Digital Riemannian Geometry and Its Application

The key characteristic of Riemannian geometry is Riemannian metric.The most important work for the discretion of Riemannian geometry is to seek a discret representation of Riemannian metric, which forms the foundation of digital Riemannian geometry.This paper initiated the conception of Digital Riemannian geometry which imposes a Riemannian metric on a rectangle grid to make them curved and induced a weighted distance on them.The main task of Digital Riemannian geometry is to obtain quantitative information about objects in pictures with the help of a discrete Riemannian metric defined on them.