This paper presents a method for 3D segmentation of kidneys from patients with autosomal dominant polycystic kidney disease (ADPKD) and severe renal insufficiency, using computed tomography (CT) data. ADPKD severely alters the shape of the kidneys due to non-uniform formation of cysts. As a consequence, fully automatic segmentation of such kidneys is very challenging. We present a segmentation method with minimal user interaction based on a random forest classifier. One of the major novelties of the proposed approach is the usage of geodesic distance volumes as additional source of information. These volumes contain the intensity weighted distance to a manual outline of the respective kidney in only one slice (for each kidney) of the CT volume. We evaluate our method qualitatively and quantitatively on 55 CT acquisitions using ground truth annotations from clinical experts.