The task of fundus image registration aims to find matching keypoints between an image pair. Traditional methods detect the keypoint by hand-designed features, which fail to cope with complex application scenarios. Due to the strong feature learning ability of deep neural network, current image registration methods based on deep learning directly learn to align the geometric transformation between the reference image and test image in an end-to-end manner. Another mainstream of this task aims to learn the displacement vector field between the image pair. In this way, the image registration has achieved significant advances. However, due to the complicated vascular morphology of retinal image, such as texture and shape, current widely used image registration methods based on deep learning fail to achieve reliable and stable keypoint detection and registration results. To this end, in this paper, we aim to bridge this gap. Concretely, since the vessel crossing and branching points can reliably and stably characterize the key components of fundus image, we propose to learn to detect and match all the crossing and branching points of the input images based on a single deep neural network. Moreover, in order to accurately locate the keypoints and learn discriminative feature embedding, a brain-inspired spatially-varying adaptive pyramid context aggregation network is proposed to incorporate the contextual cues under the supervision of structured triplet ranking loss. Experimental results show that the proposed method achieves more accurate registration results with significant speed advantage.