ConeGaussian

Anti-Aliased Gaussian Ray-Tracing for Generic Central Cameras
arXiv preprint · September 2026
Deheng Zhang1,*,†, Letian Shi1,*, Runyi Yang1, Zhendong Li1, Lei Sun1, Kanzhi Wu2, Ajad Chhatkuli1,‡, Danda Pani Paudel1, Luc Van Gool1,‡
1 INSAIT, Sofia University “St. Kliment Ohridski”  ·  2 vivo Mobile Communication Co., Ltd.
* equal contribution  ·  project lead  ·  equal supervision
0:00 / 0:00
Mip-NeRF 360 bicycle, 3DGEER (left) vs. ConeGaussian (right). First chapter: a natively trained pair zoomed out ×4 and orbited at wide field of view: the baseline's spokes and grass break into speckle, ours stays band-limited. Second chapter: a pair trained at 1/8 resolution and magnified ×16 into the grass: the baseline exposes sub-pixel “needle” Gaussians, ours stays smooth. The inset magnifies a fixed world region at native render pixels.

TL;DR. A camera is a sampling operator that maps each finite pixel to a bundle of rays. ConeGaussian builds an anisotropic pixel footprint directly from the neighbouring rays of any calibrated central camera's inverse projection, filters the exact ray–Gaussian response with it in closed form, and derives a per-Gaussian training-frequency floor from the same geometry. One implementation gives anti-aliased zoom-out and artifact-free zoom-in for pinhole and strongly distorted fisheye cameras, and ports unchanged across two Gaussian ray-rendering backbones (3DGEER and 3DGUT).

Abstract

In rendering, a camera is a sampling operator that maps each finite pixel to a bundle of rays. Different camera models change the geometry of this bundle, thus making a unified and faithful rendering formulation challenging. Consequently, Gaussian ray tracing supports generic cameras (with optical center) through their inverse ray mappings, yet typically reduces every pixel to a single center ray. This ignores the camera-dependent pixel footprint, causing aliasing under minification, while unconstrained Gaussians expose unsupported frequencies under magnification. We present ConeGaussian, a camera-model-agnostic anti-aliasing framework for Gaussian ray-based rendering. Instead of defining the pixel filter on a camera-specific image plane, ConeGaussian constructs an anisotropic footprint directly from neighboring rays produced by the camera's native inverse mapping. We derive a closed-form response under a locally linear, depth-local, moment-matched approximation of the finite pixel footprint, while the same geometry defines a per-Gaussian training-frequency floor. Notably, by construction, our filtering principle can be used unmodified across calibrated central camera models and multiple Gaussian ray-rendering backbones. Additionally, unlike in Mip-Splatting, our scene-space frequency floor and filtering enable trivial composition at render time, allowing us to remove excess blurring. On pinhole and strongly distorted fisheye captures, ConeGaussian consistently improves two distinct ray-based backbones, by up to 4.3 dB at 1/8 resolution, and reduces fisheye LPIPS by 30% where perspective screen-plane footprint formulations are not directly applicable.

Method

ConeGaussian pixel-footprint filter: edge-ray differentials, whitened anisotropic footprint, response error vs supersampled reference
Original paper overview. Panel (b) independently centres covariance shapes; it is not the translated cross-section of panel (a). Panels (c, d) show the original illustrative sweeps, not the live slider settings. The interactive geometry below retains the ray–Gaussian offset and labels the coordinate space.

Build the footprint yourself interactive

Move the pixel across the sensor, switch the camera model or reshape the Gaussian. The 3D geometry and both rows of filters update together.

Filter covariance, drawn at sqrt(3) standard deviations on one shared scale, in the . Green: the pixel footprint; dots: exact sub-ray crossings.
3DGEER
VKRayGS-style
Isotropic reduction
ConeGaussian
Filtered Gaussian (coloured 1σ contour) around the whitened Gaussian (grey), with the footprint at the centre ray's offset.
3DGEER
T = · error
VKRayGS-style
T = · error
Isotropic reduction
T = · error
ConeGaussian
T = · error
Results · zoom-out

