Loc$^{2}$: Interpretable Cross-View Localization via Depth-Lifted Local Feature Matching
Authors: Zimin Xia
Chenghao Xu
Alexandre Alahi
Venue: ICLR 2026 Poster (2026)
Keywords: Cross-view localization
ground-to-aerial image matching
visual localization
computer vision
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: We propose an accurate and interpretable fine-grained cross-view localization method that estimates the 3 Degrees of Freedom (DoF) pose of a ground-level image by matching its local features with a reference aerial image. Unlike prior approaches that rely on global descriptors or bird’s-eye-view (BEV) transformations, our method directly learns ground–aerial image-plane correspondences using weak supervision from camera poses. The matched ground points are lifted into BEV space with monocular depth predictions, and scale-aware Procrustes alignment is then applied to estimate camera rotation, translation, and optionally the scale between relative depth and the aerial metric space. This formulation is lightweight, end-to-end trainable, and requires no pixel-level annotations. Experiments show state-of-the-art accuracy in challenging scenarios such as cross-area testing and unknown orientation. Furthermore, our method offers strong interpretability: correspondence quality directly reflects localization accuracy and enables outlier rejection via RANSAC, while overlaying the re-scaled ground layout on the aerial image provides an intuitive visual cue of localization performance.

Published as a conference paper at ICLR 2026
Loc?: INTERPRETABLE PROSS-VIEV LOCALIZATION VIA DEPTH-LIFTED LOCAL FEATURE MATCHING
Zimin Xia", Chenghao Xu & Alexandre Alahi
Eoole Polytechnique Fédérale de Lausanne (EPFL), Switzerland
{2 tmmmn...e xia, chenghao... xu, alexardre. "Equal contribution
ABSTRACT
We propose an accurate and interpretable fine-grained cross-view localization method that estimates the 3 Degrees of Freedom (DoF) pose of ground-level image by matching its local features with a reference aerial image. Unlike prior approaches that rely global descriptors or bird s-eee-view view (BEV) transforma- tions, our method directly learns ground-acts aerial image-plane correspondences us- ing weak supervision from camera poses. The matched ground points are lifted into BEV space with monocular depth predictions, and scale-aware Procrustes alignment is then applied to estimate camera rotation, translation, and optionally the scale between relative depth and the aerial metric space. This formulation is lightweight, end-to-end trainable, and requires no pixel-level annotations. Exper- iments show state-of-the-ee art accuracy in challenging scenarios such as cross-area testing and unknown orientation. Furthermore, our method offers strong inter- pretability: correspondence quality directly reflects localization accuracy and en- ables outlier rejection via RANSAC, while overlaying the re-scaled ground layout on the aerial image provides an intuitive visual cue of localization performance.
INTRODUCTION
Visual localization, a fundamental task in computer vision and mobile robotics, aims to estimate the camera pose with respect to representation of the environment [Thrun 20020. In dense urban areas, specialized positioning sensors, such as Global Navigation Satellite System (GNSS), have errors up to tens of meters (Xia et al. 202T). Fine-grained cross-view localization has recently emerged promising complement. It estimates the 3 Degrees Freedom (DoF) camera pose, i.e., 2D planar location and yaw orientation, by comparing captured ground-level images to aerial image of the surroundings, identified using coarse GNSS measurements.
The key cross-view localization is establish associations between ground-level and aerial im- ages. However, the extreme visual differences between the two views make it challenging for recent advances image matching (Leroy et al., 2024, Sun et al., 202T, Wang al., 2025) produce reliable correspondences, and there is no ground-acrial pixel-level ground truth to finetune these methods. In practice, the majority of cross-view localization approaches seek global alignment be- tween two views by matching global image descriptors (Xia et al.] 2023) or aligning ground-view transformed bird's-eye --eye-view (BEV) features with aerial images (Fervers et al. 2023b Wang al.) 20246). However, these methods offer limited interpretability, as they cannot explicitly identity which objects in the ground view correspond to those in the aerial view.
Recently, 2G2 (Xia & Alahi, 2025) demonstrated the feasibility of establishing local feature cor- respondences between ground and aerial images by propagating BEV point matches to the image plane. However, performing the matching in BEV is suboptimal, since warping ground image into BEV inevitably introduces ray- directicai distortions (Song et al., 2024h and discards informa- tion along the height dimension (Xia & Alahi 2025 Wang et al. 2024a). This loss of information hinders matching to aerial images and, as a result, degrades localization performance, especially in challenging settings such as unknown camera orientation.

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Published as a conference paper at ICLR 2026
Ours
Figure 1: Loc": Interpretable cross-view localization via local feature matching. Loc² establishes accurate correspondences between aerial and ground views, with colors indicating distinct corre- spondence regions. Using the estimated rotation, translation, and scale, the ground view is warped onto the aerial image, providing a visual interpretation of localization quality.
Therefore, we propose to establish correspondences directly between ground and aerial images. In- stead of relying on pixel-level annotations (Leroy et al.) [024] Wang et al. 20250, our approach is weakly supervised using only 3-DoF camera poses. To infer the pose from image-plane correspon- dences, we lift the sampled ground points into the BEV space with the help of monocular depth models (Yang et al. 2024a by Piccinelli et al., 2025 Wang & Liu 2024). In unseen environments, usually only the non- non-metric relative depth prediction, i.e., depth up an unknown scale, is reliable. Therefore, our method supports both metric and relative depth, and jointly estimates the camera pose and depth scale using scale-aware Procrustes alignment (Umeyama) 199T..
As shown in Fig. D our method offers superior interpretability. Since the pose is computed analyt- ically from the matches, the quality of local feature correspondences directly reflects localization accuracy, and we find that the number of inlier correspondences shows a strong correlation with lo- calization accuracy. Moreover, by overlaying the scaled, rotated, and translated ground BEV layout onto aerial images, our method provides an additional visual cue of localization accuracy.
Concretely, our main contributions are: (1) We propose simple and accurate fine-grained cross- view localization method that matches local features across views. Our method achieves superior localization accuracy under challenging conditions such as cross-area generalization and unknown orientation. (2) Our method is highly interpretable. The pose is computed analytically from the estimated correspondences, which also enable outlier filtering via RANSAC. When relative depth is used at inference, our method estimates its scale, and the alignment between the re-scaled ground layout and the acrial image further provides a visual cue of localization quality. (3) By leverag- ing differentiable scale-aware Procrustes aligmment, our local feature matching becomes end-to-end trainable using only camera pose supervision, without requiring pixel-Ievel annotations.
2 RELATED WORK
Fine-grained cross-view localization is challenging due to the drastic viewpoint differences and asynchronous capture times between ground and aerial imagery. State-of-the-ar approaches tackle this domain gap primarily by learning a deep network for camera pose estimation. Global descriptor- based methods (Xia et al. 2022 Lentsch et al. 2023 Xia al.
2023) leverage contrastive learning
to pull the ground and aerial features to a common representation space, and compare the ground im- age descriptor aerial descriptors extracted at different candidate poses. Geometry transformation-
based methods (Fervers et al. 2023b Wang et al. 2023 [arllnn et al. [2024] [aag et al. 2024a) Song
al. 2024 (Shi al.] 2023 Wang et al. 2024b] Fervers al. [023a] Xia & Alahi 2025) first warp the ground image into BEV representation, and then either perform a Bolding-windeee
search over the aerial image to find the best alignment (Sarlin al. 2024 Fervers et al.) 20236 Shi et al., 2023) or estimate the relative pose by matching features between the BEV and aerial view (Song et al.,
2024 Wang et al. 2024b 2023 2024a Xia & Alahi 2025). Despite the increasing localization ac- curacy, most methods do not explicitly identify matched local features across views, offering limited interpretability. A recent work (Xia & Alahi 2025) demonstrated, for the first time, the ability to find arrral local feature correspondences by defining dense 3D point cloud and querying image features for each point. However, this process is inefficient due to the sparse nature of 3D space, and this method performs poorly when camera orientation is unknown.
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Local Feature Matching
Camera Pose Estimation
FA
Acrial Image
Maichina Scoce M
Ground Image G
Honerlle Doysk Miser
Depth Map D
Figure 2: Overview of our proposed method. Our method first matches local features between ground and aerial images. The matched ground points are then lifted the BEV space using monoc- ular depth priors. By aligning these correspondences using scale-aware Procrustes alignment, we estimate the rotation, translation, and scale between the ground and aerial views.
Ground-view visual localization typically follows highly interpretable pipeline (Sarlin et al. 2019 Sattler et al. 2016). which involves finding local feature correspondences (Sarlin et al. 2020 Sun et al. 2021) and then estimating camera pose using geometry- solver (Lepetit et al. 2009). However, this pipeline becomes challenging in the cross-view setting due to the significant domain gap and the lack of labeled correspondences. We propose learn such correspondences for cross-view localization using only camera pose supervision, facilitated by monocular depth priors.
