This paper focuses on pose registration of different object instances from the same category. This is required in online object mapping because object instances detected at test time usually differ from the training instances. Our approach transforms instances of the same category to a normalized canonical coordinate frame and uses metric learning to train fully convolutional geometric features. The resulting model is able to generate pairs of matching points between the instances, allowing category-level registration. Evaluation on both synthetic and real-world data shows that our method provides robust features, leading to accurate alignment of instances with different shapes.