Past seminars at the Faculty of Informatics
Space Deformation with Harmonic Maps
The Faculty of Informatics is pleased to announce a seminar given by Craig Gotsman
DATE: Monday, July 12th 2010
PLACE: University of Lugano, room SI-008, Informatics building (Via G. Buffi 13)
A space deformation is a mapping from a source region to a target region within Euclidean space, which best satisfies some user specified constraints. This mapping can be used to deform shapes embedded in the ambient space and represented in various forms - polygon meshes, point clouds or volumetric data. We show how harmonic maps - a mapping whose components are harmonic functions - may be used to generate space deformations which will satisfy constraints specified by the user, yet also be detail-preserving, and intuitive to control.
We generate harmonic mappings as a linear combination of a set of harmonic basis functions, which have a closed-form expression when the source region boundary is piecewise linear.
This is done by defining an energy functional of the mapping, and minimizing it within the linear span of these basis functions. The resulting mapping is harmonic, and a natural "As-Rigid-As-Possible" deformation of the source region. Unlike other space deformation methods, our approach does not require an explicit discretization of the domain. It is shown to be much more efficient, yet generate comparable deformations to state-of-the-art methods.
Beyond using harmonic maps to interactively generate natural deformations in an editing scenario, they may also be exploited to reuse animation of quite complicated 3D models by "deformation transfer". The technique requires only the solution of linear systems of equations, hence is very robust and efficient.
Craig Gotsman received a Ph.D. in Computer Science from the Hebrew University of Jerusalem in 1991. He is currently a Professor in the Faculty of Computer Science at the Technion - Israel Institute of Technology, working in 3D computer graphics, geometric modeling and computational geometry, and a co-founder of the Technion Center for Graphics and Geometric Computing (CGGC), which houses three faculty and dozens of graduate students. He is the first incumbent of the Technion's Hewlett-Packard Chair in Computer Engineering.
Prof. Gotsman has published over 150 papers in the professional literature and has been awarded five US patents. He has been awarded a number of best paper awards, and has served on the Editorial Boards of ACM Transactions on Graphics, IEEE Transactions on Visualization and Computer Graphics, The Visual Computer and Computer-Aided Geometric Design. He is also a frequent member of the leading graphics and geometry conference program committees and a frequent invited speaker at these conferences. Gotsman serves on Springer's Editorial Advisory Board for its Geometry and Computing Book Series.
Prof. Gotsman is currently a visiting professor at ETH Zurich. In the summer of 2006 he was a visiting professor at INRIA Sophia Antipolis in France. During 2003-2005, he was a visiting professor at Harvard University's computer science department and research scientist at MIT's CSAIL. Many of his summers during the mid-90's were spent at Hewlett-Packard Research Labs in Palo Alto, CA.
HOST: Prof. Kai Hormann