Statistitical Shape Analysis for Image Segmentation
and Physical Model-Based Non-Rigid Registration



A Dissertation
Presented to the Faculty of the Graduate School
of
Yale University
in Candidacy for the Degree of
Doctor of Philosophy

by

Yongmei Wang


Dissertation Director: Lawrence Hamilton Staib

May 1999

(All Rights Reserved)

Abstract


This dissertation presents novel statistical shape analysis methods for both segmentation and non-rigid registration, which are two of the most important topics in medical image analysis.

For the proposed approaches to boundary finding, the correspondence of a subset of boundary points to a model is simultaneously determined. Global shape parameters derived from the statistical variation of object boundary points in a training set are used to model the object. A Bayesian formulation, based on this prior knowledge and the edge information of the input image, is employed to find the object boundary with its subset points in correspondence with boundaries in the training set or the mean boundary. In order to demonstrate the power of this statistical information, the use of a generic smoothness prior and a uniform independent prior are compared with the training set prior. An integrated approach is also described and validated which uses a combined prior of the smoothness and statistical variation modes when few training example shapes are available. This approach adapts gradually to use more statistical modes of variation as larger data sets are available.

The resulting corresponding boundary points derived from the segmentation are then incorporated into our physical model-based non-rigid registration. The two new atlas-based methods of 2D single modality non-rigid registration proposed in this work use the combined power of physical and statistical shape models. A Bayesian formulation, based on each physical model (elastic solid and viscous fluid), an intensity similarity measure, and statistical shape information embedded in corresponding boundary points, is employed to derive more accurate and robust approaches to non-rigid registration.

Finally, the 3D generalization to volumetric segmentation is addressed with emphasis on the new techniques required, which include the identification of corresponding surface points in the training set and 3D surface triangulation. They are efficiently computed together in a new hierarchical approach.

Throughout all the work in this thesis, the key link is statistical shape, which is the prior model in segmentation, as well as the extra source of information in non-rigid registration.

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