On GDM's: Geometrically Deformed Models for the Extraction of Closed Shapes from Volume Data

The advent of nondestructive sensing equipment (CT, MRI) created an entirely new eld of research for image engineers. The equipment generates a point sampling of a true three-dimensional object. Typically, this point sampling is presented as a series of slices through the 3D object. It has become apparent, however, that displaying individual slices does not lend itself to conveying the true three-dimensional structure of the scanned object. Research, therefore, has focused on alternative methods of presenting volume data. This thesis proposes an approach that will generate a topologically closed simple geometric model of an object within a scalar eld. A Geometrically Deformed Model, GDM, is created by placing an initial simple model in the data set which is then deformed by minimizing a set of constraints. The constraint functions evaluated at each vertex in the model control the local deformation, the interaction between the model and the data set, and maintain the shape and topology of the model. Once generated, a GDM can be used for visualization, shape recognition, geometric measurements, or subjected to a series geometric operations. viii Chapter