Bi-Level Meta-Learning for Reliable Remote Sensing Image Registration

Highlights

What are the main findings?

• A saliency-aware bi-level optimization framework is proposed to address the challenges of extreme radiometric and temporal variations in heterogeneous remote sensing image matching.
• A novel Saliency Judgment module is developed to intelligently prioritize geometrically stable landmarks while suppressing spurious matches in weakly informative regions.

What are the implications of the main findings?

• The bi-level meta-learning strategy establishes a new paradigm for UAV localization by enabling effective model training under weakly labeled data regimes, reducing the reliance on large-scale expert annotations.
• The framework significantly enhances registration accuracy and reduces ghosting artifacts, providing a robust “quality-over-quantity” correspondence selection strategy for autonomous aerial localization.

Abstract

Unmanned aerial vehicle (UAV) visual navigation relies critically on robust image matching between UAV-acquired aerial imagery and pre-existing satellite reference maps. However, extreme cross-domain heterogeneity—encompassing temporal, radiometric, viewpoint, and sensor variations—causes severe performance degradation in existing deep learning-based matchers trained on conventional benchmarks. Furthermore, manual annotation of ground-truth correspondences is prohibitively expensive. This paper proposes a semi-supervised saliency-aware image matching framework with bi-level meta-learning. Our approach comprises two synergistic stages: (1) automated dense correspondence generation via parameterized geometric synthesis, which constructs a large-scale coarse dataset ${\mathcal{D}}_c$ (approximately 50,000 pairs) without dense manual point annotation, serving as the primary training corpus for the feature matching network; (2) expert-validated meta-data curation producing a high-quality meta-dataset ${\mathcal{D}}_m$ (500 pairs) that supervises the training of a Saliency Judgment Network through bi-level meta-optimization, enabling the network to identify and prioritize geometrically reliable correspondences. Experimental results on the proposed RS-Hetero-50K benchmark and cross-domain FuJian-Mountain dataset demonstrate substantial improvements over representative sparse and detector-free matchers, including LoFTR, SuperGlue, and LightGlue. The complete CNN-attention and saliency-aware framework achieves 95.4% matching precision, which is consistent with the best result reported in the experimental section. The plug-and-play experiments further confirm that the proposed saliency module consistently improves representative sparse and detector-free matchers, indicating that the performance gain stems from both stronger feature representation and saliency-guided correspondence selection. The largest terrain-specific gain is observed in gobi scenes, where the AUC@5 px improves by 16.8% relative to the LoFTR baseline, demonstrating improved robustness in weakly textured remote sensing environments.

1. Introduction

Unmanned aerial vehicle (UAV) visual navigation has emerged as a critical measure capable of autonomous positioning in environments where global navigation satellite system (GNSS) signals are degraded or unavailable [1,2,3]. At the core of visual navigation pipelines lies image matching—the task of establishing dense feature correspondences between real-time UAV-acquired aerial imagery and pre-existing satellite reference maps [4,5]. Accurate matching enables subsequent pose estimation and geolocalization, directly determining the reliability and safety of autonomous flight operations in remote sensing scenarios [6].

Despite its foundational importance, cross-domain image matching between UAV aerial imagery and satellite reference maps presents extraordinary challenges that fundamentally differentiate it from conventional matching benchmarks. Specifically, the extreme heterogeneity between these two domains encompasses four critical dimensions: temporal variations in scene appearance due to seasonal changes and land-cover evolution; radiometric disparities arising from differences in illumination conditions, atmospheric effects, and sensor response functions; viewpoint distortions caused by large variations in camera pose and perspective between aerial and satellite acquisition geometries; and sensor modality differences in resolution, spectral sensitivity, and image quality [7,8]. The cumulative effect of these cross-domain factors produces visually dissimilar image pairs in which corresponding regions may exhibit drastically different textures, colors, and structural patterns. Consequently, state-of-the-art deep learning-based matchers, which achieve remarkable performance on benchmark datasets such as MegaDepth and ScanNet [9,10], suffer from catastrophic performance degradation when deployed in high-heterogeneity remote sensing scenarios without extensive domain-specific retraining. The root cause lies in the substantial domain gap between the structured indoor/outdoor environments of existing training datasets and the unstructured, highly variable nature of remote sensing imagery spanning diverse terrain types including urban, suburban, and gobi regions.

Compounding these technical challenges is a fundamental data scarcity problem. Training high-capacity deep matchers requires large-scale datasets of accurately annotated dense correspondences. However, manual annotation of ground-truth correspondences between aerial and satellite imagery is prohibitively expensive, time-consuming, and error-prone due to the visual dissimilarity between domains and the enormous search space of potential correspondences across high-resolution images [8]. Existing remote sensing datasets remain limited in both scale and diversity, rendering direct supervised training on annotated remote sensing pairs impractical for most applications. This creates a critical need for semi-supervised or self-supervised training paradigms that can leverage unlabeled or weakly labeled remote sensing imagery to bridge the domain gap.

To address these challenges, this paper proposes a semi-supervised saliency-aware image matching framework with bi-level meta-learning for UAV visual navigation in high-heterogeneity remote sensing scenarios. Our approach comprises two synergistic stages. First, we introduce an automated dense correspondence generation mechanism based on parameterized geometric synthesis, which constructs training pairs with known ground-truth correspondences without requiring dense manual point annotation for every training pair. This synthesis pipeline models realistic cross-domain transformations through carefully designed geometric, photometric, and noise parameters that capture the essential characteristics of the aerial-to-satellite domain gap. Second, we develop a saliency-based selection strategy centered on a Saliency Judgment Network (SJN) that learns to assess the reliability and informativeness of individual correspondences. The SJN is trained through bi-level meta-optimization supervised by an expert-validated meta-dataset ${\mathcal{D}}_m$: the inner loop adapts the feature matching network on the large-scale coarse dataset ${\mathcal{D}}_c$, while the outer loop updates the SJN to prioritize correspondences that maximize matching performance on ${\mathcal{D}}_m$. This bi-level formulation effectively learns a data-driven curriculum that guides the training of the underlying matcher toward robust cross-domain generalization. The proposed framework is model-agnostic and can be integrated with various feature matching architectures.

The principal contributions of this work are threefold:

• We propose a semi-supervised learning framework that decouples automated correspondence generation from saliency-based selection, substantially reducing the dependency on costly large-scale dense manual annotations while enabling effective training on high-heterogeneity remote sensing imagery. The parameterized geometric synthesis pipeline generates diverse training pairs with accurate ground-truth correspondences, while the saliency-based selection mechanism filters unreliable samples to improve training efficiency and model robustness.
• We design a Saliency Judgment Network trained through bi-level meta-learning that adaptively identifies and prioritizes reliable correspondences for matcher optimization. The bi-level formulation treats correspondence selection as an inner optimization and matcher performance as an outer objective, enabling the network to learn a principled, data-driven criterion for sample importance without hand-crafted heuristics.
• We introduce RS-Hetero-50K, a large-scale remote sensing dataset encompassing approximately 50,000 high-heterogeneity image pairs across diverse terrain types including urban, suburban, and gobi scenes with extreme cross-domain variations. Extensive experimental evaluations demonstrate that the complete framework reaches 95.4% matching precision and that the plug-and-play saliency module consistently improves LoFTR, SuperGlue, and LightGlue backbones.

2. Related Work

2.1. Deep Learning-Based Image Matching in Natural Scenes

Image matching constitutes a foundational component of numerous computer vision systems, including visual navigation, 3D reconstruction, augmented reality, and robotics. The core objective is to establish robust and accurate pixel-level correspondences between two or more images of the same scene. Early approaches relied exclusively on hand-crafted feature detectors and descriptors. Scale-Invariant Feature Transform (SIFT) [11] detects extrema in the Difference-of-Gaussian scale-space and describes local neighborhoods using 128-dimensional histograms of oriented gradients, achieving remarkable invariance to scale, rotation, and moderate illumination and viewpoint changes. Speeded-Up Robust Features (SURF) [12] accelerates detection and description through integral-image-based approximations of the Hessian matrix determinant and Haar wavelet responses, offering comparable robustness with substantially reduced computational cost. Oriented FAST and Rotated BRIEF (ORB) [13] further improves efficiency by combining the FAST corner detector with a rotation-aware binary descriptor, making it suitable for real-time applications on resource-constrained platforms. Despite their widespread adoption, these methods rely on low-level gradient statistics and intensity patterns, rendering them highly sensitive to severe appearance disparities that violate photometric consistency assumptions—a critical limitation in cross-domain scenarios.

The advent of deep learning has catalyzed a paradigm shift, enabling learned feature representations that substantially outperform hand-crafted alternatives. Early CNN-based local-feature methods first replaced hand-crafted detectors and descriptors with trainable detect–describe modules. SuperPoint [14] introduced a fully convolutional network trained via self-supervision on synthetic homographic warps, jointly optimizing keypoint detection and descriptor computation in a single forward pass. R2D2 [15] further improved this paradigm by explicitly optimizing detector repeatability and descriptor reliability, thereby enhancing robustness under appearance changes. D2-Net [16] relaxed the explicit detector design by extracting keypoints from CNN activation maps, while DELF [17] incorporated attention to select semantically meaningful local features. These methods mark the transition from hand-crafted local descriptors to learned local feature representations.

A subsequent line of work improves the matching stage built upon sparse or local features. SuperGlue [18] integrates SuperPoint features with a graph neural network and formulates correspondence estimation as an optimal assignment problem, using self-attention and cross-attention before Sinkhorn-based matching. LightGlue [19] can be viewed as an efficiency-oriented improvement of this sparse matching pipeline, introducing a lightweight Transformer matcher with confidence-based early stopping to reduce inference latency while maintaining competitive accuracy. Following the same efficiency-oriented direction, XFeat [20] revisits compact CNN-based local features and provides both sparse and semi-dense matching modes, making it particularly relevant to resource-constrained UAV platforms.

In parallel, detector-free dense and semi-dense matching methods aim to overcome the dependence on repeatable keypoint detection. LoFTR [21] pioneered this direction by combining CNN feature extraction with alternating self-attention and cross-attention Transformer layers, establishing correspondences over dense feature maps rather than only at detected keypoints. MatchFormer [22] advanced the LoFTR-style framework by interleaving cross-view attention within the feature extraction backbone, enabling earlier information fusion across image pairs. ASpanFormer [23] further improved dense Transformer matching through adaptive span attention, which adjusts the effective receptive field according to local feature distributions. Efficient LoFTR [24] directly extends the LoFTR lineage by reducing redundant full-map Transformer computation through aggregated attention and adaptive token selection, moving semi-dense matching toward sparse-like speed.

Despite these remarkable advances in standard benchmarks, a fundamental challenge persists: matchers trained on natural-scene datasets such as MegaDepth [9] and ScanNet [10] still exhibit significant performance degradation when deployed in remote sensing scenarios. The domain gap between structured indoor/outdoor natural-scene benchmarks and the unstructured, highly variable nature of remote sensing imagery fundamentally limits cross-domain generalization.

