GOFish: Full Field-of-View Gaussian Splatting and Mesh Extraction
Authors: Allen Tu, Meher Gitika Karumuri, Shifan Zhu, Hailing Wang, Yen-Liang Lin, David Held, Matthias Zwicker, Tom Goldstein
Organizations: Amazon · University of Maryland, College Park · University of Massachusetts Amherst · Northeastern University · Carnegie Mellon University
Robots, autonomous vehicles, and consumer 360° cameras use fisheye lenses for wide fields of view (FoVs). Simulation-ready digital twins require photorealistic rendering across the full FoV and an aligned collision mesh. However, prior fisheye Gaussian Splatting methods only rasterize up to 180° and do not produce meshes, while Gaussian surface reconstruction methods assume pinhole training images. We present GOFish, the first 3D Gaussian Splatting surface reconstruction method to train directly on fisheye images, rasterize FoVs beyond 180°, and extract an aligned mesh from the same scene. Calibrated densification recovers the surface across the entire FoV, while Calibrated Mip Filtering and Wide-Angle Appearance Modeling keep pixel blur and lens falloff out of the scene and mesh. Across the 200° FIORD and 205° FullCircle benchmarks, GOFish improves PSNR over the best prior method by 2.28 and 1.97 dB, respectively. It also outperforms fisheye rendering baselines within their own FoVs and achieves the highest mesh F-score on FIORD and the main ScanNet++ set. Together, the Gaussian scene and mesh form a LiDAR-free, simulation-ready digital twin that renders in real time, ray traces the full FoV, and provides collision geometry.
Figures & tables
FIORD [ 8 ]
FullCircle [ 5 ]
ScanNet++ [ 34 ]
Full ( 200∘ )
GOFish @ FoV
Full ( 205∘ )
GOFish @ FoV
Full ( 127∘ )
Method
FoV
PSNR ↑
SSIM ↑
LPIPS ↓
Δ PSNR ↑
Δ SSIM ↑
Δ LPIPS ↑
PSNR ↑
SSIM ↑
LPIPS ↓
Δ PSNR ↑
Δ SSIM ↑
Δ LPIPS ↑
PSNR ↑
SSIM ↑
LPIPS ↓
Fisheye-GS ∗ [ 22 ]
145∘
17.78
0.685
0.395
+5.06
+0.119
+0.167
14.01
0.630
0.495
+14.05
+0.263
+0.397
26.28
0.895
0.256
3DGUT [ 31 ]
160∘
19.86
0.740
0.316
+3.95
+0.057
+0.046
21.58
0.842
0.262
+1.62
+0.013
+0.030
28.93
0.913
0.214
3DGUT + PPISP [ 31 , 4 ]
160∘
20.18
0.743
0.312
+4.04
+0.058
+0.048
21.45
0.841
0.262
+1.88
+0.014
+0.030
28.93
0.913
0.213
3DGEER ∗ [ 14 ]
178∘
12.79
0.679
0.328
+2.03
+0.026
+0.027
12.65
0.715
0.336
+4.25
+0.040
+0.036
28.59
0.914
0.201
Table 1: Quantitative comparison against wide-angle rendering baselines. The Ag best , Ag second best , and Ag third best entries are highlighted. GOFish’s gain at each baseline’s FoV is Ag highlighted . ∗ Appendix B.3 details baseline adaptations for wide-angle rendering.
Figure 2: 3DGUT failures over a full field of view. (a) Its half-angle limit cuts rays beyond 80∘ from the axis ( orange ), and its positive-depth test fails beyond 90∘ ( red ). (b) Tiles come from the projected sigma-point extent ( blue ) but alpha from the exact ray response ( red ), so the Gaussian is skipped in the hatched tiles. (Bottom) 3DGUT + PPISP leaves a cutoff ring and tile-shaped smears, while GOFish renders the full FoV cleanly.
Figure 3: Calibrated Mip Filtering. The finest training view’s Jacobian sets the 3D filter +ϵi2I3 in the stored Gaussian covariance Σi ( blue ). Rendering view v adds the footprint +γJ+J+⊤ and rescales opacity by m ( orange ), while meshing uses Σi directly.
