Minimum Description Length: An information-theoretic approach to the groupwise study of image information

Imagine we present an untrained human volunteer with a set of images of a single type of object, for example, Magnetic Resonance (MR) images of the human brain. It would be quite a simple task for this volunteer to recognize similar structures across the set of images, and to draw round them on the images. So that although the structures varied in shape and exact appearance between brains, a volunteer could nevertheless identify them as structures which persisted across the group of images.

We can present a computer with a similar set of images, and try to program it to learn, in a similar manner to our human volunteer. The standard approach to this problem is to use non-rigid image registration~--~we imagine that each image is printed on a rubber sheet, which can be stretched and deformed. The process of image registration can then be thought of as deforming each of the images in the set, so that as far as is possible, each image is similar to all other images in the set. So, if doing this with images of faces, we would be deforming the rubber sheet so as to align the eyes, nose, chin etc of each face. By then considering the deformation applied to each image, we then have information as to how the shape of the structures varies across the set. One algorithm that can be used to perform this task of groupwise registration is based on the information-theoretic concept of Minimum Description Length (MDL) ('Computing Accurate Correspondences Across Groups of Images', Cootes et al, 2009 and 'A minimum description length objective function for groupwise non-rigid image registration', Marsland et al., 2008).

However, this result, although useful, does not achieve the result that we might get from our human volunteer~--~there is no automatic identification of different tissues within the brain (gray matter, white matter etc), and no delineation of significant structures. A human presented with faces, and asked to perform this task, might be expected to draw round the eyes, chin etc as being significant structures common across the group.

We can of course segment individual images into different tissue types using standard algorithms in image processing. The aim of this project is to apply the concept of MDL to this extended task, to not only register a group of images, but also to identify tissue classes and structures that are significant across the group.

The general concept of automatically identifying common structure across a group of images could also be applied to other imaging tasks, such as reconstructing a high-resolution image of an object from a set of low-resolution images of the same object.

This project will involve considerable mathematical content.