Dataset

The FIRE dataset is widely recognized as a benchmark for evaluating retinal image registration algorithms. It comprises 134 colour fundus image pairs derived from 129 individual images, each captured at a resolution of 2,912 × 2,912 pixels with a 45° field of view using a NIDEK AFC-210 fundus camera [20]. To enable systematic performance assessment, the dataset is divided into three difficulty categories based on field-of-view overlap and anatomical variation: Class S (71 pairs) represents easy cases with substantial image overlap (> 75%) without anatomical changes between images; Class A (14 pairs) consists of cases with > 75% overlap that additionally exhibit anatomical changes as shown in Figure 1, and Class P (49 pairs) comprises the most challenging cases with limited overlap (< 75%) without anatomical differences between images. Each image pair includes 10 manually annotated ground-truth landmarks, typically located at vessel bifurcations and crossings, which provide a reference standard for quantitative evaluation of registration accuracy [20]. A visual overview of representative image pairs from each FIRE class is shown in Figure 2.

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Figure 1. Class A anatomical changes on the FIRE dataset. A: Reference retinal image showing normal fundus appearance; B: Test image with pathological features highlighted. Red circles indicate hard exudates; green circles denote cotton wool spots. Prominent optic disc swelling is observed in the test image.

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Figure 2. Pre-registration visual summary of the FIRE dataset. Columns show the fixed (reference) image, the moving (test) image, and their unregistered overlay. Ground-truth landmarks are shown as yellow (fixed) and blue (moving) points.

RetinaRegNet

RetinaRegNet is a zero-shot framework designed to register pairs of retinal images by identifying correspondences within semantic diffusion features and subsequently warping one image onto the other. The process follows a broadly three-stage pipeline encompassing feature extraction, correspondence refinement, and hierarchical transformation (Figure 3).

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Figure 3. Overview of the RetinaRegNet registration pipeline. Moving and fixed fundus images are processed using diffusion-based feature extraction. Keypoints are detected with SIFT and RANSAC, correspondences established via cosine similarity, and outliers removed through two-stage filtering. Two-stage hierarchical registration applies homography for global alignment and third-order polynomial transformation for local alignment, producing the final registered output.

First, rich feature maps are extracted from both the fixed and moving images using a pretrained Stable Diffusion model. Each image is passed through the model at a low noise step, producing intermediate feature tensors that capture both vessel patterns and broader retinal anatomy while remaining robust to variations in illumination and contrast.

With these features in hand, the method selects a balanced set of control points, approximately half from SIFT (to capture textured vessel regions) and half sampled uniformly at random (to cover smooth areas), ensuring that correspondence estimation is not biased toward densely textured regions. It then computes correspondences by cosine similarity in feature space so that a point p in the fixed image is paired with the most similar location q in the moving image. This approach provides invariance to photometric variations and tolerates moderate geometric drift.

Matched pairs are then refined through a two-step filtering process that eliminates outliers. First, a forward–backward (inverse consistency) check ensures that correspondences agree in both directions; mismatches that fail this test are discarded. Second, a geometric filtering step removes any pairs that deviate significantly from a globally consistent transformation. This combination of semantic matching and hierarchical outlier rejection produces a dense but reliable correspondence field that can support both global and local alignment.

Finally, RetinaRegNet performs a coarse-to-fine warp in two stages. Stage 1 estimates a global homography to absorb overall eye or camera motion, followed by Stage 2, a smooth local polynomial warp to correct small residual deformations. In practice, this combination of semantic feature matching, rigorous yet efficient filtering, and sequential global-to-local warping achieves high registration accuracy, particularly in low-overlap scenarios. The diffusion features enable recognition of vascular and anatomical patterns even where traditional pixel-based methods fail, while the two-stage transformation mitigates overfitting and preserves anatomical coherence.

EyeLiner

EyeLiner replicates clinical assessment patterns through modular anatomical structure analysis. The pipeline can be understood as a four-stage process that algorithmically mimics how clinicians track pathological changes relative to stable anatomical landmarks. An overview of the EyeLiner pipeline is shown in Figure 4. The image pairs are first segmented to extract the retinal vasculature and optic disc. A standard U-Net architecture was used for training on established vessel segmentation datasets to generate vascular masks for both the fixed and moving images. For reproducibility, we relied on AutoMorph [21] instead, a publicly available deep learning pipeline for vessel segmentation. Optic disc segmentation is performed using MaskFormer [22], a transformer-based architecture for general-purpose image segmentation. The resulting disc mask can be used to filter out keypoints detected (in the following step) within the optic disc region, as vessels inside the disc are subject to biological motion and thus are less reliable for geometric alignment.

