Imaging and Computing Seminar

Eric Miller, ECE, Tufts University

Geometric Methods for Inverse Problems and Image Segmentation

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.