| Topology evolutions of silhouettes |
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| 作者姓名： | DAI Jun-fei KIM Junho ZENG Hua-yi GU Xian-feng YAU Shing-tung |
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| 作者单位： | Visualization Laboratory State University of New York Stony Brook NY 11794 USA，Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China Department of Mathematics Harvard University Boston MA02138 USA |
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| 基金项目： | Project supported by the NSF CAREER Award （Nos. CCF-0448339 and DMS-0528363） of the USA, and the National Natural Science Foundation of China （No. 60503067）
We thank Stanford University for providing the surface models. |
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| 摘 要： | We give the topology changing of the silhouette in 3D space while others study the projections in an image. Silhou- ettes 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 enu- merative 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.
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| 关 键 词： | 拓扑转变 侧面影象 测地线 尖点 |
| 收稿时间： | 2007-03-28 |
| 修稿时间： | 2007-04-20 |
Topology evolutions of silhouettes |
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| DAI Jun-fei KIM Junho ZENG Hua-yi GU Xian-feng YAU Shing-tung.Topology evolutions of silhouettes[J].Journal of Zhejiang University Science,2007,8(10):1671-1680. |
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| Authors: | Dai Jun-fei Kim Junho Zeng Hua-yi Gu Xian-feng Yau Shing-tung |
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| Institution: | (1) Center of Mathematical Sciences, Zheijiang University, Hangzhou, 310027, China;(2) Visualization Laboratory, State University of New York, Stony Brook, NY 11794, USA;(3) Department of Mathematics, Harvard University, Boston, MA 02138, USA |
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| Abstract: | We give the topology changing of the silhouette in 3D space while others study the projections in an image. Silhou- ettes 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 enu- merative 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. |
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| Keywords: | Topological change Silhouette Geodesic curvature Cusp |
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