We propose a way to train deep learning based keypoint descriptors that makes them approximately equivariant for locally affine transformations of the image plane. The main idea is to use the representation theory of GL(2) to generalize the recently introduced concept of steerers from rotations to affine transformations. Affine steerers give high control over how keypoint descriptions transform under image transformations. We demonstrate the potential of using this control for image matching. Finally, we propose a way to finetune keypoint descriptors with a set of steerers on upright images and obtain state-of-the-art results on several standard benchmarks. Code will be published at github.com/georg-bn/affine-steerers.

翻译：我们提出了一种训练基于深度学习的关键点描述符的方法，使其对图像平面的局部仿射变换具有近似等变性。主要思想是利用GL(2)的表示理论，将最近提出的导向器概念从旋转变换推广到仿射变换。仿射导向器能够高度控制关键点描述在图像变换下的变换方式。我们展示了利用这种控制进行图像匹配的潜力。最后，我们提出了一种在正立图像上使用一组导向器微调关键点描述符的方法，并在多个标准基准测试中取得了最先进的结果。代码将在github.com/georg-bn/affine-steerers发布。