Keypoint detection and matching is a fundamental task in many computer vision problems, from shape reconstruction, to structure from motion, to AR/VR applications and robotics. It is a well-studied problem with remarkable successes such as SIFT, and more recent deep learning approaches. While great robustness is exhibited by these techniques with respect to noise, illumination variation, and rigid motion transformations, less attention has been placed on image distortion sensitivity. In this work, we focus on the case when this is caused by the geometry of the cameras used for image acquisition, and consider the keypoint detection and matching problem between the hybrid scenario of a fisheye and a projective image. We build on a state-of-the-art approach and derive a self-supervised procedure that enables training an interest point detector and descriptor network. We also collected two new datasets for additional training and testing in this unexplored scenario, and we demonstrate that current approaches are suboptimal because they are designed to work in traditional projective conditions, while the proposed approach turns out to be the most effective.

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