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Polygonal Shape Blending with Topological Evolutions

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Abstract

This paper presents a new general approach to blend 2D shapes with different topologies. All possible topological evolutions are classified into three types by attaching three different topological cells. This formalism is resulted from Morse theory on the behavior of the 3D surface around a non-degenerate critical point. Also we incorporate degenerate topological evolutions into our framework which produce more attractive morphing effects. The user controls the morph by specifying the types of topological evolutions as well as the feature correspondences between the source and target shapes. Some techniques are also provided to control the vertex path during the morphing process. The amount of user input required to produce a morph is directly proportional to the amount of control the user wishes to impose on the process. The user may allow the system to automatically generate the morph as well. Our approaches are totally geometric based and are easy and fast enough in fully interactive time. Many experimental results show the applicability and flexibility of our approaches.

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Authors and Affiliations

  1. Institute of Computer Image and Graphics, Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Li-Gang Liu

  2. Microsoft Research Asia, Beijing, 100080, P.R. China

    Bo Zhang, Bai-Ning Guo & Heung-Yeung Shum

Authors
  1. Li-Gang Liu
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  2. Bo Zhang
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  3. Bai-Ning Guo
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  4. Heung-Yeung Shum
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Corresponding author

Correspondence to Li-Gang Liu.

Additional information

Li-Gang Liu is working at Zhejiang University now. This research was done when he was working at Microsoft Research Asia.

Li-Gang Liu is an associate professor of Department of Mathematics, Zhejiang University, P.R. China. He received his B.S. and Ph.D. degrees of applied mathematics from Zhejiang University in 1996 and 2001, respectively. He joined the Internet Graphics Group at Microsoft Research Asia in 2001 as an associate researcher. He is currently a member of Institute of Computer Image and Graphics in Zhejiang University. His main research interests include curve and surface modeling and design, digital geometry processing, image and texture processing. He has published over 10 papers in refereed journals and conference presentations.

Bo Zhang is an associate researcher at Microsoft Research Asia. He received the B.S. degree in 1996 and the Ph.D. degree in 2001, both in computer science, from University of Science and Technology of China. His main research interests include 2D vector graphics, computer animation and game AI.

Bai-Ning Guo is the research manager of the Internet Graphics Group at Microsoft Research Asia. Before joining Microsoft, he was a senior staff researcher in the Microcomputer Research Labs at Intel Corporation in Santa Clara, California, where he worked on Intel’s next-generation graphics architecture. He was also managing Intel’s graphics research and development in Russia. Before moving to the Silicon Valley, Dr. Guo worked at University of Colorado, University of Toronto, and York University. He was also a visiting professor at Ecole Nationale Superieure Des Telecommunications and Princeton University. He received his Ph.D. and M.S. degrees from Cornell University and his B.S. degree from Peking University. His research interests are mainly in modeling and rendering areas, including texture synthesis, reflectance and shading models, real-time rendering, natural phenomena. In addition he enjoys working on facial animation.

Heung-Yeung Shum is currently managing director of Microsoft Research Asia (MSRA). He joined Microsoft Research in 1996, after receiving a Ph.D. degree in Robotics from the School of Computer Science at Carnegie Mellon University. He has authored and co-authored over 100 papers in computer vision, computer graphics and robotics, and received more than 20 US patents. He is on the editorial boards for IEEE Trans. Circuit System Video Technology (CSVT), IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), International Journal of Computer Vision, and Graphical Models. His research interests include computer vision, computer graphics, human computer interaction, pattern recognition, statistical learning and robotics. He serves as the General Co-Chair of the 10th International Conference on Computer Vision (ICCV 2005 Beijing).

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Liu, LG., Zhang, B., Guo, BN. et al. Polygonal Shape Blending with Topological Evolutions. J Comput Sci Technol 20, 77–89 (2005). https://doi.org/10.1007/s11390-005-0009-1

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  • DOI: https://doi.org/10.1007/s11390-005-0009-1

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