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


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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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


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