Recent works in deep-learning have shown that second-order information is beneficial in many computer-vision tasks. Second-order information can be enforced both in the spatial context and the abstract feature dimensions. In this work, we explore two second-order components. One is focused on second-order spatial information to increase the performance of image descriptors, both local and global. It is used to re-weight feature maps, and thus emphasise salient image locations that are subsequently used for description. The second component is concerned with a second-order similarity (SOS) loss, that we extend to global descriptors for image retrieval, and is used to enhance the triplet loss with hard-negative mining. We validate our approach on two different tasks and datasets for image retrieval and image matching. The results show that our two second-order components complement each other, bringing significant performance improvements in both tasks and lead to state-of-the-art results across the public benchmarks. Code available at: http://github.com/tonyngjichun/SOLAR
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