# February Fourier Talks 2008

## Leo Grady

### Title:

A general purpose image segmentation algorithm using analytically
evaluated random walks

### Abstract:

An ideal image segmentation algorithm could be applied equally to the
problem of isolating organs in a medical acquisition volume or to
editing a digital photograph without modifying the algorithm, changing
parameters, or sacrificing segmentation quality. However, a
general-purpose, multiway segmentation of objects in an image/volume
remains a challenging problem. In this talk, I will describe a recently
developed approach to this problem that inputs a few training points
from a user (e.g., from mouse clicks) and produces a segmentation by
computing the probabilities that a random walker leaving unlabeled
pixels/voxels will first strike the training set. By exact mathematical
equivalence with a combinatorial Laplace equation, these probabilities
may be computed analytically and deterministically. The algorithm is
developed on an arbitrary, weighted, graph in order to maximize the
breadth of application. I will illustrate the use of this approach with
examples from several image segmentation problems (without modifying the
algorithm or the single free parameter), compare this algorithm to other
approaches and discuss the theoretical properties that describe its
behavior.