2.2. Image Matching in Remote Sensing and UAV Navigation

Image matching for UAV visual navigation presents challenges that fundamentally differentiate it from conventional matching tasks. The primary objective is to establish robust correspondences between UAV-acquired aerial imagery and pre-existing satellite reference maps under substantial cross-domain appearance variations. Piasco et al. [5] surveyed visual-based localization methods and identified the substantial benefit of heterogeneous data for robust navigation in GPS-degraded environments. Toft et al. [6] proposed semantic match consistency for long-term localization, leveraging high-level semantic information to improve matching reliability across seasonal and illumination changes. Li et al. [7] developed a multi-modal image fusion framework specifically designed for end-to-end remote sensing image registration, addressing sensor heterogeneity through learned feature fusion.

For cross-domain adaptation, unsupervised domain adaptation methods [25,26] attempt to align feature distributions between source and target domains, reducing annotation dependency. However, these approaches typically assume relatively mild domain shifts and may fail when multiple cross-domain factors—cross-season, cross-illumination, cross-scale, and cross-sensor variations—compound to produce extreme appearance disparities that exceed the adaptation capacity of standard techniques.

Saliency-guided visual perception offers a promising complementary approach. Saliency detection aims to identify the most visually conspicuous and structurally distinctive regions in an image. In remote sensing contexts, high-saliency regions typically correspond to building corners, road intersections, terrain discontinuities, and distinctive vegetation boundaries—features that tend to persist across different viewing conditions and seasonal variations. Conversely, low-saliency regions such as homogeneous water surfaces, repetitive agricultural fields, and visually uniform terrain often generate ambiguous correspondences that degrade matching performance. Several studies have explored saliency-aware strategies for remote sensing image retrieval and registration, demonstrating that prioritizing matches in salient regions can substantially improve accuracy. However, the systematic integration of saliency guidance with modern deep learning-based matching architectures remains under-investigated.

Semi-supervised learning provides a principled framework for addressing the annotation bottleneck. Active learning strategies [27,28] intelligently select the most informative samples for annotation through uncertainty-based acquisition functions that prioritize samples about which the model is most uncertain. Deep Bayesian active learning [29] extends these ideas by incorporating epistemic uncertainty estimates derived from Bayesian neural network approximations, enabling more principled selection criteria that distinguish between aleatoric uncertainty (inherent ambiguity) and epistemic uncertainty (lack of model knowledge). Despite these advances, significant gaps remain: existing approaches have been developed primarily for natural scenes, and the integration of saliency guidance with semi-supervised learning for modern matchers has not been explored.

The present work addresses these gaps by proposing a unified framework combining semi-supervised learning with saliency-aware correspondence selection for UAV visual navigation. We decouple automated correspondence generation from saliency-based meta-data selection, introduce a Saliency Judgment Network with bi-level meta-learning, and demonstrate consistent improvements across multiple backbone architectures including detector-free and sparse matching paradigms.

3. Materials and Methods

This section presents the proposed semi-supervised saliency-aware image matching framework in detail. We first describe the dataset preparation pipeline, including automated coarse correspondence generation and expert-validated meta-data curation. We then elaborate on the network architecture, comprising a CNN-Attention feature matching module and a Saliency Judgment Network with bi-level optimization. Finally, we outline the inference pipeline.

For clarity,

Table 1. Summary of main symbols used in the proposed framework.

Symbol	Meaning
S, A	Satellite reference image and UAV/aerial orthomosaic.
$I^{\mathrm{src}}$, $I^{\mathrm{tgt}}$	Source and target images fed into the matching network.
$T_{\mathrm{sim}}$, $W_{\mathrm{TPS}}$, $T_{\mathrm{crop}}$	Similarity transform, TPS residual warp, and crop-normalization transform.
$T_{\mathrm{total}}$	Composite synthetic mapping used for coarse correspondence generation.
${\mathcal{D}}_c$, ${\mathcal{D}}_m$	Automatically generated coarse dataset and expert-validated meta-dataset.
${\Phi }_{\mathsf{\omega }}$, ${\mathcal{S}}_{\mathsf{\psi }}$	Feature matching network and Saliency Judgment Network.
$\mathcal{C}$, $r_l$	Putative correspondence set and its l-th correspondence.
$P_{ij}$, $s_l$, $z_l$	Dual-softmax confidence, saliency score, and differentiable selection weight.

summarizes the main symbols used throughout the methodology.

3.1. Dataset Preparation

The acquisition of high-quality training data constitutes a critical prerequisite for learning-based image matching in remote sensing scenarios. This subsection describes the complete pipeline for constructing both the coarse correspondence dataset and the expert-validated meta-dataset. The overall data preparation pipeline is illustrated in Figure 1.

3.1.1. Initial Correspondence Generation

This stage employs an automated pipeline to establish dense, full-image correspondences by synthesizing parameterized geometric transformations based on the geographic alignment between satellite and UAV imagery. This process requires no dense manual point annotation for the automatically generated coarse pairs and is therefore highly scalable.

We utilize two complementary remote sensing data sources:

Satellite Imagery: Sourced from authorized GIS and satellite imagery platforms, these orthorectified images have a spatial resolution of $0.3$–$1.0$ m/pixel. They serve as the geometric reference due to their minimal perspective distortion and precise georeferencing (GeoTIFF format).

Aerial Imagery: Acquired via UAV flight campaigns at altitudes of 100–1000 m, with a Ground Sampling Distance (GSD) of $0.5$–$2.0$ m/pixel. Raw captures are processed using Structure-from-Motion (SfM) to generate large-scale orthomosaics, where each pixel is geolocated based on integrated GNSS/IMU data.

Let S and A denote a satellite image and an aerial orthomosaic covering the same geographic region, respectively. We establish their relationship using a hierarchical progressive strategy:

1. Initial Geographic Alignme: Using georeferencing, both images are transformed into a unified coordinate system. Given the geographic transformations ${\mathcal{T}}_S$ and ${\mathcal{T}}_A$, the pixel-level correspondence is defined as:

$$x_S={\mathcal{T}}_S^{-1}\left({\mathcal{T}}_A\left(x_A\right)\right),$$

(1)

where $x_S$ and $x_A$ denote corresponding pixel coordinates in the satellite and aerial images, respectively. This step achieves coarse alignment, resulting in an aligned pair ${\mathcal{P}}_{\mathrm{align}}$ sharing the same geographic extent.

2. Source Region Selection: A rectangular region R is randomly sampled within ${\mathcal{P}}_{\mathrm{align}}$, defined by its center $C(x_c,y_c)$ and dimensions $(W_R,H_R)$, where $x_c$ and $y_c$ denote the center coordinates, and $W_R$ and $H_R$ denote the width and height of the selected region, respectively. Selection constraints include: (i) the region must lie entirely within the image boundaries, and (ii) the proportion of valid pixels must exceed $90\%$.

3. Tri-level Composite Geometric Transformation: To simulate realistic imaging distortions encountered during UAV flight, we apply a cascade of three transformations to the selected source region. Let R denote the source crop and let $\mathbf{p}={[p_x,p_y]}^{\top }\in {\mathbb{R}}^2$ be a point in R.

Level 1: Global Similarity Transformation (simulating global camera pose changes):

$${\mathbf{H}}_{\mathrm{sim}}=\left[\begin{array}{ccc}scos\theta & -ssin\theta & t_x\\ ssin\theta & scos\theta & t_y\\ 0& 0& 1\end{array}\right].$$

(2)

Here,  $s\in [0.5,2.0]$ denotes the scale factor, simulating scale changes from half to twice the original crop scale; $\theta \in [0,2\pi ]$ denotes the in-plane rotation angle; and $(t_x,t_y)$ are translation parameters used to align the transformed crop center with the target crop center. For a point $\mathbf{p}$, its homogeneous coordinate is denoted as $\overline{\mathbf{p}}={[p_x,p_y,1]}^{\top }$. The corresponding intermediate coordinate after the similarity transformation is

$$\mathbf{q}=T_{\mathrm{sim}}\left(\mathbf{p}\right)=\Pi \left({\mathbf{H}}_{\mathrm{sim}}\overline{\mathbf{p}}\right),$$

(3)

where $\Pi \left({[x,y,z]}^{\top }\right)={[x/z,y/z]}^{\top }$ converts homogeneous coordinates to Cartesian coordinates.

Level 2: TPS-based Low-Frequency Residual Deformation (simulating relief and platform motion-induced non-rigid perturbations): After the global similarity transformation, we apply a Thin Plate Spline (TPS) residual deformation in the intermediate coordinate system [30]. Let ${\left\{{\mathbf{c}}_k\right\}}_{k=1}^K$ be the TPS control points placed on the transformed crop $T_{\mathrm{sim}}\left(R\right)$, and let ${\mathbf{u}}_k\in {\mathbb{R}}^2$ be the synthetic displacement assigned to the k-th control point. In our implementation, $K=4$ control points are arranged as a $2\times 2$ grid. This sparse grid is intentionally used to generate smooth low-frequency deformation rather than high-frequency elastic distortion.

The TPS warp is defined as

$${\mathbf{q}}^{\prime }=W_{\mathrm{TPS}}\left(\mathbf{q}\right)=\mathbf{q}+f_{\mathrm{TPS}}\left(\mathbf{q}\right),$$

(4)

where $\mathbf{q}=T_{\mathrm{sim}}\left(\mathbf{p}\right)$ is the intermediate coordinate, ${\mathbf{q}}^{\prime }$ is the coordinate after residual deformation, and $f_{\mathrm{TPS}}:{\mathbb{R}}^2\to {\mathbb{R}}^2$ is the two-dimensional TPS displacement field. The displacement field is written as

$$f_{\mathrm{TPS}}\left(\mathbf{q}\right)={\mathbf{W}}^{\top }\kappa \left(\mathbf{q}\right)+{\mathbf{B}}^{\top }\left[\begin{array}{c}1\\ q_x\\ q_y\end{array}\right],$$

(5)

where $\mathbf{W}\in {\mathbb{R}}^{K\times 2}$ contains the non-rigid TPS coefficients, $\mathbf{B}\in {\mathbb{R}}^{3\times 2}$ contains the affine coefficients of the residual field, and 

$$\kappa \left(\mathbf{q}\right)={\left[\varphi (\parallel \mathbf{q}-{\mathbf{c}}_1{\parallel }_2),\dots ,\varphi (\parallel \mathbf{q}-{\mathbf{c}}_K{\parallel }_2)\right]}^{\top }.$$

(6)

The radial basis function is $\varphi \left(r\right)=r^{2}log(r+\epsilon )$, with $\epsilon ={10}^{-6}$ used to avoid the singularity at $r=0$. The TPS parameters are obtained by solving the regularized interpolation system

$$\left[\begin{array}{cc}{\mathbf{K}}_{\mathrm{tps}}+{\lambda }_{\mathrm{tps}}{\mathbf{I}}_K& \mathbf{P}\\ {\mathbf{P}}^{\top }& {\mathbf{0}}_{3\times 3}\end{array}\right]\left[\begin{array}{c}\mathbf{W}\\ \mathbf{B}\end{array}\right]=\left[\begin{array}{c}\mathbf{U}\\ {\mathbf{0}}_{3\times 2}\end{array}\right],$$

(7)

where ${\left({\mathbf{K}}_{\mathrm{tps}}\right)}_{ij}=\varphi (\parallel {\mathbf{c}}_i-{\mathbf{c}}_j{\parallel }_2)$, ${\mathbf{P}}_{k,:}=[1,c_{k,x},c_{k,y}]$, and ${\mathbf{U}}_{k,:}={\mathbf{u}}_k^{\top }$. The lower block ${\mathbf{P}}^{\top }\mathbf{W}={\mathbf{0}}_{3\times 2}$ imposes the standard TPS affine null-space constraints. Since the four control points are non-collinear and arranged as a rectangular $2\times 2$ grid, $\mathbf{P}$ has full column rank, making the regularized system well posed. We set ${\lambda }_{\mathrm{tps}}=0.1$ to suppress unstable high-curvature deformation.

