[CCoE Notice] 2011 Amundson Lectures -- This week

[Lewis, Lindsay R]

Greetings,



On behalf of Robert Azencott and Jeff Morgan, I am pleased to announce the 2011 University of Houston Amundson Lectures. For information about the lecture series and a short biography of Neal

Amundson, visit http://www.math.uh.edu/amundsonlectureseries/



Our speaker this year is Professor Laurent Younes from Johns Hopkins University.  Professor Younes is affiliated with the Center for Imaging Science and the Institute for Computational Medicine at Johns Hopkins. His research interests include statistical properties of Markov random fields, image analysis, deformation analysis - shape recognition, and computational anatomy.  For details, visit http://cis.jhu.edu/~younes/



The Amundson Lectures are scheduled for March 23-25, 2011 and will consist of 3 lectures:



1) Colloquium Lecture



Title: Shape Spaces and Computational Anatomy

Date: Wednesday, March 23, 2011

Time: 4-5 PM

Location: University of Houston Hilton Hotel - Shamrock Room



(reception to follow in the Shamrock Room at 5 PM)



2) Seminar Lecture



Title: Diffeomorphic Optimal Control

Date: Thursday, March 24, 2011

Time: 4-5 PM

Location: University of Houston Hilton Hotel - Shamrock Room



3) Lecture for Graduate Students



Title: An Interesting Space of Plane Curves

Date: Friday, March 25, 2011

Time: 2-3 PM

Location University of Houston Philip G. Hoffman Hall (PGH) room 343



ABSTRACTS



1) Colloquium Lecture: Shape Spaces and Computational Anatomy



A fundamental question in Computational Anatomy addresses how the shapes

of human organs are affected by disease.

This is motivated by the fact that, most cognitive disorders, for

example, result in selective atrophy of various structures in the brain.

Similarly, heart disease typically involves significant remodeling of

the cardiac muscle.

Describing how and where such shape changes occur can provide clinicians

with essential information on the nature of the disease.



We will show how these issues can be addressed within the framework of

Grenander's Metric

Pattern Theory, and more specifically by building Riemannian spaces of

shapes. This will be illustrated by two case studies, the first one on

the analysis of

atrophy in the striatum and connected brain structure in relation with

Huntington's disease, and the second on the analysis of shape variation

in cardiac disease, and its relation with different forms of

cardiomyopathy.





2) Seminar Lecture: Diffeomorphic Optimal Control



In the framework of the "large deformation diffeomorphic metric

matching" family of algorithms, one formulates the problem of finding

an optimal registration between two shapes, or two

images, as an optimal control problem where the control

specifies an Eulerian velocity associated to a time-dependent

diffeomorphism, with a cost represented by the norm of the velocity in a

suitably chosen Hilbert space of vector fields. Because this Hilbert norm

can also interpreted as the expression of a right-invariant Riemannian

metric in the Lie algebra of the diffeomorphism group, this directly relates

to the well-known geodesic equation, often called EPDiff, that expresses

momentum conservation.



We will describe this approach, with a special focus on the situation

in which additional contraints are

placed on the Eulerian velocity to ensure that it belongs to a

finite dimensional subspace of the originally considered Hilbert space. This

subspace, which is shape-dependent, is generated by a finite number of

well chosen time-dependent vector fields that we call diffeons. Based

on the resulting maximum principle, we will provide optimization

algorithms for

the registration problems (and a few related issues), with

some preliminary numerical experiments in two dimensions.





3) Lecture for Graduate Students: An Interesting Space of Plane Curves



The definition and study of spaces of plane shapes has met a

large amount of interest over the last ten years or so. It has important

applications in object

recognition (for the analysis of shape databases), and in medical

imaging. The theoretical background involves the construction of

infinite-dimensional manifolds of curves, in a Riemannian framework, which

is appealing, because it provides shapes spaces with a

rich structure, which is also useful for applications.

The presentation focuses on a particular Riemannian metric that has

very a specific property, in that

it can be characterized as an image of a Grassmann manifold by a

suitably chosen Riemannian submersion. A consequence of this is that

its analysis becomes relatively easy, with, for example, the

possibility to compute geodesics explicitly.



-William Ott

Assistant Professor of Mathematics

University of Houston


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