Beyond scalar morphology: A theoretical framework for mathematical morphology on colour and tensor-valued images

Mathematical morphology is an approach for processing shapes, commonly used on monochrome images. Unfortunately, it is not straightforward to extend this framework to colour images, let alone diffusion MRI scans of the brain. The problem is that although we can formally extend the theory, the results often become unintuitive. This thesis argues that this is because such extensions conflict with our interpretation of the data (for example, unlike computers, humans typically do not experience colours as mixtures of red, green and blue). By changing the representation of the data, or using a new formalism, it turns out we can avoid such problems. It is hoped that in future this will make it easier to analyse not just colour images, but also brain scans, fluid flows, and more.