METHODOLOGY
Fine-grained cross-view localization estimates the 3-DoF pose, i.e., the 2D metric location t E R and the yaw orientation E [-Tr, x), of a ground-level image G by matching aerial image A covering the local area. As shown in Fig. 2 our method first establishes correspon- dences between and A (Sec. 3.T. then lifts the matched ground points to the BEV using the predicted depth map D = D()) from off-the-shelf monocular depth models, and finally computes the 3-DoF pose via scale-aware Procrustes alignment (Sec. B.2). This fully differentiable pipeline enables end-to-end learning of image-plane matching under weak supervision from camera poses.
geo-referenced
3.1 LOCAL FEATURE MATCHING
We estimate the 3-DoF metric camera pose by learning image-plane local feature correspondences between ground and aerial images. Our model has two feature extraction branches that share the same architecture. Each branch consists followed by our lightweight projection head, which is composed of several convolutional layers and a self-attention layer (Vaswani et al., 2017). The two branches map the aerial image and the ground image G to feature maps F, and F G. respectively.
frozen DINOv2 feature extractor (Oquab et al. 2024)
Afterwards, we compute the pairwise matching scores M between F, and F using cosine similar- ity, .M cosine( F FA, FG)/T, where is temperature parameter. Following DeTone et al. 2018); Sarlin et al. (2020). we append a learnable dusthin to both the rows and columns M, allowing the model reject uncertain or unmatched points. On this extended matching score matrix M we apply dual softmax normalization over rows and columns obtain a match probability matrix M
Mis
Mig
My
6
(1)
Exeuo
Mi
Finally, we drop the dustbin row and column from M and sample N correspondences for subse- quent pose estimation. We denote the matching probability of the sampled correspondences as w,, [1,..., N), which will be used as the weight in the scale-aware Procrustes alignment.
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3.2 CAMERA POSE ESTIMATION
Coordinate assignment: Given the N sampled correspondences, we leverage off-the-shelf monoc- ular depth estimators to assign coordinates these correspondences. which are then used to estimate the camera pose. Importantly, monocular depth prediction is a geometrically ill-posed problem, as there is no unique mapping from a single image to absolute metric depth. State-of-the-an methods either learn generalizable metric depth from diverse training data (Piccinelli et al. (225) Zhu et al. 2024], or predict depth that accurate only up to an unknown per-image scale (Wang & Liu 2024
Yang et al. 2024a). To generalize across diverse scenarios and image types, our method accom- modates both metric and relative depth, and explicitly estimates a scale factor to convert relative depth into metric space. This scale estimation leverages the metric information, i.e., meters per pixel, available in geo-referenced aerial imagery.
Specically, we denote the metric coordinates of the 2D point associated with the n-th acrial feature as (a v. ). with the origin defined at the center of the acrial image. For the corresponding ground feature, we retrieve its depth from D and use its associated ray direction to compute its 3D location in space. The resulting 3D point is denoted as (Ie G 2, / with the origin defined at the ground camera. Here, is unknown scale factor from the ground coordinate system to the aerial metric space, and = 1 when a reliable metric depth model is used. We retain all matched ground points without explicitly selecting them based on their height (z-coordinate). Our ablation study will show that explicitly selecting the topmost point does not improve performance.
Scale-aware Procrustes alignment: As shown in Fig. right, once we have the point correspon- dences {<> v2",, (I Yn /s). and their matching probabilities Wy, we can compute the rota- tion R. translation t, and the scale between the ground points and the metric space aerial points an- alytically in a differentiable manner using 2D scale-aware Procrustes alignment (Umeyama) 1991
For simplicity, we denote the planar coordinates 0 of all ground points as = Ps//, assuming they differ from the metric coordinates, P = {x w/) .... (= vn"), by an unknown scale The coordinates of all aerial points are denoted as Q. The objective to estimate the scale 8, rotation
matrix R and metric translation t that satisfy the transformation Q s(R. P) + t.
First, we compute the weighted centroids of the aerial and ground point sets,
N Quy
N
W Σ
P
Wn
Pa. with W- = Σ Wp.
W n=1
n=1
==1
In Eq. 2] the better matched points will contribute more the centroids of the point sets. Then, center the point sets and compute their covariance matrix C,
N Σ 1=1
C
Wn Pn
@m
(3)
where P,, and Qn are the n-th points in the centered point sets Q Q Q and P - covariance matrix C' captures how the centered ground points relate to the centered aerial points, encoding the direction and strength of their mutual variation.
P. The
Next, we perform Singular Value Decomposition (SVD) on C, where C = UΣVT, and the optimal rotation can be recovered as R VU which derives the estimated yaw orientation o. The seale and translation from the ground points P to the aerial points Q are then computed as,
Tr(E)
t= Q - -RR(RR. P).
(4)
2 Wn P
Recall that P = /s/s. Substituting this into Eq. the estimated scale s* can be expressed using the (unscaled) metric coordinates P", with Σ" computed from the SVD between Q and P*:
In Xia Alahi 2025 ; Barroso-I Laguna et al. 2024 all coordinates are in metric space, so they
orthogonal Procrustes (Gower 1975 and ignore scale.
We assume that the ground camera's 's viewing direction is orthogonal to the gravity direction, since this can he reliably calibrated /eeccht al. 2024) obtained from an IMU accelerometer.
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Tr(E"/3) pp' /s/
(Tr(E*)
(5)
Σ n= Wn
Σ n=1
Wn
p
Since P lies in the same metric space as the aerial points Q, and there no scale difference between them, have Tr(E) Σn P must be scaled by to align them with the metric aerial points Q-
W/ P.. This leads to s* indicating that the ground points
Practical implication:
This derivation shows that, regardless of the unknown scale of the ground points, scale-aware Procrustes alignment yields consistent estimate of the camera pose and can recover the scale Its differentiability makes it particularly well-suited for learning local feature matching through pose supervision, while also enabling inference using only relative depth.
3.3 MODEL SUPERVISION
We follow Xia & Alahi 2025 to provide supervision both the pose and correspondences. For camera pose, we adopt the Virtual Correspondence Error (VCE) loss. Specifically, we define a set of No virtual points P. in a 2D metric space, where the hyperparameter controls the spatial extent of the space. We apply both the ground truth transformation, Rgt, tgt. and the estimated transformation, R, t. to these virtual points. The loss LyCe then minimizes the mean Euclidean distance between the corresponding transformed points,
LvCr
No Σ II
Pottel (R.P., ...P, F.+tt)l
When metric depth is available during training, we the ground-truth pose find for the ground points, their corresponding aerial points and compute an infoNCE loss (Oord et al. 2018). Lass, encourage these correspondences. We also find, for the acrial points, their corresponding ground points. However, multiple ground points may exist at different heights but share similar BEV loca- tions. We select the ground point closest the projected location and compute the Ls2g, using only ground points outside defined local neighborhood as negatives. The detailed formulation is pro- vided in the Appendix. The total loss is then a weighted combination of the VCE loss and infoNCE losses, L LVCr + B(Lozs + Ls2a)/2.
EXPERIMENT
We first introduce the datasets and metries, followed by implementation details. We then compare method with prior state-of-the-art vision-based methods and showcase inference using different monocular depth predictors. Next, we present qualitative results on local feature matching and interpretable layout alignment, along with cross-datase generalization and our ablation studies.
4.1 DATASETS AND EVALUATION METRICS
KITTI Geiger et al. 2013) provides forward-facing ground-level images with limited field of view. Aerial images for KITTI were collected by Shi & Li (022). who also split the dataset into Training, Testl, and Test2 subsets. Testl includes images from the same region as the Training set, while Test2 contains images from a different unseen region. We refer to Testl and Test2 as the same-area and cross-area test sets, respectively. We use the metric depth predictions from DepthAnything V2 Yang et al. 2024b) for our experiments on KITTI.
VIGOR Zhu et al. 2021 a widely used cross-view localization dataset, containing ground-level panoramas and aerial images from four U.S. cities. It also provides same-area and cross-area splits. In the same-area split, training and test images are collected from all four cities, while in the cross- area split, the training and test sets come from two different cities. During training, adopt recent metric depth model, Unik3D (Piccinelli et al. 2025), which has shown strong performance outdoor panoramic images. At test time, report results using both Unik3D and relative depth
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models (Wang & Liu 2024 Jiang al., 2021 Wang et al. 2022
Additionally, we include results in the Appendix where both training and testing are performed using only relative depth.
Metrics: We report the mean and median localization and orientation enrors. Following Xia et al. 2203), we train and test with both known and unknown orientations on VIGOR, and apply orien- tation noise sampled from 10 or 1880 on KITTI. For KITTI, we also decompose localization emoos into longitudinal and lateral components based on the driving direction and report the per- centage of samples within the defined error thresholds.
