The segmentation of MR images of the neonatal brain is an essential step in the study and evaluation of infant brain development. State-of-the-art methods for adult brain MRI segmentation are not applicable to the neonatal brain, due to large differences in structure and tissue properties between newborn and adult brains. Existing newborn brain MRI segmentation methods either rely on manual interaction or require the use of atlases or templates, which unavoidably introduces a bias of the results towards the population that was used to derive the atlases. We propose a different approach for the segmentation of neonatal brain MRI, based on the infusion of high-level brain morphology knowledge, regarding relative tissue location, connectivity and structure. Our method does not require manual interaction, or the use of an atlas, and the generality of its priors makes it applicable to different neonatal populations, while avoiding atlas-related bias. The proposed algorithm segments the brain both globally (intracranial cavity, cerebellum, brainstem and the two hemispheres) and at tissue level (cortical and subcortical gray matter, myelinated and unmyelinated white matter, and cerebrospinal fluid). We validate our algorithm through visual inspection by medical experts, as well as by quantitative comparisons that demonstrate good agreement with expert manual segmentations. The algorithm's robustness is verified by testing on variable quality images acquired on different machines, and on subjects with variable anatomy (enlarged ventricles, preterm- vs. term-born).