The displacement magnitude is controlled in the image domain. Specifically, for low-, medium-, and high-altitude settings, the control point displacements are sampled as ${\mathbf{u}}_k\sim \mathcal{U}\left({[-\rho ,\rho ]}^2\right)$ with $\rho =5$, 10, and 20 pixels, respectively. After solving the TPS system, we evaluate the displacement field on the sampled grid points. If ${max}_{\mathbf{x}\in \mathcal{G}}{\parallel f_{\mathrm{TPS}}\left(T_{\mathrm{sim}}\left(\mathbf{x}\right)\right)\parallel }_{\infty }>\rho$, the whole residual field is uniformly rescaled by the factor

$$\eta =min\left(1,{\displaystyle \frac{\rho }{{max}_{\mathbf{x}\in \mathcal{G}}{\parallel f_{\mathrm{TPS}}\left(T_{\mathrm{sim}}\left(\mathbf{x}\right)\right)\parallel }_{\infty }}}\right),f_{\mathrm{TPS}}(·)\leftarrow \eta f_{\mathrm{TPS}}(·).$$

(8)

Level 3: Rectangular Bounding Crop (generating standardized input): After the similarity and TPS transformations, we compute the minimal axis-aligned bounding box B enclosing the deformed crop. A crop-normalization transformation $T_{\mathrm{crop}}$ maps this bounding box to the standardized target image window T. The complete synthetic transformation is therefore

$$T_{\mathrm{total}}=T_{\mathrm{crop}}\circ W_{\mathrm{TPS}}\circ T_{\mathrm{sim}}.$$

(9)

Equivalently, for any source point $\mathbf{p}\in R$, its final target coordinate is

$${\mathbf{p}}^{\prime }=T_{\mathrm{total}}\left(\mathbf{p}\right)=T_{\mathrm{crop}}\left(W_{\mathrm{TPS}}\left(T_{\mathrm{sim}}\left(\mathbf{p}\right)\right)\right).$$

(10)

This composite formulation retains both global pose variation and smooth residual deformation. Therefore, it is more appropriate for UAV-to-satellite data synthesis than approximating the entire transformation with a single homography.

It should be noted that the TPS residual deformation is used for training-time correspondence synthesis and local matching supervision. The final registration evaluation in Section 4 is performed on held-out homography-compatible pairs, for which the reference transformation is represented by a planar projective mapping obtained from geographic alignment and verified control points. Therefore, the non-rigid TPS component improves training diversity but is not used as the reference model for homography-level evaluation.

We construct a regular grid $\mathcal{G}$ within the source region R with step size $\delta$; in all experiments, $\delta =8$ pixels. For each grid point ${\mathbf{x}}_i\in \mathcal{G}$, the corresponding point in the target image is computed as

$${\mathbf{x}}_i^{\prime }=T_{\mathrm{total}}\left({\mathbf{x}}_i\right).$$

(11)

Only correspondences whose transformed coordinates remain inside the valid target image region are retained. The dense correspondence set is defined as

$${\mathcal{M}}_{\mathrm{dense}}=\left\{({\mathbf{x}}_i,{\mathbf{x}}_i^{\prime })|{\mathbf{x}}_i\in \mathcal{G},{\mathbf{x}}_i^{\prime }=T_{\mathrm{total}}\left({\mathbf{x}}_i\right),{\mathbf{x}}_i^{\prime }\in T\right\}.$$

(12)

The automated correspondence generation pipeline produces the large-scale coarse dataset ${\mathcal{D}}_c$.

3.1.2. Preferred Correspondence Selection

While the automatically generated dense correspondence set provides extensive spatial coverage, it inevitably contains a high proportion of low-quality candidates due to the synthetic nature of the geometric transformations, as well as points situated in weakly textured or repetitive regions that offer limited discriminative information. To distill a subset of semantically salient and geometrically reliable correspondences, we implement a two-stage selection strategy combining automated pre-filtering and expert-in-the-loop refinement.

Automated Pre-Filtering

A multi-index joint filtering mechanism is designed to rapidly eliminate low-quality candidates prior to expert review. The evaluation metrics are defined as follows.

(1) Local Texture Richness: For a candidate point p, we define its local texture richness as the mean gradient magnitude within its neighborhood:

$$\mathrm{Texture}\left(p\right)={\displaystyle \frac{1}{\left|\mathcal{W}\right|}}\sum _{q\in \mathcal{W}\left(p\right)}∥\nabla I\left(q\right)∥,$$

(13)

where $\mathcal{W}\left(p\right)$ denotes a $16\times 16$ local window centered at p, $\left|\mathcal{W}\right|=256$ denotes the number of pixels in the window, and $\nabla I\left(q\right)={[I_x\left(q\right),I_y\left(q\right)]}^{\top }$ represents the image gradient vector at pixel q, with $I_x$ and $I_y$ denoting the partial derivatives of the image intensity I with respect to the horizontal and vertical directions, respectively. Candidates satisfying $\mathrm{Texture}\left(p\right)<{\tau }_{\mathrm{tex}}$ (with ${\tau }_{\mathrm{tex}}=10$) are discarded to filter out points in homogeneous areas such as water bodies or cloud cover.

(2) Local Distinctiveness (Harris Response): We employ the Harris corner detector to evaluate structural saliency:

$$R\left(p\right)=det\left(\mathbf{M}\right)-k·{\mathrm{trace}}^2\left(\mathbf{M}\right),$$

(14)

where $\mathbf{M}$ is the structure tensor (autocorrelation matrix):

$$\mathbf{M}=g\ast \left[\begin{array}{cc}{I}_x^2& I_x{I}_y\\ I_x{I}_y& I_y^2\end{array}\right],$$

(15)

in which g denotes a Gaussian weighting window, ∗ denotes the convolution operator, $I_x^2$, $I_y^2$, and $I_x{I}_y$ denote the squared horizontal gradient, squared vertical gradient, and cross-gradient terms, respectively, and $k=0.04$ is an empirical constant. Only candidates within the top $20\%$ of Harris response values are retained to ensure that the selected points possess robust corner or edge structures.

Through this joint pre-screening process, a large number of low-quality matching point pairs can be eliminated.

Expert-in-the-Loop Refinement

After automated pre-filtering, the remaining candidate correspondences are further examined through an expert-in-the-loop validation procedure. Three experts with experience in photogrammetry and remote sensing independently inspect the candidate regions in each satellite–UAV image pair. During this process, the experts are asked to select regions that are both geometrically stable and semantically persistent across the two images, such as building corners, road intersections, terrain boundaries, and other long-term landmarks. Ambiguous areas caused by weak texture, repetitive patterns, transient shadows, seasonal vegetation changes, cloud cover, or severe occlusion are rejected.

For the q-th candidate correspondence in the p-th image pair, the vote of the m-th expert is denoted as $v_{pq}^{\left(m\right)}\in \{0,1\}$, where $v_{pq}^{\left(m\right)}=1$ means that the expert considers this candidate reliable and $v_{pq}^{\left(m\right)}=0$ otherwise, with $m\in \{1,2,3\}$. We adopt a simple majority-voting rule to determine the final meta-label:

$$y_{pq}^{\mathrm{meta}}=\mathbb{I}\left({\displaystyle \sum _{m=1}^3}{v}_{pq}^{\left(m\right)}\ge 2\right),$$

(16)

where $\mathbb{I}(·)$ denotes the indicator function. A candidate correspondence is regarded as reliable only when it is selected by at least two experts. Candidates selected by only one expert, or by none of the experts, are not included in the preferred positive correspondence set. This two-out-of-three rule suppresses subjective single-annotator bias and ensures that the retained correspondences reflect consistent expert agreement.

For each image pair, the positively selected correspondences are further checked under a spatial distribution constraint. Specifically, when too many positive candidates concentrate in a small highly textured region, only a subset is retained so that the final preferred points are distributed as uniformly as possible over the image. This prevents the Saliency Judgment Network from overfitting to local texture clusters and encourages it to learn reliable correspondence selection over the whole scene. In practice, each validated image pair contains approximately 2000–3000 preferred positive correspondences after expert voting and spatial balancing. On average, each expert required approximately 3 min to verify one image pair, and the annotation of the entire meta-dataset could be completed within two to three working days.

The relationship between the coarse dataset and the expert-validated meta-dataset is therefore defined at the image-pair level. The coarse dataset ${\mathcal{D}}_c$ contains approximately $50,000$ automatically generated image pairs, while the meta-dataset ${\mathcal{D}}_m$ consists of 500 image pairs selected from ${\mathcal{D}}_c$ and further annotated by the experts:

$${\mathcal{D}}_m={\left\{\left(I_p^{\mathrm{src}},I_p^{\mathrm{tgt}},{\mathcal{M}}_p^{\mathrm{meta}}\right)\right\}}_{p=1}^{500},{\mathcal{D}}_m\subset {\mathcal{D}}_c.$$

(17)

Here, $I_p^{\mathrm{src}}$ and $I_p^{\mathrm{tgt}}$ denote the source and target images of the p-th meta pair, respectively. The expert-validated correspondence set associated with this pair is defined as

$${\mathcal{M}}_p^{\mathrm{meta}}={\left\{\left({\mathbf{x}}_{pq}^{\mathrm{src}},{\mathbf{x}}_{pq}^{\mathrm{tgt}},y_{pq}^{\mathrm{meta}}\right)\right\}}_{q=1}^{N_p},$$

(18)

where ${\mathbf{x}}_{pq}^{\mathrm{src}}$ and ${\mathbf{x}}_{pq}^{\mathrm{tgt}}$ denote the source and target coordinates of the q-th candidate correspondence in the p-th image pair, $y_{pq}^{\mathrm{meta}}\in \{0,1\}$ is the expert-derived meta-label, and $N_p$ is the number of candidate correspondences evaluated in that pair. In this formulation, $y_{pq}^{\mathrm{meta}}=1$ indicates a reliable and salient correspondence agreed upon by at least two experts, whereas $y_{pq}^{\mathrm{meta}}=0$ indicates an unreliable or insufficiently agreed candidate. The positive subset

$${\mathcal{M}}_{p,+}^{\mathrm{meta}}=\left\{\left({\mathbf{x}}_{pq}^{\mathrm{src}},{\mathbf{x}}_{pq}^{\mathrm{tgt}}\right)\mid y_{pq}^{\mathrm{meta}}=1\right\}$$

(19)

is used as the preferred positive correspondence set for qualitative visualization and for constructing reliability-aware meta-batches. During bi-level meta-learning, both positive and negative expert-derived labels in ${\mathcal{M}}_p^{\mathrm{meta}}$ are used in the meta-loss, as defined in Equation (45).