4.2 IMPLEMENTATION DETAILS
On both datasets, we use A Loshchilov & Hutter, 2019) with learning rate of 1 x 10-4. Training is conducted on a single H100 GPU with a batch size of 80 for VIGOR and 224 for KITTI. We follow the setting from Xia & Alahi 2025): the temperature parameter in matching score computation is set to 0.1, the aerial feature map F resized to generate 41 x 41 aerial points, LVCe uses N, 10 x 10 points, with / set to m, and N 1024 correspondences pose estimation. For Ls2g. negatives are m away in planar distance from the projected location. We use B = 1 for VIGOR and / 0.1 for KITTL RANSAC (Fischler & Bolles 198 is applied on VIGOR, but omitted on KITTI as it did not yield improvements localization accuracy. When using metric depth, we apply maximum depth threshold of 35 for VIGOR and 40 for KITTI, setting the matching score of points exceeding this threshold to zero. For relative depth predictors, apply fixed initial scale (identified by visually inspecting few examples) all relative depth maps and then use the threshold to filter out matches corresponding to sky and distant objects.
sampled for
4.3 QUANTITATIVE RESULTS
Table 1: KITTI test results. Best in bold. The 'ori.' column shows orientation noise used in training and testing, uniformly sampled within +00 or 180%.
Loc. (m)
? Lateral (%)
Long. (%)
Orien. (?)
1 Orien. (%)
Ori. Methods
Mcan
Median
R@
R@5m
R@ Im
R@5m
Mean
Median
R@1"
R@5"
GGCVT
57.72
91.16
14.15
45.00
98.98
100.00
CCVPE
9.16
3.33
44.06
90.23
23.08
64.31
1.55
0.84
57.72
96. 19
Cross-area
#1 DenseFlow
HC-Net
8.47
4.57
75.00
97.76
58.93
76.46
3.22
1.63
33.58
83.78
7.97
3.52
54.19
91.74
23.10
61.75
2.17
1.21
43.44
89.31
FG2
7.31
4.15
37.89
85.65
21.98
60.77
3.62
2.37
23.03
77.84
Ours
5.60
3.01
45.29
92.43
27.01
68.26
3.32
2.12
26.03
80.68
+180
SliceMatch
14.85
11.85
24.00
72.89
7.17
33.12
23.64
7.96
31.69
31.69
CCVPE
13.94
10.98
23.42
60.46
11.81
42.12
77.84
63.84
3.14
14.56
Ours
11.71
9.11
13.64
50.88
14.04
50.73
55.18
33.23
2.53
12.78
GGCVT
76.44
98.89
23.54
62.18
99.10
100.00
CCVPE
1.22
0.62
97.35
99.71
77.13
97.16
0.67
0.54
77.39
99.95
+100
HC-Net
0.80
0.50
99.01
99.73
92.20
99.25
0.45
0.33
91.35
99.84
Same-area
DenseFlow
1.48
0.47
95.47
99.79
87.89
94.78
0.49
0.30
89,40
99.31
FG2
0.75
0.51
95.81
99.66
92.50
99.05
0.93
0.66
67.27
98.91
Ours
1.13
0.77
93.59
99.97
71.51
98.17
1.97
1.43
36.68
92.84
+180
SliceMatch
7.96
4.39
49.09
98.52
15.19
57.35
4.12
3.65
13.41
64.17
CCVPE
6.88
3.47
53,30
85.13
25.84
68.49
15.01
6.12
8.96
42.75
Ours 1.85
1.31
62.18
97.80
59.37
97.48
9.70
6.17
9.46
41.64
KITTI: We compare our method with both global descriptor- methods, CCVPE Xia et al. 2023) and SliceMatch (Lentsch et al.] (023). and geometry transformation-busee methods,
GGCVT (Shi et al. 2023). HC-Net (Wang et al. 2024b). DenseFlow (Song et al.) 2024h. and FG2 (ia & Alahi 2025) As shown in Tab. our method sets a new state-of-the-art in mean and median localization errors on the cross-area test under both 10 and 180 orientation noise. On the same-area test, although our method has higher error under +0 noise, it shows a large improvement over the previous state-of of-te-of-the-rr the-art method in the more challenging +880 setting, re- ducing the mean error from 6.88 to 1.85 m. For orientation prediction, method is less accurate than the state of the art. Since our method computes orientation analytically from local feature correspondences, it cannot take full advantage of the prior that most ground images in KITTI

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aligned with the road direction. Under 10 noise, our performance is comparable FG?, while under +180 noise, our method outperforms CCVPE but falls short of SliceMatch.
VIGOR: Overall, method demonstrates strong and consistent performance in both localization and orientation estimation on the same-area and cross-area test sets (see Tab. 2 For instance, while FG2 attains lower localization error when the orientation is known, method significantly outperforms it in the more challenging unknown orientation setting. Compared to the previous state of the art under unknown orientation (Xia
2023), our method achieves comparable localization accuracy, showing slightly higher mean error on the same-area test set but lower mean error on the cross-area set. Notably, for panoramic images, the richer matchable information between ground and aerial views leads to substantial gains, with our method achieving the lowest mean orientation error both same-area and cross-area tests.
Table 2: VIGOR test results. Best in bold. Training uses metric depth from Unik3D (Piccinelli al.
The row 'ours' reports results with metric depth from the same model, while "ours- XXX shows results with different relative depth inputs. Relative depth predictors, BiFuse++ (Wang
2025
al.
2022) and UniFuse (Jiang et al. 2021), are provided by (Wang & Liu 2024). "OursUnni33D,
denotes the study where metric depth is manually scaled by an arbitrary factor.
Cross-area area
Same-ane area
Ori. Methods
Localization (m)
L. Orientation (*)
Localization (m)
J Orientation (*)
Mean
Median
Mean
Median
Mean
Median
Mean
Median
SliceMatch
7.22
25.97
4.51
6.49
3.13
25.46
4.71
CCVPE
5.41
1.89
27.78
13.58
3.74
1.42
12.83
6.62
DenseFlow
7.67
3.67
17.63
2.94
4.97
1.90
11.20
1.59
Unknown
FG2
10.02
8.14
31.41
5.45
8.95
7.32
15.02
2.94
Ours
2.09
11.67
2.21
3.94
1.78
9.54
2.00
Ours-BiFuse++
4.43
2.26
12.27
2.47
4.12
1.94
TO.13
2.31
Fuise
4.36
2.21
12.10
2.43
4.03
1.89
9.81
2.21
SliceMatch
5.53
2.55
5.18
2.58
CCVPE
4.97
1.68
3.60
1.36
GGCVT
5.16
1.40
4.12
1.34
DenseFlow
5.01
2.42
3,03
0.97
Known
HIC-Net
3.35
1.59
2.65
1.17
FG
2.41
1.37
1.95
1.08
Ours
3.43
1.90
3.06
1.59
Ours- Burs-Unii3DDet
3.43
1.90
3,06
1.59
Ours-Bitr Birs+++
3.56
2.02
3.17
1.69
Ours-UniFuse
3.54
3.14
We evaluate the consistency of our pose estimation against different depth predictors in inference through two additional experiments VIGOR. The first one applies arbitrary scale factors to the metric depth predicted by Unik3D. We vary the scale from 0.001 to 1000 and observe that the resulting variation in both mean and median localization error remains below cm ( "Ours-Unik3DD. in Tab. D demonstrating strong scale invariance. This robustness is due to both the accurate correspondence matching and the spatial distribution of the matched points.
Inference with relative depth:
Second, we evaluate a practical scenario where only relative depth model (Wang et al. 2022 Jiang al. 202T, Wang & Liu 2024) is available inference. We plug in different relative depth models with our estimated correspondences, without retraining or finetuning. As shown in the bottom two rows of the known and unknown orientation entries in Tab. relative depth increases localization error by less than 0.2 m. This flexibility in depth predictors highlights the practicality and robustness of our method for real-world deployment, especially when a compact depth predictor is required.
4.4 INTERPRETABILITY
Local feature matching: Since our pose is computed analytically from the estimated correspon- dences, these correspondences directly reflect localization quality, an interpretability advantage ab- sent in most prior cross-view localization methods. Although FG² also estimates correspondences, its localization fails when the orientation is unknown, whereas method remains accurate.

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Dus
(d)
Dun
Figure 3: Local feature matching results the VIGOR same-area test under unknown orienta- tion. We visualize the top 50 correspondences, ranked by matching score.
As shown in Fig. (a) and (b), when road markings repetitive, e.g., highways, method leverages other landmarks such as overhead road signs and streetlights for localization, demonstrat- ing that the matching is not solely appearance-basee but also reflects strong semantic understanding. In (c), the partially occluded 'bus' marking is difficult even for humans to identify, yet our model matches it correctly. In (d), both streetlights and road markings while (e) shows that without restricting matches to object tops, our method aligns the upper facades of buildings in the ground view with rooftops the aerial view. Finally, (f) shows a failure case, though interestingly our method predicts a more reasonable position aligned with the visible path, whereas the ground truth appears erroneous. More VIGOR and KITTI results are in the Appendix.
anchors for localization,
The ability to estimate correspondences makes our method well-suited for outlier detection using RANSAC. For each test sample, we record the number of inlier correspondences and use it for outlier detection. As shown in Fig. the pose error decreases sharply the inlier ratio rises from 10% to 50%, followed by a slower decline after 50%. This trend reveals strong negative correlation between inlier ratio and pose error, consistent with the expectation that more accurate correspondences yield more accurate pose estimates.
