Three-dimensional attenuation map reconstruction using geometrical models and free-form deformations

We address the issue of using deformable models to reconstruct an unknown a ttenuation map of the torso from a set of transmission scans, We assume the three-dimensional (3-D) distribution of attenuation coefficients to be pie cewise uniform. We represent the unknown distribution by a set of closed su rfaces defining regions having the same attenuating properties. The methods of reconstruction published so far tend to directly deform the surfaces, t he parameters being the surface elements. Rather than deforming the surface s, we explore the possibility of deforming the space in which the geometric al primitives are contained. We focus on the use of free-form deformations (FFD's) to describe the continuous transformation of space used to match a set of transmission measurements. We illustrate this approach by reconstruc ting realistically simulated transmission scans of the torso with various n oise levels and compare the results to standard reconstruction methods.