The IMAGE section at DIKU hosts experts in fields including nonlinear statistics, applied differential geometry, shape modelling, image analysis & processing, computer vision, computer simulation, and machine learning. Their work ranges from theoretical analyses, over algorithm development, to solving concrete problems for science, industry, and society. Biomedical imaging is a central application area, including neuroimaging. The section contributes to the theory of image analysis by studying nonlinear statistics, variational problems, and geometry on manifolds and metric spaces. The section conducts core machine learning research, including deep learning, transfer learning, online learning, kernel methods, stochastic optimization, and concentration of measure inequalities. For further information, please visit http://www.diku.dk/english/research/imagesection/ 

Human organs change shape when exposed to disease processes. For example, shape changes in the human brain is linked to the progression of Alzheimer’s disease due to the degeneration of brain tissue. Organ shape can therefore be used as a biomarker for understanding disease progression. However, due to the nonlinearity of shape spaces, classical methods from multivariate and functional statistics cannot be used for quantifying shape variation. The PhD project aims at developing methods for performing statistical analysis of shapes as elements of infinite dimensional nonlinear spaces. Recent probabilistic shape models use stochastic processes to encode variation of shapes, and likelihoods arise from the processes conditioned on observed data. The conditioned processes are examples of stochastic bridges. Particular aims of the project is to develop and prove validity of methods for sampling stochastic shape bridges, to use this to analyze shape variation among Alzheimer’s patients, and thereby to reveal distinct temporal progression patterns within Alzheimer’s disease. 

The PhD student will focus on both theoretical aspects of stochasticity in nonlinear, infinite dimensional spaces, on developing actual statistical tools to analyze shape variation, and on evaluation the methodology on medical image data. The project will thus have both theoretical and applied focus. The PhD student will be part of the Probabilistic Shape Statistics for Disentangling Subtypes in Alzheimer’s Disease project, funded by a grant from the Novo Nordisk foundation. The applicant must have documented experience in aspects of theoretical statistics, stochastic analysis, differential geometry and/or machine learning. The project will require computer implementation of the developed numerical algorithms.

 

Principal supervisor is Associate Professor Stefan Sommer, Department of Computer Science, sommer@di.ku.dk, Direct Phone: +4521179125.