The detection of optic disc and macula is an essential step for ROP (Retinopathy of prematurity) zone segmentation and disease diagnosis. This paper aims to enhance deep learning-based object detection with domain-specific morphological rules. Based on the fundus morphology, we define five morphological rules, i.e., number restriction (maximum number of optic disc and macula is one), size restriction (e.g., optic disc width: 1.05 +/- 0.13 mm), distance restriction (distance between the optic disc and macula/fovea: 4.4 +/- 0.4 mm), angle/slope restriction (optic disc and macula should roughly be positioned in the same horizontal line), position restriction (In OD, the macula is on the left side of the optic disc; vice versa for OS). A case study on 2953 infant fundus images (with 2935 optic disc instances and 2892 macula instances) proves the effectiveness of the proposed method. Without the morphological rules, naïve object detection accuracies of optic disc and macula are 0.955 and 0.719, respectively. With the proposed method, false-positive ROIs (region of interest) are further ruled out, and the accuracy of the macula is raised to 0.811. The IoU (intersection over union) and RCE (relative center error) metrics are also improved.