Outlier detection:
Moan Thardattnn Emor (m)
12.50
Same-area
50
28
Same-area
11
Cross-area
(osg)
40
Croek
20
30
25.95 95
7.38
8-
5.30
20-
20"28 35
4.35
3
73
2.84
2.13
1.90
1.63
1.93
1.53
11762
6.64
47
4.92
7.13
4.30
3.30
2.48
2
2.11
186
20
60
50
70
90
10
30
40
60
80
90
Quantle
Quantiic
Figure 4: Outlier detection using RANSAC on VIGOR same/cross-area test sets.
Ground-acrial layout alignment: With relative depth predictor (Wang al. 2022,. our method estimates both the camera pose and the scale between relative depth and the aenal metric space. As shown in Fig. the rotated, translated, and scaled ground layout be overlaid onto the aerial image, providing a clear and interpretable visual cue of localization quality. For example, (a) and (b) show precise alignment of the projected intersection and building with those in the aerial view,
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corresponding to accurate localization. Interestingly, (c) also shows good alignment, revealing error in the ground truth location: the vehicle should be in front the zebra crossing rather than on it. (d) shows localization failure, which is easily identifiable from the misalignment. The strong correlation between alignment and localization quality offers a powerful tool for interpretability.
a
Figure 5: Ground layout overlaid on the aerial image after applying the predicted rotation, transla- tion, and scale transformations. The alignment directly reflects localization quality: the first three examples show successful localization, while the last illustrates failure case. Notably, the alignment in example (c) helped us to identify the error ground truth location.
4.5 CROSS-DATASET GENERALIZATION
Additionally, we demonstrate the strong generalization capability our model by directly applying the model trained on VIGOR to the CVACT dataset ([.iu & Li 2019). CVACT is cross-view image retrieval dataset collected in Canberra, Australia, where the rural and natural landscapes present significant domain gap compared to VIGOR. Notably, CVACT lacks precise localization labels (Shi et al. 2022). Therefore, we provide local feature matching results and evaluate localization perfor- by overlaying the transformed ground layout onto the aerial image.
In general, our model exhibits strong generalization capability across datasets collected in different countries. As shown in Fig. our model establishes reasonable feature correspondences, In sam- ples (a) and (c), features extracted along trees in the ground view accurately match the corresponding blobs in the aerial view. In samples (b) and (d), the curbs and road markings the ground view are correctly matched to those in the acrial view. Reliable feature matching leads to accurate localiza- tion. As shown, the transformed ground layout consistently aligns well with the aerial image across all samples. In (a) and (b), road markings and lane boundaries projected from the ground view form seamless continuations of those in the aerial view. In (c) and (d), both ground-lever structures (e.g., curbs) and above-ground objects (e.g., buildings and trees) exhibit strong alignment.
4.6 ABLATION STUDY
Our main ablation study focuses two key design choices: (1) the coordinate assignment strategy (Sec. (S2c. comparing using all points within the depth range versus only the topmost points along height; and (2) the effect of ignoring scale in Procrustes alignment (reducing formulation to

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(b)
(a)
Direct generalization to the CVACT dataset. We visualize the top 50 correspondences, ranked by matching score, and overlay the ground layout the aerial image after using the predicted rotation, translation, and scale transformations. We use the metric depth prediction from Unik3D.
Figure 6:
the orthogonal Procrustes of Xia & Alahi (025);; Barroso-Laguna et al. (2024)). )) As shown in Tab. g explicitly selecting the topmost points does improve localization accuracy. The side view of an object's top does not necessarily exhibit the most consistent semantics with the acrial image. Therefore, enforcing the use of topmost points may hinder cross-view localization. For scale- awareness, excluding scale forces the model to align features strictly to metric depth predictions, which are imperfect. Allowing the model also estimate scale from correspondences yields more accurate and robust matching. Moreover, without modeling scale, the method cannot support relative depth predictors, as orthogonal Procrustes assumes that all coordinates lie the same scale space. Additional ablation study other hyperparameters in both inference and training is included in Appendix. Sec.
Table 3: Ablation study on VIGOR same-area validation set with unknown ori. Best in bold.
Method design choices
Mean loc. (m)
Median loc. (m)
Mean ori. (9)
Median ori. (9)
(1) Top points only
3.95
1.78
9.37
1.77
(2) Not consider scale
5.47
2.75
19.92
4.45
Ours (all points, scale-aware)
3.86
1.75
9.30
1.93
CONCLUSION
We propose simple, accurate, and interpretable fine-grained cross-view localization method that matches local features between ground and aerial images. Our method learns correspondences from camera pose supervision and leverages monocular depth predictors with scale-aware Procrustes alignment to estimate the camera pose and recover the scale of relative depth. Experiments demon- strate state-of- the-art performance in challenging scenarios, including cross-area generalization and unknown camera orientation. Furthermore, our local feature matching enhances interpretability. enabling visual identification of erroneous predictions as well as RANSAC-based outlier detection.
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Reproducibility statement: Our method combines deep learning model with classic algorith- mic component, scale-aware Procrustes aligmment. The deep learning component is described in Sec. 322 while the derivation of the scale-aware Procrustes alignment is detailed in Sec. 3.2 with complete proof provided the Appendix, ensuring that the theoretical foundation of our approach transparent and verifiable. The implementation is lightweight and relies only standard compo- nents, with all hyperparameters and training settings fully described in Sec. 4.2 To further support reproducibility, will release our code together with configuration files and evaluation scripts, enabling the community to reproduce all experiments and results reported in this paper.
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APPENDIX
Here we provide supplementary material to support the main paper:
A. Additional ablation study.
A.I. Ablation on inference settings.
A.2. Ablation on training settings.
B. Test on non-road facing samples on KITTI.
C. Additional local feature matching results.
Additional results on cross-dataset generalization.
E. Additional results on using relative depth in inference.
F. Training and testing with relative depth.
G. Additional proof for scale-aware Procrustes alignment.
H. Additional details infoNCE losses.
I. Discussion of standard and true digital orthophoto maps.
J. Runtime and memory usage.
K. LLM usage statement.
A ADDITIONAL ABLATION STUDY
We conduct additional ablation studies on the VIGOR same-area validation set with unknown ori- entation, analyzing the effects of various hyperparameters in both inference and training.
During inference, we vary the number of sampled correspondences N, the number of aerial points, the resolution (meters per pixel) of the input aerial image, and the use of RANSAC in trained model using the default settings.
During training, we investigate the influence of various hyperparameters, including the number of sampled correspondences N, the number of aerial points, the feature map resolution, and the temper- ature parameter т. Additionally, we compare our formulation umage-plane matching scale-award aware Procrustes alignment) with two homography- based formulation: (1) Replacing image-plane match- ing with BEV-plane matching by first transforming the ground images into a BEV, and then feed it to the same feature extractor, matcher, and Procrustes alignment. (2) Replacing the scale-aware Procrustes alignment with homography for pose estimation.
A.1 ABLATION STUDY ON INFERENCE SETTINGS
Number of sampled correspondences N: Our default setting N 1024 (following Xia
& Alahi 2025 ) during inference. If RANSAC is used, we sample only 3 correspondences per RANSAC doop to compute the pose and scale. In this case, we vary only in inference: model trained with N = 1024 is evaluated with N = 256, 512, 1024, and 2048 (without RANSAC).
As shown in Tab. the number of correspondences N does not have strong impact on perfor- mance. When varying N during inference, the difference in mean localization error is less than 0.2 m for N 512, 1024, 2048. The error increases more noticeably when smaller N, such as 256, is used.
Number of aerial points: Next, we examine how the number of aerial points affects performance. Our default setting, following Xia & Alahi (225). uses 41 41 acrial points for fair comparison. As shown in Tab. 5 our model is robust to small variations in the number of acrial points. When more than 36 36 points used, the change in
localization error is less than 0.2 m. However, when the number of points is significantly reduced (e.g., 31 x 31), performance degrades noticeably.
Aerial image resolution: We also study the effect of varying aerial image resolution in inference. As shown in Tab 6 our model robust to such variations. All aerial images are first processed by the pre-trained DINOv2 feature extractor. Regardless of input resolution, consistently sample fixed
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Table 4: Ablation on the number of sampled correspondences N. Best in bold..
Localization (m)
Orientation (?)
