Nondistorting flattening maps and the 3-D visualization of colon CT images

Considers a novel three-dimensional (3-D) visualization technique based on surface flattening for virtual colonoscopy. Such visualization methods could be important in virtual colonoscopy because they have the potential for noninvasively determining the presence of polyps and other pathologies. Further, the authors demonstrate a method that presents a surface scan of the entire colon as a cine, and affords the viewer the opportunity to examine each point on the surface without distortion. The authors use certain angle-preserving mappings from differential geometry to derive an explicit method for flattening surfaces obtained from 3-D colon computed tomography (CT) imagery. Indeed, the authors describe a general method based on a discretization of the Laplace-Beltrami operator for flattening a surface into the plane in a conformal manner. From a triangulated surface representation of the colon, the authors indicate how the procedure may be implemented using a finite element technique, which takes into account special boundary conditions. They also provide simple formulas that may be used in a real-time cine to correct for distortion.