From Real-Time Shape Deformation to Geometric Flows in Shape Space
Klaus Hildebrandt (Delft University of Technology, The Netherlands)
The optimization of deformable, flexible or non-rigid shapes is essential for many tasks in geometric modeling and processing. In the first part of this talk, I will introduce model reduction techniques that can be used to construct fast approximation algorithms for shape optimization problems. The goal is to obtain run times that are independent of the resolution of the discrete shapes to be optimized. As an example, we will discuss a method for real-time elasticity-based shape interpolation.
In the second part, we will broaden the perspective and discuss how concepts from elasticity can be used to obtain geometric structures on shape spaces, in which a shape is a single point. We will see how these structures can be used for the processing of motion and animations of non-rigid shapes. The idea is to treat the motions as curves in shape space and to transfer concepts from curve processing in Euclidean space to the processing of motion of non-rigid shapes. We will discuss explicit examples including a geometric flow of curves in shapes space that can be used for reducing jittering artifacts in motion capture data, the construction of subdivision curves in shape space and the efficient computation of geodesics in shape space.
|Klaus Hildebrandt is a faculty member at the Intelligent Systems Department at Delft University of Technology, The Netherlands. Previous to that he was a Senior Researcher at the Max Planck Institute for Informatics in Saarbrücken, Germany, where he headed the Applied Geometry group. He received his PhD in mathematics from Freie University Berlin. His research interests are in geometric modeling and geometry processing, computational and discrete differential geometry and physics-based computer animation.|
Topology-aware Modeling from Curves
Tao Ju (Washington University in St. Louis, USA)
Many applications of surface models, such as mesh processing, simulation, and manufacturing, are sensitive to the topological properties of the models. To create a surface with the desirable topology, a common strategy is to first reconstruct the surface from the input data using a topology-oblivious algorithm and then fix any topological errors in a post-process. We advocate a different strategy that reconstructs the surface with topology constraints in mind. The talk reviews several recent work in this direction that revolve around reconstructing surfaces from a network of spatial curves. We will consider a variety of topological constraints, such as manifoldness, connected components, and genus.
|Tao Ju is a Professor in the Department of Computer Science and Engineering at the Washington University in St. Louis. He obtained his M.S. and PhD degrees in Computer Science at Rice University in 2005.He conducts research in computer graphics and bio-medical applications, and is particularly interested in geometric modeling and processing. He has served as an associated editor for journals IEEE Transactions on Visualization and Computer Graphics, Computer Graphics Forum, Computer-Aided Design, and Graphical Models. His research is funded by NSF and NIH, including an NSF CAREER award in 2009.|
Geodesic Voronoi diagrams and medial axes on 2-manifold meshes
Yong-Jin Liu (Tsinghua University, China)
In computer graphics and machine perception, three-dimensional objects such as terrain and brain cortex are usually represented by 2-manifold meshes M. Compared to Euclidean metric spaces, the Voronoi diagrams based on geodesic metric on M exhibit many distinct properties that fail all existing Euclidean Voronoi diagram. In this talk, the combinatorial structure of geodesic Voronoi diagrams with complexity analysis is presented. If the generator is a closed curve bounding a 2D shape on M, the geodesic Voronoi diagram is also related to a geodesic medial axis of the 2D shape on M. Several properties that make geodesic medial axis on M distinct from it Euclidean counterpart are also presented. Finally practical algorithms for constructing geodesic Voronoi diagram and medial axis on M, as well as some applications in computer graphics and pattern analysis are presented.
|Dr. Yong-Jin Liu received his B.Eng from Mechano-Electronic Engineering, Tianjin University in 1998, and his PhD degree from Mechanical Engineering, The Hong Kong University of Science and Technology in 2004. He joined the Department of Computer Science at Tsinghua University in 2006 and he now is an associate professor. His research interests include computational geometry, computer graphics, and computer-aided design, and pattern analysis. He received the Second-Class National Technology Invention Award in 2011, a Best Reviewer Award in CAD/Graphics 2013, a Gold Medal Award at the 41st International Exhibition of Inventions of Geneva, Switzerland, 2013, and a Best Paper Award in Symposium on Solid and Physical Modeling (SPM) 2014. Started from 2014, he was supported by Distinguished Young Scholar Program in the Natural Science Foundation of China. For more information, visit his website.|