Title: Statistics of the anatomic geometry of multi-object complexes via m-reps
Speaker: Stephen M. Pizer, PhD,
Kenan Professor of Computer Science, Radiology, Radiation Oncology, &
Biomedical Engineering
and Head, UNC Medical Image Display & Analysis Group
University of North Carolina


Both dense multi-object complexes and non-dense complexes are important in
such medical areas as neuroscience and radiation treatment planning. A
probabilistic point of view on anatomic geometry is important for such
objectives as segmentation by posterior optimization and hypothesis testing
as to differences in object complex geometry between classes. I will review
why the medial representation called m-reps is particularly well suited both
to statistics on individual objects and statistics on multi-object complexes
and review how a generalization of mean and principal component methods to
the underlying curved abstract spaces can be done. Using novel statistical
techniques, which I will briefly explain, I will show by how much m-reps of
single objects together with the appropriate non-linear statistics yields a
requirement of smaller training samples. For multi-object complexes it is
particularly important that the probabilistic algorithms be at multiple
scale levels, each with its own characteristic entity, e.g., object complex,
object (and interstitial region), figure, figural section, voxel; and that
they provide probabilities the geometry relationships between neighboring
entities. The Markov random field framework that this produces and the means
of simultaneously representing probabilities on entity and inter-entity
geometry will be discussed.