Geometric Sampling of Manifolds for Image Representation and Processing

摘要

It is often advantageous in image processing and computer vision to consider images as surfaces imbedded in higher dimensional manifolds. It is therefore important to consider the theoretical and applied aspects of proper sampling of manifolds. We present a new sampling theorem for surfaces and higher dimensional manifolds. The core of the proof resides in triangulation results for manifolds with or without boundary, not necessarily compact. The proposed method adopts a geometric approach that is considered in the context of 2-dimensional manifolds (i.e surfaces), with direct applications in image processing. Implementations of these methods and theorems are illustrated and tested both on synthetic images and on real medical data.