| During the past decade, lots of progress has been made in biomedical image processing with the help of modern computers. These technological advances allow the use of large-scale computational algorithms and techniques of which the implementation was almost impossible just few years ago.; This dissertation is about biomedical imaging processing. More precisely, it is about the incorporation of the level set method, computational anatomy and other related fields in biomedical imaging processing.; A general framework of level set based object matching technique is developed in this dissertation. In order to apply the level set method, it has to be re-formulated in the semi-Lagrangian reference formulation rather than the Eulerian reference in the original level set method. The level set based object matching techniques is then incorporated to the framework of diffeomorphisms generated by infinite dimensional group actions in computational anatomy. With this formulation, a metric can be rigorously defined by quantifying the underlying grid deformation based on ideas borrowed from continuum mechanics. Moreover, a geodesic flow can be defined and computed that links one object to the other. A unifying approach for matching objects of different types including shapes, open curves, and landmarks in both two-dimensional and three-dimensional space will be presented.; Formulations for taking into account the equivalence of objects under the action of translation, scaling and rotation will also be discussed. Furthermore, we show that the method of level set based object matching is closely related to minimizing the Hausdorff metric between objects, a classic result in geometric measure theory. This provides a sound and rigorous foundation for the level set based object matching. |
