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Malignant pleural mesothelioma (MPM) is a form of aggressive tumour that is almost always associated with prior exposure to asbestos. Currently responsible for over 47,000 deaths worldwide each year and rising, it poses a serious threat to global public health. Many clinical studies of MPM, including its diagnosis, prognostic planning, and the evaluation of a treatment, necessitate the accurate quantification of tumours based on medical image scans, primarily computed tomography (CT). Currently, clinical best practice requires application of the MPM-adapted Response Evaluation Criteria in Solid Tumours (MPM-RECIST) scheme, which provides a uni-dimensional measure of the tumour's size. However, the low CT contrast between the tumour and surrounding tissues, the extensive elongated growth pattern characteristic of MPM, and, as a consequence, the pronounced partial volume effect, collectively contribute to the significant intra- and inter-observer variations in MPM-RECIST values seen in clinical practice, which in turn greatly affect clinical judgement and outcome. In this thesis, we present a novel computer-assisted approach to evaluate MPM patient response to treatments, based on the volumetric segmentation of tumours (VTA) on CT. We have developed a 3D segmentation routine based on the Random Walk (RW) segmentation framework by L. Grady, which is notable for its good performance in handling weak tissue boundaries and the ability to segment any arbitrary shapes with appropriately placed initialisation points. Results also show its benefit with regard to computation time, as compared to other candidate methods such as level sets. We have also added a boundary enhancement regulariser to RW, to improve its performance with smooth MPM boundaries. The regulariser is inspired by anisotropic diffusion. To reduce the required level of user supervision, we developed a registration-assisted segmentation option. Finally, we achieved effective and highly manoeuvrable partial volume correction by applying a reverse diffusion-based interpolation. To assess its clinical utility, we applied our method to a set of 48 CT studies from a group of 15 MPM patients and compared the findings to the MPM-RECIST observations made by a clinical specialist. Correlations confirm the utility of our algorithm for assessing MPM treatment response. Furthermore, our 3D algorithm found applications in monitoring the patient quality of life and palliative care planning. For example, segmented aerated lungs demonstrated very good correlation with the VTA-derived patient responses, suggesting their use in assessing the pulmonary function impairment caused by the disease. Likewise, segmented fluids highlight sites of pleural effusion and may potentially assist in intra-pleural fluid drainage planning. Throughout this thesis, to meet the demands of probabilistic analyses of data, we have used the Non-Parametric Windows (NPW) probability density estimator. NPW outperforms the histogram in terms of its smoothness and kernel density estimator in its parameter setting, and preserves signal properties such as the order of occurrence and band-limitedness of the sample, which are important for tissue reconstruction from discrete image data. We have also worked on extending this estimator to analysing vector-valued quantities; which are essential for multi-feature studies involving values such as image colour, texture, heterogeneity and entropy.