Smooth partition of unity with Hermite interpolation: applications to image processing

摘要

We explore the one-to one correspondence between parametric surfaces in 3D and two dimensional color images in the RGB color space. For the case of parametric surfaces defined on general parametric domains recently a new approximate geometric representation has been introduced which also works for manifolds in higher dimensions. This new representation has a form which is a generalization to the Bezier representation of parametric curves and tensor-product surfaces. The main purpose of the paper is to discuss how the so generated technique for modeling parametric surfaces can be used for respective modification (re-modeling) of images. We briefly consider also some of the possible applications of this technique.