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Figure 4. Overview of the EyeLiner registration pipeline. Fixed and moving fundus images are first compared using a checkerboard overlay. Vessel and optic disc regions are segmented to guide correspondence estimation. Keypoints are detected with SuperPoint and matched using LightGlue along vascular structures. A Thin-Plate Spline model then warps the moving image, producing the registered output and improved checkerboard alignment.

Once the vascular regions are defined, EyeLiner detects and matches distinctive vessel features in a unified process. The SuperPoint [23] network is used to identify salient keypoints along the segmented vessels and to compute descriptor vectors that capture the local appearance of each point. These descriptors are then passed directly to LightGlue [24], a lightweight transformer that performs feature matching. Rather than relying on direct numerical comparison of descriptor values, LightGlue interprets the geometric layout and contextual relationships among vessels in both images, producing more reliable correspondences even when illumination, scale, or focus differ between acquisitions. This combination of SuperPoint and LightGlue therefore establishes anatomically grounded, context-aware correspondences that are robust to the variations that typically challenge conventional intensity-based registration methods.

The final stage of the EyeLiner pipeline performs the actual alignment by warping the moving image to match the fixed reference. Once correspondences are confirmed, a thin-plate spline transformation is used to model the deformation between the two images. This smooth, flexible transformation captures both global displacement and local non-rigid motion in the retinal vasculature while maintaining overall anatomical plausibility. In practice, the combination of anatomically guided segmentation, context-aware matching, and smooth deformation modelling enables EyeLiner to produce clinically interpretable and geometrically stable registrations, offering a strong balance between accuracy, computational efficiency, and biological realism.

Geoformer

GeoFormer builds upon the existing LoFTR framework and employs a geometry-aware transformer to learn dense correspondences between retinal images without relying on explicit keypoint detectors. The method can be broadly divided into three stages. A schematic overview of the GeoFormer framework is presented in Figure 5. GeoFormer begins with a ResNet-FPN backbone [25] that extracts multiscale feature maps from the fixed and moving retinal images. The model captures coarse-level features at one-eighth resolution, encoding global anatomical information such as optic disc shape and overall curvature, and fine-level features at one-half resolution, which preserve local vessel structures, edge patterns, and texture details. This multi-level representation ensures that both global context and fine anatomical information are passed to the transformer network.

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Figure 5. GeoFormer architecture and methodology. Stage 1: ResNet-FPN extracts multi-scale features at 1/2 and 1/8 resolution. Stage 2: Transformer blocks perform self-attention and cross-attention to generate confidence maps, followed by geometry-aware RANSAC and refinement for sub-pixel accuracy. Stage 3: The final homography matrix is computed and applied to produce the registered output.

The extracted features are processed through transformer blocks that perform self-attention within each image to capture contextual dependencies and cross-attention between the image pair to infer correspondences. This produces a confidence map that indicates how likely each feature in one image matches a feature in the other. The resulting matches are filtered using a geometry-aware RANSAC procedure, which removes correspondences inconsistent with a plausible geometric transformation and estimates an initial homography matrix. These verified matches are then refined through a second transformer stage that focuses attention only on local regions surrounding the geometrically consistent points, improving computational efficiency and accuracy in vessel-dense areas. Finally, the model revisits the fine-scale feature maps to achieve sub-pixel correspondence accuracy, accommodating vessel curvature and illumination variations that coarse features cannot fully capture.

The refined correspondences are used to compute a final homography matrix that maps coordinates from the moving image onto the fixed image. The moving image is then warped according to this transformation, completing the registration process.

Evaluation metrics

MLE in pixels for each evaluated method. MLE measures registration accuracy by calculating the average distance between the corresponding anatomical landmarks and their estimated locations obtained from the registration method, with lower values indicating better alignment:

where (x^′_i ,y_i^′) represent manually annotated ground truth landmarks and (x^′′_i ,y_i^′′) are transformed coordinates.

