Mathematical Imaging Methods for Mitosis Analysis in Live-Cell Phase Contrast Microscopy
This project is 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, mitotic cells are detected by using the circular Hough transform. Then, we use variational level-set methods for subsequent tracking of the cells to determine the length and the outcome of mitosis.
Video (Made for a contest of the Cantab Capital Institute for the Mathematics of Information)
J. Pike, P. Mascalchi, JSG, S. Reichelt. Event Driven Automated Microscopy. Applications in Cancer Research. Imaging & Microscopy, 2017. (article)
JSG, J.A. Harrington, S.B. Koh, J.A. Pike, A. Schreiner, M. Burger, C.-B. Schönlieb, S. Reichelt. Mathematical Imaging Methods for Mitosis Analysis in Live-Cell Phase Contrast Microscopy. Methods, 115: 91-99, 2017. Image Processing for Biologists. (article) (arXiv)
Learning Filter Functions in Regularisers by Minimising Quotients
The aim of this project is 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 are currently investigating the potential to extend our model in the context of classification problems.
M. Benning, G. Gilboa, JSG, C.-B. Schönlieb. Learning Filter Functions in Regularisers by Minimising Quotients. In Scale Space and Variational Methods in Computer Vision, pages 511-523. Springer, 2017. (article) (arXiv)
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 show that our model generalises well-established TV-type first- and second-order regularisers.
E.-M. Brinkmann, M. Burger, JSG. Unified Models for Second-Order TV-Type Regularisation in Imaging – A New Perspective Based on Vector Operators. Journal of Mathematical Imaging and Vision, 2018. (article) (arXiv)
E.-M. Brinkmann, M. Burger, JG. Regularization with Sparse Vector Fields: From Image Compression to TV-Type Reconstruction. In Scale Space and Variational Methods in Computer Vision, pages 191-202. Springer, 2015. (article) (arXiv)
Regularisation by Circular Hough Transform
In this project, we investigate 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
During my time at The Alan Turing Institute, I was involved in a project aiming to develop computer-aided detection tools with expertise from radiology, image processing, statistics and machine learning (see more extended project description on CMIH webpage here).