Seminar: Shape Analysis Using Overcomplete Wavelets of the Sphere

December 3, 2007

Polina Golland
Computer Science and Artificial Intelligence Laboratory (CSAIL)
Massachusetts Institute of Technology

Dec. 3rd, 2007 at 15:30 in TASC 9204.

In this talk I will discuss our recent work in extending the theory of
wavelets to the sphere and its applications to shape analysis of
cortical folding. The theories of signal sampling, filter banks,
wavelets and overcomplete wavelets are well-established for the
Euclidean spaces and are widely used in the processing and analysis of
images. While recent advances have extended some filtering methods to
spherical images, many key challenges remain. In this work, we develop
theoretical conditions for the invertibility of filter banks under
continuous spherical convolution. We use the theoretical results to
establish a general framework for the design of invertible filter
banks on the sphere.

Bi-orthogonal spherical wavelets have been shown to be powerful tools
in the segmentation and shape analysis of 2D closed surfaces, but
unfortunately they suffer from aliasing problems and are therefore not
invariant under rotations of the underlying surface parameterization.
We demonstrate the theoretical advantage of over-complete wavelets
over bi-orthogonal wavelets and illustrate their utility on both
synthetic and real data. In particular, we show that over-complete
spherical wavelets allow us to build more stable cortical folding
development models.

Joint work with Thomas Yeo and Peng Yu, MIT.

Bio: Polina Golland is an assistant professor in the EECS Department
and the Computer Science and Artificial Intelligence Laboratory
(CSAIL) at MIT. Her primary research interest is developing novel
techniques for image analysis and understanding. Polina got her PhD
from MIT and her Bachelor and Masters degree from Technion,
Israel. She has worked on various problems in computer vision, motion
and stereo, shape modeling and representation, predictive modeling and
visualization of statistical models. Her current research focuses on
modeling biological shape and function using images (from MRI to
microscopy) as a source of information.

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