Advertisement

GPU Accelerated Computation of Geometric Descriptors in Parametric Space

  • Anthousis AndreadisEmail author
  • Georgios Papaioannou
  • Pavlos MavridisEmail author
Part of the Communications in Computer and Information Science book series (CCIS, volume 598)

Abstract

We present a novel generic method for the fast and accurate computation of geometric descriptors. While most existing approaches perform the computations directly on the geometric representation of the model, our method operates in parametric space, decoupling the computational complexity from the underlying mesh geometry. In contrast to other parametric space approaches, our method is not restricted to specific descriptors or parameterisations of the surface. By using the parametric space representation of the mesh geometry, we can trivially exploit massive parallel GPU architectures and achieve interactive computation times, while maintaining high accuracy. This renders the method suitable for computations involving large areas of support and animated shapes.

Keywords

Geometric descriptors Parametric space Mesh geometry GPU acceleration 

Notes

Acknowledgements

This work was supported by EC FP7 STREP Project PRESIOUS, grant no. 600533. Armadillo, Lucy, Bunny and XYZ RGB Dragon models are from Stanford 3D Scanning Repository. Angel model is from the Large Geometric Models Archive of Georgia Institute of Technology. Rim model is from TurboSquid. All other models used are from the PRESIOUS project data collection.