Zoom-out: minification without aliasing

3DGEER: Mip-NeRF 360 · bicycle
ConeGaussian: Mip-NeRF 360 · bicycle
3DGEERConeGaussian
Mip-NeRF 360 · bicyclepinhole · 19.1 → 22.7 dB (+3.7)
Ground truth: Mip-NeRF 360 · bicycle
ground truth
3DGEER: Mip-NeRF 360 · garden
ConeGaussian: Mip-NeRF 360 · garden
3DGEERConeGaussian
Mip-NeRF 360 · gardenpinhole · 21.3 → 27.0 dB (+5.7)
Ground truth: Mip-NeRF 360 · garden
ground truth
3DGEER: Zip-NeRF london
ConeGaussian: Zip-NeRF london
3DGEERConeGaussian
Zip-NeRF londonfisheye · 28.7 → 30.6 dB (+1.9)
Ground truth: Zip-NeRF london
ground truth
Results · zoom-in

Zoom-in: magnification without needle artifacts

3DGEER bicycle zoom-in
ConeGaussian bicycle zoom-in
3DGEERConeGaussian
bicyclegrass tuft at the front wheel
3DGEER garden zoom-in
ConeGaussian garden zoom-in
3DGEERConeGaussian
gardenhedge foliage
3DGEER stump zoom-in
ConeGaussian stump zoom-in
3DGEERConeGaussian
stumptall grass blades

One scene, any central camera

Performance in the wild own capture
Results · paper figures

Qualitative comparisons against ground truth

Choose Zoom-out or Zoom-in, then a scene, to compare 3DGEER → ConeGaussian → ground truth. The 6 zoom-out and 5 zoom-in comparisons are kept separate, with their original detail insets and scale labels. Scene/view names are descriptive because the source figures do not list scene IDs.

Zoom-out · 1/8 sampling rate. Select a scene below.

Window sill Zoom-out · 1/8 sampling rate

3DGEER
3DGEER: Office · windows, Window sill, Zoom-out · 1/8 sampling rate
ConeGaussian
ConeGaussian: Office · windows, Window sill, Zoom-out · 1/8 sampling rate
Ground truth
Ground truth: Office · windows, Window sill, Zoom-out · 1/8 sampling rate

Supplementary zoomout figure, row 6. Full source figure ↗

Results · quantitative

Comparisons with other methods

Every cell reads PSNR↑ / SSIM↑ / LPIPS↓. Real-scene benchmarks: ScanNet++ and Zip-NeRF (fisheye, metrics inside a 3-pixel-eroded valid-domain mask) and Mip-NeRF 360 (pinhole); every eighth image is held out. Zoom-in / zoom-out change only the image sampling resolution with consistently scaled calibration, never the optical zoom or the pose. Green = best, orange = second best per column and metric among the generalizable ray-based methods.

Multi-scale training and testing, two backbones

DatasetMethod1½¼Avg.
ScanNet++fisheye3DGUT29.33/.915/.24830.38/.934/.19331.47/.954/.11230.24/.953/.07830.36/.939/.158
ConeGaussian w. 3DGUT29.67/.921/.23930.61/.938/.18531.66/.956/.10831.65/.963/.05930.90/.944/.148
3DGEER27.59/.911/.25728.53/.929/.20228.53/.946/.12328.02/.946/.08428.17/.933/.167
ConeGaussian w. 3DGEER27.65/.917/.24328.29/.931/.18929.27/.950/.11129.93/.962/.05228.78/.940/.149
Zip-NeRFfisheye3DGUT23.40/.781/.41324.18/.835/.29924.73/.867/.19224.58/.865/.14724.22/.837/.263
ConeGaussian w. 3DGUT23.48/.791/.40324.22/.840/.29224.82/.871/.18525.14/.880/.12824.42/.845/.252
3DGEER24.32/.806/.38825.02/.854/.26825.64/.893/.16225.45/.895/.12125.11/.862/.235
ConeGaussian w. 3DGEER24.42/.815/.37725.16/.860/.26125.89/.898/.15326.37/.915/.09425.46/.872/.221
Mip-NeRF 360Pinhole3DGS26.55/.779/.27428.00/.854/.16228.51/.891/.10227.45/.888/.08727.63/.853/.156
Mip-Splatting†27.20/.802/.24428.74/.870/.14629.90/.915/.09030.66/.944/.05629.12/.883/.134
Analytic-Splatting†27.50/.808/.23128.99/.874/.13230.35/.919/.07731.21/.945/.05129.51/.887/.123
3DGUT26.68/.768/.34126.80/.788/.24126.97/.823/.15924.02/.716/.23826.12/.774/.245
ConeGaussian w. 3DGUT26.98/.782/.33226.94/.798/.23427.21/.831/.15225.00/.762/.21026.53/.793/.232
3DGEER26.01/.739/.32627.55/.820/.21228.56/.880/.12826.74/.860/.12827.21/.825/.199
ConeGaussian w. 3DGEER27.05/.792/.27528.44/.841/.17630.03/.905/.09531.08/.945/.05229.15/.871/.149