Figure 2 illustrates representative annotation examples from ${\mathcal{D}}_m$. The selected positive correspondences are concentrated on persistent semantic structures that can be reliably identified across satellite and UAV imagery, while ambiguous candidates in weakly textured or temporally unstable regions are excluded from the preferred correspondence set.

3.2. Network Architecture

As shown in Figure 3, the proposed framework comprises two principal components: (1) a CNN-Attention feature matching module ${\Phi }_{\mathsf{\omega }}$ that extracts discriminative descriptors and establishes initial correspondences, and (2) a Saliency Judgment Network ${\mathcal{S}}_{\mathsf{\psi }}$ optimized through a bi-level meta-learning strategy. In the inner level, the matcher is adapted on the automatically generated coarse dataset ${\mathcal{D}}_c$ under the guidance of saliency-weighted correspondence losses. In the outer level, the saliency network is updated according to the performance of the adapted matcher on the expert-validated meta-dataset ${\mathcal{D}}_m$. This formulation enables the saliency network to learn which correspondences are useful for improving registration reliability, rather than merely selecting matches according to raw confidence scores. The specific input resolution, feature-grid stride, model hyperparameters, and optimization settings are reported in Section 4.2.

3.2.1. CNN-Attention Feature Matching Module

Feature extraction. Given a source image $I^{\mathrm{src}}$ and a target image $I^{\mathrm{tgt}}$, we use a shared ResNet backbone together with a feature pyramid network (FPN) [31,32] to extract multi-scale convolutional features. The FPN fuses hierarchical features from different backbone stages and projects them to a unified descriptor dimension. The feature maps used for matching are denoted as

$$F_c^{\mathrm{src}}\in {\mathbb{R}}^{H_c\times W_c\times d},F_c^{\mathrm{tgt}}\in {\mathbb{R}}^{H_c\times W_c\times d},$$

(20)

where $H_c$ and $W_c$ denote the spatial size of the matching feature grid, and d is the descriptor dimension. The corresponding grid stride is denoted as ${\rho }_c$. Since the proposed framework does not include an additional fine-level coordinate refinement module, each output correspondence is represented by the center of its associated feature-grid cell.

The coordinate of a token at grid location $(u_i,v_i)$ is defined as the center of the corresponding feature-grid cell:

$${\mathbf{p}}_i={\left[{\rho }_c\left(u_i+{\displaystyle \frac{1}{2}}\right),{\rho }_c\left(v_i+{\displaystyle \frac{1}{2}}\right)\right]}^{\top }.$$

(21)

All token coordinates are represented in the resized input-image coordinate system. When evaluation or visualization is performed at the original image size, the predicted coordinates are mapped back using the corresponding resizing scale.

A schematic illustration of the CNN-Attention feature matching module is provided in Figure 4. The module first extracts multi-scale CNN-FPN features, then performs contextual feature enhancement, and finally establishes putative correspondences through dual-softmax matching.

Contextual feature enhancement. The dense feature maps are flattened into token sequences

$$X_0^{\mathrm{src}}={\left\{{\mathbf{x}}_{i,0}^{\mathrm{src}}\right\}}_{i=1}^{N_s}\in {\mathbb{R}}^{N_s\times d},X_0^{\mathrm{tgt}}={\left\{{\mathbf{x}}_{j,0}^{\mathrm{tgt}}\right\}}_{j=1}^{N_t}\in {\mathbb{R}}^{N_t\times d},$$

(22)

where $N_s=H_c{W}_c$ and $N_t=H_c{W}_c$ denote the numbers of source and target tokens, respectively. The image coordinate locations associated with the i-th source token and the j-th target token are denoted as ${\mathbf{p}}_i^{\mathrm{src}}$ and ${\mathbf{p}}_j^{\mathrm{tgt}}$. Positional encodings are added to the token features before attention is applied.

The feature interaction module contains stacked self-attention and cross-attention layers [33,34].  At the ℓ-th layer, self-attention first aggregates intra-image context, and cross-attention then exchanges information between the two images:

$${\overline{X}}_{\ell }^{\mathrm{src}}=X_{\ell -1}^{\mathrm{src}}+{SelfAttn}_{\ell }^{\mathrm{src}}\left(X_{\ell -1}^{\mathrm{src}}\right),$$

(23)

$${\overline{X}}_{\ell }^{\mathrm{tgt}}=X_{\ell -1}^{\mathrm{tgt}}+{SelfAttn}_{\ell }^{\mathrm{tgt}}\left(X_{\ell -1}^{\mathrm{tgt}}\right),$$

(24)

$$X_{\ell }^{\mathrm{src}}={\overline{X}}_{\ell }^{\mathrm{src}}+{CrossAttn}_{\ell }^{\mathrm{src}}\left({\overline{X}}_{\ell }^{\mathrm{src}},{\overline{X}}_{\ell }^{\mathrm{tgt}}\right),$$

(25)

$$X_{\ell }^{\mathrm{tgt}}={\overline{X}}_{\ell }^{\mathrm{tgt}}+{CrossAttn}_{\ell }^{\mathrm{tgt}}\left({\overline{X}}_{\ell }^{\mathrm{tgt}},{\overline{X}}_{\ell }^{\mathrm{src}}\right).$$

(26)

Here, $SelfAttn\left(X\right)$ denotes multi-head self-attention using X as query, key, and value. $CrossAttn(X,Y)$ denotes multi-head cross-attention using X as the query sequence and Y as the key–value sequence. For each attention head, the scaled dot-product attention is

$$Attention(Q,K,V)=softmax\left({\displaystyle \frac{Q{K}^{\top }}{\sqrt{d_k}}}\right)V,$$

(27)

where Q, K, and V denote query, key, and value matrices, respectively, and $d_k$ is the channel dimension of each attention head. After the interaction layers, the output sequences are reshaped back to dense feature maps, denoted as ${\tilde{F}}_c^{\mathrm{src}}$ and ${\tilde{F}}_c^{\mathrm{tgt}}$.

Correspondence establishment via feature matching. Let ${\left\{{\mathbf{f}}_i^{\mathrm{src}}\right\}}_{i=1}^{N_s}$ and ${\left\{{\mathbf{f}}_j^{\mathrm{tgt}}\right\}}_{j=1}^{N_t}$ denote the enhanced descriptors obtained from ${\tilde{F}}_c^{\mathrm{src}}$ and ${\tilde{F}}_c^{\mathrm{tgt}}$, respectively. Each descriptor is ${\ell }_2$-normalized before similarity computation. The pairwise cosine similarity is

$$S_{ij}={\displaystyle \frac{{\left({\mathbf{f}}_i^{\mathrm{src}}\right)}^{\top }{\mathbf{f}}_j^{\mathrm{tgt}}}{\parallel {\mathbf{f}}_i^{\mathrm{src}}{\parallel }_2{\parallel {\mathbf{f}}_j^{\mathrm{tgt}}\parallel }_2}},i=1,\dots ,N_s,j=1,\dots ,N_t.$$

(28)

A dual-softmax operation is applied to obtain the matching confidence matrix:

$$P_{ij}=softmax{\left(S_{i,:}/\tau \right)}_j·softmax{\left(S_{:,j}/\tau \right)}_i,$$

(29)

where $\tau$ is the temperature parameter. A token pair $(i,j)$ is accepted as a putative correspondence when it satisfies

$$P_{ij}>{\theta }_p,j=arg\underset{j^{\prime }}{max}{P}_{i{j}^{\prime }},i=arg\underset{i^{\prime }}{max}{P}_{i^{\prime }j},$$

(30)

where ${\theta }_p$ is the matching confidence threshold. The resulting putative correspondence set is

$$\mathcal{C}={\left\{r_l=\left(i_l,j_l,{\mathbf{p}}_l^{\mathrm{src}},{\mathbf{p}}_l^{\mathrm{tgt}},P_l,{\mathbf{f}}_l^{\mathrm{src}},{\mathbf{f}}_l^{\mathrm{tgt}}\right)\right\}}_{l=1}^M,$$

(31)

where ${\mathbf{p}}_l^{\mathrm{src}}={\mathbf{p}}_{i_l}^{\mathrm{src}}$, ${\mathbf{p}}_l^{\mathrm{tgt}}={\mathbf{p}}_{j_l}^{\mathrm{tgt}}$, $P_l=P_{i_l{j}_l}$, ${\mathbf{f}}_l^{\mathrm{src}}={\mathbf{f}}_{i_l}^{\mathrm{src}}$, and ${\mathbf{f}}_l^{\mathrm{tgt}}={\mathbf{f}}_{j_l}^{\mathrm{tgt}}$.

