For a long time, the local descriptors learning for
image matching benefits from the use of L2 normalization, which projects the descriptor space onto the hypersphere. However, there is no free lunch in the world. Although hypersphere description space stabilizes the optimization and improves the repeatability of the descriptors, it causes the descriptors to have a denser distribution, which reduces the discrimination between descriptors and leads to some incorrect matches. To alleviate this problem, we propose the cross normalization technology as an alternative to L2 normalization, which can achieve a consistent improvement in the several current popular local descriptors. In addition, we provide a distribution consistent loss that can optimize local descriptors based on description space distribution consistency constraint to further stimulate the performance of the local descriptors. Based on the above inovations, we carefully design a novel local descriptors extraction network (CNDesc) via our densely connected backbone. We perform experiments on image matching, homography estimation, 3D reconstruction, and visual localization tasks, and the results demonstrate that our method surpasses the current state-of-the-art local descriptors.