Aerial visual localization is crucial for autonomous drone navigation in urban environments where GNSS signals are often degraded. Lightweight textureless Level-of-Detail (LoD) city models provide a geometric map alternative to textured assets. Existing silhouette-based methods rely on image-space alignment, which can leave different camera poses indistinguishable and favor incorrect poses when segmentation errors distort the building outlines. We present PlanarCityLoc, which moves beyond silhouette overlap by leveraging the planar geometry of building facades and roofs. Following geometry-aware initialization, we match image-side planar patches to LoD model planes and use the resulting 3D-to-2D correspondences to refine pose with Perspective-n-Point (PnP). The framework uses off-the-shelf geometry and segmentation models without dataset-specific training or fine-tuning. Experiments on UAVD4L-LoDv2 and Swiss-EPFLv2 achieve state-of-the-art localization recall among the evaluated off-the-shelf LoD-based methods. By grounding image-space alignment in 3D planes, PlanarCityLoc enables more accurate aerial localization with lightweight, textureless city maps.

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