This work investigates a new partial volume (PV) image segmentation framework with comparison to a previous PV approach. The new framework utilizes an expectation-maximization (EM) algorithm to estimate simultaneously (1) tissue fractions in each image voxel and (2) statistical model parameters of the image data under the principle of maximum a posteriori probability (MAP). The previous EM approach models the PV effect by down-sampling a voxel and then labels each subvoxel as a pure tissue type, where the number of subvoxels labeled by a given tissue type over the total number of subvoxels reflects the fraction of that tissue type inside the original voxel. The tissue fractions in each voxel in this discrete PV model are represented by a limited number of percentage values. In the new MAPEM approach, the PV effect is modeled in a continuous space and estimated directly as the fraction of each tissue type in the original voxel. The previous discrete PV model would converge to the proposed continuous PV tissue-mixture model if there is an infinite number of subvoxels within a voxel. However, in practice a voxel is usually down-sampled once or twice for computational reasons. A simulation study reveals that the continuous PV model is not only more realistic but also more accurate than the discrete PV model.