FIORD [ 8 ]
ScanNet++ [ 34 ]
Full ( 200∘ )
Common ( 90∘ )
Geometry
Full ( 127∘ )
Geometry
Method
FoV
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
P↑
R↑
F↑
PSNR ↑
SSIM ↑
LPIPS ↓
P↑
R↑
F↑
GOF [ 37 ]
Rectified
17.03
0.676
0.353
28.20
0.883
0.278
0.168
0.248
0.198
27.54
0.904
0.212
0.579
0.629
0.601
PGSR [ 2 ]
Rectified
16.81
0.670
0.363
28.44
0.892
0.273
0.225
0.293
0.239
27.39
0.898
0.241
0.698
0.677
0.687
SOF [ 26 ]
Rectified
16.62
0.660
0.363
26.15
0.852
0.311
0.163
0.240
0.192
27.10
0.898
0.218
0.620
0.667
0.641
MiLo [ 7 ]
Rectified
17.05
0.680
0.368
28.21
0.882
0.297
0.180
0.261
0.210
27.61
0.903
0.234
0.651
0.701
0.675
Table 2: Quantitative comparison against surface reconstruction baselines. The Ag best , Ag second best , and Ag third best entries are highlighted. Full scores each calibrated FoV and Common the shared rectified images; Section 5 defines both.
Figure 4: Qualitative rendering results on FIORD [ 8 ] and FullCircle [ 5 ] . Held-out views span the full FoV; metrics are per-scene.
Figure 5: Qualitative mesh results on FIORD [ 8 ] and FullCircle [ 5 ] . GOFish uses the Geometry Objective. Metrics are per-scene.
Figure 6: Ray tracing and mesh-based physics simulation. 3DGUT ray traces its 160∘ FoV using 3DGRT [ 24 ] and does not produce a mesh, so simulated objects have no surface to collide with. GOFish covers the full 200∘ FoV and supports collisions.
Figure 7: Rendering gain by ray angle on FIORD [ 8 ] ( cyan ) and FullCircle [ 5 ] ( magenta ). PSNR gain of GOFish over 3DGUT + PPISP [ 31 , 4 ] (solid) and over GOFish without Wide-Angle Appearance (dashed). As in Fig. 2 , 3DGUT + PPISP cuts rays beyond 80∘ ( orange ) and fails beyond 90∘ ( red ).
Variant
FoV
PSNR ↑
SSIM ↑
LPIPS ↓
F ↑
Train ↓
FPS ↑
GOF [ 37 ]
90°
17.03
0.676
0.353
0.198
104m
11.0
3DGRT + PPISP [ 24 , 4 ]
Full
18.42
0.712
0.313
0.159
108m
22.3
3DGUT + SOF [ 31 , 26 ]
160°
18.46
0.671
0.374
0.168
111m
17.9
3DGUT + PPISP [ 31 , 4 ]
160°
20.18
0.743
0.312
0.141
29m
84.3
+ Full-FoV Rasterization
Full
21.21
0.798
0.253
0.139
162m
91.1
+ Calibrated Mip Filtering
Full
21.19
0.804
0.239
0.240
103m
81.1
Table 3: Component analysis on FIORD [ 8 ] . Components are added cumulatively. + Calibrated Mip Filtering includes calibrated densification, and + Wide-Angle Appearance completes base GOFish. Appendix B.2 details the configurations.
Appendix figures & tables16 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 8: FIORD capture and calibration diagnostics [ 8 ] . (Top) SfM reconstructions are overlaid on LiDAR ( gray ). Points within 10 cm of LiDAR are green and others orange . Night_Out has no LiDAR. Cameras are black ; red marks those more isolated than any retained camera, including one off-panel (arrow). (a) Full-FoV 95th-percentile training luma (left) and a rim crop (right) for Building_In camera 2. Curves mark total field angles of 167∘ ( blue ) and 200∘ ( orange ), while magenta marks the dark band. (b) Held-out ground truth (left) and GOFish rendering (right) at the rim, with the calibrated edge in white.
