Liver and liver cyst volume measurements are important quantitative imaging biomarkers for assessment of disease progression in autosomal dominant polycystic kidney disease (ADPKD) and polycystic liver disease (PLD). To date, no study has presented automated segmentation and volumetric computation of liver and liver cysts in these populations. In this paper, we proposed an automated segmentation framework for liver and liver cysts from bounded abdominal MR images in patients with ADPKD. To model the shape and variations in ADPKD livers, the spatial prior probability map (SPPM) of liver location and the tissue prior probability maps (TPPMs) of liver parenchymal tissue intensity and cyst morphology were generated. Formulated within a three-dimensional level set framework, the TPPMs successfully captured liver parenchymal tissues and cysts, while the SPPM globally constrained the initial surfaces of the liver into the desired boundary. Liver cysts were extracted by combined operations of the TPPMs, thresholding, and false positive reduction based on spatial prior knowledge of kidney cysts and distance map. With cross-validation for the liver segmentation, the agreement between the radiology expert and the proposed method was 84% for shape congruence and 91% for volume measurement assessed by the intra-class correlation coefficient (ICC). For the liver cyst segmentation, the agreement between the reference method and the proposed method was ICC=0.91 for cyst volumes and ICC=0.94 for % cyst-to-liver volume.