Tree representation of digital picture embeddings

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).

► We study the relationship between low- and high-resolution images of an object.
► Rooted component trees are used to represent these images.
► We establish conditions for a low-resolution image to be embedded in a high-resolution image.
► We illustrate how this work has potential to be useful in structural biology.