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Issue No.06 - November/December (2009 vol.15)
pp: 1201-1208
Gregory Cipriano , University of Wisconsin
George N. Phillips Jr. , University of Wisconsin
Michael Gleicher , University of Wisconsin
ABSTRACT
Local shape descriptors compactly characterize regions of a surface, and have been applied to tasks in visualization, shape matching, and analysis. Classically, curvature has be used as a shape descriptor; however, this differential property characterizes only an infinitesimal neighborhood. In this paper, we provide shape descriptors for surface meshes designed to be multi-scale, that is, capable of characterizing regions of varying size. These descriptors capture statistically the shape of a neighborhood around a central point by fitting a quadratic surface. They therefore mimic differential curvature, are efficient to compute, and encode anisotropy. We show how simple variants of mesh operations can be used to compute the descriptors without resorting to expensive parameterizations, and additionally provide a statistical approximation for reduced computational cost. We show how these descriptors apply to a number of uses in visualization, analysis, and matching of surfaces, particularly to tasks in protein surface analysis.
INDEX TERMS
Curvature, descriptors, npr, stylized rendering, shape matching.
CITATION
Gregory Cipriano, George N. Phillips Jr., Michael Gleicher, "Multi-Scale Surface Descriptors", IEEE Transactions on Visualization & Computer Graphics, vol.15, no. 6, pp. 1201-1208, November/December 2009, doi:10.1109/TVCG.2009.168
REFERENCES
[1] S. Buss and J. Fillmore, Spherical averages and applications to spherical splines and interpolation. ACM Trans. Graph., 20 (2): 95–126, 2001.
[2] Y. Cai and F. Dong, Surface hatching for medical volume data. In Computer Graphics, Imaging and Vision: New Trends, 2005. International Conference on, pages 232–238, 2005.
[3] C. Chua and R. Jarvis, Point signatures: A new representation for 3D object recognition. International Journal of Computer Vision, 1997.
[4] R G. Coleman, M A. Burr, D L. Souvaine, and A C. Cheng, An intuitive approach to measuring protein surface curvature. Proteins: Structure, Function, and Bioinformatics, 61 (4): 1068–1074, 2005.
[5] D. DeCarlo, A. Finkelstein, S. Rusinkiewicz, and A. Santella, Suggestive contours for conveying shape. ACM Trans. Graph., 22 (3): 848–855, 2003.
[6] R. Gal and D. Cohen-Or, Salient geometric features for partial shape matching and similarity. ACM Trans. Graph., 25 (l): 130–150, 2006.
[7] T. Gatzke and C. Grimm, Estimating curvature on triangular meshes. International Journal of Shape Modeling, 12 1: 12–1, June 2006.
[8] T. Gatzke, C. Grimm, M. Garland, and S. Zelinka, Curvature maps for local shape comparison. In Shape Modeling and Applications, 2005 International Conference, pages 244–253, 2005.
[9] A. Girshick, V. Interrante, S. Haker, and T. Lemoine, Line direction matters: an argument for the use of principal directions in 3D line drawings. In Proceedings of the 1st international symposium on Non-photorealistic animation and rendering, pages 43–52, Annecy, France, 2000. ACM.
[10] J. Goldfeather and V. Interrante, A novel cubic-order algorithm for approximating principal direction vectors. ACM Trans. Graph., 2004.
[11] B. Goldman and W T. Wipke, Quadratic shape descriptors. 1. rapid superposition of dissimilar molecules using geometrically invariant surface descriptors. Journal of Chemical Information and Computer Sciences, 40 (3): 644–658, May 2000.
[12] R. Gonzalez and R. Woods, Digital Image Processing. Prentice-Hall, 2002.
[13] G. Gorla, V. Interrante, and G. Sapiro, Texture synthesis for 3D shape representation. Visualization and Computer Graphics, IEEE Transactions on, 9 (4): 512–524, 2003.
[14] S. Gumhold, Maximum entropy light source placement. In Proceedings of the conference on Visualization '02, pages 275–282, Boston, Massachusetts, 2002. IEEE Computer Society.
[15] P. Huber, Robust Statistics. Wiley-Interscience, Feb. 1981.
