VIRD: View-Invariant Representation through Dual-Axis Transformation for Cross-View Pose Estimation

Juhye Park; Wooju Lee; Dasol Hong; Changki Sung; Youngwoo Seo; Dongwan Kang; Hyun Myung

cs.CVMar 13, 2026

VIRD: View-Invariant Representation through Dual-Axis Transformation for Cross-View Pose Estimation

Authors: Juhye Park, Wooju Lee, Dasol Hong, Changki Sung, Youngwoo Seo, Dongwan Kang, Hyun Myung

Organizations: Urban Robotics Lab, School of Electrical Engineering, KAIST · Hanwha Aerospace

Abstract

Accurate global localization is critical for autonomous driving and robotics, but GNSS-based approaches often degrade due to occlusion and multipath effects. As an emerging alternative, cross-view pose estimation predicts the 3-DoF camera pose corresponding to a ground-view image with respect to a geo-referenced satellite image. However, existing methods struggle to bridge the significant viewpoint gap between the ground and satellite views mainly due to limited spatial correspondences. We propose a novel cross-view pose estimation method that constructs view-invariant representations through dual-axis transformation (VIRD). VIRD first applies a polar transformation to the satellite view to facilitate horizontal correspondence, then uses context-enhanced positional attention on the ground and polar-transformed satellite features to mitigate vertical misalignment, explicitly bridging the viewpoint gap. To further strengthen view invariance, we introduce a view-reconstruction loss that encourages the derived representations to reconstruct the original and cross-view images. Experiments on the KITTI and VIGOR datasets demonstrate that VIRD outperforms the state-of-the-art methods without orientation priors, reducing median position and orientation errors by 50.7% and 76.5% on KITTI, and 18.0% and 46.8% on VIGOR, respectively.

Figures & tables

Figure 1: Ground-view and satellite-view images exhibit a large viewpoint gap due to misalignment along both the horizontal and vertical axes on the image plane. Previous geometry-based methods, such as polar and projective transformations, partially mitigated this issue by ensuring horizontal correspondence but could not fully address vertical misalignment. For example, projective transformations often produce severe artifacts around vertical structures such as buildings. VIRD overcomes these limitations through dual-axis transformation, introducing a shared virtual vertical axis $a$ to establish consistent cross-view correspondence.

Figure 2: Overview of VIRD. VIRD constructs view-invariant descriptors through dual-axis transformation. The process begins by applying a polar transformation to transform the satellite features $F_{s}$ into a horizontally corresponding representation to the ground features $F_{g}$ for each candidate pose $\mathbf{p}_{c}\in\mathcal{P}$ (the set of candidate poses), generating the polar-transformed features $F_{s2p}$ . The context-enhanced positional attention (CEPA) module then vertically transforms cross-view features through a positional attention mechanism. The resulting satellite and ground features, $F_{s2p^{\prime}}$ and $F_{g^{\prime}}$ , are compressed along the vertical axis to generate orientation-aware descriptors $D_{s2p}$ and $D_{g}$ . During training, a view-reconstruction loss is computed at the ground-truth pose $\mathbf{p}^{*}$ to enforce view invariance by reconstructing both original and cross views. At inference, the final 3-DoF pose is estimated by combining descriptor matching with residual regression.

Figure 3: Schematic illustration of the context-enhanced positional attention (CEPA) module consisting of positional attention (PA) and context enhancement (CE). PA generates attention weights $\mathcal{A}_{g}$ and $\mathcal{A}_{s2p}$ by comparing the shared virtual positional encodings $P_{a}$ with the positional encodings of the ground and satellite views, $P_{g}$ and $P_{s2p}$ , respectively. CE then adaptively refines the ground attention weights $\mathcal{A}_{g}$ using contextual information from the ground feature $F_{g}$ , resulting in $\mathcal{A}_{g^{\prime}}$ . These attention weights vertically transform the cross views by weighting the features $F_{g}$ and $F_{s2p}$ with $\mathcal{A}_{g^{\prime}}$ and $\mathcal{A}_{s2p}$ , respectively.

Figure 4: Visualization of attention weights. It shows the activations corresponding to each shared virtual positional encoding (PE). Red indicates stronger activations. Orange and green dots indicate the real spatial correspondence between the views.

