# G-ray: Ray-Level Relative Geometric Position Encoding in Multi-View Vision Transformers under Camera Heterogeneity

arXiv: https://arxiv.org/abs/2609.15018 · HTML: https://mlsanity.com/paper/2609.15018/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 89 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 30 of 69)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [Matterport3D: Learning from RGB-D Data in Indoor Environments](https://mlsanity.com/paper/1709.06158/) (2017)
- [BEVFormer: Learning Bird's-Eye-View Representation from Multi-Camera Images via Spatiotemporal Transformers](https://mlsanity.com/paper/2203.17270/) (2022)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [MVSNet: Depth Inference for Unstructured Multi-view Stereo](https://mlsanity.com/paper/1804.02505/) (2018)
- [ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenes](https://mlsanity.com/paper/2308.11417/) (2023)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [pixelSplat: 3D Gaussian Splats from Image Pairs for Scalable Generalizable 3D Reconstruction](https://mlsanity.com/paper/2312.12337/) (2023)
- [DETR3D: 3D Object Detection from Multi-view Images via 3D-to-2D Queries](https://mlsanity.com/paper/2110.06922/) (2021)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [Hypersim: A Photorealistic Synthetic Dataset for Holistic Indoor Scene Understanding](https://mlsanity.com/paper/2011.02523/) (2020)
- [Habitat-Matterport 3D Dataset (HM3D): 1000 Large-scale 3D Environments for Embodied AI](https://mlsanity.com/paper/2109.08238/) (2021)
- [MVSplat: Efficient 3D Gaussian Splatting from Sparse Multi-View Images](https://mlsanity.com/paper/2403.14627/) (2024)
- [PETR: Position Embedding Transformation for Multi-View 3D Object Detection](https://mlsanity.com/paper/2203.05625/) (2022)
- [TartanAir: A Dataset to Push the Limits of Visual SLAM](https://mlsanity.com/paper/2003.14338/) (2020)
- [BlendedMVS: A Large-scale Dataset for Generalized Multi-view Stereo Networks](https://mlsanity.com/paper/1911.10127/) (2019)
- [ARKitScenes: A Diverse Real-World Dataset For 3D Indoor Scene Understanding Using Mobile RGB-D Data](https://mlsanity.com/paper/2111.08897/) (2021)
- [Conditional Positional Encodings for Vision Transformers](https://mlsanity.com/paper/2102.10882/) (2021)
- [Fast3R: Towards 3D Reconstruction of 1000+ Images in One Forward Pass](https://mlsanity.com/paper/2501.13928/) (2025)

## Built on by (most cited first, 1 of 1)

- [Many Eyes, One World: Feed-Forward 3D Reconstruction from Mixed Cameras](https://mlsanity.com/paper/2609.35658/) (2026)

## Abstract (arXiv)

We study relative position encoding for multi-view vision Transformers under camera heterogeneity, including varying fields of view (FoVs) or projection models. Existing rotary relative position encodings commonly use image-plane positional coordinates, producing projection-dependent relative phases and inconsistent geometric cues for cross-projection attention. We introduce G-ray, a ray-level relative position encoding whose rotary phases are parameterized by camera-local ray angles. The same camera-local ray pair induces the same relative phase across projections, providing projection-invariant positional consistency. G-ray can be used directly or integrated with existing encodings, retaining complementary geometric cues without additional learned parameters. We validate G-ray in three host encodings, RoPE, GTA, and RayRoPE, across 3D reconstruction and novel-view synthesis (NVS). Across three heterogeneous 3D reconstruction benchmarks at 50 views, G-ray leads all six averaged metrics and reduces mean pointmap relative error by 45.8% over MapAnything, with calibration supplied to both. Trained exclusively on homogeneous pinhole images, the 3D reconstruction model handles mixed pinhole and non-pinhole inputs without retraining and remains competitive on homogeneous pinhole 3D reconstruction protocols. For NVS, GTA and RayRoPE improve with G-ray under joint viewpoint and FoV variation. The project's webpage is available at https://g-ray-project.github.io/.