Matching 3D-images and 3D-movies by elastic deformations

Organized by Robert Azencott
Location: PGH 646

Time: every Monday starting at 10:00am
Mon. Sept. 22nd to Mon. Oct. 27th 2008 Robert Azencott, Mathematics, Univ.of Houston
Nov. and Dec. 2008 talks To be announced

Seminar outline : The space of Soft Shapes

Given two piecewise smooth surfaces S1 and S2 in R3, the applicative goal is to determine an R3 diffeomorphism F realizing the "best" matching of S1 and S2

This means that one wants to simultaneously have the deformed soft shape F(S1) very close to S2 and the "elastic deformation energy" of F to be reasonably low. This difficult variational problem is linked to the computation of "geodesics" in the (infinite dimensional) group of diffeomorphisms in R3. We will present recent mathematical approaches relying on elegant results of A Trouve (ENSC France), L Younes (Johns Hopkins) J Glaunes (Brown Univ)

Fascinating medical applications to the actual matching of brain substructures across patients have been developed mostly at Johns Hopkins in M Miller's laboratory

We have started a research group at UH Maths (jointly with Roland Glowinski, Jiwen He, Ronald Hoppe), to apply these approaches to medical 3D-movies of soft organs such as echocardiographic movies of beating hearts. In this case one actually has to deal with diffeomorphisms in R4, which is a serious computational challenge.

Our research group is currently supported by a recently awarded 3 years NSF grant.

For any further questions, contact the seminar organizer:
Robert Azencott, Prof. of Mathematics
Univ.of Houston and Ecole Normale Sup. (France)
email : ; cellphone 832 330 4706