  This paper addresses the problem of estimating the 3-DoF camera pose for a
ground-level image with respect to a satellite image that encompasses the local
surroundings. We propose a novel end-to-end approach that leverages the
learning of dense pixel-wise flow fields in pairs of ground and satellite
images to calculate the camera pose. Our approach differs from existing methods
by constructing the feature metric at the pixel level, enabling full-image
supervision for learning distinctive geometric configurations and visual
appearances across views. Specifically, our method employs two distinct
convolution networks for ground and satellite feature extraction. Then, we
project the ground feature map to the bird's eye view (BEV) using a fixed
camera height assumption to achieve preliminary geometric alignment. To further
establish content association between the BEV and satellite features, we
introduce a residual convolution block to refine the projected BEV feature.
Optical flow estimation is performed on the refined BEV feature map and the
satellite feature map using flow decoder networks based on RAFT. After
obtaining dense flow correspondences, we apply the least square method to
filter matching inliers and regress the ground camera pose. Extensive
experiments demonstrate significant improvements compared to state-of-the-art
methods. Notably, our approach reduces the median localization error by 89%,
19%, 80% and 35% on the KITTI, Ford multi-AV, VIGOR and Oxford RobotCar
datasets, respectively.