Training objective for feature matching. The coarse dataset ${\mathcal{D}}_c$ provides geometric supervision because each synthesized image pair has a known transformation $T_{\mathrm{total}}$. Before assigning labels, $T_{\mathrm{total}}$ is converted to the resized input coordinate system. For a sampled token pair $(i,j)$, the binary geometric label is defined as

$$Y_{ij}=\mathbb{I}\left({∥{\mathbf{p}}_j^{\mathrm{tgt}}-T_{\mathrm{total}}^{\mathrm{res}}\left({\mathbf{p}}_i^{\mathrm{src}}\right)∥}_2\le {ϵ}_{\mathrm{gt}}\right),$$

(32)

where $T_{\mathrm{total}}^{\mathrm{res}}$ denotes the transformation in the resized input coordinate system, and ${ϵ}_{\mathrm{gt}}$ is the positive-label tolerance. Let $\mathsf{\Omega }$ denote the sampled set of positive and negative token pairs used for supervised matcher training. To avoid ambiguity between the loss of an individual token pair and the batch-level matching objective, we first define the local pairwise matching loss as

$${\ell }_{\mathrm{local},ij}=-\left[{\alpha }_{\mathrm{focal}}{Y}_{ij}{(1-P_{ij})}^{\gamma }log(P_{ij}+{\epsilon }_p)+(1-{\alpha }_{\mathrm{focal}})(1-Y_{ij})P_{ij}^{\gamma }log(1-P_{ij}+{\epsilon }_p)\right].$$

(33)

Here, ${\ell }_{\mathrm{local},ij}$ denotes the focal loss of a single source–target token pair $(i,j)$, ${\alpha }_{\mathrm{focal}}$ is the class-balancing factor, $\gamma$ is the focusing parameter, and ${\epsilon }_p$ is used for numerical stability. The overall matching loss is then obtained by averaging the local pairwise losses over all sampled token pairs:

$${\mathcal{L}}_{\mathrm{match}}={\displaystyle \frac{1}{\left|\mathsf{\Omega }\right|}}\sum _{(i,j)\in \mathsf{\Omega }}{\ell }_{\mathrm{local},ij}.$$

(34)

Therefore, ${\ell }_{\mathrm{local},ij}$ measures the supervision signal of one candidate token pair, whereas ${\mathcal{L}}_{\mathrm{match}}$ is the batch-level objective used to train the feature matching module. For the l-th putative correspondence $r_l=(i_l,j_l,{\mathbf{p}}_l^{\mathrm{src}},{\mathbf{p}}_l^{\mathrm{tgt}},P_l,{\mathbf{f}}_l^{\mathrm{src}},{\mathbf{f}}_l^{\mathrm{tgt}})$, we write

$${\ell }_{\mathrm{local},l}={\ell }_{\mathrm{local},i_l{j}_l}.$$

(35)

3.2.2. Saliency Judgment and Bi-Level Optimization

Although the feature matching module generates confidence-ranked putative correspondences, high matching confidence does not necessarily imply geometric reliability in heterogeneous satellite–UAV imagery. Matches on transient shadows, seasonal vegetation, repetitive textures, water surfaces, or weakly structured regions may still degrade transformation estimation. We therefore introduce a Saliency Judgment Network to estimate correspondence-level reliability and guide the matcher toward geometrically stable regions.

Saliency network architecture. The Saliency Judgment Network ${\mathcal{S}}_{\mathsf{\psi }}$ is implemented as a lightweight MLP. For the l-th putative correspondence $r_l\in \mathcal{C}$, the saliency input is

$${\mathbf{x}}_l=\left[{\mathbf{f}}_l^{\mathrm{src}}\parallel {\mathbf{f}}_l^{\mathrm{tgt}}\parallel c_l\right]\in {\mathbb{R}}^{2d+1},c_l=-log(P_l+{\epsilon }_p).$$

(36)

The cue $c_l$ is computed only from the predicted matching confidence and is therefore available during both training and inference. A smaller $c_l$ corresponds to higher matching confidence. We use $c_l$ rather than ${\mathcal{L}}_{\mathrm{match}}$ as the saliency input because ${\mathcal{L}}_{\mathrm{match}}$ is a batch-level objective, while the SJN requires a correspondence-level confidence cue. The saliency score is

$$s_l={\mathcal{S}}_{\mathsf{\psi }}\left({\mathbf{x}}_l\right)=\sigma \left({MLP}_{\mathsf{\psi }}\left({\mathbf{x}}_l\right)\right),$$

(37)

where $s_l$ represents the estimated reliability of correspondence $r_l$.

Differentiable correspondence selection. During training, hard correspondence selection is approximated by a binary Gumbel-softmax relaxation [35,36]:

$$z_l={\displaystyle \frac{exp\left((log(s_l+{\epsilon }_g)+g_l^1)/ϵ\right)}{exp\left((log(s_l+{\epsilon }_g)+g_l^1)/ϵ\right)+exp\left((log(1-s_l+{\epsilon }_g)+g_l^0)/ϵ\right)}},$$

(38)

where $g_l^1$ and $g_l^0$ are independent samples from $\mathrm{Gumbel}(0,1)$, $ϵ$ is the Gumbel-softmax temperature, and ${\epsilon }_g$ ensures numerical stability. During inference, Gumbel noise is not used; correspondences are ranked deterministically by $s_l$.

Bi-level meta-learning framework. The proposed saliency-guided training is formulated as a bi-level meta-learning problem. The objective is to learn saliency parameters $\mathsf{\psi }$ such that the saliency-weighted correspondences selected from the coarse dataset ${\mathcal{D}}_c$ can produce a matcher that performs well on the expert-validated meta-dataset ${\mathcal{D}}_m$. In this sense, ${\mathcal{S}}_{\mathsf{\psi }}$ is not trained as an isolated binary classifier; instead, it is optimized according to the downstream registration-oriented behavior of the adapted matcher.

For a coarse batch from ${\mathcal{D}}_c$, let ${\mathcal{C}}_c={\left\{r_l^c\right\}}_{l=1}^{M_c}$ denote the putative correspondences produced by the current matcher. Each correspondence $r_l^c$ corresponds to a token pair $(i_l,j_l)$ and has a geometric label

$$y_l^c=Y_{i_l{j}_l}^c.$$

(39)

The local loss of the l-th coarse putative correspondence is defined as

$${\ell }_{\mathrm{local},l}^c={\ell }_{\mathrm{local},i_l{j}_l}^c={\ell }_{\mathrm{local}}\left(P_l^{c,\mathsf{\omega }},y_l^c\right),$$

(40)

where $P_l^{c,\mathsf{\omega }}$ is the matching confidence of the l-th coarse correspondence predicted by the matcher ${\Phi }_{\mathsf{\omega }}$. The inner-level objective updates the matcher using saliency-weighted local correspondence losses:

$${\mathcal{L}}_{\mathrm{inner}}(\mathsf{\omega },\mathsf{\psi })={\displaystyle \frac{1}{M_c}}{\displaystyle \sum _{l=1}^{M_c}}{z}_l^c{\ell }_{\mathrm{local},l}^c.$$

(41)

Thus, ${\mathcal{L}}_{\mathrm{inner}}$ is a saliency-weighted version of the local correspondence losses.

To make the bi-level update both explicit and implementable, we use a first-order meta-gradient approximation. For each coarse correspondence, we first compute the per-correspondence matcher gradient and stop its gradient when forming the one-step adapted matcher:

$${\tilde{\mathbf{g}}}_l^c=sg\left({\nabla }_{\mathsf{\omega }}{\ell }_{\mathrm{local},l}^c\right),$$

(42)

where $sg(·)$ denotes the stop-gradient operation. The adapted matcher parameters are then obtained by

$${\mathsf{\omega }}^{\prime }\left(\mathsf{\psi }\right)=\mathsf{\omega }-{\displaystyle \frac{\alpha }{M_c}}{\displaystyle \sum _{l=1}^{M_c}}{z}_l^c\left(\mathsf{\psi }\right){\tilde{\mathbf{g}}}_l^c.$$

(43)

Here, $\alpha$ is the inner-level learning rate. This formulation retains the gradient path from the outer meta-loss to $\mathsf{\psi }$ through the saliency weights $z_l^c\left(\mathsf{\psi }\right)$, i.e., through $\partial z_l^c/\partial \mathsf{\psi }$, while avoiding exact second-order Hessian–vector products through the matcher gradient.

For a meta-batch from ${\mathcal{D}}_m$, let ${\mathcal{C}}_m={\left\{r_l^m\right\}}_{l=1}^{M_m}$ denote expert-validated candidate correspondences. Each correspondence has a binary reliability label $y_l^m\in \{0,1\}$ determined by the expert validation protocol. Since $y_l^m$ is assigned to a candidate correspondence, it is interpreted as a correspondence-level reliability label. To make the meta-loss implementable on the feature grid, each expert-validated coordinate pair $({\mathbf{x}}_l^{m,\mathrm{src}},{\mathbf{x}}_l^{m,\mathrm{tgt}})$ is mapped to its nearest source and target feature-grid tokens:

$$i_l^m=arg\underset{i}{min}{∥{\mathbf{p}}_i^{\mathrm{src}}-{\mathbf{x}}_l^{m,\mathrm{src}}∥}_2,j_l^m=arg\underset{j}{min}{∥{\mathbf{p}}_j^{\mathrm{tgt}}-{\mathbf{x}}_l^{m,\mathrm{tgt}}∥}_2,P_l^{m,{\mathsf{\omega }}^{\prime }\left(\mathsf{\psi }\right)}=P_{i_l^m{j}_l^m}^{{\mathsf{\omega }}^{\prime }\left(\mathsf{\psi }\right)}.$$

(44)

The outer-level meta-objective then evaluates whether the adapted matcher assigns high confidence to expert-validated reliable correspondences and low confidence to unreliable ones:

$${\mathcal{L}}_{\mathrm{meta}}\left(\mathsf{\psi }\right)={\displaystyle \frac{1}{M_m}}{\displaystyle \sum _{l=1}^{M_m}}{\ell }_{\mathrm{BCE}}\left(P_l^{m,{\mathsf{\omega }}^{\prime }\left(\mathsf{\psi }\right)},y_l^m\right).$$

(45)

The saliency parameters are updated by minimizing the meta-loss:

$$\mathsf{\psi }\leftarrow \mathsf{\psi }-\beta {\nabla }_{\mathsf{\psi }}{\mathcal{L}}_{\mathrm{meta}}\left(\mathsf{\psi }\right),$$

(46)

where $\beta$ is the outer-level learning rate. In practice, Equation (43) provides a one-step unrolled first-order bi-level update. The outer gradient is implemented as

$${\nabla }_{\mathsf{\psi }}{\mathcal{L}}_{\mathrm{meta}}={\displaystyle \frac{\partial {\mathcal{L}}_{\mathrm{meta}}}{\partial {\mathsf{\omega }}^{\prime }}}{\displaystyle \frac{\partial {\mathsf{\omega }}^{\prime }}{\partial {\mathbf{z}}^c}}{\displaystyle \frac{\partial {\mathbf{z}}^c}{\partial \mathsf{\psi }}},$$

(47)

while the exact Hessian–vector terms inside ${\tilde{\mathbf{g}}}_l^c$ are omitted by the stop-gradient operation. The exact number of unrolled inner updates and the optimizer settings are specified in Section 4.2.

Matcher update with spatial diversity regularization. After the outer-level update of $\mathsf{\psi }$, the matcher is further optimized using the saliency-weighted matching loss and a spatial diversity regularizer. Let ${\mathcal{C}}_{c,d}$ denote the subset of coarse correspondences used for diversity regularization. The diversity loss is

$${\mathcal{L}}_{\mathrm{div}}={\displaystyle \frac{1}{max\left(\right|{\mathcal{C}}_{c,d}\left|\right(|{\mathcal{C}}_{c,d}|-1),1)}}\sum _{\begin{array}{c}r,t\in {\mathcal{C}}_{c,d}\\ r\ne t\end{array}}exp\left(-{\displaystyle \frac{\parallel {\mathbf{p}}_r^{c,\mathrm{src}}-{\mathbf{p}}_t^{c,\mathrm{src}}{\parallel }_2^2}{2{\sigma }_d^2}}\right)z_r^c{z}_t^c.$$

(48)

The matcher is updated by minimizing

$${\mathcal{L}}_{\mathsf{\omega }}={\mathcal{L}}_{\mathrm{inner}}+{\lambda }_{\mathrm{div}}{\mathcal{L}}_{\mathrm{div}},$$

(49)

where ${\lambda }_{\mathrm{div}}$ controls the strength of the diversity regularization.