ScanNet++ (3DGUT set) [ 34 , 31 ]
ScanNet++ (CoMe set) [ 34 , 27 ]
Full ( 127∘ )
Common
Geometry
Full ( 127∘ )
Common
Geometry
Method
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
P↑
R↑
F↑
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
P↑
R↑
F↑
GOF [ 37 ]
27.54
0.904
0.212
30.01
0.920
0.208
0.579
0.629
0.601
26.10
0.874
0.234
27.34
0.889
0.233
0.578
0.693
0.630
PGSR [ 2 ]
27.39
0.898
0.241
29.66
0.916
0.229
0.698
0.677
0.687
25.69
0.870
0.258
26.94
0.887
0.249
0.694
0.728
0.710
SOF [ 26 ]
27.10
0.898
0.218
28.83
0.914
0.214
0.620
0.667
0.641
26.29
0.876
0.221
27.20
0.889
0.225
0.603
0.724
0.657
MiLo [ 7 ]
27.61
0.903
0.234
29.75
0.916
0.231
0.651
0.701
0.675
26.35
0.877
0.247
27.50
0.891
0.247
0.652
0.726
0.687
Appendix
Table 4: Quantitative comparison on both ScanNet++ scene sets [ 34 ] . Left uses the six scenes of 3DGUT and Fisheye-GS [ 31 , 22 ] ; right uses CoMe’s six [ 27 ] . Full is the native 127∘ image and Common the official undistortion. GOFish is mapped to Common with the official map and a 2× box downsample; geometry uses CoMe’s 5 cm protocol. The Ag best , Ag second best , and Ag third best entries are highlighted.
Rendering
Geometry
Method
PSNR ↑
SSIM ↑
LPIPS ↓
P↑
R↑
F↑
Fisheye-GS ∗ [ 22 ]
24.71
0.838
0.236
3DGUT [ 31 ]
25.11
0.852
0.221
3DGUT + PPISP [ 31 , 4 ]
26.51
0.868
0.199
3DGEER ∗ [ 14 ]
24.42
0.837
0.235
Self-Calibrating GS ∗ [ 3 ]
22.66
0.759
0.332
Appendix
Table 5: Quantitative comparison on Tanks & Temples [ 18 ] . The Ag best , Ag second best , and Ag third best entries are highlighted. ∗ Appendix B.3 details baseline adaptations.
FIORD [ 8 ]
ScanNet++ [ 34 ]
Tanks & Temples [ 18 ]
Method
Train ↓
Mesh ↓
Total ↓
FPS ↑
Gaussians
Triangles
Train ↓
Mesh ↓
Total ↓
FPS ↑
Gaussians
Triangles
Train ↓
Mesh ↓
Total ↓
FPS ↑
Gaussians
Triangles
3DGS [ 17 ]
23m
23m
124
0.95M
16m
16m
168
0.97M
22m
22m
107
1.31M
Fisheye-GS ∗ [ 22 ]
42m
42m
135
0.60M
119m
119m
74.0
0.96M
21m
21m
115
1.49M
3DGUT [ 31 ]
28m
28m
92.1
1.03M
10m
10m
238
0.37M
24m
24m
105
1.00M
3DGUT + PPISP [ 31 , 4 ]
29m
29m
84.3
1.03M
11m
11m
209
0.35M
25m
25m
96.5
1.00M
3DGEER ∗ [ 14 ]
51m
51m
46.7
1.90M
67m
67m
112
1.41M
71m
71m
97.2
4.27M
Appendix
Table 6: Efficiency and representation size. Dataset averages follow Appendix B.2 . Training, meshing, and FPS are measured on an NVIDIA A10G GPU. GOFish FPS uses the real-time renderer detailed in Appendix A.6 . ⋆ denotes an NVIDIA A100 GPU run detailed in Appendix B.3 .
Figure 9: Representative surface-reconstruction failure cases. Panels (a)–(c) compare ground truth (left) with GOFish meshes (right). Panel (d) shows GOFish’s rendering (left) and mesh (right).
Dataset
Abbreviation
Scene
FIORD [ 8 ]
Kit.
Kitchen_In
Cor.