Mode
N
Mean + Median
Mean 4
Median +
Inference
2048
4.66
2.88
11.13
3.92
1024 (default)
4.60
2.81
11.19
4.04
512
4.71
2.91
12.06
4.20
256
4.90
2.98
12.97
4.78
Table 5: Ablation on the number of aerial points. Best in bold.
Localization (m) Median
Orientation (9)
Number of Aerial Points
Mean
Mean
Median
31 x11
4.27
2.16
10.01
2.49
36x36
3.98
1.88
9.38
2.10
41 41 (default)
3.86
1.75
9.30
1.93
x6
3.86
1.72
9.31
1.91
51x51
3.82
1.70
9.18
1.90
x66
3.91
1.68
9.61
1.97
41 x 41 grid of aerial points from the feature map. Since a downsampled aerial image still covers the same geographic area, the sampled points correspond to the same geo-locations, independent of resolution. Thus, any effect pose estimation accuracy mainly stems from changes in DINOv2 features due to downsampling in lower-resolution inputs.
Table Ablation on aerial image resolution. Best in bold.
Localization (m)
Orientation (9)
Resolution
Mean
Median
Mean +
Median J
630x630 (default)
3.86
1.75
9.30
1.93
574x574
3.77
1.71
9.52
1.95
518x 518
3,82
1.76
9.17
1.94
448 4488
3.90
1.77
9.49
1.97
392 392
3.99
1.84
10.22
2.13
336x 336
4.17
1.96
10.36
2.28
RANSAC:
Finally, we report results of in inference with without RANSAC. As shown in Tab. using RANSAC yields a ~0.74 m reduction in mean localization error.
A.2 ABLATION STUDY ON TRAINING SETTINGS
We first investigate the impact of several hyperparameters involved in our local feature matching during training, including the number of sampled correspondences, the number of aerial points, and the temperature parameter. After this, we vary our formulation by using homography-transtonn inputs bomography-based pose estimator.
Number of sampled correspondences N: Our default setting uses N 1024 (following Xia & Alahi (225)) during training. In this case, vary N in both training and inference: validation results (with RANSAC) of models trained with N = 256, 512, 1024, and 2048. As shown in Tab g the model remains robust to different N during training, long N is not too small (e.g.. N 256).
Number of aerial points & Feature Map Resolution: We train additional models using 31 31, 36 x 36, 46 46, 51 x 51, 56 x 56 acrial points. Meanwhile, to investigate the impact of feature map resolution, also trained model that upsamples the aerial DINO feature map from its original
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Table 7: Ablation on RANSAC. Best in bold.
Localization (m)
Orientation (?)
RANSAC
Mcan
Median 4
Mean J
Median J
Without RANSAC
4.60
2.81
11.19
4.04
With RANSAC
3.86
1.75
9.30
1.93
Table 8: Ablation on the number of sampled correspondences N. Best in bold..
Localization (m)
Orientation (?)
Mode
N
Mean +
Median
Mean 4
Median +
Training
2048
3.91
1.76
9.25
1.73
1024 (default)
3.86
1.75
9.30
1.93
512
4.12
1,80
9.71
1.80
256
4.31
1.90
11.27
2.17
45 x 45 resolution to 180 x 180 using two stages of bilinear interpolation followed by convolutional layers. We then sample a 41 41 grid of points from this higher-resolution feature map.
As shown in Tab. higher resolution of aerial points provides only a modest improvement in per- formance (0.16 meters reduction mean localization error). However, such setting substantially increases memory usage and training time. Notably, Tab. TC indicates that this marginal improve- ment mainly comes from RANSAC, which benefits from larger pool of correspondences. When inferring without RANSAC, the 41 x 41 setting even performs slightly better. By contrast, upsam- pling the feature maps does not lead to any measurable performance improvement.
Table 9:
Ablation different resolution configurations. Best in bold.
Number of aerial points (N)
Mean loc. (m)
Median loc. (m)
Mean ori. (*)
Median ori. (9)
31
4,22
1,90
9.68
1.99
36
1.82
9.42
41 x 41 (default)
3.86
1.75
9,30
1.93
41 x 41 (upsampled feature)
4.55
1.94
11.46
1.96
46 46
3,90
1.72
9.07
1.72
51
3.75
1.67
8.76
1.73
56 56
3.70
1.65
8.75
1.69
Temperature Parameter 7: This parameter directly affects the matching score matrix M Fol- lowing Barroso-Laguua al. (2024); [Sun et al. (202T: Xia & Alahi (025), adopt the com- monly used setting - = 0.1. To further investigate its impact, we perform a grid search over 0.5, 0.1, 0.05, 0.01. As shown in Tab. T 0.1 and 7 0.05 yield very similar perfor- mance, while both larger and smaller values lead to a noticeable degradation in accuracy.
BEV-pl matching: Transforming ground images into BEV via a homography typically intro- duces ray- direcciiali distortions, which degrade correspondence quality when matching these BEV. transformed views directly to the aerial image. To validate this, we construct bird --ee (BEV) variant of Loc² by first transforming the ground-level images into BEV representations and then feeding the transformed images into the same feature extractor and matching head, followed by scale-aware Procrustes alignment using the same loss functions. We adopted the BEV transforma- tion from HC-Net (Wang et al. 2024b) with its default hyperparameters.
As shown in the Tab. the BEV variant yields substantially worse performance. The BEV transfor- mation inevitably introduces distortions to elevated or grove-g structures. More importantly, such structures often occupy large portion of the input image, restricting matching to small undis- torted region or forcing the model to match features on distorted objects, which ultimately degrades performance (see Fig.
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Table 10: Different resolution configurations (inference without RANSAC). Best in bold.
Number of acrial points (N)
Mcan loc. (m)
Median loc. (m)
Mean ori. ())
Median ori. (*)
41 (default)
4.60
2.81
11.19
4.04
51 x 51
4.70
2.89
11.38
4.03
56 x 56
4.68
2.91
11.59
3.92
Table 11: Different values for the temperature parameter. Best in bold.
Temperature
Mean loc. (m)
Median loc. (m)
Mean ori. (*)
Median ori. (*)
0.5
9.58
6.18
39.03
15.33
0.1 (default)
3,86
1.75
9.30
1.93
0.05
3.78
1.80
9.25
2.17
0.01
4.58
2.46
13.70
4.78
Homography-based pose estimation: We next replace pose estimation module with homography-based formulation instead of 2D similarity transformation. Specifically, we use the sampled correspondences estimate homography matrix and supervise it through translation and orientation, following a strategy similar to HC-Net (Wang et al. 2024b).
As shown in the Tab. 12 the homography-base formulation leads significant drop in localiza- tion accuracy. A homography has eight degrees of freedom and, beyond translation and rotation, can model anisotropic scaling and shear. As result, can disregard the contour and shape information encoded in the (relative) depth prior. Meanwhile, it also reduces interpretability: the inferred ground layout may become skewed or non-uniformly scaled across different directions in order satisfy the point correspondences in the aerial view.
B TEST ON NON-ROAD FACING SAMPLES ON KITTI
In Sec. noted that our method computes orientation from correspondences, making it difficult to exploit the prior that most ground images in KITTI are aligned with the road direction. Here, provide additional quantitative comparison between method and CCVPE manually selected KITTI samples that are not aligned with the road direction, denoted as non-road.
As shown in Tab. B method consistently outperforms CCVPE (which directly regresses orien- tation and can easily capture the soad-facing bias). This setting better reflects real-world scenarios, where the orientation rough alignment) is required. When comparing the "non-road" subset to the full test set (Tab. []]. both CCVPE and our method exhibit increased orientation errors. However, the increase is signifi- cantly smaller for our method, indicating greater robustness to challenging viewpoints. Interestingly, we observe that localization errors in the non-road subset are lower than those on the full set. This is likely due to reduced location ambiguity at intersections compared to the more monotonous structure of ali-neieedd scenes.
be arbitrary and pre-processing (such rotating the aerial image for
C ADDITIONAL LOCAL FEATURE MATCHING RESULTS
First, we present additional results on local feature matching. Fig. 3 shows success cases where the pose estimation is accurate, while Fig. T0 presents failure cases.
presents results on VIGOR. (a)-(f, we demonstrate that our model effec- tively matches various types of road markings across views, including painted text (a)-(d) and lines (f)-(). In general, road markings are distinctive across views, and accurately matching them signif- icantly aids localization. Besides road markings, our method also leverages other landmarks, such as overhead road signs and streetlights, to help anchor the keypoint locations. ban areas, there is typically rich visual information available for matching across ground and aerial views (Fig. B (i)-()), including buildings, zebra crossings, and lane lines. Our model effectively exploits all of these cues for localization.
Success cases: Fig.
{g) (h)). ur-
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Table Comparison between the proposed Loc² and its BEV variant. Best in bold.
Method design choices
Mcan loc. (m)
Median loc. (m)
Mean ori. (*)
Median ori. (?)
