Segmentation is an indispensable initial step in image analysis and computer vision. New advanced scanners and large scale imaging facilities have spiked the interest of researchers across fields to investigate the internal structures of objects in a noninvasive manner. However, with new machines come new artefacts and challenges that need to be addressed before subsequent analysis can be conducted.

This thesis presents six novel variational methods for the recovery of segments in tomographic reconstructions. Two primary types of volumetric datasets are used as target application; porous chalk rocks, from X-ray computerised microtomography (X-ray μCT) and rat cranial scans, acquired through magnetic resonance imaging (MRI). Several types of artefacts are addressed, with an emphasis on bias fieldsthat corrupts both acquisition modalities.