DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Saurabh Jain, Johns Hopkins University

**Title: ***
Optimal Control Problems in Computational Anatomy
*

**Abstract:**
Computational Anatomy characterizes the anatomical shapes via the action of deformations on templates or exemplars. The statistical variabilities are then studied using probability models on the set of deformations. A Bayesian classification and testing approach can be used for the detection of anomalies based on these deformations.The idea of studying anatomy via transformations dates back to the work of D'Arcy Thompson's "On Growth and Form" published in 1917. A rigorous mathematical formulation of Thompson's idea was developed by Grenander and Miller following ideas from Grenander's global pattern theory.
We begin with a brief description of Computational Anatomy, and introduce a class of diffeomorphic registration algorithms known as Large Deformation Diffeomorphic Metric Mapping (LDDMM), which are key to the study of anatomical shape variation. This algorithm can be formulated as an optimal control problem. The optimal control point of view gives rise to further refinements of the algorithm. In particular, we discuss a realistic model for human heart motion based on fiber orientations of the cardiac muscles, and applications of computational anatomy in Neuroscience.

**Time:** Friday, November 1, 2013, 1:30-2:30 p.m.

**Place:** Exploratory Hall (formerly S & T II), Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491