BEV-plane matching
9.49
8.20
53.42
31.84
Homography pose estimation
14.46
13.43
90.98
91.17
Ours
3.86
1.75
9.30
1.93
BCV verteri
BCY eatiri
MEV wrarrt
MVV autirt
Figure 7: Matching results of the BEV variant of our method on the VIGOR same-area test set under unknown orientation. We visualize the top 50 correspondences, ranked by matching score.
Fig. presents results on KITTI. Our method primarily leverages structures such as roads, sidewalks, and fences in front of the vehicle establish correspondences with the aerial view.
Failure cases: Typical failure cases are shown in Fig. 10 When there is dense vegetation (Fig. 10 (a),b)), the matchable information across views very limited, making precise localization ex- tremely challenging, even for humans. Interestingly, in Fig. 10 (b), our method still correctly matches the gap between two buildings in the ground view the corresponding gap in the acrial view. In Fig. I0 (c), the two narrow roads with trees and zebra crossing in front appear visually similar. At the true location, a tree partially blocks the zebra crossing in the aerial view, making harder to distinguish. As result, our method matches the zebra crossing to an incorrect one, lead- ing to an erroneous location estimate, In Fig. TO (d), it nearly impossible to determine the exact location over the water due to the lack of distinctive features. Finally, Fig. 10 (h) shows that occlusions from dense high-rise buildings make cross-view matching more difficult. Importantly, believe these scenarios represent common challenges for most cross-view localization methods, rather than limitations specific to our approach. Furthermore, our local feature matching frame- work provides strong interpretabilityy enabling straightforward identification of such failure cases and supporting RANSAC-based outlier filtering.
D ADDITIONAL RESULTS ON PROSS-DATASED GENERALIZATION.
In addition to Sec. 4.5 we present more qualitative results on cross-datased generalization. As shown in Fig. II our model establish reliable correspondences buildings (a), road markings (b, c, g, D, and trees (d, e). The layout alignments also demonstrate our superior localization quality with recovered rotation, translation and scale.
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Table 13: Test on non-road facing samples on KITTI. Best in bold.
Setting
Localization (m)
Orientation (?)
Orientation
Test Set
Method
Mean 4
Median !
Mean
Median !
Unknown
Cross-area (non-road)
CCVPE
8.33
5.99
89.78
93.97
Cross-area (non-road)
Ours
7.04
5.00
58.97
47.98
Same-area (non-road)
CCVPE
3.19
1.81
26.10
16.88
Same-area (non-road)
Ours
1.17
1.01
9.79
8.00
(a)
(b)
(C)
Ous
(d)
Our
Oun
(h)
Oue
(k)
Figure 8: Success cases for localization the VIGOR same-area test set under unknown orientation. We visualize the top 50 correspondences, ranked by matching score.
E ADDITIONAL RESULTS ON USING RELATIVE DEPTH IN INFERENCE
We conduct additional experiments using relative depth inference time for model (trained with metric depth predictions from UniK3D (Piceinelli et al., 2025)). Specifically, we use Bi- Fuse++ (Wang al. 2022) relative depth predictor for these experiments.
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Figure 9: Success cases for localization on the KITTI same-area test set under 10 orientation
noise. We visualize the top 50 correspondences, ranked by matching score
(d)
Figure 10: Failure cases for localization on the VIGOR same-area test set under unknown orienta- tion. We visualize the top 50 correspondences, ranked by matching score.
when using relative depth, we apply an initial scaling factor all relative depth maps bring the values into reasonable depth range, determined by visually inspecting a few examples. We then apply a predefined maximum depth threshold, the same one used for the metric depth model, to filter out matches corresponding to sky and distant objects. In practice, the initial scale and maximum depth threshold can be determined for each dataset by visually inspecting few examples. Here, we study how consistent the model's predictions are when these settings are varied.
Initial scale and maximum depth threshold: As mentioned in Sec. 4.2
First, we evaluate the model's robustness against different scales of the relative depth. We apply an additional scaling factor on top of the initial scale. To ensure the same objects are kept for pose estimation, the same scaling factor is also applied to the maximum depth threshold. As shown in Fig. 12 the test errors remain stable across different scaling factors during inference. This observa- tion is consistent with our findings on applying scaling factors to metric depth in Sec. 4.3 Therefore, in practice, when using relative depth, people do not need to carefully select initial scale.
We then evaluate the effect of different maximum depth thresholds. Our default setting uses a threshold of 35 and we additionally test thresholds of 25 and 45 m. Note that although 35
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(a)
(c)
(b)
(d)
(c)
Dup
(c)
(h)
Direct generalization to the CVACT dataset. We visualize the top 50 correspondences, ranked by matching score, and overlay the ground layout the aerial image after using the predicted rotation, translation, and scale transformations.
Figure 11:
threshold is used during training with metric depth, applying the same 35 m threshold to relative depth does not select exactly the same set of objects, as our initial scale estimate only roughly maps the relative depth values reasonable range. As shown in Tab, [4 the impact of the maximum depth choice is minor, less than 0.2 m difference localization errors. Since our feature matching excluding relatively distant objects has little effect pose estimation.
accurate, including Combined with the method's robustness to the initial scale, this makes our approach highly practical, users do not need to carefully select an initial scale or depth cutoff for accurate pose estimation.
Ground-aerial layout alignment: Next, we present additional results on ground-aerial layout alignment. We visualize the bird's-eye view ground layout after applying estimated pose and
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Same-aree
Crass area
4.5
4.222
6.199
4:224
4,225
4,323
4.325
422
4,425
427
4.427
4.477
4,427
4,426
4,427
Localzatinn Enter (m)
Median
3.0
2.211
200
2261
2761
220
2.0
1.942
1.342
1.041
1,922
942
10"
10"1
Extra scale factor
Extra scale factor
Figure 12: VIGOR test errors when different scaling factors are applied to the relative depth during inference. We use the model trained with metric depth from UniK3D (Piccinelli et al. (025). with unknown orientation. inference time, we use relative depth from BiFuse++ (Wang et 2022).
Table 14: Robustness to different maximum depth thresholds. We apply different maximum depth thresholds during inference to remove sky and distant objects (after applying the initial scale to the relative depth from BiFuse++ (Wang et al., 2022)). Best results are shown in bold. During training, use metric depth predictions from UniK3D UniK3D(Piccinelll al. 2025). with maximum depth threshold of 35 m.
Same-area
Cross-area
Max depth
+ Localization (m)
4 OOrientation ())
J. Localization (m)
Orientation (*)
Mean
Median
Mean
Median
Mean
Median
Mean
Median
25 m
4.04
9,91
2.27
4.39
2.23
12.17
2.46
45 m
4.20
1.97
10.46
2.35
4.47
2.27
12.30
2.51
35 m (default)
4.12
1.94
10.13
2.31
4.43
2.26
12.27
2.47
scale. As shown in Fig. 13 the quality of alignment directly reflects localization accuracy: when the alignment is precise, the estimated pose is accurate; when the alignment is off, as in the last exam- ple, localization also fails. This interpretability provides practical means of identifying potentially erroneous predictions.
F TRAINING AND TESTING WITH RELATIVE DEPTH
also experimented with training and testing using only relative depth. This setup is more challenging, since inducing correct correspondences on the BEV plane requires both ground-truth pose and scale (i.e., metric depth). As result, the infoNCE loss cannot be directly applied and we lack direct supervision two settings. (1) Training without infoNCE losses, i.e., setting the weight 3 0. (2) With pseudo ground truth for infoNCE losses: At each training iteration, we estimate the scale and use it to generate pseudo ground-truth positive matches for the infoNCE losses.
As mentioned in Sec. 3
the correspondences during training. We then explored
As expected, using relative depth during training leads to worse performance than using metric depth (see Tab. 15). When the orientation is known, finding correct correspondences between ground and aerial images is easier. In this setting, the estimated scale may quickly converge to a reasonable range, and using it to supervise correspondences (B 1) results better performance compared to not using it (3 0). In contrast, when the orientation is unknown, identifying correct matches becomes significantly more difficult, making it hard to recover the correct scale. In this case, corporating the infoNCE loss (5 1) introduce conflicting gradients to the pose supervision: correspondences derived from an inaccurate scale may reinforce incorrect matches, thereby degrad- ing pose estimation performance.
As shown Fig without explicit supervision on the correspondences (6 = 0), our model still learns establish accurate local feature matches across views. It demonstrates strong semantic understanding. For example, in Fig dd), different points on the streetlight in the ground view are correctly matched to the corresponding BEV of the streetlight in the aerial view.
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GT
Outs
Ours
Ours
Ours
Figure 13: Ground layout overlaid on the aerial image after applying the predicted rotation, trans- lation, and scale transformations. The alignment directly reflects localization quality: the first three examples show successful localization, while the last one illustrates a failure case. Relative depth is obtained from BiFuse++ (Wang et al. 2022).
