3-DIMENSIONAL RECONSTRUCTION OF VASCULAR TREES - THEORY AND METHODOLOGY

In this paper we examine the few-view reconstruction problem as it app lies to imaging vascular trees. A fully automated reconstruction algor ithm is described that circumvents the traditional ''correspondence pr oblem,'' using only notions of consistency and connectivity. It is ass umed that the vascular tree is a connected structure and that its cent erlines have been identified in three or more images. The first of thr ee steps in the procedure involves generating a connected structure th at represents the multiplicity of solutions that are consistent with a ny two (different) projections. The second step assigns to each branch in this structure a measure of agreement based on its relationship wi th one or more additional views of the vasculature. The problem then b ecomes one of propagating this information, via connectivity relations hips and consistency checks, throughout the above structure to disting uish between the branches comprising the imaged structure and the acco mpanying artifacts. In this paper we present the theory and methodolog y of the technique, while in a companion paper we address the issue of validation via simulations and experiments. Together, these papers sh ed some light on why ambiguities arise and often lead to errors in the few-view reconstruction problem. Strategies to handle these errors ar e described and results are presented that demonstrate the ability to obtain adequate reconstructions with as few as three distinct views. ( C) 1996 American Association of physicists in Medicine.