Tree representation of digital picture embeddings

摘要

It is often the case that the same object is imaged in different ways, resulting in digital pictures of (some parts of) it at different resolutions. This leads to the combinatorial problem of "embedding" one of these pictures into the other in a way that corresponds to physical truth. In this paper we present a mathematical formulation of this intuitive concept of embedding. We also show, using a tree representation of digital pictures, how picture embedding relates to tree embedding, which has been a subject of much study in combinatorial computer science (mostly for reasons other than application to digital pictures).