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Spectral methods based on the finite difference discretization for Laplacian eigenvalue problems are emerging as a very robust tool in computer vision applications such as shape recognition and image retrieval. Features that arise naturally in the theoretical study of eigenvalue estimates and bounds--based on combinations of eigenvalues, or on dimensionless combinations of these physical attributes with various geometric quantities--are invariant under rotation and translation and are tolerant to noise, and thus can be used to uniquely characterize and (statistically) "hear" objects.
In this talk, I will describe some of the algorithms and demonstrate these notions through various applications, including some recent experiments on the SQUID Databases (Shape Queries Using Image Databases).
I also give a flavor of how one goes about deriving some of the theoretical bounds for such spectral functions.

Note special day.