Geometric and Topological Modelling of Organs and Vascular Structures from CT Data

Automatic segmentation of organs in CT scans is a field of rising interest for the generation of 3D models that can help surgery planning, training and support during surgical procedures. However, the reconstruction and visualization of 3D models of organs with vascular structures present several modelling problems. In this chapter, we review these problems and describe a methodology that allows for the reconstruction to be automatic. In particular this chapter describes and illustrates: how to transform and extract 3D geometry from sets of planar contours/polygons annotated on DICOM images, a solution for enforcing polygon vertex order consistency, polygon triangulation by ear clipping and respective inner angle calculation for irregular polygons, a polygon tiling algorithm for stitching contours in adjacent slices, a file format for storing multiple polygons per slice and support for storing their correspondences with other polygons in other slices. Finally, we show how these algorithms can be used together to build different reconstruction solutions: surface-based reconstruction for organs with simple topology, composite surfaces for organs with branching, single surface with branching and polygon extrusion for topologically complex vascular structures. We conclude by showing how organs and vascular structures can be viewed together using transparency.