DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Gunay Dogan, NIST

**Title: ***
Shape Optimization for Image Analysis
*

**Abstract:**
Image segmentation, namely, detection of regions, objects and their boundaries in given images, is a fundamental problem in image analysis. It is the basis of many important practical applications, such as biological cell analysis, robotic vision, image-based material simulations. One of the most successful approaches to solving this problem builds on energy minimization formulations. In this approach, one designs special segmentation energies, in which the main variables are the candidate geometries or shapes, such as curves or surfaces, and the sought region boundaries correspond to minima of the segmentation energies. Then one needs to solve a shape optimization problem to detect the regions and their boundaries in the images. Energy minimization approaches are popular in image analysis because of the freedom and flexibility to customize and address applications; they enable us to incorporate data fidelity terms, geometric regularity criteria and prior information on the shapes expected in the images. In this talk, I will describe our work on how we can formulate such energies and solve the resulting shape optimization problem. I will emphasize critical components, such as numerical discretization of the shapes, geometric adaptivity, computation of descent direction.

**Time:** Friday, April 11, 2014, 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