GRLoc: Geometric Representation Regression for Visual Localization

Absolute Pose Regression (APR) has emerged as a compelling paradigm for visual localization. However, APR models typically operate as black boxes, directly regressing a 6-DoF pose from a query image, which can lead to memorizing training views rather than understanding 3D scene geometry. In this work, we propose a geometrically-grounded alternative. Inspired by novel view synthesis, which renders images from intermediate geometric representations, we reformulate APR as its inverse that regresses the underlying 3D representations directly from the image, and we name this paradigm Geometric Representation Regression (GRR). Our model explicitly predicts two disentangled geometric representations in the world coordinate system: (1) a ray bundle's directions to estimate camera rotation, and (2) a corresponding pointmap to estimate camera translation. The final 6-DoF camera pose is then recovered from these geometric components using a differentiable deterministic solver. This disentangled approach, which separates the learned visual-to-geometry mapping from the final pose calculation, introduces a strong geometric prior into the network. We find that the explicit decoupling of rotation and translation predictions measurably boosts performance. We demonstrate state-of-the-art performance on 7-Scenes and Cambridge Landmarks datasets, validating that modeling the inverse rendering process is a more robust path toward generalizable absolute pose estimation.