kim, Y., Yu, J., Yu, X., and Lee, S. (2008). Line-art illustration of dynamic and specular surfaces. In ACM SIGGRAPH Asia 2008 Papers, SIGGRAPH Asia 7808, pages 156:1-156:10. ACM.
- Koenderink, J. J. and van Doorn, A. J. (1992). Surface shape and curvature scales. Image Vision Comput., 10(8):557-565.
- Manay, S., Hong, B.-W., Yezzi, A., and Soatto, S. (2004). Integral invariant signatures. In Computer Vision - ECCV 2004, volume 3024 of Lecture Notes in Computer Science, pages 87-99. Springer.
- McGuire, M., Osman, B., Bukowski, M., and Hennessy, P. (2011). The alchemy screen-space ambient obscurance algorithm. In Proc. of the ACM SIGGRAPH Symp. on High Performance Graphics, HPG 7811, pages 25-32. ACM.
- Mellado, N., Barla, P., Guennebaud, G., Reuter, P., and Duquesne, G. (2013). Screen-space curvature for production-quality rendering and compositing. In ACM SIGGRAPH 2013 Talks, SIGGRAPH 7813, pages 42:1-42:1. ACM.
- Meyer, M., Desbrun, M., Schrder, P., and Barr, A. (2003). Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and Mathematics III, Mathematics and Visualization, pages 35-57. Springer.
- Museth, K. (2013). Vdb: High-resolution sparse volumes with dynamic topology. ACM Trans. Graph., 32(3):27:1-27:22.
- Novatnack, J. and Nishino, K. (2007). Scale-dependent 3D geometric features. In Computer Vision, 2007. ICCV 2007. IEEE 11th International Conference on, pages 1-8. IEEE.
- Pottmann, H., Wallner, J., Huang, Q.-X., and Yang, Y.-L. (2009). Integral invariants for robust geometry processing. Comput. Aided Geom. Des., 26(1):37-60.
- Pottmann, H., Wallner, J., Yang, Y.-L., Lai, Y.-K., and Hu, S.-M. (2007). Principal curvatures from the integral invariant viewpoint. Computer Aided Geometric Design, 24(8):428-442.
- Rusinkiewicz, S. (2004). Estimating curvatures and their derivatives on triangle meshes. In Proceedings of the 3D Data Processing, Visualization, and Transmission, 2Nd International Symposium, 3DPVT 7804, pages 486-493. IEEE Computer Society.
- Sander, P. V., Snyder, J., Gortler, S. J., and Hoppe, H. (2001). Texture mapping progressive meshes. In Proc. of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 7801, pages 409-416. ACM.
- Sander, P. V., Wood, Z. J., Gortler, S. J., Snyder, J., and Hoppe, H. (2003). Multi-chart geometry images. In Proc. of the 2003 Eurographics/ACM SIGGRAPH Symp. on Geometry Processing, SGP 7803, pages 146- 155. Eurographics Association.
- Sheffer, A., Praun, E., and Rose, K. (2006). Mesh parameterization methods and their applications. Found. Trends. Comput. Graph. Vis., 2(2):105-171.
- Shirley, P. and Chiu, K. (1997). A low distortion map between disk and square. J. Graph. Tools, 2(3):45-52.
- Taubin, G. (1995). Estimating the tensor of curvature of a surface from a polyhedral approximation. In Proceedings of the Fifth International Conference on Computer Vision, ICCV 7895, pages 902-. IEEE Computer Society.
- Yang, Y.-L., Lai, Y.-K., Hu, S.-M., and Pottmann, H. (2006). Robust principal curvatures on multiple scales. In Symp. on Geometry Processing, pages 223- 226.
- Yoshizawa, S., Belyaev, A., and Seidel, H.-P. (2004). A fast and simple stretch-minimizing mesh parameterization. In Proc. of the Shape Modeling International 2004, SMI 7804, pages 200-208. IEEE Computer Society.
- Zhou, K., Synder, J., Guo, B., and Shum, H.-Y. (2004). Iso-charts: Stretch-driven mesh parameterization using spectral analysis. In Proc. of the 2004 Eurographics/ACM SIGGRAPH Symp. on Geometry Processing, SGP 7804, pages 45-54. ACM.
Paper Citation
in Harvard Style
Andreadis A., Papaioannou G. and Mavridis P. (2015). A Parametric Space Approach to the Computation of Multi-scale Geometric Features . In Proceedings of the 10th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2015) ISBN 978-989-758-087-1, pages 5-15. DOI: 10.5220/0005225700050015
in Bibtex Style
@conference{grapp15,
author={Anthousis Andreadis and Georgios Papaioannou and Pavlos Mavridis},
title={A Parametric Space Approach to the Computation of Multi-scale Geometric Features},
booktitle={Proceedings of the 10th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2015)},
year={2015},
pages={5-15},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005225700050015},
isbn={978-989-758-087-1},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 10th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2015)
TI - A Parametric Space Approach to the Computation of Multi-scale Geometric Features
SN - 978-989-758-087-1
AU - Andreadis A.
AU - Papaioannou G.
AU - Mavridis P.
PY - 2015
SP - 5
EP - 15
DO - 10.5220/0005225700050015