Establishing accurate anatomical correspondences is critical for medical image registration. Although many hand-engineered features have been proposed for correspondence detection in various registration applications, no features are general enough to work well for all image data. Although many learning-based methods have been developed to help selection of best features for guiding correspondence detection across subjects with large anatomical variations, they are often limited by requiring the known correspondences (often presumably estimated by certain registration methods) as the ground truth for training. To address this limitation, we propose using an unsupervised deep learning approach to directly learn the basis filters that can effectively represent all observed image patches. Then, the coefficients by these learnt basis filters in representing the particular image patch can be regarded as the morphological signature for correspondence detection during image registration. Specifically, a stacked two-layer convolutional network is constructed to seek for the hierarchical representations for each image patch, where the high-level features are inferred from the responses of the low-level network. By replacing the hand-engineered features with our learnt data-adaptive features for image registration, we achieve promising registration results, which demonstrates that a general approach can be built to improve image registration by using data-adaptive features through unsupervised deep learning.