[16] A. Johnson, Spin-images: a representation for 3-D surface matching. Carnegie Mellon University, The Robotics Institute, 1997.
[17] E. Kalogerakis, D. Nowrouzezahrai, P. Simari, J. Mccrae, A. Hertzmann, and K. Singh, Data-driven curvature for real-time line drawing of dynamic scenes. ACM Trans. Graph., 28 1: 28–1, 2009.
[18] G. Kindlmann, R. Whitaker, T. Tasdizen, and T. Moller, Curvature-Based transfer functions for direct volume rendering: Methods and applications. In Proceedings of the 14th IEEE Visualization 2003 (VIS'03), page 67. IEEE Computer Society, 2003.
[19] M. Körtgen, G. Park, M. Novotni, and R. Klein, 3D shape matching with 3D shape contexts. In the 7th Central European Seminar on Computer Graphics, Apr. 2003.
[20] C. Lee, X. Hao, and A. Varshney, Geometry-dependent lighting. Visualization and Computer Graphics, IEEE Transactions on, 2006.
[21] Q. Li and J. Griffiths, Least squares ellipsoid specific fitting. In Geometric Modeling and Processing, 2004. Proceedings, pages 335–340, 2004.
[22] A. Mangan and R. Whitaker, Partitioning 3D surface meshes using watershed segmentation. Visualization and Computer Graphics, IEEE Transactions on, 5 (4): 308–321, 1999.
[23] M. Mortara, G. Patan, M. Spagnuolo, B. Falcidieno, and J. Rossignac, Blowing bubbles for Multi-Scale analysis and decomposition of triangle meshes. Algorithmica, 38 (l): 227–248, 2003.
[24] D. Page, Y. Sun, A. Koschan, J. Paik, and M. Abidi, Normal vector voting: crease detection and curvature estimation on large, noisy meshes. Graph. Models, 64 (3/4): 199–229, 2002.
[25] S. Petitjean, A survey of methods for recovering quadrics in triangle meshes. ACM Computing Surveys, 2: 161, 2002.
[26] V. Pratt, Direct least-squares fitting of algebraic surfaces. SIGGRAPH Comput. Graph., 21 (4): 145–152, 1987.
[27] E. Praun, M. Webb, and A. Finkelstein, Real-time hatching. IN PROCEEDINGS OF SIGGRAPH 2001, pages 579—584, 2001.
[28] S. Rusinkiewicz, Estimating curvatures and their derivatives on triangle meshes. In Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium, pages 486–493. IEEE Computer Society, 2004.
[29] M. Sanner, A. Olson, and J. Spehner, Fast and robust computation of molecular surfaces. In Proceedings of the eleventh annual symposium on Computational geometry, pages 406–407, Vancouver, British Columbia, Canada, 1995. ACM.
[30] R. Schmidt, C. Grimm, and B. Wyvill, Interactive decal compositing with discrete exponential maps. ACM Transactions on Graphics, 25 (3): 603–613, 2006.
[31] A. Sheffer and J C. Hart, Seamster: inconspicuous low-distortion texture seam layout. In Proceedings of the conference on Visualization '02, pages 291–298, Boston, Massachusetts, 2002. IEEE Computer Society.
[32] E. Stokely and S. Wu, Surface parametrization and curvature measurement of arbitrary 3-D objects: five practical methods. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 14 (8): 833–840, 1992.
[33] V. Surazhsky, T. Surazhsky, D. Kirsanov, S. Gortler, and H. Hoppe, Fast exact and approximate geodesies on meshes. ACM Trans. Graph., 24 (3): 553–560, 2005.
[34] C. Toler-Franklin, A. Finkelstein, and S. Rusinkiewicz, Illustration of complex real-world objects using images with normals. In Proceedings of the 5th international symposium on Non-photorealistic animation and rendering, pages 111–119, San Diego, California, 2007. ACM.
[35] R. Vergne, P. Barla, X. Granier, and C. Schlick, Apparent relief: a shape descriptor for stylized shading. In Proceedings of the 6th international symposium on Non-photorealistic animation and rendering, pages 23–29, Annecy, France, 2008. ACM.
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