			Position						Orientation
			Error (m) ↓		Lateral recall (%) ↑		Lon. recall (%) ↑		Error ( ∘ ) ↓		Recall (%) ↑
Method	Backbone	Area	Mean	Med.	R@1m	R@5m	R@1m	R@5m	Mean	Med.	R@1 ∘	R@5 ∘
HighlyAccurate [ 18 ]	VGG16	Same	15.51	15.97	5.17	25.44	4.66	25.39	89.91	90.75	0.61	2.89
SliceMatch [ 11 ]	VGG16	Same	9.39	5.41	39.73	87.92	13.63	49.22	8.71	4.42	11.35	55.82
CCVPE [ 35 ]	EfficientNet-B0	Same	6.88	3.47	53.30	85.13	25.84	68.49	15.01	6.12	8.96	42.75
DenseFlow ∗ [ 23 ]	ResNet18 [ 6 ]	Same	6.47	4.26	73.87	97.27	14.82	58.50	3.72	0.99	50.62	90.06

Table 1: Position and orientation estimation errors on the KITTI [ 5 ] dataset without orientation priors. Lon. and Med. are abbreviations for longitudinal and median, respectively. ∗ denotes results reproduced from the official implementations. Best in bold , second best underlined .

			Same-Area				Cross-Area
			Position (m) ↓		Orientation ( ∘ ) ↓		Position (m) ↓		Orientation ( ∘ ) ↓
Method	Backbone	Aligned	Mean	Median	Mean	Median	Mean	Median	Mean	Median
MCC [ 34 ]	VGG16	✓	6.94	3.64	-	-	9.05	5.14	-	-
SliceMatch [ 11 ]	VGG16	✓	5.18	2.58	-	-	5.53	2.55	-	-
CCVPE [ 35 ]	EfficientNet-B0	✓	3.60	1.36	-	-	4.97	1.68	-	-
DenseFlow [ 23 ]	ResNet18	✓	3.03	0.97	-	-	5.01	2.42	-	-

Table 2: Position and orientation estimation errors on the VIGOR [ 38 ] dataset. ‘Aligned’ refers to the case where the ground image orientation is known. For unaligned images, the models estimate the full 360-degree. † indicates the use of a two-step inference specific to the method in [ 31 ] to boost performance. Best in bold , second best underlined .

	Pos. error (m) ↓		Orien. error ( ∘ ) ↓
	Mean	Med.	Mean	Med.
Projective (S2G)	14.37	10.59	37.92	3.84
Projective (G2S)	17.10	15.20	47.62	5.44
Polar	15.26	11.75	39.92	4.00
Polar + PA (Ours)	13.92	9.76	35.17	3.44
Polar + CEPA (Ours)	13.83	8.88	31.35	3.36

Table 3: Ablation study of dual-axis transformation on KITTI [ 5 ] .

Panel of Figure 5 — Figure 5: Visualization of CEPA’s attention weights, view reconstruction, and pose estimation results from VIRD.

	Pos. error (m) ↓		Orien. error ( ∘ ) ↓
	Mean	Med.	Mean	Med.
Polar + CEPA	13.83	8.88	31.35	3.36
+ $\mathcal{L}_{\text{origin}}$	13.34	8.29	28.26	3.31
+ $\mathcal{L}_{\text{cross}}$	12.84	8.10	26.30	3.21
+ $\mathcal{L}_{\text{origin}}$ + $\mathcal{L}_{\text{cross}}$	12.72	7.90	21.91	3.05
+ $\mathcal{L}_{\text{origin}}$ + $\mathcal{L}_{\text{cross}}$ + $\mathcal{L}_{\text{reg}}$	12.30	7.05	25.10	2.22

Table 4: Ablation study of model components on KITTI [ 5 ] .

Figure 6: Ablation study of robustness to orientation noise on KITTI [ 5 ] . Larger markers denote higher noise levels (

\pm 10^{\circ}

\pm 60^{\circ}

\pm 120^{\circ}

, and

\pm 180^{\circ}

Figure A : Comparison of content-based attention (CBA) and context-enhanced positional attention (CEPA) on KITTI [ 5 ] .

