A Fast Algorithm for Variational Level Set Image Segmentation

Tony Chan
Department of Mathematics
UCLA
Los Angeles, USA


I'll first give an overview of a family of variational image segmentation models based on using level set representation of segment boundaries that L. Vese and I have developed over the last few years. The distinctive feature is use of regional information without using edge detection explicitly. The methodology can handle scalar and multi-valued images, multiple level sets, and logical combinations of information from different channels. In the 2nd part of the talk, I'll present a fast computational algorithm for computing the solution of these variational segmentation models. Instead of the typical PDE-based gradient descent algorithms, the new algorithm is optimization-based and make use of the objective function directly, without the need for any gradient information. The new algorithm speeds up the traditional algorithms dramatically. For 2-phase images, we prove that the algorithm finds the correct segmentation with only one sweep over the pixels of the image, regardless of the ordering of the pixels or the initial level set.

The second part of the talk is joint work with my PhD student Bing Song.

Brief Biography:

Tony F. Chan received both his B.S. (Engineering) and M.S. (Aeronautics) degrees from the California Institute of Technology in 1973, and his Ph.D. degree in computer science from Stanford University in 1978.

He was an Assistant and then Associate Professor of computer science at Yale University from 1979-1986, when he was lured to UCLA. He served as the Chair of the UCLA Mathematics Department from 1997-2000, until he became Director of the, newly established Institute for Pure and Applied Mathematics (IPAM), one of only 3 NSF-funded national math institutes at that time, which he helped bring to UCLA. He became Dean of the Division of Physical Sciences in July 2001.

As Dean of the Division of Physical Sciences, he oversees 6 departments, several research institutes, over 200 ladder faculty, 1700 undergraduates, and 700 graduate students. The division brings in over $60M in annual research awards. His responsibilities include policy, planning, budget, faculty recruitment, retention and promotion, education and research programs, and fund raising.

Dr. Chan has been an active member of the Society of Industrial and Applied Math and the American Math Society. He served on the SIAM Council, the editorial board of SIAM Review and the SIAM Committee on Human Rights. Currently, he serves on the SIAM Committee on Science Policy and the AMS Editorial Board Committee. He also serves on the editorial boards of the SIAM Journal of Scientific Computing, Numerische Matematik, the Asian Journal of Math, and Numerical Algorithms. He was a co-chair of the Organizing Committee of the July 2000 National SIAM Meeting held in Puerto Rico.

Dean Chan has served on a number of national and professional panels, including the NSF Math and Physical Sciences Advisory Committee, the AMS Committee on Committees, the University Space Research Association (USRA) Science Council for Applied Mathematics and Computer Science, the Lawrence Livermore National Laboratory's Computation Directorate Advisory Committee, the NSF's Division of Mathematical Science Committee of Visitors.

Some of his many honors include: Chairing the Search Committee for the NSF Director of the Division of Mathematical Sciences (2002) and Chairing the Local Organizing Committee for the AMS "Mathematical Challenges of the 21st Century" Conference held in August 2000 at UCLA. He has served as the Plenary speaker at the Joint Mathematics Meeting held in San Diego, in January 2002; the International Congress of Chinese Mathematicians in held in Taipei, in December 2001; and the SIAM National Meeting held in San Diego, in July 1989. His latest honor is the Distinguished Visiting Lectureship at the United College Chinese University of Hong Kong in November 2002.

Dean Chan's general research interest is interdisciplinary mathematics. Specific current projects include differential equation based image processing and computer vision, multiscale computational methods, optimizational and algebraic multigrid methods for VLSI circuit layout and algorithms on advanced architecture parallel computers.