## 3DGEER: 3D Gaussian Rendering
Made Exact and Efficient for Generic Cameras

- In Anonymous Submission

Can Gaussian rendering be both exact and fast
without relying on lossy splatting? Checkout our 3D-GEER!

### Abstract

3D Gaussian Splatting (3DGS) achieves an appealing balance between rendering quality and efficiency, but relies on approximating 3D Gaussians as 2D projections—an assumption that degrades accuracy, especially under generic large field-of-view (FoV) cameras. Despite recent extensions, no prior work has simultaneously achieved both projective exactness and real-time efficiency for general cameras. We introduce 3DGEER, a geometrically exact and efficient Gaussian rendering framework. From first principles, we derive a closed-form expression for integrating Gaussian density along a ray, enabling precise forward rendering and differentiable optimization under arbitrary camera models. To retain efficiency, we propose the Particle Bounding Frustum (PBF), which provides tight ray–Gaussian association without BVH traversal, and the Bipolar Equiangular Projection (BEAP), which unifies FoV representations, accelerates association, and improves reconstruction quality. Experiments on both pinhole and fisheye datasets show that 3DGEER outperforms prior methods across all metrics, runs 5x faster than existing projective exact ray-based baselines, and generalizes to wider FoVs unseen during training—establishing a new state of the art in real-time radiance field rendering.

### Video

### Visual Result (click to zoom-in.)

#### High-Quality Large FoV Results

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#### Highly Distorted & Close-Up Views

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#### Cross-Camera Rendering (train: FE 1/8; test: PH 1/4)

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### Visual Comparison (check more results.)

3DGEER outperforms both 3DGS-based (Gaussian Splatting) and 3DPRT-based (Particle Ray Tracing) approaches on novel view synthesis benchmarks — including MipNeRF360 (pinhole), ScanNet++ (fisheye) and ZipNeRF (mix). 3DGEER achieves high rendering fidelity while remaining runtime-efficient — 5× faster than 3DPRT (e.g., EVER, 3DGRT) and comparable to 3DGS, with no sacrifice in projective exactness.

#### MipNeRF360 (Pinhole)

3DGS (PSNR: 27.21; FPS: 343) v.s. 3DGRT (PSNR: 27.20; FPS: 52) v.s. 3DGEER (Ours) (PSNR: 27.76; FPS:327)

3DGS Ours | 3DGRT Ours | Groundtruth Ours

#### ScanNet++ (Fisheye)

FisheyeGS (PSNR:27.81; FPS:213) v.s. EVER (PSNR: 29.47; FPS: 13) v.s. 3DGEER (Ours) (PSNR: 31.50; FPS: 251)

FisheyeGS Ours | EVER Ours | Groundtruth Ours

#### ZipNeRF Close-Up Views (click to zoom-in.)

Our method (3DGEER) can handle soft shadow / lights or close views where the solid ellipsoid-based model (EVER) suffers.

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#### ZipNeRF Large FoV Views (click to zoom-in.)

3DGUT and FisheyeGS are based on equidistant model for representations, which fail in much wider FoV. (See paper Fig. 5). Our method (3DGEER) can effectively sample rays in larger FoV regions and show much better results.

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### Acknowledgements

The website template was borrowed from Michaël Gharbi and MipNeRF360.