The extremely low tissue contrast in white matter during an infant's isointense stage (6-8 months) of brain development presents major difficulty when segmenting brain image regions for analysis. We sought to develop a label-fusion-aided deep-learning approach for automatically segmenting isointense infant brain images into white matter, gray matter and cerebrospinal fluid using T1- and T2-weighted magnetic resonance images. A key idea of our approach is to apply the fully convolutional neural network (FCNN) to individual brain regions determined by a traditional registration-based segmentation method instead of training a single model for the whole brain. This provides more refined segmentation results by capturing more region-specific features. We show that this method outperforms traditional joint label fusion and FCNN-only methods in terms of Dice coefficients using the dataset from iSEG MICCAI Grand Challenge 2017.