Table 15: VIGOR test results. Best in bold. (1) and (2): Training and testing with relative depth predicted by BiFuse++(Wang et al. 2022). For reference, we also include the model trained and tested with metric depth from Unik3D metric depth and tested with relative depth.
et al. 2025), as well as the model trained with
Same-area
Cross-area
Ori. Settings
Localization (m)
J Orientation (*)
Localization (m)
+ Orientation (9)
Mean
Median
Mean
Median
Mean
Median
Mean
Median
(1)3=0
3.85
2.33
4.37
2.74
Known
(2) ==
3.34
1.99
3.92
2.39
Metric
3,06
1.59
3.43
1.90
Metric + rel.
3.17
1.69
3.56
2.02
Unknown
(1) =
3.83
23.09
9.29
6.72
4.57
29.44
12.77
(2) 1
6.25
4.31
33.40
16.05
7.28
4.96
41.05
20.44
Metric
3.94
1.78
9.54
2.00
4.23
2,09
11.67
2.21
Metric + rel.
4.12
1.94
10.13
2.31
4.43
2.26
12.27
2.47
G ADDITIONAL PROOF FOR SCALE-AWARE PROCRUSTES ALIGNMENT
As discussed in Sec. 3.2 the main paper, we estimate pose and scale using scale-aware Procrustes alignment (Umeyama] 1991) from local correspondences. Let ((P., Qn, wn) J.V ) denote weighted correspondences between ground points P and aerial points Q with weights w,, 2 0 and >,, Wn.
1. We denote the weighted centroids as P and Q and the centered point sets as P P P and
Q Q Q. The objective is to find the optimal rotation R. translation t, and scale satisfying.
sRR P) +t.
Below provide proofs for two key steps:
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Da
(b)
cc)
(d)
Figure 14:
Local feature matching results on the VIGOR same-area test set under unknown orienta- tion. We visualize the top 50 correspondences, ranked by matching score. The model train and test with relative depth.
The optimal rotation from ground points to aerial points is R VUT.
(2) When ground and aerial points lie in the same metric space, i.e., there is no scale difference
between them, we obtain Tr(E) Σ Wn
T
(1) Rotation computation: The optimal rotation between the ground and aerial points is indepen- dent of their relative scale and translation. Therefore, it is computed using only the centered point sets, Q and P. We express the objective function
Σ Wn R. P. Qn Q
arg min R
(8)
R
72
The term
R P,, - -2 can be rewritten as (for simplicity, we omit the explicit dot product):
R.P, 2 = RRP, -RPP,
Q..) RP,,
-Q..)
-(Pm)) T - -QQ.)) RRP, QQ,))
Q2.
(P.) R RP, -Q,,) RPP, (P,) TR. T + (Q.)) = P Q 2 - TT,TP.P..
Note that Pn and @ are fixed, so the optimal rotation depends only on the inner product R. n- Hence, the objective in Eq. which sums over all correspondences, can be written in matrix form as:
2
R = arg max Σ (wn (Q.) TRP..
(9)
arg max Tr(Q RPW)
(10)
R
arg max (r(((PQQT))
(11)
where W a diagonal matrix with entrie W Wn,, = wr. Eq. 11
the matrix product PWQ
constructs a x 2 square matrix C, which be decomposed using singular value decomposition
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(SVD) as C UEVT. Accordingly. the objective function in Eq. 11
be reformulated as:
R arg max Tr(R(UEVT))
(12)
arg max Tr RU).
(13)
Since a 2 diagonal matrix with nonnegative elements, the optimal rotation is achieved when RU RU
I, where R VUT.
(2) Scale computation: As mentioned above, the x 2 square matrix C obtained from the matrix product PWQ can also be formulated as:
C
Wyy
Pr.
Q
UEV
(14)
The centered target points Qn can be obtained by rotating and scaling the centered source points
P satisfying Q. = sRP,,. n. With estimated rotation R = VU Eq. 14 can be formulated as
Σ
Wn P,
(VVTTP,) -EEV,
(15)
Wn
PUPTTUVT = UEVT,
P n
(16)
N
8
UUTPPPTTU) = E.
(17)
n=l
Then we take the trace of both sides of Eq.
17 as
Tr
Wn
U UU) Tr(E),
(18)
P (PrP) = Tr(E). =TrEE)
Wn
(19)
The trace of P.P equivalent to the norm of P n. Thus, the scale can be computed by
N
Wn
Tr(E),
(20)
Tr(E)
(21)
>m Wn
|P,,111
Hence, when s = 1, we have Tr(E) = ΣN Wn P
H ADDITIONAL DETAILS ON INFONCE LOSSES
Here, we provide details on the applied infoNCE losses, Lazs and Ls2g. These losses encourage correspondences that align with the ground-truth pose while discouraging incorrect matches.
Given the sampled N corresponding ground points P and aerial points Q, we compute the true aerial correspondences for P as Q = s(Rg P) + tgt. the true ground correspondences for Q as P = R (QQ ts), and = 1 when we use metric depth during training. Then, we find in the pairwise matching score matrix M for the scores for these correspondences, denoting as MP..C and Q.P. which will serve as the positives in the infoNCE loss.
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Assuming there are Np valid scores in MP.Q (excluding points whose correspondences fall outside the aerial image), and denoting the n-th score as M,,. the loss La2s is computed as:
Np
Lazs
Σ
log
e
(22)
NP
EeM,
where M, is the i-th column correspond to the current ground point in the pairwise matching score matrix M. Essentially, Lass encourages each sampled ground point to match the aerial point found by the ground-truth pose and scale, while discouraging matches to all other aerial points.
For LSsG. we do not simply encourage the matching score MQP while discouraging all other matches. This is because multiple ground points may share similar planar coordinates but differ in height (i.e., the coordinate). As described in Section 3.3 of the main paper, we define local neighborhood and use only matching scores correspond to ground points outside this neighborhood as negatives. The loss LsgG then computed as:
No
e M.P
Ls20
log
(23)
NQ
Σ e.Muux
where NQ is the number of valid scores in MQ.P. and Maeg are the negatives for each sampled aerial point.
I DISCUSSION OF STANDARD AND TRUE DIGITAL ORTHOPHOTO MAPS
A standard Digital Orthophoto Map (DOM) is an aerial or satellite image that has been orthorecti- fied using a Digital Elevation Model (DEM), which typically represents only the bare-earth terrain. Unlike raw aerial photographs, DOM has uniform scale and corrected geometric distortions, abling it to serve as a metrically accurate base map for overlaying additional geospatial information.
The aerial imagery in datasets such VIGOR Zhuu et al. 2021 and KITTI (Shi & Li 2022) falls into this category, as these images provide uniform scale, they still contain building facades and occlusions due the absence of bbbove-ground structures in the underlying DEM.
A True Digital Orthophoto Map (TDOM), in contrast, is generated using Digital Surface Model (DSM) that captures both the terrain and above-ground objects such as buildings and vegetation. As a result, TDOM removes facade distortions and yields an image that is geometrically much closer to true nadir (top-down) projection. Our formulation estimates similarity transformation (rotation, translation, and scale) between ground-level and aerial points, implicitly assuming that the aerial image behaves like TDOM.
Despite this approximation, our method mitigates the resulting geometric inconsistencies through two key mechanisms: (1) Deep feature representations, which encode not only local appearance but also contextual information aggregated over large receptive fields, making them less sensitive to small misalignments between acrial and ground views; and (2) Confidence-basse correspondence sampling, applied during both training and inference, which ensures that pose estimation relies primarily on high-quality matches. As illustrated in the main paper Fig. 3(c), the model avoids unreliable points on building facades and instead focuses on stable cues such as road markings. Likewise, in examples (a) and (d), streetlights are matched via the pole base to their aerial footprint rather than the poles themselves, which is more susceptible to perspective distortion.
J RUNTIME AND MEMORY USAGE
Next, we report the runtime and memory usage of our method on VIGOR in Tab. 16
Runtime: On single H100 GPU, our method achieves 14.74 FPS without RANSAC Fischler 1981h (0.03s for our model and 0.04s for the depth predictor Unik3D PPicimelli et al.
& Bolles
2025)) and 0.42 FPS with RANSAC. This is faster than the previous local feature matching method FG (Xia & Alahi 2025), which runs at 9.26 EPS without RANSAC and 0.32 FPS with it. Notably, when prioritizing speed, omitting RANSAC results in only small increase in localization error,
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Runtime (FPS)
Method
Memory Usage
No RANSAC
With RANSAC
FG2
9.26
0.32
811.52 MB
726.74 MB (base) 1368.81 MB (Unik3D)
Ours
14.74
0.42
726.74 74 MB (base) 117.44 MB (UniFuse)
726.74 MB (base) 200.23 MB (BiFuse++)
Table 16: Runtime and memory usage comparison.
e.g., VIGOR same-area test set with known orientation the mean error increases from 3.06 to 3.29 m. Furthermore, one can use faster depth predictor to further reduce inference time.
