Design and recovery of 2-D and 3-D shapes using rational Gaussian curves and surfaces

摘要

A new representation for parametric curves and surfaces is introduced here. It is in rational form and uses rational Gaussian bases. This representation allows design of 2-D and 3-D shapes, and makes recovery of shapes from noisy image data possible. The standard deviations of Gaussians in a curve or surface control the smoothness of a recovered shape. The control points of a surface in this representation are not required to form a regular grid and a scattered set of control points is sufficient to reconstruct a surface. Examples of shape design, shape recovery, and image segmentation using the proposed representation are given.