Mathematical Analysis of Image Matching Techniques

Finding matching keypoints between images is a core problem in 3D computer vision. However, modern matchers struggle with large in-plane rotations. A straightforward mitigation is to learn rotation invariance via data augmentation. However, it remains unclear at which stage rotation invariance should be incorporated. In this paper, we study this in the context of a modern sparse matching pipeline. We perform extensive experiments by training on a large collection of 3D vision datasets and evaluating on popular image matching benchmarks. Surprisingly, we find that incorporating rotation invariance already in the descriptor yields similar performance to handling it in the matcher. However, rotation invariance is achieved earlier in the matcher when it is learned in the descriptor, allowing for a faster rotation-invariant matcher. Further, we find that enforcing rotation invariance does not hurt upright performance when trained at scale. Finally, we study the emergence of rotation invariance through scale and find that increasing the training data size substantially improves generalization to rotated images. We release two matchers robust to in-plane rotations that achieve state-of-the-art performance on e.g. multi-modal (WxBS), extreme (HardMatch), and satellite image matching (SatAst). Code is available at https://github.com/davnords/loma.

The deep-learning based image matching networks can now handle significantly larger variations in viewpoints and illuminations while providing matched pairs of pixels with sub-pixel precision. These networks have been trained with ground-based image datasets and, implicitly, their performance is optimized for the pinhole camera geometry. Consequently, you get suboptimal performance when such networks are used to match satellite images since those images are synthesized as a moving satellite camera records one line at a time of the points on the ground. In this paper, we present EpiMask, a semi-dense image matching network for satellite images that (1) Incorporates patch-wise affine approximations to the camera modeling geometry; (2) Uses an epipolar distance-based attention mask to restrict cross-attention to geometrically plausible regions; and (3) That fine-tunes a foundational pretrained image encoder for robust feature extraction. Experiments on the SatDepth dataset demonstrate up to 30% improvement in matching accuracy compared to re-trained ground-based models.

Dense image matching establishes pixel-wise correspondences and underpins broad applications in computer vision and photogrammetry. However, extending dense matching to global-scale remote sensing remains challenging because image pairs may differ in acquisition time, season, viewpoint, spatial resolution, and land-cover state. The resulting large geometric offsets, partial overlap, and intrinsically unmatchable regions make direct dense correspondence prediction unreliable and inefficient. We thus reformulate dense matching as localization-and-registration: first localizing the matchable overlap and affine geometry, then refining dense residuals within the aligned frame. Based on this formulation, we propose LoRetta, a foundation model coupling matchability-aware affine localization with guided dense registration. We also introduce LEVIR-GM, a global-scale multi-temporal optical matching benchmark with dataset-native matchability labels (103K aligned, 827K augmented pairs, six continents, five years, 0.5-1024 m resolution). We further establish a unified evaluation protocol for sparse, semi-dense, and dense matchers. On LEVIR-GM, LoRetta achieves an area under the curve (AUC) of 83.3%, outperforming the strongest baseline RoMa v2 by 1.6 points, with larger percentage of correct keypoints (PCK) gains of 6.5 and 8.2 points at 1 and 2 pixels, while reducing inference latency by 47.8%. Astronaut-to-satellite and unmanned aerial vehicle (UAV)-to-satellite geolocalization experiments further demonstrate its transferability as a reusable geometric aligner.