Corridor_Out
Road
Road_Out
Bld.
Building_In
Meet.
MeetingRoom_In
Bri.
Bridge_Out
Appendix
Scene abbreviations for Tables 7 – 10 .
FIORD [ 8 ]
FullCircle [ 5 ]
Full ( 200∘ )
GOFish @ FoV
Full ( 205∘ )
GOFish @ FoV
Method
FoV
Kit.
Cor.
Road
Bld.
Meet.
Bri.
Hall
Kit.
Cor.
Road
Bld.
Meet.
Bri.
Hall
Dark
F1
F2
Lab
Lou.
Per.
R1
R2
R3
Dark
F1
F2
Lab
Lou.
Per.
R1
R2
R3
PSNR ↑
Fisheye-GS ∗ [ 22 ]
145∘
18.72
16.22
17.19
18.18
16.28
17.47
20.42
+5.66
+2.93
+2.59
+6.56
+9.65
+3.43
+4.63
13.44
13.87
14.53
14.38
12.80
13.25
14.97
14.59
14.28
+15.05
+13.98
+14.05
+14.29
+8.24
+15.82
+15.51
+15.64
+13.88
3DGUT [ 31 ]
160∘
20.20
17.62
19.49
19.03
19.62
24.25
18.84
+3.99
+4.01
+2.48
+6.36
+5.27
− 1.51
+7.04
22.17
21.06
20.44
20.32
20.14
22.55
22.30
23.21
22.06
+1.40
+2.69
+1.15
+1.71
− 1.46
+2.63
+2.13
+2.68
+1.63
3DGUT + PPISP [ 31 , 4 ]
160∘
20.34
18.78
19.70
19.68
19.48
24.38
18.93
+4.36
+3.26
+2.14
+6.51
+6.12
− 1.17
+7.09
22.03
20.99
20.58
20.31
20.00
22.06
22.09
23.07
21.93
+1.74
+2.53
+1.44
+1.82
− 1.42
+3.13
+2.84
+3.00
+1.82
3DGEER ∗ [ 14 ]
178∘
14.19
10.39
11.52
12.29
13.50
10.06
17.55
− 0.39
+4.80
+3.55
+1.53
+0.46
+4.85
− 0.60
13.45
12.96
10.02
10.36
13.07
14.75
13.57
13.47
12.19
+4.66
+3.70
+5.22
+5.34
+1.48
+4.35
+4.86
+4.87
+3.72
Appendix
Table 7: Per-scene rendering results on FIORD [ 8 ] and FullCircle [ 5 ] for fisheye baselines. The Ag best , Ag second best , and Ag third best entries are highlighted. GOFish’s gain at each baseline’s FoV is Ag highlighted . Protocols follow Appendix B.2 .
FIORD [ 8 ]
FullCircle [ 5 ]
Full ( 200∘ )
Common ( 90∘ )
Full ( 205∘ )
Method
FoV
Kit.
Cor.
Road
Bld.
Meet.
Bri.
Hall
Kit.
Cor.
Road
Bld.
Meet.
Bri.
Hall
Dark
F1
F2
Lab
Lou.
Per.
R1
R2
R3
PSNR ↑
GOF [ 37 ]
Rectified
18.02
17.42
14.92
17.64
19.35
12.86
19.03
30.96
24.15
22.44
28.19
31.88
30.60
29.20
21.48
22.62
19.94
22.81
18.67
22.97
22.36
22.95
22.77
PGSR [ 2 ]
Rectified
17.82
17.12
14.56
18.36
18.81
12.59
18.43
30.37
25.14
24.34
29.31
31.00
29.34
29.54
21.08
23.35
20.04
23.30
18.31
23.08
22.46
23.10
23.59
SOF [ 26 ]
Rectified
18.08
16.92
13.26
17.00
19.30
12.73
19.05
30.07
21.53
17.87
26.00
30.57
28.65
28.32
21.13
22.41
19.55
22.72
19.62
22.03
22.02
22.67
23.63
MiLo [ 7 ]
Rectified
17.57
17.87
14.94
18.21
18.86
12.26
19.67
30.02
25.18
24.35
29.46
30.25
29.19
29.01
21.30
23.10
19.79
22.89
20.82
23.17
22.26
23.35
22.70
Appendix
Table 8: Per-scene rendering results on FIORD [ 8 ] and FullCircle [ 5 ] for surface baselines. The Ag best , Ag second best , and Ag third best entries are highlighted. Protocols follow Appendix B.2 .
