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

In this paper, we consider a novel three-dimensional (3-D) visualization te chnique based on surface flattening for virtual colonoscopy, Such visualiza tion methods could be important in virtual colonoscopy because they have th e potential for noninvasively determining the presence of polyps and other pathologies. Further, we demonstrate a method that presents a surface scan of the entire colon as a cine, and affords the viewer the opportunity to ex amine each point on the surface without distortion. We use certain angle-preserving mappings from differential geometry to deri ve an explicit method for flattening surfaces obtained from 3-D colon compu ted tomography (CT) imagery. Indeed, me 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 represent ation of the colon, we indicate how the procedure may be implemented using a finite element technique, which takes into account special boundary condi tions. We also provide simple formulas that may be used in a real-time cine to correct for distortion.