GeLoc3r: Geometric Consistency in Pose Estimation

• GeLoc3r is a relative camera pose estimation method that integrates Geometric Consistency Regularization (GCR) to embed dense geometric supervision into regression networks.
• It employs a FusionTransformer for context-sensitive correspondence weighting and weighted RANSAC to refine pose predictions with improved precision.
• The approach decouples complex geometric computations from inference, delivering high accuracy and low latency suitable for real-time applications.

GeLoc3r is a relative camera pose estimation approach that advances the speed-accuracy trade-off in pose regression by introducing Geometric Consistency Regularization (GCR) during training, thereby enabling regression networks to approach the geometric precision of correspondence-based methods like MASt3R with the computational efficiency of single-pass pose regressors such as ReLoc3R (Li et al., 27 Sep 2025). The method is designed to produce geometrically consistent pose representations without the need for inference-time geometric computations, transferring knowledge from dense, geometrically-grounded supervision into neural network parameters. At inference, GeLoc3r retains the low latency of regression models, achieving improvements in angular and translation accuracy across diverse benchmarks.

1. Geometric Consistency Regularization (GCR) Framework

Geometric Consistency Regularization is applied exclusively during network training and leverages ground-truth depth for privileged geometric supervision. For each training image pair:

• Ground-truth depth maps are unprojected with camera intrinsics to yield a dense set of 3D points from the source view.
• The regression head predicts a relative camera pose, $\mathbf{P}_{\textrm{regression}}$, and the corresponding transformation is used to project 3D points into the target view.
• Local image descriptors at the projected image locations are extracted (using frozen MASt3R heads) and paired with descriptors from the source view; these pairs serve as 3D-2D correspondences for geometric optimization.
• The FusionTransformer module computes per-correspondence weights, $\mathbf{w}$, reflecting the contextual reliability and discriminative value of each correspondence.

Weighted RANSAC is executed on the correspondence set to recover a geometrically optimal pose, $\mathbf{P}_{\textrm{solver}}$. The consistency loss

$$\mathcal{L}_{\textrm{consistency}} = \textrm{AngularError}(\mathbf{P}_{\textrm{regression}}, \mathbf{P}_{\textrm{solver}})$$

is computed to align the regression output with the correspondence-based solution. Additionally, a descriptor similarity loss is calculated:

$$\mathcal{L}_{\textrm{descriptor}} = -\sum_{i} w_i \cdot \textrm{sim}\bigl(\mathbf{d}_i^{\textrm{src}}, \mathbf{d}_i^{\textrm{proj}}\bigr)$$

where $w_i$ are FusionTransformer weights and $\textrm{sim}$ denotes, e.g., cosine similarity. The overall training objective aggregates the standard pose regression loss and the new geometric supervision terms:

$$\mathcal{L}_{\textrm{total}} = \lambda_{\textrm{pose}}\,\mathcal{L}_{\textrm{pose}} + \lambda_{\textrm{consistency}}\,\mathcal{L}_{\textrm{consistency}} + \lambda_{\textrm{desc}}\,\mathcal{L}_{\textrm{descriptor}}$$

This multi-objective training ensures that the regression network learns to respect the underlying scene geometry, as validated by correspondence-based optimization, while maintaining direct learning of camera pose parameters.

2. FusionTransformer and Correspondence Weighting

FusionTransformer is an attention-based module specifically designed to evaluate and weight dense 3D-2D correspondences for the geometric consistency branch. For each spatial location:

• Descriptor pairs $(\mathbf{d}_{1,j}, \mathbf{d}_{2,j})$ are concatenated into an embedding vector.
• The transformer processes these embeddings via self-attention, enabling context-sensitive assessment of correspondence reliability—outliers (occlusions, textureless regions) are assigned low weights.
• The output is passed through an MLP followed by softmax normalization to produce sampling weights for weighted RANSAC and weighting coefficients for descriptor matching.

