A wide range of applied imaging problems are concerned with the
determination of the three dimensional structure of anomalous areas in
a larger field of regard. In the context of medical imaging, there is great interest in the characterization of cancerous tumors using non-ionizing modalities such as diffuse optical tomography or quantitative ultrasonic imaging. In this work, we introduce a new,
flexible approach to the modeling and estimation of 3D shapes.
A complex three dimensional volume is defined by a set of 2D shape "primitives" representing the cross section of the object in essentially arbitrary planes. Each primitive is itself a 2D shape (specifically an ellipse for this paper) the structure of which is easily defined by a low dimensional vector of parameters (center location, axis lengths, and orientation angles). Given a set of primitives, we devise an interpolation scheme that correlates the structure of the individual primitives from one to the next. A nonlinear estimation algorithm is described for determining the parameters of our elliptic primitives i.e., the location of the centers in 3D, the lengths of their axes, and their orientation in space. Simulated results show the effectiveness of this method.