We propose a semantic similarity metric for image registration. Existing metrics like Euclidean Distance or Normalized Cross-Correlation focus on aligning intensity values, giving difficulties with low intensity contrast or noise. Our approach learns dataset-specific features that drive the optimization of a learning-based registration model. We train both an unsupervised approach using an auto-encoder, and a semi-supervised approach using supplemental segmentation data to extract semantic features for image registration. Comparing to existing methods across multiple image modalities and applications, we achieve consistently high registration accuracy. A learned invariance to noise gives smoother transformations on low-quality images.