Noname manuscript No. (will be inserted by the editor) 3D Segmentation of Abdominal CT Imagery with Graphical Models, Conditional Random Fields and Learning

Abstract Probabilistic graphical models have had a tremendous impact in machine learning and approaches based on energy function minimization via techniques such as graph-cuts are now widely used in image seg-mentation. However, the free parameters in energy func-tion based segmentation techniques are often set by hand or using heuristic techniques. In this paper we ex-plore parameter learning in detail. We show how prob-abilistic graphical models can be used for segmentation problems to illustrate Markov random fields (MRFs), their discriminative counterparts conditional random fields (CRFs) as well as kernel CRFs. We discuss the re-lationships between energy function formulations, MRFs, CRFs, hybrids based on graphical models and their re-lationships to key techniques for inference and learning. We then explore a series of novel 3D graphical models and present a series of detailed experiments comparing and contrasting different approaches for the complete volumetric segmentation of multiple organs within com-puted tomography (CT) imagery of the abdominal re-gion. Further, we show how these modelling technique