Statistical and Topological Quantification of Shape Features in Biomedical Images
This project will develop new methods for medical image analysis by combining techniques from statistical and topological data analysis.
The overall objective is to robustly detect morphological features in biomedical images obtained by label-free ‘finger-printing’ vibrational spectroscopy methods and classify the images according to their disease status. Such advanced spectroscopy and novel imaging methods are able to extract the chemical composition of biological systems, including living cells, to an unprecedented level of detail, and thus can be used for accurate medical diagnosis and early detection of diseases. The imaging techniques give multicomponent spectral information bearing chemical and structural information that can be complex to disentangle in a robust non-subjective manner. However, at the moment, the diagnosis depends solely on the clinician’s expertise, while machine learning data-driven classifiers are limited by the typically small number of training samples.
This project will develop novel statistical models which use topological summaries to create powerful methods for image classification without the need of vast training sets. Topology is the mathematical study of shape, and modern methods, including persistent homology, have been extremely successful at detecting key morphological features (‘shape’) in multiple application domains, including brain morphology or material science.
The first objective of this project is to develop statistically robust topological summaries of morphological features from single or multicomponent ‘chemical maps’ in biomedical images. These shape descriptors can be quantified and presented to the clinician to inform her/his decision. The second objective is to develop a classifier based on a statistical model that uses topological summaries. The integration of topological summaries in statistical models is a rapidly growing area which has provided several important results to date.
The successful applicant will be exposed to a truly interdisciplinary environment in the interface between Mathematics and Medicine, and will be trained in advanced statistical and topological techniques, as well as contribute to state-of-the-art tools for biomedical image analysis.
The ideal candidate will have at least an upper second-class undergraduate degree, or a merit at masters, in Mathematics, Statistics, Physics or related area, with an interest in biomedical problems and a positive attitude towards interdisciplinary research.