Multi-scale training and testing at {1, ½, ¼, ⅛}. PSNR↑ / SSIM↑ / LPIPS↓. Gray rows are author-reported, pinhole-only screen-space methods (3DGS rasterizer) that do not support generic cameras; green / orange mark the best / second-best generalizable ray-based method per column and metric.

Zoom-out (train native, render 1 → ⅛)
DatasetMethod1½¼Avg.
ScanNet++fisheye3DGEER (baseline)27.89/.921/.24328.18/.930/.19827.10/.930/.15526.58/.918/.13127.44/.925/.182
VKRayGS z/f26.20/.919/.24425.89/.922/.20521.57/.885/.19320.54/.833/.18523.55/.890/.207
ConeGaussian (isotropic)27.96/.921/.24228.45/.932/.19427.34/.937/.13727.37/.938/.08927.78/.932/.165
ConeGaussian (anisotropic)27.97/.922/.23928.45/.932/.19328.25/.942/.12827.93/.942/.07928.15/.934/.160
Zip-NeRFfisheye3DGEER (baseline)24.13/.787/.40924.92/.845/.27825.87/.899/.15025.82/.906/.10425.19/.859/.235
VKRayGS z/f23.37/.786/.40624.61/.846/.27626.00/.902/.14825.92/.913/.09224.97/.862/.230
ConeGaussian (isotropic)24.16/.794/.40125.01/.850/.27125.97/.901/.14826.41/.918/.08925.39/.866/.227
ConeGaussian (anisotropic)24.25/.795/.39825.02/.851/.27025.96/.901/.14826.43/.919/.08825.41/.867/.226
Mip-NeRF 360pinhole3DGEER (baseline)27.03/.797/.30027.68/.832/.21427.19/.836/.17125.29/.784/.18326.80/.812/.217
VKRayGS z/f27.14/.798/.29827.25/.832/.21925.68/.839/.17522.96/.786/.18325.76/.814/.219
ConeGaussian (isotropic)27.17/.799/.29628.10/.843/.20728.80/.884/.13528.53/.903/.09628.15/.857/.183
ConeGaussian (anisotropic)27.11/.803/.29628.06/.829/.20628.87/.876/.13128.67/.909/.08728.18/.854/.180

Zoom-out (STMT): trained at native resolution, rendered at {1, ½, ¼, ⅛} without retraining. Isotropic / anisotropic rows differ only in footprint shape; the VKRayGS row re-implements only its paraxial z/f footprint sizing inside the same renderer.

Zoom-in (train at the lowest resolution, render ×1 → ×4)
DatasetMethod×1×2×4Avg.Corner ×4
ScanNet++fisheye3DGEER (baseline)27.28/.944/.12227.74/.918/.22127.33/.895/.27927.45/.919/.20822.73/.871/
3DGEER (+ Mip-Splatting floor)29.49/.951/.11127.19/.918/.21627.25/.896/.27227.98/.922/.20022.40/.872/
3DGEER (+ footprint floor)28.73/.949/.11228.13/.921/.21327.42/.897/.27128.09/.922/.19922.82/.879/
ConeGaussian (ours)28.80/.950/.11128.32/.924/.20427.52/.900/.26428.21/.925/.19322.88/.879/
Zip-NeRFfisheye3DGEER (baseline)25.87/.899/.15024.92/.845/.27824.13/.787/.40924.97/.844/.27921.72/.780/
3DGEER (+ Mip-Splatting floor)25.88/.899/.15024.92/.845/.27924.13/.787/.40924.98/.844/.27921.73/.779/
3DGEER (+ footprint floor)25.91/.900/.15024.94/.845/.27924.14/.787/.40925.00/.844/.27921.72/.780/
ConeGaussian (ours)25.96/.901/.14825.02/.851/.27024.25/.795/.39825.08/.849/.27221.74/.781/
Mip-NeRF 360pinhole3DGEER (baseline)29.73/.898/.12826.92/.790/.25525.62/.720/.37927.42/.803/.25425.77/.718/
3DGEER (+ Mip-Splatting floor)29.93/.902/.12527.03/.794/.25225.74/.727/.37227.57/.808/.25025.94/.726/
3DGEER (+ footprint floor)30.05/.906/.11827.11/.798/.24325.77/.728/.36527.64/.811/.24225.96/.726/
ConeGaussian (ours)30.15/.907/.11727.18/.802/.23925.79/.731/.35927.71/.813/.23825.96/.729/

