We propose a new method, called curvature similar- ity extractor (CSE), for improving local feature matching across images. CSE calculates the curvature of the local 3D surface patch for each detected feature point in a viewpoint- invariant manner via fitting quadrics to predicted monocu- lar depth maps. This curvature is then leveraged as an addi- tional signal in feature matching with off-the-shelf matchers like SuperGlue and LoFTR. Additionally, CSE enables end- to-end joint training by connecting the matcher and depth predictor networks. Our experiments demonstrate on large- scale real-world datasets that CSE consistently improves the accuracy of state-of-the-art methods. Fine-tuning the depth prediction network further enhances the accuracy. The proposed approach achieves state-of-the-art results on the ScanNet dataset, showcasing the effectiveness of incor- porating 3D geometric information into feature matching.