Representing 3D regions with rational Gaussian surfaces
Marcel Parolin Jackowski, Ardeshir Goshtasby, Martin R. Satter · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
The 3-D regions obtained as a result of a volume image segmentation often need to be geometrically modeled and rendered. In this paper, use of rational Gaussian (RaG) surfaces in modeling and rendering 3-D regions is described. A new parametrization technique is introduced that morphs a sphere in a coarse-to-fine fashion to a 3-D region. Knowing parameters of points on the sphere, parameters of voxels on the region are determined. Having the parameters of the voxels, a RaG surface is then fitted to the voxels to obtain a smooth representation for the region. Examples of the proposed representation on various 3-D regions are presented.