	Pos. error (m) ↓		Orien. error ( ∘ ) ↓
	Mean	Med.	Mean	Med.
Sinusoidal pe	13.92	9.76	35.17	3.44
Sinusoidal learnable pe	14.28	10.63	33.82	3.41
Learnable pe	15.23	12.06	36.23	4.04
2D sinusoidal pe	14.68	10.31	33.57	3.57

Table A : Positional attention performance with various positional encoding variants on KITTI [ 5 ] .

Figure B : Effect of the view-reconstruction loss on CEPA. The first row presents example (a), and the second row presents example (b). For each example, the satellite attention $\mathcal{A}_{s2p}$ and the context-enhanced ground attention $\mathcal{A}_{g^{\prime}}$ are visualized at the same vertical position in the shared virtual positional encoding space. The view-reconstruction loss stabilizes the learning of vertical transformations in CEPA, yielding stronger roof activations in example (a) and successful detection of overpass structures in example (b). Regions with stronger activations are highlighted in red.

	Pos. error (m) ↓		Orien. error ( ∘ ) ↓
	Mean	Med.	Mean	Med.
$\ell_{1}$	12.72	7.90	21.91	3.05
$\ell_{2}$	13.14	8.30	25.74	3.31
SSIM	12.92	8.00	25.23	3.34
Percep	14.00	9.78	29.55	3.31

Table B : Comparison of different reconstruction loss types on KITTI [ 5 ] .

Cylindrical	Pos. error (m) ↓		Orien. error ( ∘ ) ↓
projection	Mean	Med.	Mean	Med.
×	15.26	11.75	39.92	4.00
✓	15.10	11.62	38.97	4.13

Table C : Impact of cylindrical projection on pinhole camera on KITTI [ 5 ] .

	Pos. error (m) ↓		Orien. error ( ∘ ) ↓
$\tau$	Mean	Med.	Mean	Med.
0.1	16.09	13.21	38.54	4.34
0.05	15.26	11.75	39.92	4.00
0.01	17.18	14.93	53.59	6.17

Table D : Ablation study of the temperature parameter on KITTI [ 5 ] .

			Pos. error (m) ↓		Orien. error ( ∘ ) ↓
$\alpha_{1}$	$\alpha_{2}$	$\beta$	Mean	Med.	Mean	Med.
0.1	0	0	13.43	8.54	30.08	3.30
1	0	0	13.34	8.29	28.26	3.31
5	0	0	13.90	9.04	27.01	3.34
1	5	0	12.61	7.64	25.72	3.16
1	10	0	12.72	7.90	21.91	3.05

Table E : Ablation study of the loss coefficients on KITTI [ 5 ] .

		Lat. (%) ↑	Lon. (%) ↑	Orien. (%) ↑
Range	Area	R@1m	R@1m	R@1 ∘
$\pm 2$ m, $\pm 2$ m, $\pm 1.8^{\circ}$	Same	79.30	29.21	44.16
$\pm 4$ m, $\pm 4$ m, $\pm 3.6^{\circ}$	Same	79.46	31.65	49.32
$\pm 6$ m, $\pm 6$ m, $\pm 4.8^{\circ}$	Same	74.77	28.49	51.63
$\pm 2$ m, $\pm 2$ m, $\pm 1.8^{\circ}$	Cross	44.37	12.98	26.81
$\pm 4$ m, $\pm 4$ m, $\pm 3.6^{\circ}$	Cross	43.61	12.88	27.65

Table F : Ablation study of the regression search range on KITTI [ 5 ] .

Figure C : Ablation study of

H_{Q}

on KITTI [ 5 ] .

Figure D : Ablation study of candidate pose sampling density, compared with SliceMatch [ 11 ] and CCVPE [ 35 ] . For the proposed method, the number of orientation candidates is fixed to 70 during position sampling, and the position grid size is fixed to 20

\times

20 during orientation sampling. SliceMatch performs matching only on 15

\times

\times

64 candidate poses. For CCVPE, position prediction is performed at the original resolution, while orientation prediction first matches 20 candidates and then performs regression. Because CCVPE is independent of the number of position samples, its performance is shown as a horizontal line.

Figure E : Error statistics across five random seeds for the proposed method. Error bars indicate

\pm 2\sigma

standard deviations, computed from five independent runs.

