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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.10 P.1671~1680

http://doi.org/10.1631/jzus.2007.A1671


Topology evolutions of silhouettes


Author(s):  DAI Jun-fei, KIM Junho, ZENG Hua-yi, GU Xian-feng, YAU Shing-tung

Affiliation(s):  Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   jfdai@cms.zju.edu.cn, jkim@cs.sunysb.edu, hzeng@cs.sunysb.edu, gu@cs.sunysb.edu, yau@math.harvard.ed

Key Words:  Topological change, Silhouette, Geodesic curvature, Cusp


DAI Jun-fei, KIM Junho, ZENG Hua-yi, GU Xian-feng, YAU Shing-tung. Topology evolutions of silhouettes[J]. Journal of Zhejiang University Science A, 2007, 8(10): 1671~1680.

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author="DAI Jun-fei, KIM Junho, ZENG Hua-yi, GU Xian-feng, YAU Shing-tung",
journal="Journal of Zhejiang University Science A",
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year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1671"
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A1 - YAU Shing-tung
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A1671


Abstract: 
We give the topology changing of the silhouette in 3D space while others study the projections in an image. silhouettes play a crucial role in visualization, graphics and vision. This work focuses on the global behaviors of silhouettes, especially their topological evolutions, such as splitting, merging, appearing and disappearing. The dynamics of silhouettes are governed by the topology, the curvature of the surface, and the view point. In this paper, we work on a more theoretical level to give enumerative properties of the silhouette including: the integration of signed geodesic curvature along a silhouette is equal to the view cone angle; in elliptic regions, no silhouette can be contained in another one; in hyperbolic regions, if a silhouette is homotopic to a point, then it has at least 4 cusps; finally, critical events can only happen when the view point is on the aspect surfaces (ruled surface of the asymptotic lines of parabolic points with surface itself). We also introduce a method to visualize the evolution of silhouettes, especially all the critical events where the topologies of the silhouettes change. The results have broad applications in computer vision for recognition, graphics for rendering and visualization.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Arnold, V.I., 1986. Catastrophe Theory (2nd Ed.). Springer-Verlag.

[2] Bottino, A., Laurentini, A., 2003. Introducing a new problem: shape from silhouette when the relative positions of the viewpoints is unknown. IEEE Trans. on Pattern Anal. Machine Intell., 25(11):1484-1493.

[3] Boyer, E., Berger, M.O., 1995. Smooth Surface Reconstruction from Image Sequences. IEEE Int. Conf. on Image Processing, p.398-401.

[4] Boyer, E., Berger, M.O., 1997. 3D surface reconstruction using occluding contours. Int. J. Computer Vision, 22(3):219-233.

[5] Cipolla, R., Zisserman, A., 1992. Qualitative surface shape from deformation of image curves. Int. J. Computer Vision, 8:53-69.

[6] Cipolla, R., Fletcher, G.J., Giblin, P.J., 1995. Surface Geometry from Cusps of Apparent Contours. Int. Conf. on Computer Vision, p.858-863.

[7] Cipolla, R., Fletcher, G.J., Giblin, P.J., 1997. Following cusps. Int. J. Computer Vision, 23:115-129.

[8] Cyr, C.M., Kimia, B.B., 2001. 3D Object Recognition Using Shape Similarity-based Aspect Graph. Int. Conf. on Computer Vision, p.254-261.

[9] Ebert, D., Rheingans, P., 2000. Volume Illustration: Non-Photorealistic Rendering of Volume Models. In: Ertl, T., Hamann, B., Varshney, A. (Eds.), Proc. Visualization, p.195-202.

[10] Forsyth, D., 1993. Recognizing Algebraic Surfaces from Their Outlines. Int. Conf. on Computer Vision, 93:476-480.

[11] Forsyth, D.A., Ponce, J., 2002. Computer Vision: A Modern Approach. Prentice Hall. FOR d 02:1 1.Ex.

[12] Gooch, B., Gooch, A., 2001. Non-Photorealistic Rendering. A K Peters.

[13] Hertzmann, A., Zorin, D., 2000. Illustrating Smooth Surfaces. ACM SIGGRAPH, p.517-526.

[14] Isenberg, T., Halper, N., Schlechtweg, S., Strothotte, T., 2003. A developer’s guide to silhouette algorithms for polygonal models. IEEE Computer Graph. Appl., 23(4):28-37.

[15] Kalnins, R.D., Davidson, P.L., Markosian, L., Finkelstein, A., 2003. Coherent stylized silhouettes. ACM Trans. on Graph., 22(3):856-861.

[16] Koenderink, J., van Doorn, A.J., 1976. The singularities of the visual mapping. Biol. Cybern., 24:51-59.

[17] Koenderink, J., 1984. What Does the Occluding Contour Tell Us about Solid Shape? Volume 13. Mit Press, Cambridge.

[18] Landis, E.E., 1981. Tangential singularities. Funct. Anal. & Its Appl., 15(2):103-114.

[19] Laurentini, A., 1995. How far 3D shapes can be understood from 2D silhouettes. IEEE T-PAMI, 17:188-195.

[20] Lee, J., Moghaddam, B., Pfister, H., Machiraju, R., 2003. Silhouette Based 3D Face Shape Recovery. Proc. Graphics Interface, p.21-30.

[21] Marr, D., 1977. Analysis of occluding contour. Proc. Royal Soc. B, p.441-475.

[22] Marr, D., 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. W.H. Freeman & Company.

[23] McCrory, C., 1980. Profiles of Surfaces. University of Warwick, in press.

[24] Northrup, J.D., Markosian, L., 2000. Artistic Silhouettes: A Hybrid Approach. Proc. 1st Int. Symp. on Non-Photorealistic Animation and Rendering, p.31-37.

[25] Pae, S., Ponce, J., 2001. On computing structural changes in evolving surfaces and their appearance. Int. J. Computer Vision, 43(2):113-131.

[26] Platonova, O.A., 1981. Singularities of contact of a surface and a line. Uspekhi Mat. Nauk, 36(1).

[27] Ponce, J., Kriegman, D., 1989. On Recognising and Positioning Curved 3 Dimensional Objects from Image Contours. Proc. DARPA IU Workshop.

[28] Ponce, J., Petitjean, S., Kriegman, D.J., 1992. Computing Exact Aspect Graphs of Curved Objects: Algebraic Surfaces. European Conf. on Computer Vision, p.599-614.

[29] Strothotte, T., Schlechtweg, S., 2002. Non-Photorealistic Computer Graphics: Modeling, Rendering, and Animation. Morgan Kaufmann Publishers.

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