In addition to the mean landmark error, we evaluate registration performance using the success rate. A registration is considered successful if a transformed landmark lies within a predefined pixel threshold of its corresponding ground-truth location. For each image pair, this criterion is applied independently to the ten annotated landmarks, yielding a binary outcome (success or failure) per point. The success rate is then computed as the proportion of successful landmarks out of the ten ground-truth points for that image pair. The threshold τ is set to 12.5 pixels, following [17], to ensure comparability with prior results.

where I(⋅) is the indicator function, $d_i=\sqrt{{\left(x_i^{\text{'}}-x_i^{\text{'}\text{'}}\right)}^2+{\left(y_i^{\text{'}}-y_i^{\text{'}\text{'}}\right)}^2}$ and τ = 12.5 pixels.

Finally, we quantify overall registration robustness using the Area Under the Curve (AUC) of the cumulative success-rate curve. For a range of pixel thresholds, the success rate is computed as the proportion of landmarks whose registration error falls below each threshold. The resulting curve characterises how registration performance degrades as the tolerance increases. The AUC provides a single scalar summary of this behaviour, with higher values indicating consistently higher success rates across a wide range of error thresholds:

where T_max is the maximum error threshold, set to 25 pixels for the FIRE dataset.

We also evaluated registration results using Normalized Cross Correlation (NCC), an intensity-based metric that quantifies linear correlation between image intensities. In retinal imaging, NCC reflects global photometric consistency after warping but is influenced by acquisition-related factors and appearance changes due to disease progression. As NCC is computed over the full image domain, the metric does not explicitly encode pointwise anatomical correspondence. NCC is therefore reported as a complementary measure of global intensity agreement rather than a primary indicator of anatomical registration accuracy.

Where ∑ is 2-dimensional summation across (x, y), I_f (x,y) is the intensity of the fixed image at location (x, y) and I_m (x,y) is the intensity of the moving image at the location I_m (x,y), and μ_f and μ_m are the mean intensities of fixed and moving images, respectively.

Experimental setup

All three registration pipelines were reproduced and evaluated in the same environment to ensure consistency and comparability across methods. All experiments were executed on a workstation equipped with an NVIDIA GeForce RTX 3090 GPU (24 GB VRAM) running CUDA 12.6. The implementations used Python 3.11.13, PyTorch 2.2.2, and torchvision 0.17.2 as the primary deep learning frameworks. For methods requiring vessel segmentation (EyeLiner), AutoMorph was used for reproducibility. All runtime and accuracy measurements reported in Results section reflect executions under this standardised environment. The code for data processing is available at: https://github.com/ThenukaDharmaseelan/image_Registration.

Exact parametric configurations used for each registration pipeline are provided in the Tables S2, 3, 4.

Overall performance analysis

As shown in Table 1 and Figure 6, RetinaRegNet achieved the lowest overall MLE of 3.12 (± 2.43 pixels) across the FIRE dataset. A Friedman test confirmed significant differences between the three methods (χ²(2) = 134.37, P = 2 × 10^–16). Post-hoc Wilcoxon signed-rank tests with Bonferroni correction demonstrated that RetinaRegNet achieved significantly lower MLE than both EyeLiner (3.81 ± 3.13 pixels, P = 1 × 10^–4) and GeoFormer (6.06 ± 4.86 pixels, P = 2 × 10^–21), while EyeLiner also significantly outperformed GeoFormer (Table 2).

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Figure 6. Overall comparison of registration methods across all classes on the FIRE dataset (n = 134). Box plots show the distribution of MLE in pixels for the three methods.

Box plot analysis in Figure 6 reveals distinct distributional characteristics. RetinaRegNet demonstrates the most compact error distribution with a median of approximately 2.0 pixels and relatively few outliers. EyeLiner shows a slightly wider distribution with a median around 2.5 pixels and a comparable outlier pattern. In contrast, GeoFormer exhibits substantially higher variability, with a median of approximately 4 pixels and a significantly larger interquartile range.

Success rate analysis (Table 1) showed RetinaRegNet achieved 97.76%, EyeLiner 97.01%, and GeoFormer 88.06% overall, demonstrating RetinaRegNet’s superior reliability in completing registration tasks successfully.

AUC analysis (Table 1) confirmed RetinaRegNet’s superior performance with an overall AUC of 0.89, compared to EyeLiner (0.85) and GeoFormer (0.76), representing a 5% improvement over EyeLiner and 17% over GeoFormer.

NCC analysis (Table 1) revealed contrasting patterns. GeoFormer achieved the highest overall NCC (0.64), followed by RetinaRegNet and EyeLiner (both 0.56). Notably, NCC rankings contradicted landmark-based metrics. Despite GeoFormer achieving the highest intensity correlation, it exhibited the poorest landmark accuracy (MLE: 6.06 pixels), lowest AUC (0.76), and poorest success rate (88.06%). These findings indicate that intensity-based similarity does not reliably reflect geometric alignment accuracy.

