Preterm birth is a multifactorial condition associated with increased morbidity and mortality. Diffuse excessive high signal intensity (DEHSI) has been recently described on T2-weighted MR sequences in this population and thought to be associated with neuropathologies. To date, no robust and reproducible method to assess the presence of white matter hyperintensities has been developed, perhaps explaining the current controversy over their prognostic value. The aim of this paper is to propose a new semi-automated framework to detect DEHSI on neonatal brain MR images having a particular pattern due to the physiological lack of complete myelination of the white matter. A novel method for semi-automatic segmentation of neonatal brain structures and DEHSI, based on mathematical morphology and on max-tree representations of the images is thus described. It is a mandatory first step to identify and clinically assess homogeneous cohorts of neonates for DEHSI and/or volume of any other segmented structures. Implemented in a user-friendly interface, the method makes it straightforward to select relevant markers of structures to be segmented, and if needed, apply eventually manual corrections. This method responds to the increasing need for providing medical experts with semi-automatic tools for image analysis, and overcomes the limitations of visual analysis alone, prone to subjectivity and variability. Experimental results demonstrate that the method is accurate, with excellent reproducibility and with very few manual corrections needed. Although the method was intended initially for images acquired at 1.5T, which corresponds to usual clinical practice, preliminary results on images acquired at 3T suggest that the proposed approach can be generalized.