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Machine learning (ML) has become a powerful tool, with remarkable success across a wide range of areas. In medical image analysis, ML has shown great potential for supporting diagnosis, treatment planning, and disease monitoring by extracting patterns from complex imaging data.

This thesis focuses on structure-aware ML methods for medical image analysis. Medical images exhibit strong spatial structure rather than consisting of independent pixel or voxel intensities. The central idea in the work is to incorporate this prior knowledge into the learning process. The work combines theoretical method development with empirical evaluation on medical imaging applications. The work begins by introducing mathematical morphology as a form of regularization, encouraging the selection of spatially coherent features while also controlling the size of the selected structures (Paper I). The proposed methods are further developed for the multi-class classification task, with particular emphasis on identifying spatially coherent and interpretable image regions associated with disease progression (Paper II).

The work then develops a structured prior distribution based on total variation (TV) within a Bayesian regression framework. Specifically, a well-defined family of structured priors that combines TV with an lp norm is constructed and proven to be proper. The resulting Bayesian formulation enables the estimation of tissue-specific parameter maps together with the quantification of their associated uncertainty (Paper III & Paper IV).

Finally, an input-dependent model is developed in which a neural network generates sample-specific regression coefficients. The Fisher information is used to quantify uncertainty in these coefficients, providing both interpretable predictions and uncertainty estimates (Paper V).

These contributions demonstrate how incorporating prior structure knowledge can guide models toward anatomically plausible solutions. By additionally quantifying uncertainty in estimated parameters, the developed methods provide information about how certain a model is in its outputs, thereby improving the reliability and interpretability of ML methods for medical image analysis.