Fuzzy and probabilistic segmentation, and appropriate validation, applied to cardiac magnetic resonance images

Algorithms producing fuzzy and probabilistic (i.e. 'soft') segmentations are becoming increasingly popular. However, many of the unique strengths of such algorithms get overlooked, especially when used in the context of deterministic frameworks, which typically treat softness as label uncertainty, and tend to discard it as the final step. We maintain that such treatment results in loss of potentially useful information, which could be used to improve outcomes further. This is particularly the case with regard to validation algorithms, where such loss of information effectively renders validation unreliable. When 'softness' is treated as a fuzzy measure, defined with respect to a suitable criterion, the uncertainty over such a measure can be further characterised and put to use. We explore the role of fuzziness and probability theory in characterising such notions of uncertainty over 'softness', and use it to a) fuse soft segmentations via their uncertainties, leading to improved outcomes compared to fusing by simple consensus, and b) to enable clinicians to optimise algorithms using clinically intuitive measures as opposed to fine-tuning unintuitive algorithmic parameters by hand. We also make theoretical predictions based on the semantics of fuzziness in the context of spatial overlap, and use them to propose the notion of a 'directional t-norm' and show that it leads to more reliable validation. Finally we propose ways of characterising modes of segmentation failure through the use of local-performance maps, fuzzy spatial / anatomical relationship masks, and validation sweeps. In summary, this thesis provides a better understanding of the types of uncertainty that can be defined over an already 'soft' segmentation, and how they could be put to use to improve segmentation outcomes; and a better understanding of the semantics of fuzziness with respect to the validation of soft segmentations, leading to more reliable validation and evaluation in general. While the applications presented in this dissertation have been demonstrated in the context of medical image segmentation, the methods and theory should also be more widely applicable to non-medical image analysis and computer vision in general.