Overall, RetinaRegNet demonstrates lower mean error, higher success rate, and superior AUC compared with EyeLiner and GeoFormer across all landmark-based metrics, while GeoFormer exhibits the widest error distribution despite achieving higher intensity-based correlation.

Across difficulty classes, RetinaRegNet achieves superior overall performance (3.12 pixels), with the lowest MLE in Classes S and P and mean performance in Class A that is close to EyeLiner. EyeLiner attains the lowest mean MLE in Class A, although its advantage over RetinaRegNet is not statistically significant in this subset. Both methods consistently outperform GeoFormer, which shows particularly large errors in Class P. These findings underscore the importance of class specific evaluation in assessing the robustness and generalization capabilities of retinal registration methods.

Class specific performance analysis

Class S performance

Class S, representing the largest subset with 71 samples, proves to be the least challenging for all methods (Figure 7A). RetinaRegNet obtained the best performance with an MLE of (1.70 pixels), outperforming EyeLiner (1.80 pixels) and GeoFormer (2.42 pixels) by 6% and 42%, respectively. The consistently low error rates across all methods indicate that Class S images possess favourable characteristics for vessel landmark localisation. These differences were statistically significant, as shown in Table 3 (Friedman P = 2 × 10^–14; all pairwise comparisons reached significance after Bonferroni correction with P ≤ 8 × 10^–4). AUC analysis (Table 1) demonstrated RetinaRegNet’s superior performance (0.95), followed by EyeLiner (0.93) and GeoFormer (0.91). All three methods achieved 100% success rates (Table 1), confirming the relative ease of Class S registration tasks. NCC values (Table 1) were comparable across methods (RetinaRegNet: 0.75, EyeLiner: 0.74, GeoFormer: 0.72), indicating similar intensity-based alignment in high-overlap scenarios. Overall, RetinaRegNet provides consistently lower landmark error and higher AUC than EyeLiner and GeoFormer in this class.

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Figure 7. Mean Landmark Error distribution by class and method on the FIRE dataset. Boxplots show the performance comparison of the three methods across the three classes. Diamond markers indicate mean values, horizontal lines show medians, boxes represent interquartile ranges (IQR), whiskers extend to 1.5 × IQR, and red circles represent outliers. Lower values indicate better registration accuracy.

Table 3. Statistical comparison of MLE for Class S images (n = 71).

Comparison	Test	Statistic	Raw P-value	Bonferroni P-value	Mean Difference (A–B)
Friedman	χ²(2)	63.577	2 × 10–14	–	–
RetinaRegNet vs EyeLiner	Wilcoxon V	640	2 × 10–4	8 × 10–4 ***	−0.204
RetinaRegNet vs GeoFormer	Wilcoxon V	51	2 × 10–12	6 × 10–12 ***	−0.729
EyeLiner vs GeoFormer	Wilcoxon V	339	8 × 10–8	2 × 10–7 ***	−0.524

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Asterisks denote Bonferroni-adjusted significance: * P < 0.05, ** P < 0.01, *** P < 0.001.

Runtime analysis

Table 6 presents the runtime performance analysis of the evaluated methods. GeoFormer demonstrates the fastest processing speed at 0.32 seconds per image, offering real-time processing capability. EyeLiner achieves moderate computational efficiency at 4.92 seconds per image. This includes 4.22 seconds for AutoMorph vessel segmentation and 0.70 seconds for the registration process itself, making it approximately 15 times slower than GeoFormer. RetinaRegNet exhibits the highest computational cost at 31.23 seconds per image, representing 98 times increase compared to GeoFormer and 6.4 times increase compared to EyeLiner.

These computational differences highlight the trade-offs between different architectural approaches. EyeLiner’s reliance on explicit vessel segmentation via AutoMorph adds substantial preprocessing overhead compared to end-to-end approaches. Due to its complex architecture, RetinaRegNet’s multi-stage registration pipeline with iterative refinement steps results in considerably longer processing times. In contrast, GeoFormer’s transformer-based architecture enables direct processing of raw retinal images without intermediate segmentation steps, resulting in significantly faster inference times suitable for clinical deployment. The theoretical computational complexity and scalability characteristics of each pipeline across individual processing stages are analysed in Table S5.