The bi-level meta-learning framework is shown in Figure 5 and Algorithm 1.

Algorithm 1 Bi-level meta-learning for saliency-aware matching

Require:  Coarse dataset ${\mathcal{D}}_c$, meta-dataset ${\mathcal{D}}_m$, matcher ${\Phi }_{\mathsf{\omega }}$, saliency network ${\mathcal{S}}_{\mathsf{\psi }}$, learning rates $\alpha$ and $\beta$ Ensure:  Optimized parameters ${\mathsf{\omega }}^{*}$ and ${\mathsf{\psi }}^{*}$   1: for each training iteration do   2:    Sample a coarse batch from ${\mathcal{D}}_c$   3:    Compute $F_c^{\mathrm{src}}$, $F_c^{\mathrm{tgt}}$, ${\tilde{F}}_c^{\mathrm{src}}$, and ${\tilde{F}}_c^{\mathrm{tgt}}$ using Equations (20)–(26)   4:    Compute S and P using Equations (28) and (29)   5:    Construct ${\mathcal{C}}_c={\left\{r_l^c\right\}}_{l=1}^{M_c}$ using Equation (30)   6:    Assign labels $y_l^c=Y_{i_l{j}_l}^c$ using Equations (32) and (39)   7:    Compute local correspondence losses ${\ell }_{\mathrm{local},l}^c$ using Equation (40)   8:    Compute ${\mathbf{x}}_l^c$, $s_l^c$, and $z_l^c$ using Equations (36)–(38)   9:    Compute the stopped per-correspondence gradients ${\tilde{\mathbf{g}}}_l^c$ using Equation (42) 10:    Inner level: compute ${\mathcal{L}}_{\mathrm{inner}}$ and form the first-order adapted matcher ${\mathsf{\omega }}^{\prime }\left(\mathsf{\psi }\right)$ using Equations (41) and (43) 11:    Sample a meta-batch from ${\mathcal{D}}_m$ and construct ${\mathcal{C}}_m={\left\{(r_l^m,y_l^m)\right\}}_{l=1}^{M_m}$ 12:    Outer level: evaluate ${\Phi }_{{\mathsf{\omega }}^{\prime }\left(\mathsf{\psi }\right)}$ on ${\mathcal{C}}_m$ and compute ${\mathcal{L}}_{\mathrm{meta}}$ using Equation (45) 13:    Update $\mathsf{\psi }$ using Equation (46) 14:    Recompute $s_l^c$ and $z_l^c$ with the updated $\mathsf{\psi }$ 15:    Compute ${\mathcal{L}}_{\mathrm{div}}$ and ${\mathcal{L}}_{\mathsf{\omega }}$ using Equations (48) and (49) 16:    Update $\mathsf{\omega }$ by descending ${\nabla }_{\mathsf{\omega }}{\mathcal{L}}_{\mathsf{\omega }}$ 17: end for 18: return ${\mathsf{\omega }}^{*}$ and ${\mathsf{\psi }}^{*}$

3.3. Inference Pipeline

During inference, the proposed framework operates in a feed-forward manner. The method outputs feature-grid correspondences represented by cell-center coordinates, and no additional fine-level refinement is applied.

Stage 1: Feature extraction and initial matching. The CNN-Attention feature matching module computes enhanced descriptors and the matching confidence matrix P. Candidate correspondences satisfying Equation (30) are collected into

$$\mathcal{C}={\left\{r_l=\left({\mathbf{p}}_l^{\mathrm{src}},{\mathbf{p}}_l^{\mathrm{tgt}},P_l,{\mathbf{f}}_l^{\mathrm{src}},{\mathbf{f}}_l^{\mathrm{tgt}}\right)\right\}}_{l=1}^M.$$

(50)

Stage 2: Saliency scoring. For each $r_l\in \mathcal{C}$, the saliency input is

$${\mathbf{x}}_l^{\inf }=\left[{\mathbf{f}}_l^{\mathrm{src}}\parallel {\mathbf{f}}_l^{\mathrm{tgt}}\parallel c_l\right],c_l=-log(P_l+{\epsilon }_p),$$

(51)

and the saliency score is

$$s_l={\mathcal{S}}_{\mathsf{\psi }}\left({\mathbf{x}}_l^{\inf }\right).$$

(52)

Stage 3: Saliency-based correspondence selection. If $M=0$, the image pair is regarded as a registration failure. Otherwise, we compute

$${\theta }_s={\mu }_s+{\sigma }_s,$$

(53)

where ${\mu }_s$ and ${\sigma }_s$ are the mean and standard deviation of ${\left\{s_l\right\}}_{l=1}^M$. The preliminary selected set is

$${\mathcal{C}}_{\theta }=\{r_l\in \mathcal{C}\mid s_l\ge {\theta }_s\}.$$

(54)

The final selected set is

$${\mathcal{C}}^{*}=\left\{\begin{array}{cc}TopK(\mathcal{C},{\overline{K}}_{min};s),\hfill & |{\mathcal{C}}_{\theta }|<{\overline{K}}_{min},\hfill \\ TopK({\mathcal{C}}_{\theta },K_{max};s),\hfill & |{\mathcal{C}}_{\theta }|>K_{max},\hfill \\ {\mathcal{C}}_{\theta },\hfill & \mathrm{otherwise},\hfill \end{array}\right.$$

(55)

where ${\overline{K}}_{min}=min(K_{min},M)$. The values of $K_{min}$ and $K_{max}$ are given in Section 4.2.

Stage 4: Geometric verification. If $|{\mathcal{C}}^{*}|<4$, the image pair is regarded as a registration failure because homography estimation requires at least four correspondences. Otherwise, ${\mathcal{C}}^{*}$ is verified by RANSAC-based homography estimation [37]. Correspondences with a reprojection error larger than the threshold specified in Section 4.2 are treated as outliers. The retained inlier set is denoted as ${\mathcal{C}}^{\mathrm{final}}$.

Stage 5: Transformation estimation. Given ${\mathcal{C}}^{\mathrm{final}}$, the final homography matrix $\mathbf{H}\in {\mathbb{R}}^{3\times 3}$ is estimated using the Direct Linear Transform followed by least-squares refinement over the RANSAC inliers. The final correspondences and estimated transformation are mapped back to the original image coordinate system when reporting evaluation metrics or producing visualizations.

4. Experiments and Results

This section evaluates the proposed bi-level meta-learning framework under heterogeneous satellite–UAV matching conditions. We first describe the datasets and implementation details, then report quantitative comparisons with representative local-feature, sparse matching, semi-dense matching, and recent lightweight matching methods. We further analyze the plug-and-play compatibility of the proposed Saliency Judgment Network and evaluate the cross-domain generalization ability of the framework.

4.1. Datasets

We use two datasets in the experiments. RS-Hetero-50K is used as the primary benchmark for training, validation, and final testing, while FuJian-Mountain is used as an independent zero-shot test set to evaluate cross-domain generalization. To prevent data leakage, all RS-Hetero-50K splits are constructed at the geographic-tile level; image pairs from the same geographic tile are assigned to only one split. The expert-validated meta-dataset ${\mathcal{D}}_m$ is selected exclusively from the training partition and is never used for validation or final testing.

RS-Hetero-50K: RS-Hetero-50K is a self-built heterogeneous remote sensing image matching dataset containing approximately 50,000 satellite–UAV image pairs. The image pairs were collected or synthesized from remote sensing scenes acquired between 2018 and 2023, covering three representative terrain categories: urban scenes with dense buildings and structured road networks, suburban scenes with mixed residential, agricultural, and natural regions, and gobi scenes with sparse vegetation, weak texture, and repetitive rocky patterns. Each pair consists of a satellite reference image and a UAV-derived aerial image covering the same geographic region. The satellite images have a ground resolution of approximately 0.3–1.0 m/pixel, while the UAV images have a Ground Sampling Distance of approximately 0.5–2.0 m/pixel.

The dataset is partitioned as summarized in

Table 2. Dataset partitioning and usage. The 500-pair meta subset is selected from the training partition only; it is included in the 40,000 training pairs and is not an additional subset.

Subset	Pairs	Usage	Geographic Overlap with Test
RS-Hetero-50K training split, including the 500-pair meta subset	40,000	Matcher training on ${\mathcal{D}}_c$; source of ${\mathcal{D}}_m$	No
RS-Hetero-50K meta subset ${\mathcal{D}}_m$	500	SJN bi-level meta-training only	No
RS-Hetero-50K validation split	5000	Hyperparameter validation	No
RS-Hetero-50K test split	5000	Final in-domain evaluation	–
FuJian-Mountain	500	Independent zero-shot evaluation	No

. The training partition is used to train the matcher on automatically generated correspondences. The 500-pair meta-dataset is selected only from the training partition and is used for bi-level meta-learning of the Saliency Judgment Network. The validation and test partitions are geographically disjoint from the training and meta partitions. For homography-based evaluation, validation and test pairs are constructed or selected to be homography-compatible; samples with strong non-planar residual deformation are excluded from the reported homography metrics.

FuJian-Mountain. FuJian-Mountain is an independently collected mountainous test set containing 500 satellite–UAV image pairs from the Wuyi Mountain region in Fujian Province, China. This dataset is not used during training, validation, or meta-training, and it has no geographic overlap with RS-Hetero-50K. It contains scenes with complex relief, dense vegetation, seasonal appearance changes, and non-uniform illumination. The reference transformations are obtained from georeferencing information and manually checked control points. For quality control, each retained pair contains at least 12 spatially distributed control points inspected by two remote sensing experts, and only pairs whose fitted homography has a reprojection RMSE below 3 pixels in the resized evaluation coordinate system are included in the reported metrics. The control points are used only for constructing the evaluation reference and are not used for training or meta-training.

4.2. Implementation Details

Training configuration. The proposed framework is implemented in PyTorch v.2.4.0 [38]. Unless otherwise specified, all training experiments are conducted on four NVIDIA RTX 4090 GPUs. All input images are resized to $512\times 512$ pixels before being fed into the network. The CNN backbone in the feature matching module is ResNet-34 initialized with ImageNet-pretrained weights [39]. The FPN projects the fused descriptors to $d=256$ dimensions. Contextual feature interaction and dual-softmax matching are performed on the $1/4$ feature grid, where each image contains $128\times 128=16,384$ tokens. The grid stride is ${\rho }_c=4$ pixels. Since no additional fine-level refinement is used, each correspondence is represented by the center of its feature-grid cell. The maximum center quantization error is approximately ${\displaystyle \frac{\sqrt{2}}{2}}{\rho }_c=2.83$ pixels, which is below the 5-pixel threshold used for matching precision and RANSAC verification.

