**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

Abstract

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.