What can we learn from discrete images about the continuous world?

Abstract

Image analysis attempts to perceive properties of the continuous real world by means of digital algorithms. Since discretization discards an infinite amount of information, it is difficult to predict if and when digital methods will produce reliable results. This paper reviews theories which establish explicit connections between the continuous and digital domains (such as Shannon's sampling theorem and a recent geometric sampling theorem) and describes some of their consequences for image analysis. Although many problems are still open, we can already conclude that adherence to these theories leads to significantly more stable and accurate algorithms. © 2008 Springer-Verlag Berlin Heidelberg.