Memory: model uses 74 MB, with 580.54 MB for the frozen DINOv2 (Oquab al. 2024 while the metric depth predictor Unik3D (Piccinelli et al. 2025) uses 1368.81 MB. Notably, as shown in Tab. 2 method is also compatible with more lightweight depth models, such Uni- Fuse Diang et al. 2021 and BiFuse++ Wang et al. (2022).
K LLM USAGE STATEMENT
We used a large language model (LLM) exclusively for text polishing, limited to minor grammar corrections, wording refinements, and improvements in readability. The LLM was not involved in the design of the method, the implementation of experiments, the analysis of results, or the gen- eration of any scientific content. All technical ideas, experiments, and conclusions presented in this work are entirely the authors' own. The role of the LLM was purely editorial, comparable to language editing support.
27


Reviews:
[{"review_id": "nmb8EXQ0t8", "reviewer": "Reviewer_uio4", "summary": "Loc² proposes an interpretable fine-grained cross-view localization method to estimate the 3-DoF pose of ground-level images by matching local features directly with aerial images. Unlike BEV transformation-based or global descriptor-based prior works, it learns image-plane correspondences under weak camera pose supervision, lifts ground points to BEV via monocular depth predictions, and estimates pose/scale using differentiable scale-aware Procrustes alignment. Key contributions include: direct cross-view local feature matching avoiding BEV distortion, strong interpretability via explicit correspondences and layout overlay, compatibility with both metric/relative depth, and state-of-the-art performance on KITTI and VIGOR.", "questions": "The paper argues that BEV transformation causes ray-directional distortions and height information loss, but does not conduct a direct comparative experiment between \"direct image-plane matching\" and \"BEV transformation + matching\". Have you ever constructed a BEV variant of Loc² (e.g., converting ground-level images to BEV first, then using the same DINOv2 feature extractor, matching head, and scale-aware Procrustes alignment as the original method) and compared its performance with the original direct matching？", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- **Strong interpretability and practicality**: Explicit local correspondences enable RANSAC outlier rejection, and scaled ground layout overlay provides intuitive localization quality cues, addressing the \"black box\" issue of prior methods.\n- **Robust and flexible depth adaptation**: Compatible with both metric and relative depth predictors, with minimal performance degradation when using lightweight relative depth models, enhancing real-world deployment potential.", "weaknesses": "The paper claims that 'However, these methods offer limited interpretability, as they cannot explicitly identify which objects in the ground view correspond to those in the aerial view.'  However, there is no experiments to directly compare the advantages and disadvantages of \"direct image-plane matching (used in Loc²)\" and \"BEV transformation followed by matching\". Specifically, the paper does not construct a BEV variant of Loc² (e.g., keeping the DINOv2 feature extractor, scale-aware Procrustes alignment, and loss function unchanged, but only converting the ground-level image to BEV as input for feature matching) for comparison. Without such a comparison, even though Loc² uses depth information, it cannot quantitatively prove: (1) how much performance loss BEV transformation actually causes in ground-aerial matching; (2) whether the direct matching method truly avoids the information loss of BEV transformation (e.g., whether the height information retained by direct matching with depth contributes to better correspondence accuracy).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "myHAsfj5AY", "reviewer": "Reviewer_aLNR", "summary": "This paper estimates the 3-DoF pose of a ground-level image based on a reference aerial image. This task is achieved by conduct local feature matching, monocular depth predictions and scale-aware Procrustes alignment in an end-to-end framework. Experiments show state-of-the-art accuracy and strong interpretability.", "questions": "1 In the introduction, the term \"scale-aware Procrustes alignment\" is used. For clarity, could the authors confirm if this refers specifically to a ​2D similarity transformation​? A more detailed explanation in the text would be helpful.\n\n2 The method seems to assume that the ground-level query images are oriented orthogonal to gravity. Could the authors explicitly state this assumption? Its practical limitation should be discussed, as consumer-grade images (e.g., from mobile phones) with arbitrary orientations may not easily be transformed into a canonical BEV space.\n\n3 The satellite imagery used is a Digital Orthophoto Map (DOM), which does not account for building facades, unlike a True Digital Orthophoto Map (TDOM). This creates a fundamental misalignment with BEV images, especially in urban areas with tall structures. ​How does the proposed method account for or mitigate this inherent domain discrepancy?​​\n\n4 The accuracy of the pose (location and orientation) annotations in KITTI and VIGOR is critical, as they provide the supervision signal. ​Have the authors validated the accuracy of these annotations?​​ If there is inherent noise, how does the method ensure reliable supervision? \n\n5 Since the method establishes correspondences, an informative ablation would be to compare the performance of using a ​homography​ versus the proposed ​scale-aware Procrustes alignment.\n\n6 The authors mention using RANSAC. ​For which specific geometric model is RANSAC employed?​​ Is it used to estimate a homography for outlier rejection before the Procrustes alignment?", "limitations": "", "rating": 2, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1 The paper is well-written and easy to follow. The  proposed framework are presented clearly.\n\n2 The attempt to formulate cross-view matching within a differentiable training pipeline is a commendable direction.", "weaknesses": "1 The authors claim the method's effectiveness, but the experimental results show that it does not achieve state-of-the-art (SOTA) performance on several key metrics.\n\n2 The method appears to be a straightforward composition of existing modules. The core challenges of cross-view matching do not seem to be fundamentally addressed by a novel technical contribution. This relates to my questions Q2-Q4.\n\n3 The generalization ability is a major concern. The method is evaluated on a limited data split. To better validate robustness, I strongly suggest an additional cross-dataset evaluation, for instance, ​training on KITTI and testing on VIGOR.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "bglDPXrZH9", "reviewer": "Reviewer_rY3A", "summary": "This paper proposes a cross-view localization method that first builds matches between ground and aerial images, and then analytically computes the camera pose from these matches. The idea is reasonable and demonstrates good generalization ability.", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is well-written and easy to follow. The idea is clear and makes sense to me.", "weaknesses": "1. **Purpose of “aerial points” (Line 696)**  \n   - What are the “aerial points” used for? I did not find a clear explanation. Do you match ground images to **regular grids** sampled on the aerial images? If yes, please justify this design choice. My concern is that downsampling features to a grid may degrade matching accuracy.\n\n2. **Resolution vs. Accuracy: feature maps and aerial-grid density**  \n   - I suspect localization accuracy depends on (i) the **feature-map resolution**, (ii) the **grid resolution** on the aerial images, and (iii) the **original image resolution**. How do you balance these factors? A deeper analysis would help clarify the sensitivity to these design choices. Please provide ablations such as:  \n     - Fix the aerial grid and vary the **backbone** to increase feature-map resolution.  \n     - Fix the feature-map resolution and vary the **aerial-grid resolution**.  \n     - Optionally, explore multi-scale/FPN settings to study trade-offs.  \n\n3. **Temperature parameter in Equation (1)**  \n   - Are the matching results sensitive to the temperature parameter \\( \\tau \\)? Please include a sensitivity analysis (e.g., performance vs. \\( \\tau \\)) and report the chosen value and tuning protocol.\n\n4. **Aerial image scale (ground sampling distance, GSD)**  \n   - Since you directly match ground to aerial features, the **GSD** (e.g., meters per pixel) will influence representational fidelity and, hence, matching accuracy. Have you evaluated aerial images captured at **higher altitudes** (coarser GSD)? Please report performance across different GSDs/heights to quantify robustness and discuss how scale changes affect the aerial feature maps and matching.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "2czBEMFAyJ", "reviewer": "Reviewer_SVL7", "summary": "The paper presents a fine-grained cross-view localization approach that leverages off-the-shelf depth estimation and integrates local feature matching with scale estimation for robust pose estimation, featuring an analytic pose head that incorporates RANSAC for outlier filtering.", "questions": "1. Does the rotation matrix R account for pitch and roll components?\n\n2. The results show that the method improves localization accuracy more than orientation. Do the authors have an explanation for this? You mention that orientation often aligns with road direction. Why does the local feature matching fail to capture this information effectively?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The analytic pose head, combined with RANSAC and overlay-based alignment, offers reliable diagnostics of correspondence quality.\n\n2. The method leverages off-the-shelf depth estimation, which is already well-established and helps improve localization performance.", "weaknesses": "1. The method relies on off-the-shelf depth estimation, while depth provides rich geometric information, its inclusion appears to improve localization accuracy only marginally. Furthermore, were the depth models used here trained on datasets such as KITTI?\n\n2. The results in Table 3 seem unintuitive: ignoring scale should significantly impact matching quality, yet the performance remains close to the full method. How do the authors explain this?\n\n3. Running RANSAC on a large number of correspondences may be computationally expensive, and could its robustness degrade when the outlier ratio is high?\n\n4. Since the approach depends heavily on local features and depth priors, it may overfit to VIGOR-style scenes and struggle to generalize to novel or unseen environments.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)