Mathematical Imaging Methods for Mitosis Analysis in Live-Cell Phase Contrast Microscopy
This project was concerned with the development of imaging tools to automate and facilitate mitosis analysis in cancer research. In a collaboration with the Cancer Research UK Cambridge Institute we developed the MitosisAnalyser framework accompanied by a Graphical User Interface. In a first step, we detect mitotic cells by using the circular Hough transform. Then, we use variational level-set methods for subsequent tracking of the cells to determine the length of mitosis within the cell cycle as well as outcomes such as regular division or apoptosis and other statistics.
Learning Filter Functions in Regularisers by Minimising Quotients
The aim of this project was to develop learning frameworks by allowing for both fit- and misfit training data. We developed a quotient model that yields the possibility to resemble the behaviour of well-established derivative-based sparse regularisers. Moreover, we introduced novel families of non-derivative-based regularisers and were investigating the potential to extend our model in the context of classification problems.
Regularisation by Sparse Vector Fields
Inspired by works on image compression borrowing ideas from diffusion inpainting, we developed a variational model enforcing sparsity of the divergence of a vector field related to the gradient of the underlying image. We further investigated this sparse regulariser in the context of image denoising and extended it, eventually proposing a novel unified regulariser based on four natural vector field operators: the curl, the divergence and both components of the shear. We showed that our model generalises well-established TV-type first- and second-order regularisers.
Regularisation by Circular Hough Transform
In this project, we investigated potential benefits of including the circular Hough transform operator in sparse regularisation functionals, acting as a shape prior.
Computer-Aided Detection And Personalised Screening In Breast Imaging
In this project, we were aiming to develop computer-aided detection tools with expertise from radiology, image processing, statistics and machine learning.