Weighted RANSAC uses these probabilities to select high-confidence correspondences, which empirically improves the robustness and geometric accuracy of the recovered $\mathbf{P}_{\textrm{solver}}$. By integrating FusionTransformer within the training pipeline, GeLoc3r ensures that learned features encode both local appearance and global scene structure.

3. Training and Inference Protocol

GeLoc3r's pipeline is bifurcated between the training and inference phases:

Training Phase

• The encoder-decoder backbone (Siamese encoder + ViT decoder) predicts relative pose and produces dense feature maps.
• Ground-truth depth yields 3D geometry for correspondence generation.
• The geometric consistency branch, using FusionTransformer and weighted RANSAC, supervises the regression predictions with the aforementioned pose and descriptor losses.
• All geometric computations (depth usage, correspondence weighting, RANSAC) are utilized only for supervision and are not retained at test time.

Inference Phase

• Only the regression head is used. There is no overhead from geometric computations, FusionTransformer, or depth processing.
• Inference speed matches that of vanilla ReLoc3R, i.e., $\sim$25–33ms per image pair.
• The model delivers pose predictions specified by the enhanced regression network trained under geometric regularization.

This decoupling of geometric supervision from runtime computation is central to the GeLoc3r paradigm.

4. Quantitative Evaluation and Comparative Performance

Performance metrics reported in the source benchmark a range of pose regression and correspondence-based methods, with GeLoc3r showing significant gains:

Dataset	Method	AUC@5° (%)	Relative Impr. (%)
CO3Dv2	GeLoc3r	40.45	16 (vs ReLoc3R)
CO3Dv2	ReLoc3R	34.85	–
RealEstate10K	GeLoc3r	68.66	–
RealEstate10K	ReLoc3R	66.70	–
MegaDepth1500	GeLoc3r	50.45	–
MegaDepth1500	ReLoc3R	49.60	–

AUC@5° denotes the area under the curve for angular error thresholds, measuring pose precision. GeLoc3r’s improvements are supported by reduction in cosine similarity error maps (e.g., mean error dropping from 0.520 to 0.421), indicating more geometrically faithful feature representations.

The approach achieves median translation and rotation errors on par with state-of-the-art correspondence-based methods on challenging indoor and outdoor benchmarks (7-Scenes, Cambridge Landmarks) while retaining much lower inference latency.

5. Relationship to Prior Methods and Paradigm Shift

GeLoc3r redefines the architectural landscape for relative camera pose estimation by transferring geometric knowledge during training rather than enforcing geometric computations at runtime:

• Prior regression methods (e.g., ReLoc3R) lack geometric guarantees and fall short of the precision attainable by correspondence solvers such as MASt3R or feature-augmented regression frameworks like FAR.
• Correspondence-based solutions require explicit matching and RANSAC at inference, incurring significant computational cost ($\sim$300ms/pair).
• FAR maintains geometric solving at inference, combining regression and geometry—GeLoc3r eliminates this requirement by embedding geometric understanding directly into the regression weights.
• The paradigm shift lies in leveraging privileged geometric supervision during training to yield efficient, geometry-aware models for deployment.

This separation of training and inference requirements, with geometric complexity handled upfront, permits models that scale for real-time and resource-constrained applications without sacrificing accuracy.

6. Practical Implications and Use Cases

GeLoc3r’s technical innovations have direct implications for real-time localization and mapping:

• Applications in SLAM, augmented reality, and autonomous robotics benefit from integration of geometric accuracy and low-latency model inference.
• The training strategy unifies regression efficiency with geometric reliability, suitable for deployment in time-critical systems.
• The technique demonstrates that dense 3D supervision, attention-based correspondence weighting, and pose refinement can be effectively leveraged for 2-view pose estimation without runtime penalties.

A plausible implication is that future work may further capitalize on “privileged” training modalities—using not just depth but possibly additional sensor data or multi-view constraints—to embed contextual awareness into lightweight deployment architectures. This suggests a general trend toward decoupling architectural complexity during training and optimizing runtime simplicity for large-scale spatial understanding systems.

GeLoc3r thus marks a notable advancement in the integration of geometric supervision and modern regression networks for robust and efficient camera pose estimation.