The theory of active contours models the problem of contour recovery as an energy minimization process. The computational solutions based on dynamic programming require that the energy associated with a contour candidate can be decomposed into an integral of local energy contributions. In this paper we propose a grammatical framework that can model different local energy models and a set of allowable transitions between these models. The grammatical encodings are utilized to represent a priori knowledge about the shape of the object and the associated signatures in the underlying images. The variability encountered in numerical experiments is addressed with the energy minimization procedure which is embedded in the grammatical framework. We propose an algorithmic solution that combines a nondeterministic version of the Knuth-Morris-Pratt algorithm for string matching with a time-delayed discrete dynamic programming algorithm for energy minimization. The numerical experiments address practical problems encountered in contour recovery such as noise robustness and occlusion.

This paper explores the potential of multispectral analysis of density slices extracted by automatic object recognition algorithms in volumetric data sets. The object recognition algorithm is utilized to define the object surface. Each point x on the object surface is hence associated with the set of measurements in the underlying volumetric data set that is within the region of interest and projected onto x. This variable size attribute vector is converted to a fixed size attribute vector by transforming the measurements into the associated cumulative distribution vector. The fixed size attribute vectors represent a multispectral image over the manifold defined by the object surface. This image is further processed with multispectral techniques such as the Karhunen-Loeve transform and visualized as a coloring of the 3-dimensional object surface. Our numerical experiments include 3-dimensional ultrasonic catheter studies of plaque formation in arteries, MRI studies of the brain, and evaluation of customized femoral hip prostheses based on CT imaging.>