Talk by Sylvain Bouix at UNC Computer Science Dept
Location: 284 Sitterson Hall
10:00-11:00 on Wed, Oct 8, 2003

Title: "Medial Surfaces"

Abstract:The medial surface of a 3D object is comprised of the locus of
centers of its maximal inscribed spheres. Interest in this representation
stems from a number of interesting properties: i) it is a thin set, i.e.,
itcontains no interior points, ii) it is homotopic to the original shape,
iii) it is invariant under rigid transformations of the object and iv)
given the radius of the maximal inscribed sphere associated which each
skeletal point, the object can be reconstructed exactly. Hence, it
provides a compact representation while preserving the object's genus and
making certain useful properties explicit, such as its local width. These
properties have led to its application in a variety of domains, including
the analysis and quantification of the shape of volumetric structures in
medical images. Despite its popularity, its numerical computation remains
non-trivial. Most algorithms are not stable with respect to small
perturbations of the boundary, and heuristic measures for simplification
are often introduced. The study of the medial surface is the subject of
this talk.

First, we examine the sensitivity of the medial surface to boundary
perturbations by studying its evolution (locally) as the boundary
undergoes an arbitrary motion. Second, we introduce a new algorithm for
computing medial surfaces. The key idea is to measure the average outward
flux of the gradient vector field of the Euclidean distance function to
the boundary of the object. This measure has very different limiting
behaviors depending upon whether the region over which it is computed
shrinks to a medial point or a non-medial one. Finally, we illustrate the
power of this representation with two applications. One is the automatic
computation of central paths in tubular structures in order to create
virtual fly throughs. The second application is a study of the effect of
age and gender on the shape of the hippocampus (HC), a structure of the
brain related to memory. We investigate these factors in normal subjects
in young adulthood, by employing a shape analysis of the HC using medial
surfaces.