Panel of Figure 22 — Figure F : Visualization of the attention weights $\mathcal{A}_{g}$ , $\mathcal{A}_{g^{\prime}}$ , and $\mathcal{A}_{s2p}$ at selected positions in the shared virtual positional encoding space. CE and pos denote the context-enhanced attention and the positions in the shared virtual positional encoding space, respectively. Regions with stronger activations are highlighted in red.

Panel of Figure 23 — Figure G : Visualization of reconstructed images from ground and satellite descriptors in both original and cross views. Each subfigure is denoted as $i\to j$ , where $i,j\in\{s,g\}$ indicate the source and target views, respectively. The pairs $g\to g$ and $s\to s$ indicate original-view reconstructions, whereas $g\to s$ and $s\to g$ represent cross-view reconstructions.

Cross-View Geo-Localization

Cross-view geo-localization matches ground, drone, or aerial images to maps or satellite views to estimate where they were captured.

See all 94 papers

More Than Where You Are: Learning Semantics, Structure, and Geometry from Cross-View Localization
Jul 14, 2026Mao Chen, Xiangkai Zhang, Zhiyong Liu +2Multi-View Consistency Multi-View Geometry
State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, and also with the School of Artificial Intelligence, University of Chinese Academy of Sciences · Beijing Aerospace Control Center
CIPER: A Unified Framework for Cross-view Image-retrieval and Pose-estimation
Jun 3, 2026Yurim Jeon, Dongseong Seo, Seung-Woo SeoCross-View Geo-Localization Visual Place Recognition
Seoul National University, Seoul, Republic of Korea
Seeing Across Skies and Streets: Feedforward 3D Reconstruction from Satellite, Drone, and Ground Images
May 8, 2026Qiwei Wang, Zhongyao Tuo, Xianghui Ze +1Relative Pose Estimation Cross-View Geo-Localization
ShanghaiTech University Shanghai, China · Nanjing University of Science and Technology Nanjing, China

Jul 14, 2026J/K move · Enter open · S save

More Than Where You Are: Learning Semantics, Structure, and Geometry from Cross-View Localization

Mao Chen, Xiangkai Zhang, Zhiyong Liu, Chuankai Liu+1

State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, and also with the School of Artificial Intelligence, University of Chinese Academy of Sciences · Beijing Aerospace Control Center

Multi-View Consistency Multi-View Geometry Cross-View Geo-Localization Multi-View Learning

Open paper AskPDF arXiv

Consistent cross-view understanding under extreme viewpoint changes is essential for spatial intelligence, as it enables models to recognize the same scene across extreme viewpoint gaps. Cross-view localization naturally provides a promising pathway toward this ability, as it requires a model to align ground-view imagery with geo-referenced satellite-view imagery despite drastic appearance changes to estimate camera poses. Recent visual foundation models have made this long-standing localization problem increasingly feasible by providing rich 2D representations for cross-view matching. However, we argue that cross-view localization should not be viewed merely as 2D matching or pose estimation. In this work, we revisit cross-view localization as more than pose estimation and investigate how it can help the model develop consistent cross-view understanding under extreme viewpoint changes, including stable semantics, reliable structure, and transferable geometry. We identify three key limitations of existing methods that prevent them from achieving this. They usually lack explicit 3D grounding, rely on strict point-wise matching that can weaken semantic consistency, and learn from an absolute objective that provides limited guidance for geometric reasoning. To address these limitations, we propose CROSS, a unified cross-view localization framework built upon 3D-grounded alignment, structure-aware matching, and hypothesis ranking. This formulation makes structure learning an intrinsic requirement, encourages semantic representations to remain stable, and enables the model to acquire transferable geometry. Extensive experiments on the KITTI and VIGOR datasets show that CROSS achieves state-of-the-art performance in cross-view localization. More importantly, CROSS effectively learns stable semantics, reliable structure, and transferable geometry across extremely different viewpoints.

Abstract

Cross-View Geo-Localization

Explore similar work

More Than Where You Are: Learning Semantics, Structure, and Geometry from Cross-View Localization

CIPER: A Unified Framework for Cross-view Image-retrieval and Pose-estimation

Seeing Across Skies and Streets: Feedforward 3D Reconstruction from Satellite, Drone, and Ground Images