Non-distorting Flattening for Virtual Colonoscopy

In this paper, we consider a novel 3D visualization technique based on surface flattening for virtual colonoscopy. Such visualization methods could be important in virtual colonoscopy since they have the potential for non-invasively determining the presence of polyps and other pathologies. Further, we demonstrate a method which presents a surface scan of the entire colon as a cine, and affords a viewer the opportunity to examine each point on the surface without distortion. We use certain angle-preserving mappings from differential geometry in order to derive an explicit method for flattening surfaces obtained from 3D colon CT imagery. Indeed, we describe a general method based on a discretization of the Laplace-Beltrami operator for flattening a surface onto the plane in a manner which preserves the local geometry. From a triangulated surface representation of the colon, we indicate how the procedure may be implemented using a finite element technique, which takes into account special boundary conditions. We give a simple example of how the flattening map can be composed with other maps to enhance certain mapping properties. Finally, we show how the use of curvature based colorization and shading maps can be used to aid in the inspection process.