The contextual interaction module contains $N_c=4$ self-attention/cross-attention layers, and each attention layer uses $N_h=8$ heads. To reduce peak memory usage on the $1/4$ grid, self-attention, cross-attention, and dual-softmax matching are computed with memory-efficient block-wise implementation and mixed-precision training.

The Saliency Judgment Network ${\mathcal{S}}_{\mathsf{\psi }}$ is implemented as an MLP with hidden dimensions $[512,256,128]$ and a sigmoid output. Training is conducted in two stages. In the first stage, the matcher ${\Phi }_{\mathsf{\omega }}$ is trained on the coarse dataset ${\mathcal{D}}_c$ for 50 epochs using the focal matching loss in Equation (34). The batch size is set to 4 image pairs per GPU. In the second stage, we perform bi-level meta-learning for 30 epochs using both ${\mathcal{D}}_c$ and the expert-validated meta-dataset ${\mathcal{D}}_m$. For each iteration, the inner level uses a coarse batch from ${\mathcal{D}}_c$ to compute saliency-weighted correspondence losses and obtain the adapted matcher ${\mathsf{\omega }}^{\prime }\left(\mathsf{\psi }\right)$ through one unrolled inner update. The outer level evaluates the adapted matcher on a meta-batch from ${\mathcal{D}}_m$ and updates the saliency parameters $\mathsf{\psi }$ according to the meta-loss in Equation (45).

The inner-level learning rate is set to $\alpha =1\times {10}^{-3}$, and the outer-level learning rate is set to $\beta =5\times {10}^{-5}$. The matcher parameters are optimized with Adam [40] and a weight decay of ${10}^{-4}$. The focal-loss focusing parameter is $\gamma =2.0$, the focal-loss class-balancing factor is set to ${\alpha }_{\mathrm{focal}}=0.25$, the numerical stability term is ${\epsilon }_p={10}^{-8}$, and the dual-softmax temperature is $\tau =0.1$. In the Gumbel-softmax relaxation, the temperature is set to $ϵ=0.5$, and the stability term is set to ${\epsilon }_g={10}^{-10}$. The spatial diversity regularization weight is ${\lambda }_{\mathrm{div}}=0.1$, and the diversity scale is set to ${\sigma }_d=32$ pixels in the resized input coordinate system. To keep bi-level meta-learning computationally tractable, only one inner update is unrolled in each iteration. The first-order implementation retains gradients through the saliency weights $z_l^c\left(\mathsf{\psi }\right)$ but applies stop-gradient to the per-correspondence matcher gradients ${\tilde{\mathbf{g}}}_l^c$, as defined in Equations (42) and (43). The diversity loss is computed on the top-$K_d$ saliency-ranked correspondences with $K_d=min(M_c,2000)$.

Data augmentation. During training, we apply geometric and photometric augmentations to improve robustness to satellite–UAV appearance differences. Geometric augmentations include random rotation within $\pm {15}^{\circ }$, random scaling in the range $[0.5,2.0]$, and horizontal flipping. Photometric augmentations include random brightness adjustment within $\pm 20\%$, contrast adjustment in the range $[0.8,1.2]$, and additive Gaussian noise with standard deviation ${\sigma }_n\le 0.01$. These augmentations are applied only during training and are not used during validation or testing.

Baseline implementation. For comparison, we evaluate representative local-feature methods, sparse learned matchers, detector-free semi-dense matchers, and recent lightweight matching methods, including DELF, D2-Net, XFeat, LoFTR, Efficient LoFTR, SuperPoint+SuperGlue, and LightGlue. To improve fairness, trainable learning-based baselines with available training or fine-tuning recipes are adapted on the same RS-Hetero-50K training split used by the proposed matcher. The expert-validated meta-dataset ${\mathcal{D}}_m$ is not used by any baseline method; it is used only for the outer-level meta-update of the proposed SJN. For methods whose full training pipeline is unavailable or incompatible with the present setting, we use the official released model and configuration and evaluate them under the same preprocessing and RANSAC protocol. The training setting of each baseline is explicitly reported in

Table 3. Comparison of the proposed complete framework with representative image matching pipelines on RS-Hetero-50K. The training setting column specifies whether each baseline uses an official pretrained model or is fine-tuned on the RS-Hetero-50K training split.

Method	Paradigm	Training Setting	MP (%)	AUC@5 px	AUC@10 px	AUC@20 px
DELF [17]	Local feature	Official pretrained	69.1	14.4	32.1	57.9
D2-Net [16]	CNN local feature	Fine-tuned on train split	80.4	29.8	48.5	71.8
XFeat [20]	Lightweight local feature	Fine-tuned on train split	85.4	31.6	51.8	73.7
LoFTR [21]	Detector-free semi-dense	Fine-tuned on train split	89.8	35.1	54.3	75.3
Efficient LoFTR [24]	Efficient semi-dense matching	Fine-tuned on train split	90.2	36.4	55.6	75.9
SP + SG [18]	Sparse learned matching	Fine-tuned on train split	90.1	36.7	55.4	75.6
LightGlue [19]	Lightweight sparse matching	Fine-tuned on train split	91.2	36.9	55.9	76.2
Ours (Full)	Bi-level saliency-aware matching	Train split + meta subset	95.4	40.2	61.5	81.3

. All reported methods are evaluated on the same geographically disjoint RS-Hetero-50K test split. Predicted correspondences from all methods are mapped to the same resized evaluation coordinate system before computing MP and AUC. Unless a method has a mandatory internal resolution requirement, input images are resized to $512\times 512$ pixels for evaluation; for methods with an internal resizing strategy, the output correspondences are rescaled to the common evaluation coordinate system.

Inference configuration. For the proposed framework, both input images are resized to $512\times 512$ pixels during inference. Matching is performed on the $1/4$ grid, and each correspondence is represented by the center of its corresponding grid cell. The matching confidence threshold in Equation (30) is set to ${\theta }_p=0.2$. The positive-label tolerance in Equation (32) is set to ${ϵ}_{\mathrm{gt}}=5$ pixels in the resized input coordinate system. After the initial putative correspondence set $\mathcal{C}$ is obtained, the saliency score $s_l$ of each correspondence is computed by ${\mathcal{S}}_{\mathsf{\psi }}$ using Equation (51). The adaptive saliency threshold is ${\theta }_s={\mu }_s+{\sigma }_s$, where ${\mu }_s$ and ${\sigma }_s$ are computed from the saliency scores of the current image pair. The number of retained correspondences is constrained by $K_{min}=200$ and $K_{max}=2000$, consistent with Equation (55).

The selected correspondences are verified by RANSAC-based homography estimation. The reprojection-error threshold is set to 5 pixels in the resized $512\times 512$ coordinate system, and the maximum number of RANSAC iterations is set to 10,000. This 5-pixel threshold is consistent with the $1/4$ correspondence grid because the maximum center quantization error is approximately 2.83 pixels. If fewer than four correspondences are retained after saliency selection, the pair is counted as a failed registration. The final transformation is estimated from the RANSAC inliers using the Direct Linear Transform followed by least-squares refinement, and the estimated correspondences are mapped back to the original image coordinate system for evaluation.

Evaluation metrics. We report two types of metrics. First, matching precision (MP) measures the percentage of predicted correspondences whose geometric error is within 5 pixels in the resized $512\times 512$ coordinate system after projection by the reference transformation. This criterion is consistent with the $1/4$ output grid and the absence of a fine refinement stage. Second, we report AUC@t px with thresholds $t\in \{5,10,20\}$ pixels. Let $e_H$ denote the corner reprojection error of the estimated homography with respect to the reference homography in the resized evaluation coordinate system. AUC@t px is computed as the normalized area under the cumulative distribution of $e_H$ from 0 to t pixels and is reported as a percentage.

4.3. Quantitative Evaluation on RS-Hetero-50K

Overall performance of the complete framework. We first evaluate the complete proposed framework, consisting of the CNN-Attention feature matching module and the Saliency Judgment Network, on RS-Hetero-50K. The compared methods include DELF, D2-Net, XFeat, LoFTR, Efficient LoFTR, SuperPoint+SuperGlue, and LightGlue, covering local-feature, sparse matching, detector-free semi-dense matching, efficient semi-dense matching, and recent lightweight matching paradigms.

As shown in Table 3, the proposed full framework achieves the best performance among the evaluated methods. Compared with conventional local-feature and CNN-feature baselines, modern learned matchers obtain substantially better results owing to stronger feature representations and more effective correspondence estimation. However, heterogeneous satellite–UAV registration remains challenging because high matching confidence does not always imply geometric reliability under cross-season, cross-view, cross-scale, and cross-sensor variations. By combining cross-image contextual feature enhancement with bi-level meta-learned saliency selection, the proposed framework improves both correspondence-level precision and transformation-level accuracy.

Plug-and-play compatibility analysis. To evaluate whether the proposed Saliency Judgment Network can be used with different backbone matchers, we integrate it into two representative pipelines: LoFTR and SuperPoint + SuperGlue (SP + SG). As shown in

Table 4. Compatibility of the proposed Saliency Judgment Network with different backbone matchers on RS-Hetero-50K.

Backbone	Saliency Module	MP (%)	AUC@5 px	AUC@10 px
LoFTR [21]	None	89.8	35.1	54.3
LoFTR	+ Proposed	94.2	38.6	59.1
SP + SG [18]	None	90.1	36.7	55.4
SP + SG	+ Proposed	91.8	37.1	56.8

, the saliency module consistently improves both matching precision and transformation accuracy. For LoFTR, MP increases from 89.8% to 94.2%, and AUC@10 px increases from 54.3 to 59.1. For SP + SG, MP increases from 90.1% to 91.8%, and AUC@10 px increases from 55.4 to 56.8. The improvement is larger for LoFTR, suggesting that dense or semi-dense matchers benefit more from saliency-guided filtering because they typically generate more candidate correspondences in ambiguous regions.

Analysis. The results in Table 3 show that the proposed framework improves performance by jointly enhancing feature representation and learning to suppress unreliable correspondences through bi-level meta-learning before geometric verification. The CNN-Attention module improves descriptor discriminability through multi-scale feature extraction and cross-image contextual interaction, while the Saliency Judgment Network prioritizes persistent and geometrically stable matches. The plug-and-play experiments in Table 4 further indicate that the saliency module can improve existing matchers, but the best performance is achieved when it is jointly used with the proposed CNN-Attention backbone.

4.4. Ablation Study on Selection Strategy

To verify that the performance improvement stems from bi-level meta-learned saliency selection rather than merely reducing the number of correspondences, we compare the proposed selection strategy with a random pruning baseline. Random-Prune uniformly removes correspondences until the retained number is comparable to that of the proposed saliency module. This comparison is conducted on three representative backbones to evaluate whether the meta-learned selection strategy is generally effective.

