Visualizing the Evolutions of Silhouettes

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 their splitting, merging, appearing and disappearing. The dynamics of silhouettes are governed by the topology, the curvature of the surface, and the viewpoint. Some theoretical results are established: the integration of signed geodesic curvature along a silhouette is equal to the view cone angle; critical events can only happen when the view point is on the aspect surfaces (ruled surface of the asymptotic lines of parabolic points). We 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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