## Adaptive and Sparse Representations of Geometric Models

- Feb. 22, 2013
- 3:30 p.m.
- LeConte 412

## Abstract

Efficient representation of geometric models is essential in many applications in Geometric Design and Computer Graphics. In this talk, I will discuss two general approaches for efficient representations of geometric models--adaptive representation and sparse representation. For adaptive representation, we propose splines over T-meshes. We discuss some theoretic issues such as dimension calculation and basis constructions of the spline spaces. We then apply splines over T-meshes in adaptive modeling of geometric models. For sparse representation, we apply the ${L _ 1}$ optimization technique in surface denoising and segmentation. Further research problems are also discussed.

**Brief Bio**

Falai Chen is currently a professor in the Department of Mathematics, University of Science and Technology of China (USTC). He earned his B.S. and Ph.D degrees in 1987 and 1994 respectively, both from USTC. His research interests include algebraic methods in Geometric Modeling, splines over T-meshes, and applications of sparse analysis in Geometric Modelling and Computer Graphics. He has published over one hundred scientific papers in refereed journals and international conferences. He currently serves on the editorial boards of several international journals such as Computer Aided Geometric Design, Visual Computer, and Numerical Mathematics-Theory, Method and Applications. He won the Distinguished Young Investigator Award of NSF of China in 2002 and the Feng Kang Scientific Computation Award in 2009.