References

  1. 1.
    Bertrand, J., Diquet, C., Puiseux, V.: Démonstration d’un théorème de Gauss. J. Math. 13, 80–90 (1848)Google Scholar
  2. 2.
    Campagna, S., Kobbelt, L., Seidel, H.P.: Directed edges — a scalable representation for triangle meshes. J. Graph. Tools 3(4), 1–11 (1998)CrossRefGoogle Scholar
  3. 3.
    Connolly, M.L.: Measurement of protein surface shape by solid angles. J. Mol. Graph. 4(1), 3–6 (1986)MathSciNetCrossRefGoogle Scholar
  4. 4.
    De Floriani, L., Hui, A.: Data structures for simplicial complexes: an analysis and a comparison. In: Proceedings of the Third Eurographics Symposium on Geometry Processing. SGP 2005. Eurographics Association (2005)Google Scholar
  5. 5.
    Floater, M., Hormann, K.: Surface parameterization: a tutorial and survey. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds.) Advances in Multiresolution for Geometric Modelling. Mathematics and Visualization, pp. 157–186. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Griffin, W., Wang, Y., Berrios, D., Olano, M.: GPU curvature estimation on deformable meshes. In: Symposium on Interactive 3D Graphics and Games, I3D ’11, pp. 159–166. ACM (2011)Google Scholar
  7. 7.
    Gu, X., Gortler, S.J., Hoppe, H.: Geometry images. In: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH ’02, pp. 355–361. ACM (2002)Google Scholar
  8. 8.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: Proceedings of the 4th Alvey Vision Conference, pp. 147–151 (1988)Google Scholar
  9. 9.
    Hormann, K., Polthier, K., Sheffer, A.: Mesh parameterization: theory and practice. In: ACM SIGGRAPH ASIA 2008 Courses. SIGGRAPH Asia ’08, pp. 12: 1–12: 87. ACM (2008)Google Scholar
  10. 10.
    Hua, J., Lai, Z., Dong, M., Gu, X., Qin, H.: Geodesic distance-weighted shape vector image diffusion. IEEE Trans. Vis. Comput. Graph. 14(6), 1643–1650 (2008)CrossRefGoogle Scholar
  11. 11.
    Huang, Q.X., Flöry, S., Gelfand, N., Hofer, M., Pottmann, H.: Reassembling fractured objects by geometric matching. ACM Trans. Graph. 25(3), 569–578 (2006)CrossRefGoogle Scholar
  12. 12.
    Hulin, D., Troyanov, M.: Mean curvature and asymptotic volume of small balls. Am. Math. Monthly 110(10), 947–950 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kim, Y., Yu, J., Yu, X., Lee, S.: Line-art illustration of dynamic and specular surfaces. In: ACM SIGGRAPH Asia 2008 Papers. SIGGRAPH Asia ’08, pp. 156: 1–156: 10. ACM (2008)Google Scholar
  14. 14.
    Koenderink, J.J., van Doorn, A.J.: Surface shape and curvature scales. Image Vis. Comput. 10(8), 557–565 (1992)CrossRefGoogle Scholar
  15. 15.
    Manay, S., Hong, B.-W., Yezzi, A.J., Soatto, S.: Integral invariant signatures. In: Pajdla, T., Matas, J.G. (eds.) ECCV 2004. LNCS, vol. 3024, pp. 87–99. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    McGuire, M., Osman, B., Bukowski, M., Hennessy, P.: The alchemy screen-space ambient obscurance algorithm. In: Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics. HPG ’11, pp. 25–32. ACM (2011)Google Scholar
  17. 17.
    Mellado, N., Barla, P., Guennebaud, G., Reuter, P., Duquesne, G.: Screen-space curvature for production-quality rendering and compositing. In: ACM SIGGRAPH 2013 Talks. SIGGRAPH ’13, pp. 42: 1–42: 1. ACM (2013)Google Scholar
  18. 18.
    Meyer, M., Desbrun, M., Schrder, P., Barr, A.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Hege, H.-C., Polthier, K. (eds.) Visualization and Mathematics III. Mathematics and Visualization, pp. 35–57. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Museth, K.: Vdb: high-resolution sparse volumes with dynamic topology. ACM Trans. Graph. 32(3), 27:1–27:22 (2013)CrossRefzbMATHGoogle Scholar
  20. 20.
    Novatnack, J., Nishino, K.: Scale-dependent 3D geometric features. In: IEEE 11th International Conference on Computer Vision, 2007. ICCV 2007, pp. 1–8. IEEE, October 2007Google Scholar
  21. 21.
    Pottmann, H., Wallner, J., Huang, Q.X., Yang, Y.L.: Integral invariants for robust geometry processing. Comput. Aided Geom. Des. 26(1), 37–60 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Pottmann, H., Wallner, J., Yang, Y.L., Lai, Y.K., Hu, S.M.: Principal curvatures from the integral invariant viewpoint. Comput. Aided Geom. Des. 24(8), 428–442 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Rusinkiewicz, S.: Estimating curvatures and their derivatives on triangle meshes. In: Proceedings of the 2nd International Symposium on 3D Data Processing, Visualization, and Transmission. 3DPVT ’04, pp. 486–493. IEEE Computer Society (2004)Google Scholar
  24. 24.
    Sander, P.V., Wood, Z.J., Gortler, S.J., Snyder, J., Hoppe, H.: Multi-chart geometry images. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. SGP ’03, pp. 146–155. Eurographics Association (2003)Google Scholar
  25. 25.
    Sander, P.V., Snyder, J., Gortler, S.J., Hoppe, H.: Texture mapping progressive meshes. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH ’01, pp. 409–416. ACM (2001)Google Scholar
  26. 26.
    Sheffer, A., Praun, E., Rose, K.: Mesh parameterization methods and their applications. Found. Trends. Comput. Graph. Vis. 2(2), 105–171 (2006)CrossRefzbMATHGoogle Scholar
  27. 27.
    Shirley, P., Chiu, K.: A low distortion map between disk and square. J. Graph. Tools 2(3), 45–52 (1997)CrossRefGoogle Scholar
  28. 28.
    Sipiran, I., Bustos, B.: Harris 3D: a robust extension of the harris operator for interest point detection on 3D meshes. Vis. Comput. 27(11), 963–976 (2011)CrossRefGoogle Scholar
  29. 29.
    Taubin, G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. In: Proceedings of the Fifth International Conference on Computer Vision. ICCV ’95, pp. 902–907. IEEE Computer Society (1995)Google Scholar
  30. 30.
    Yang, Y.L., Lai, Y.K., Hu, S.M., Pottmann, H.: Robust principal curvatures on multiple scales. In: Symposium on Geometry Processing, pp. 223–226 (2006)Google Scholar
  31. 31.
    Yoshizawa, S., Belyaev, A., Seidel, H.P.: A fast and simple stretch-minimizing mesh parameterization. In: Proceedings of the Shape Modeling International. SMI ’04, pp. 200–208. IEEE Computer Society (2004)Google Scholar
  32. 32.
    Zhou, K., Synder, J., Guo, B., Shum, H.Y.: Iso-charts: stretch-driven mesh parameterization using spectral analysis. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. SGP ’04, pp. 45–54. ACM (2004)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of InformaticsAthens University of Economics and BusinessAthensGreece

Personalised recommendations