The Weizmann Institute of Science
Faculty of Mathematics and Computer Science
Vision and Robotics Seminar
Iddo Drori
Department of Statistics,
Stanford University
will speak on
Multiscale representations for manifold-valued data
Abstract:
We describe multiscale representations for data observed on equispaced grids
and taking values in manifolds such as: the sphere $S^2$, the special
orthogonal group $SO(3)$, and the positive definite matrices $SPD(n)$. The
representations are based on the deployment of Deslauriers-Dubuc and
Average-Interpolating pyramids ``in the tangent plane" of such manifolds, using
the Exp and Log maps of those manifolds. The representations provide wavelet
coefficients which can be thresholded, quantized, and scaled much as
traditional ``wavelet coefficients". Tasks such as compression, noise removal,
contrast enhancement, and stochastic simulation are facilitated by this
representation. The approach applies to general manifolds, but is particularly
suited to the manifolds we consider, i.e. Riemannian symmetric spaces, such as
$S^{n-1}$, $SO(n)$, where the Exp and Log maps are effectively computable.
Applications to manifold-valued data sources of a geometric nature (motion,
orientation, diffusion) seem particularly immediate. A software toolbox,
SymmLab, can reproduce the results discussed in this talk.
Joint work with Inam Ur Rahman, Victoria C. Stodden, David L. Donoho, and
Peter Schroeder.
The lecture will take place in the
Lecture Hall, Room 1, Ziskind Building
on Thursday, August 25, 2005
noon - 13:00