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Despite the fact that Second Order Similarity (SOS) has been used withsignificant success in tasks such as graph matching and clustering, it has notbeen exploited for learning local descriptors. In this work, we explore thepotential of SOS in the field of descriptor learning by building upon theintuition that a positive pair of matching points should exhibit similardistances with respect to other points in the embedding space. Thus, we proposea novel regularization term, named Second Order Similarity Regularization(SOSR), that follows this principle. By incorporating SOSR into training, ourlearned descriptor achieves state-of-the-art performance on several challengingbenchmarks containing distinct tasks ranging from local patch retrieval tostructure from motion. Furthermore, by designing a von Mises-Fischerdistribution based evaluation method, we link the utilization of the descriptorspace to the matching performance, thus demonstrating the effectiveness of ourproposed SOSR. Extensive experimental results, empirical evidence, and in-depthanalysis are provided, indicating that SOSR can significantly boost thematching performance of the learned descriptor.

SOSNet: Second Order Similarity Regularization for Local Descriptor Learning