1. A method of reconstructing a model of a path through a branching tubular organ, drawing upon a three-dimensional (3D) digital image of the surrounding anatomy and comprising the steps of: computing a segmentation of the organ using the digital image; identifying a region of interest (ROI) associated with the anatomy; selecting the path originating at the beginning of the branching organ, passing through branches of the organ, and leading to the ROI; adding branches to the organ segmentation; constructing accurate endoluminal surfaces of the organ's branches; and producing a model of the path containing accurate endoluminal surfaces at all branch junctions encountered along the path.