Pia Löthgren

Distance Metrics for Stochastic Shape Models

Abstract The purpose of this exam project is to develop mathematical
and statistical models that can be used to build stochastic models of
the shapes of a beating heart. This could then be used to construct a
decision support system to help with diagnosis of patients with
suspected cardiac infarction.

In order to establish correspondence between different shapes one
needs to find  a suitable reparametrisations for each shape. The
current most popular methods for doing so, the Minimal Description
Length methods, have problems with gathering of sample points. We
propose that this problem is because the methods are based on the
Euclidian metric on arbitrary sample points. We propose a new distance
metric that is weighted by surface area and by the Laplacian of the
surface. This new metric is invariant to any reparametrisation of the
surfaces. It can also bed used to build plausible probability
structures for the set of objects on which the metric is defined. The
models of the shapes in this metric can be used independently of any
particular measurement method.