## Imaging and Computing Seminar

### Eric Miller, ECE, Tufts University

**Title:**

Geometric Methods for Inverse Problems and Image Segmentation

**Abstract:**

One of the most fundamental problems in image processing is that of
segmentation broadly defined as determining the structure of objects in a
given scene. In almost all application areas where multidimensional data are
acquired, some portion of the processing pipeline requires the
identification and quantification of specific regions in the field of regard
either as the ultimate solution to the underlying problems or as an
intermediate step toward the extraction of higher level information. While
many methods have been proposed in the last 30 years for solving such
problems, here we concentrate on the use of level-set methods. These
techniques have attracted significant attention both due to their
mathematical elegance as well as their ability to identify disconnected area
easily. We will start by discussing level-set basics and then move on to
cover some extensions we have developed to improve the performance of such
methods in addressing challenges arising in their application both to
inverse problems as well as image segmentation. In the case of inverse
problems, we examine the use of low-order, parametrically defined level set
functions for application to severely ill-posed problems (electrical
resistance tomography for subsurface contaminant remediation) and problems
where one is interested in recovering small anomalies embedded in cluttered
background (dual energy X-ray CT for luggage inspection). Additionally,
motivated by a problem in electron microscopy segmentation, we will discuss
out recent work in building "active-ribbons" out of multiple level sets.