ScanNet++ [ 34 ]
Tanks & Temples [ 18 ]
Full ( 127∘ )
Common
Pinhole
Method
FoV
0a5c
8d56
bb87
d415
e8ea
fe17
0a5c
8d56
bb87
d415
e8ea
fe17
Barn
Cat.
Court.
Ign.
Meet.
Truck
PSNR ↑
Fisheye-GS ∗ [ 22 ]
145∘
24.50
24.17
29.21
26.13
29.28
24.40
28.30
23.75
22.58
22.35
25.90
25.41
3DGUT [ 31 ]
160∘
29.54
26.09
30.97
28.21
33.10
25.66
29.10
23.65
22.84
22.82
26.30
25.96
3DGUT + PPISP [ 31 , 4 ]
160∘
29.84
25.94
30.99
28.11
33.16
25.54
30.18
26.00
24.02
25.01
27.06
26.79
3DGEER ∗ [ 14 ]
178∘
27.50
26.29
31.22
28.37
32.16
26.01
28.63
23.50
22.91
21.84
25.23
24.39
Appendix
Table 9: Per-scene rendering results on ScanNet++ [ 34 ] and Tanks & Temples [ 18 ] . The Ag best , Ag second best , and Ag third best entries are highlighted. Protocols follow Appendix B.2 .
FIORD [ 8 ]
ScanNet++ [ 34 ]
Tanks & Temples [ 18 ]
Method
Kit.
Road
Bld.
Meet.
Bri.
Hall
0a5c
8d56
bb87
d415
e8ea
fe17
Barn
Cat.
Court.
Ign.
Meet.
Truck
Precision ↑
GOF [ 37 ]
0.488
0.016
0.108
0.292
0.031
0.074
0.539
0.546
0.615
0.647
0.562
0.566
0.522
0.402
0.432
0.726
0.400
0.585
PGSR [ 2 ]
0.647
0.025
0.176
0.346
0.066
0.090
0.702
0.643
0.696
0.786
0.648
0.715
0.521
0.337
0.190
0.831
0.368
0.611
SOF [ 26 ]
0.473
0.006
0.103
0.307
0.031
0.060
0.561
0.555
0.702
0.675
0.608
0.622
0.586
0.393
0.506
0.682
0.399
0.553
MiLo [ 7 ]
0.532
0.012
0.137
0.307
0.027
0.065
0.705
0.590
0.619
0.706
0.644
0.646
0.551
0.368
0.413
0.774
0.426
0.602
CoMe [ 27 ]
0.508
0.016
0.148
0.352
0.039
0.077
0.639
0.562
0.716
0.667
0.680
0.648
0.558
0.446
0.543
0.801
0.491
0.604
Appendix
Table 10: Per-scene geometry results. The Ag best , Ag second best , and Ag third best entries are highlighted. Protocols follow Appendix B.2 .
Figure 10: Additional qualitative rendering results on FIORD [ 8 ] . Metrics are per-scene.
Figure 11: Additional qualitative rendering and mesh results on FIORD [ 8 ] . Metrics are per-scene.
Figure 12: Additional qualitative rendering results on FullCircle [ 5 ] . Metrics are per-scene.
Figure 13: Qualitative rendering results on ScanNet++ [ 34 ] . Metrics are per-scene.
Figure 14: Qualitative rendering and mesh results on ScanNet++ [ 34 ] . Metrics are per-scene.
Figure 15: Qualitative rendering and mesh results on Tanks & Temples [ 18 ] . Metrics are per-scene.