Analysis.

Table 5. Comparison of matching performance on the RS-Hetero-50K high-heterogeneity remote sensing dataset. MP denotes matching precision (%). Bold indicates best results per backbone group.

Method	Matches	MP (%)	AUC@5 px	AUC@10 px	AUC@20 px
LoFTR (Baseline) [21]	2231	89.8	35.1	54.3	75.3
LoFTR + Random-Prune	1562	88.4	33.2	52.1	73.8
LoFTR + Proposed	1577	94.2	38.6	59.1	79.6
SP + SG (Baseline) [18]	1794	90.1	36.7	55.4	75.6
SP + SG + Random-Prune	1256	89.5	35.1	53.8	74.2
SP + SG + Proposed	1099	91.8	37.1	56.8	77.9
LightGlue (Baseline) [19]	1650	91.2	36.9	55.9	76.2
LightGlue + Random-Prune	1155	90.6	35.4	54.3	74.9
LightGlue + Proposed	1210	93.5	37.8	58.3	78.5

shows that the proposed bi-level meta-learned saliency selection consistently improves matching precision and transformation accuracy, even though it reduces the number of retained correspondences. For LoFTR, the number of matches decreases from 2231 to 1577, while MP increases from 89.8% to 94.2%. Similar trends are observed for SP + SG and LightGlue. In contrast, Random-Prune removes a comparable number of correspondences but consistently degrades performance, indicating that the proposed module does not simply reduce the match count. Instead, it preferentially retains correspondences located on geometrically stable and semantically persistent structures.

The improvement is most evident for the LoFTR backbone because dense and semi-dense matchers tend to generate many correspondences in homogeneous or repetitive regions. These additional correspondences may increase match density but can also introduce structured outliers that degrade homography estimation. The Saliency Judgment Network, optimized through the outer-level meta-objective on expert-validated correspondences, suppresses such unreliable matches before RANSAC, allowing the geometric estimator to rely on a more stable subset of matches.

Figure 6 qualitatively compares the feature extraction and registration accuracy between the baseline LoFTR and our LoFTR + Proposed method across two representative scenarios. The first two columns visualize the spatial distribution of extracted correspondences. The third column presents the registration overlay generated using the homography matrix estimated from these correspondences. The baseline LoFTR tends to produce matches in weakly textured or repetitive regions, which introduces geometric instability and visible ghosting artifacts. In contrast, the proposed saliency-aware selection prioritizes correspondences on geometrically stable structures, thereby reducing overlay misalignment.

4.5. Terrain-Specific Breakdown Analysis

To further investigate the method’s behavior across different environments, we conducted terrain-specific analysis using the LoFTR backbone.

Table 6. Terrain-specific performance breakdown on RS-Hetero-50K (LoFTR backbone).

Terrain	Method	MP (%)	AUC@5 px	AUC@20 px
Urban	Baseline	91.3	38.2	78.4
	+ Proposed	95.7	41.3	82.1
Gobi	Baseline	86.4	31.5	71.2
	+ Proposed	92.1	36.8	77.5
Suburban	Baseline	88.7	33.8	74.3
	+ Proposed	93.4	37.1	78.9

presents results for urban, gobi, and suburban terrains.

Urban terrain achieves the highest absolute performance due to the abundance of geometric structures with well-defined corners, straight edges, and distinctive shapes. In gobi terrain, where weak texture and repetitive natural patterns dominate, the baseline achieves only 31.5% AUC@5 px. Our module improves this to 36.8%, representing a 16.8% relative gain. This improvement is primarily achieved by suppressing matches on homogeneous desert surfaces and repetitive rocky textures while preserving correspondences on terrain discontinuities, road traces, and other sparse but stable geometric structures. The suburban terrain presents intermediate difficulty, with a balanced mix of man-made and natural features.

To further illustrate the cross-terrain behavior of the proposed method, Figure 7 presents qualitative feature extraction results across mountainous and gobi environments. These two environments are intentionally contrasted because mountainous regions mainly test vegetation-induced seasonal variation, whereas gobi scenes mainly test weak texture and repetitive terrain. In mountainous regions, the baseline LoFTR generates numerous feature points on forest canopy and vegetated slopes that exhibit severe seasonal appearance changes. The proposed method suppresses these unstable correspondences and preserves matches on ridge lines, trail intersections, and rock formations that provide reliable geometric constraints. In gobi terrain, where repetitive rock patterns dominate, the baseline produces matches on visually similar surfaces that confuse the geometric estimator. The saliency network filters these ambiguous correspondences and concentrates on distinctive terrain discontinuities and man-made structures.

4.6. Robustness and Cross-Domain Generalization

To assess generalization capability beyond the training domain, we evaluate zero-shot transfer to the independent FuJian-Mountain dataset. This dataset is geographically disjoint from RS-Hetero-50K and is not used during matcher training, validation, or SJN meta-training.

Table 7. Zero-shot cross-domain generalization performance on FuJian-Mountain. Proposed variants are trained on RS-Hetero-50K and evaluated without target-domain fine-tuning.

Method	MP (%)	AUC@5 px	AUC@10 px	AUC@20 px
D2-Net [16]	62.4	9.8	15.3	21.8
LoFTR (Baseline) [21]	71.5	15.1	22.4	25.3
LoFTR + Proposed	84.2	28.6	42.3	59.6
SP + SG (Baseline) [18]	73.8	16.7	23.1	25.6
SP + SG + Proposed	82.1	27.1	40.8	57.9

reports the results under the same preprocessing, pixel-based AUC, and RANSAC settings used for the RS-Hetero-50K test split.

The results show that the Saliency Judgment Network remains effective under strong domain shifts caused by mountainous terrain, dense vegetation, and seasonal spectral changes. For the LoFTR backbone, AUC@5 px increases from 15.1 to 28.6, and MP increases from 71.5% to 84.2%. Similar improvements are observed for SP + SG. These gains indicate that the learned reliability criterion is not limited to the RS-Hetero-50K training areas, although broader validation across additional geographic regions remains necessary for a more comprehensive generalization assessment.

4.7. Computational Efficiency Analysis

To evaluate the computational feasibility of the proposed bi-level meta-learning framework, we report the overall model size, total inference latency, and total training time of the complete proposed model, i.e., the CNN-Attention feature matching module together with the Saliency Judgment Network (SJN). All measurements follow the implementation settings described in Section 4.2. During inference, both input images are resized to $512\times 512$ pixels, matching is performed on the $1/4$ feature grid, and no additional fine-level refinement module is used.

Model parameter count.

Table 8. Parameter count of the proposed complete framework.

Component	Parameter Count
ResNet-34 backbone	21.285 M
FPN	2.607 M
CNN-attention interaction module	2.109 M
Saliency Judgment Network (SJN)	0.428 M
Total	26.429 M

reports the parameter count of the proposed complete model. The ResNet-34 backbone is used without the ImageNet classification head. The FPN contains four $1\times 1$ lateral projection convolutions and four $3\times 3$ smoothing convolutions. The contextual interaction module contains $N_c=4$ layers, each consisting of one self-attention block and one cross-attention block with descriptor dimension $d=256$ and $N_h=8$ attention heads. The attention parameters are shared between the source and target streams, and no additional Transformer feed-forward network is used; this is the configuration used for the parameter count in Table 8. The SJN is implemented as an MLP with dimensions $513\to 512\to 256\to 128\to 1$.

The complete proposed model contains 26.429 M parameters. The SJN contributes only 0.428 M parameters, accounting for approximately 1.62% of the complete model. This indicates that the saliency judgment mechanism introduces only a small parameter overhead while enabling reliability-aware correspondence selection through bi-level meta-learning.

Overall inference and training cost. The complete model achieves an overall inference latency of 55.6 ms per image pair on a single NVIDIA RTX 4090 GPU under mixed-precision inference, excluding image I/O and visualization, corresponding to 17.9 FPS. The total training time of the complete framework is approximately 17 h on 4× NVIDIA RTX 4090 GPUs, including both the base matcher training stage and the subsequent bi-level meta-learning stage.

These results show that the proposed framework remains computationally feasible for remote sensing image registration. Since the SJN operates on correspondence-level meta-features rather than dense image features, it adds limited computational cost compared with the CNN-attention matching module. The overall throughput is suitable for visual map-matching and localization correction tasks, while high-frequency flight control can still rely on inertial or visual odometry modules and use the proposed matcher as a robust global correction component.

5. Discussion

The experimental results in Section 4 demonstrate that the proposed bi-level meta-learning framework improves both correspondence-level reliability and transformation-level registration accuracy under heterogeneous satellite–UAV matching conditions. As shown in Table 3, the complete framework achieves the best overall performance among the evaluated methods. The ablation results in Table 5 further show that Random-Prune reduces the number of correspondences but degrades performance, whereas the proposed Saliency Judgment Network retains fewer but more reliable matches. This indicates that the improvement is not caused by simple match reduction, but by bi-level meta-learned reliability-aware correspondence selection.

The terrain-specific and cross-domain results further illustrate the behavior and limitations of the proposed method. The largest relative gain appears in gobi terrain, where weak texture and repetitive patterns often produce ambiguous correspondences, while urban scenes achieve higher absolute accuracy due to stable man-made structures. The zero-shot results on FuJian-Mountain suggest that the learned reliability criterion can transfer to unseen mountainous scenes, but this result should still be interpreted within the satellite–UAV registration setting rather than as evidence of universal superiority across all natural-scene benchmarks. The computational analysis also shows practical feasibility. Nevertheless, the current framework mainly focuses on RGB satellite–UAV imagery and 2D geometric estimation; future work will extend it to multi-modal remote sensing data, 3D-aware registration, and larger-scale cross-region evaluation.

6. Conclusions

This paper proposes a bi-level meta-learning framework for reliable heterogeneous remote sensing image registration. The framework combines a CNN-attention feature matching module with a lightweight Saliency Judgment Network to improve the geometric reliability of satellite–UAV correspondences. Unlike conventional confidence-based filtering, the saliency network is optimized through an inner–outer meta-learning process, where the matcher is adapted on automatically generated coarse correspondences and the saliency criterion is updated using expert-validated meta-correspondences. This design enables the model to suppress unreliable matches from weakly textured, repetitive, or temporally unstable regions while preserving geometrically stable landmarks for transformation estimation.

Experiments on RS-Hetero-50K demonstrate that the proposed complete framework achieves superior matching precision and transformation accuracy compared with representative local-feature, sparse matching, semi-dense matching, and lightweight matching pipelines. Ablation studies confirm that the performance gain comes from meta-learned reliability-aware correspondence selection rather than simple pruning, and zero-shot evaluation on FuJian-Mountain shows promising transferability to unseen mountainous scenes. With 26.429 M parameters and 55.6 ms inference latency per image pair, the proposed method provides a practical solution for visual map-matching and localization correction in UAV remote sensing applications.