Graph-based techniques for image processing

About the Project

These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.

Modern medical imaging systems produce a voxel image: one can regard this as a collection of voxels (cubes) in an N × N × N array, where we assign the value 1 to a voxel if it is part of the image and 0 if it is not. If one takes a scan of a body organ such as a kidney or a brain, the image has the topology of a solid ball in 3-space. Martin et al. have developed algorithms for storing and manipulating such images using techniques from graph theory [1].

This builds on work of Adams, Fishkind and Priebe [2, 3], who gave criteria for determining whether a voxel image has the topology of a 3-ball near any given point, and used this to create algorithms for removing noise from the boundary of an image. The ultimate aim is to develop an automated classifier to determine from a medical image whether an organ is healthy or diseased.

The key idea in the graph-based approach is to store not the positions of the voxels themselves, but the positions of the exterior faces. For N large, this sharply reduces the amount of data one must store (from O(N3) to O(N2)). One can then represent this data in the form of an edge-labelled graph. This graphical representation enjoys some extra robustness properties: for instance, if one translates the image within the ambient N × N × N array then the associated graphical representation does not change.

Lazovskis has implemented these algorithms using C++. He has produced some sets of samples images and computed their graphical representations. The aim of this project isto determine whether a suitable neural network can distinguish between images of different types using their graphical representations as input: for instance, can it distinguish a cube with some added noise from a sphere with some added noise? The student will design the neural networks and apply them to the sample images.

Mamen Romano (Physics) and Ben Martin (Maths) will supervise the project. Martin will advise on the underlying mathematical theory and Romano will use her expertise on image processing and neural networks.

Informal enquiries can be made by contacting Professor B Martin (B.Martin@abdn.ac.uk).

Decisions will be based on academic merit. The successful applicant should have, or expect to obtain, a UK Honours Degree at 2.1 (or equivalent) in maths, physics or a relevant subject. Some knowledge of neural networks, topology or graph theory (in the mathematical sense) would be useful but is not essential. Some experience with programming would also be helpful.

We encourage applications from all backgrounds and communities, and are committed to having a diverse, inclusive team.

Application Procedure:

Formal applications can be completed online: https://www.abdn.ac.uk/pgap/login.php.

You should apply for Degree of Doctor of Philosophy in Mathematics to ensure your application is passed to the correct team for processing.

Please clearly note the name of the lead supervisor and project titleon the application form. If you do not include these details, it may not be considered for the project.

Your application must include: A personal statement, an up-to-date copy of your academic CV, and clear copies of your educational certificates and transcripts .

Please note: you do not need to provide a research proposal with this application.

If you require any additional assistance in submitting your application or have any queries about the application process, please don't hesitate to contact us at researchadmissions@abdn.ac.uk

Funding Notes

This is a self-funding project open to students worldwide. Our typical start dates for this programme are February or October.

Fees for this programme can be found here Finance and Funding | Study Here | The University of Aberdeen.