3D Gaussian Splatting (3DGS) has enabled efficient 3D scene reconstruction from everyday images with real-time, high-fidelity rendering, greatly advancing VR/AR applications. Fisheye cameras, with their wider field of view (FOV), promise high-quality reconstructions from fewer inputs and have recently attracted much attention. However, since 3DGS relies on rasterization, most subsequent works involving fisheye camera inputs first undistort images before training, which introduces two problems: 1) Black borders at image edges cause information loss and negate the fisheye's large FOV advantage; 2) Undistortion's stretch-and-interpolate resampling spreads each pixel's value over a larger area, diluting detail density -- causes 3DGS overfitting these low-frequency zones, producing blur and floating artifacts. In this work, we integrate fisheye camera model into the original 3DGS framework, enabling native fisheye image input for training without preprocessing. Despite correct modeling, we observed that the reconstructed scenes still exhibit floaters at image edges: Distortion increases toward the periphery, and 3DGS's original per-iteration random-selecting-view optimization ignores the cross-view correlations of a Gaussian, leading to extreme shapes (e.g., oversized or elongated) that degrade reconstruction quality. To address this, we introduce a feature-overlap-driven cross-view joint optimization strategy that establishes consistent geometric and photometric constraints across views-a technique equally applicable to existing pinhole-camera-based pipelines. Our DirectFisheye-GS matches or surpasses state-of-the-art performance on public datasets. Project Page: https://yzxqh.github.io/DirectFisheye-GS/ .
Zhengxian Yang, Fei Xie, Xutao Xue +5
BNRist, Tsinghua University · Shanghai AI Lab · Beihang University +1
Omnidirectional images are increasingly used in robotics and vision due to their wide field of view. However, extending 3D Gaussian Splatting (3DGS) to panoramic camera models remains challenging, as existing formulations are designed for perspective projections and naive adaptations often introduce distortion and geometric inconsistencies. We present Spherical-GOF, an omnidirectional Gaussian rendering framework built upon Gaussian Opacity Fields (GOF). Unlike projection-based rasterization, Spherical-GOF performs GOF ray sampling directly on the unit sphere in spherical ray space, enabling consistent ray-Gaussian interactions for panoramic rendering. To make the spherical ray casting efficient and robust, we derive a conservative spherical bounding rule for fast ray-Gaussian culling and introduce a spherical filtering scheme that adapts Gaussian footprints to distortion-varying panoramic pixel sampling. Extensive experiments on standard panoramic benchmarks (OmniBlender and OmniPhotos) demonstrate competitive photometric quality and substantially improved geometric consistency. Compared with the strongest baseline, Spherical-GOF reduces depth reprojection error by 57% and improves cycle inlier ratio by 21%. Qualitative results show cleaner depth and more coherent normal maps, with strong robustness to global panorama rotations. We further validate generalization on OmniRob, a real-world robotic omnidirectional dataset introduced in this work, featuring UAV and quadruped platforms. The source code and the OmniRob dataset will be released at https://github.com/1170632760/Spherical-GOF.
Zhe Yang, Guoqiang Zhao, Sheng Wu +2
School of Artificial Intelligence and Robotics, Hunan University, China · National Engineering Research Center of Robot Visual Perception and Control Technology, Hunan University, China
Feed-forward foundation models for multi-view 3-dimensional (3D) reconstruction have been trained on large-scale datasets of perspective images; when tested on wide field-of-view images, e.g., from a fisheye camera, their performance degrades. This degradation arises from changes in spatial arrangements of pixels induced by the non-linear projection model that maps 3D points onto the 2D image plane. While one may surmise that training on fisheye images would resolve this problem, there are far fewer fisheye images with ground truth than perspective images, which limits generalization. To enable inference on imagery exhibiting high radial distortion, we propose Fisheye3R, a novel adaptation framework that extends these multi-view 3D reconstruction foundation models to natively accommodate fisheye inputs without performance regression on perspective images. To address the scarcity of fisheye images and ground truth, we introduce flexible learning schemes that support self-supervised adaptation using only unlabeled perspective images and supervised adaptation without any fisheye training data. Extensive experiments across three foundation models, including VGGT, π3, and MapAnything, demonstrate that our approach consistently improves camera pose, depth, point map, and field-of-view estimation on fisheye images. Code is available at https://github.com/android-xr/fisheye3r.