The Couinaud classification of hepatic anatomy partitions the liver into eight functionally independent segments. Detection and segmentation of the hepatic vein (HV), portal vein (PV) and inferior vena cava (IVC) plays an important role in the subsequent delineation of the liver segments. To facilitate pharmacokinetic modeling of the liver based on the same data, a 4D DCE-MR scan protocol was selected. This yields images with high temporal resolution but low spatial resolution. Since the liver's vasculature consists of many tiny branches, segmentation of these images is challenging. The proposed framework starts with registration of the 4D DCE-MRI series followed by region growing from manually annotated seeds in the main branches of key blood vessels in the liver. It calculates the Pearson correlation between the time intensity curves (TICs) of a seed and all voxels. A maximum correlation map for each vessel is obtained by combining the correlation maps for all branches of the same vessel through a maximum selection per voxel. The maximum correlation map is incorporated in a level set scheme to individually delineate the main vessels. Subsequently, the eight liver segments are segmented based on three vertical intersecting planes fit through the three skeleton branches of HV and IVC's center of mass as well as a horizontal plane fit through the skeleton of PV. Our segmentation regarding delineation of the vessels is more accurate than the results of two state-of-the-art techniques on five subjects in terms of the average symmetric surface distance (ASSD) and modified Hausdorff distance (MHD). Furthermore, the proposed liver partitioning achieves large overlap with manual reference segmentations (expressed in Dice Coefficient) in all but a small minority of segments (mean values between 87% and 94% for segments 2-8). The lower mean overlap for segment 1 (72%) is due to the limited spatial resolution of our DCE-MR scan protocol.