Zoom-in: trained at the lowest resolution, rendered at ×1–×4. Corner ×4 is PSNR / SSIM over the normalized radial band r > 0.9 of the fisheye image.

Cross-camera rendering (ScanNet++)
SettingMethod1½¼Avg.
FH → PHfull img3DGEER (baseline)27.42/.935/.25729.99/.940/.20329.66/.941/.15628.34/.930/.13628.85/.936/.188
VKRayGS-insp. z/f dilation26.99/.933/.25328.50/.937/.20225.73/.919/.17223.02/.871/.17226.06/.915/.200
ConeGaussian (ours)27.38/.934/.25530.14/.942/.19930.28/.949/.13529.56/.951/.08329.34/.944/.168
PH → FHfull img3DGEER (baseline)27.01/.919/.23427.47/.931/.18527.53/.936/.13926.66/.923/.12027.17/.927/.169
ConeGaussian (ours)27.01/.920/.23027.47/.931/.18127.69/.942/.12427.02/.939/.07727.30/.933/.153
PH → FHperipheral img3DGEER (baseline)23.82/.892/24.11/.897/24.32/.901/24.12/.890/24.09/.895/
ConeGaussian (ours)23.83/.893/24.15/.898/24.44/.907/24.36/.904/24.20/.900/

Cross-camera rendering on ScanNet++ (FH = fisheye, PH = pinhole). FH→PH: trained on native fisheye views, rendered through the matched pinhole cameras without retraining; PH→FH is the reverse. Peripheral PSNR / SSIM over the radial band r > 0.7.

Citation

If you use ConeGaussian in your work, please cite our paper. The BibTeX below follows the public arXiv record.

@article{zhang2026conegaussian,
  title   = {ConeGaussian: Anti-Aliased Gaussian Ray-Tracing for Generic Central Cameras},
  author  = {Zhang, Deheng and Shi, Letian and Yang, Runyi and Li, Zhendong and Sun, Lei and
             Wu, Kanzhi and Chhatkuli, Ajad and Paudel, Danda Pani and Van Gool, Luc},
  journal = {arXiv preprint arXiv:2609.13397},
  year    = {2026},
  url     = {https://arxiv.org/abs/2609.13397}
}

References

  1. Deheng Zhang et al. ConeGaussian: Anti-Aliased Gaussian Ray-Tracing for Generic Central Cameras. arXiv, 2026.
  2. Zixun Huang, Cho-Ying Wu, Yuliang Guo, Xinyu Huang, and Liu Ren. 3DGEER: 3D Gaussian Rendering Made Exact and Efficient for Generic Cameras. ICLR, 2026. Code.
  3. Qi Wu, Janick Martinez Esturo, Ashkan Mirzaei, Nicolas Moënne-Loccoz, and Zan Gojcic. 3DGUT: Enabling Distorted Cameras and Secondary Rays in Gaussian Splatting. CVPR, 2025.
  4. Samuel Rota Bulò, Nemanja Bartolovic, Lorenzo Porzi, and Peter Kontschieder. Hardware-Rasterized Ray-Based Gaussian Splatting (VKRayGS). CVPR, 2025.
  5. Zehao Yu, Anpei Chen, Binbin Huang, Torsten Sattler, and Andreas Geiger. Mip-Splatting: Alias-free 3D Gaussian Splatting. CVPR, 2024.