Retinopathy of prematurity (ROP) is an eye disorder that mainly affects fundus vasculature of immature infants. The effect of this disease can be mild with no observable impairments or may become severe with neovascularization, leading to retinal detachment and possibly childhood blindness. A vital sign for initiating treatment for ROP is the detection of Plus disease, which is clinically diagnosed by identifying certain morphological changes to the blood vessels present in the retina of preterm infants. The main goal of this study is to develop a diagnostic method that can distinguish between Plus-diseased and healthy infant retinal images. This work utilizes a fully convolutional deep learning architecture for achieving the desired objective. We use a semi-supervised learning technique for training the network. The proposed technique accurately predicts bounding boxes over the tortuous vessel segments present in an infant retinal image. The count of bounding boxes serve as a measure to quantify tortuosity. We also compare the proposed technique with a recently introduced ROP diagnostic method employing U-COSFIRE filters. We show the efficacy of the proposed methodology on a proprietary data set of 289 infant retinal images (89 with ROP, and 200 healthy), obtained from KIDROP Bangalore, India. We obtain sensitivity (true positive rate) and specificity (true negative rate) equal to 0.99 and 0.98, respectively in the experimented data set. The results obtained in this study show the robustness of the proposed pipeline, as a computer aided diagnostic tool, that can augment medical experts in the early diagnosis of ROP. © 2021 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences