SlowGuess/NeurIPS_2023_OCR huggingface dataset:
cube maps were converted from panoramas. To render a panoramic view for evaluation, we cast rays in IBRNet and NeuRay with spherical projection (refer to Sec. 3.1) and aggregate features with their original perspective projection. We use  $\mathrm{NeuRay}^*$  and IBRNet* to denote variants of NeuRay and IBRNet which render panoramas. We did not compare with methods based on multi-sphere images (MSI) [2, 8] as they can only render novel views within the smallest sphere of MSI, which are unsuitable for wide-baseline panoramas. In the supplementary materials, we provide additional analysis on per-scene fine-tuning of PanoGRF and also compare it with Cross Attention Renderer [7].
Table 1: Quantitative comparisons with baseline methods on Matterport3D. The best results are in bold.
baseline method	1.0m	1.5m	2.0m
WS-PSNR↑	SSIM↑	LPIPS↓	WS-PSNR↑	SSIM↑	LPIPS↓	WS-PSNR↑	SSIM↑	LPIPS↓
S-NeRF	15.25	0.579	0.546	14.16	0.563	0.580	13.13	0.523	0.607
OmniSyn	22.90	0.850	0.244	20.31	0.790	0.317	18.91	0.761	0.354
IBRNet*	25.72	0.855	0.258	21.69	0.751	0.382	20.04	0.706	0.431
NeuRay*	24.92	0.832	0.260	21.92	0.766	0.347	19.85	0.715	0.407
PanoGRF	27.12	0.876	0.195	23.38	0.811	0.282	20.96	0.761	0.352
* means models are trained with cubemap projection and evaluated with equirectangular projection.
Sample 1 (Replica)
Sample 2 (Matterport3D)
IBRNet* [32]
NeuRay* [20]
Figure 3: Qualitative comparison on Replica and Matterport3D between IBRNet*, OmniSyn, NeuRay* and PanoGRF.
PanoGRF
Analysis On Matterport3D and Replica, we quantitatively compared PanoGRF with the baseline methods. The results can be found in Table. 1 and Table. 2. Almost all the metrics show that PanoGRF outperforms other methods significantly. We show the qualitative comparisons in Fig. 3. IBRNet* and NeuRay* aggregate features based on perspective projection. Due to the limited field of view, 3D sample points are often projected somewhere behind the source perspective camera ( $z$ -depth<0) or outside the image border during pixel alignment. In this case, the aggregated features are incorrect, causing bad rendering results. As for OmniSyn, its rendering outputs exhibit ghosting artifacts, particularly notable at the boundaries of the two sofas in Sample 1 of Fig. 3. Unlike these methods, PanoGRF is a generalizable spherical NeRF which is more appropriate for panoramic images due to the use of spherical coordinates. It achieves superior accuracy in synthesizing object boundaries and demonstrates better pixel alignment, as evident from the results showcasing the sofas in Sample 1 and the desk in Sample 2 of Fig. 3). On Residential, we also compared PanoGRF with S-NeRF, IBRNet*, NeuRay*. The results of S-NeRF show severe floaters (See the ceilings of Sample 1 in Fig. 4). As
Sample 1 (Residential)
Figure 4: Qualitative comparison on Residential between S-NeRF, IBRNet*, NeuRay* and PanoGRF.
Sample 2 (Residential)
converting panoramas into perspective views brings information loss, the perspective generalization methods IBRNet* and NeuRay* have notable artifacts. In contrast, PanoGRF demonstrates excellent generalization performance on the Residential dataset, as shown in Fig. 4. Additional qualitative comparisons can be seen in the supplementary material.
Table 2: Quantitative comparison with baseline methods on Replica and Residential Dataset
Dataset	Replica (1.0m)	Residential (about 0.3m)
method	PSNR↑	WS-PSNR↑	SSIM↑	LPIPS↓	PSNR↑	WS-PSNR↑	SSIM↑	LPIPS↓
S-NeRF	16.91	16.10	0.723	0.443	23.06	22.47	0.741	0.435
OmniSyn	23.91	23.17	0.898	0.189	-	-	-	-
IBRNet*	23.35	22.65	0.854	0.291	22.95	22.47	0.735	0.498
NeuRay*	26.62	25.90	0.899	0.187	23.01	22.38	0.753	0.427
PanoGRF	30.08	29.22	0.937	0.134	31.64	31.03	0.909	0.207
We conducted ablation studies to evaluate the effectiveness of the key components in mono-guided spherical depth estimator:  $360^{\circ}$  monocular depth and multi-view stereo. We provide qualitative comparisons of  $360^{\circ}$  depth estimation quality on Matterport3D in Fig. 5, and analyze the view synthesis quality on Replica in Table. 3. More results can be found in the supplementary material.
$360^{\circ}$  monocular depth We removed the  $360^{\circ}$  monocular depth guidance and kept the total number of depth candidates unchanged ( $N_{uni} = 64$ ) in the depth sampling. Under three camera baselines, all the metrics dropped after removing the  $360^{\circ}$  monocular depth. Especially, under the camera baseline of 2.0 meters, WS-PSNR dropped by 1.33dB without monocular depth. This removal resulted in error-prone object boundaries, such as the bedside and wooden pillar (shown in Fig. 6). The guidance of monocular depth can give more accurate depth candidates and mitigates the view inconsistency problem, which  $360^{\circ}$  multi-view stereo cannot handle alone.
$360^{\circ}$  multi-view stereo We removed  $360^{\circ}$  multi-view stereo and used  $360^{\circ}$  monocular depth directly as the input of the geometry feature extraction in PanoGRF. In this case, WS-PSNR dropped
more than  $1.0\mathrm{dB}$  under the camera baselines of 1.5 and 2.0 meters. And LPIPS became 0.165 from 0.134 under the baseline of 1.0 meters. Without multi-view stereo, multi-view consistency of geometry is not guaranteed, degrading the quality of novel view synthesis results. In Fig. 6, we observed the presence of ghosting artifacts near the left wooden pillar when relying solely on  $360^{\circ}$  monocular depth.
Table 3: Ablation studies on Replica
baseline	1.0m	1.5m	2.0m
method	WS-PSNR↑	SSIM↑	LPIPS↓	WS-PSNR↑	SSIM↑	LPIPS↓	WS-PSNR↑	SSIM↑	LPIPS↓
w/o Mono	28.71	0.935	0.136	25.53	0.898	0.188	23.33	0.864	0.249
w/o MVS	28.23	0.925	0.165	25.15	0.888	0.227	23.15	0.855	0.274
full	29.22	0.937	0.134	26.38	0.903	0.187	24.48	0.885	0.223
In this paper, we propose PanoGRF, generalizable spherical radiance fields for wide-baseline panoramas. We aggregate the appearance and geometry features from input panoramas through spherical projection to avoid panorama-to-perspective conversion. To address the view inconsistency problem, we use  $360^{\circ}$  monocular depth to guide the spherical depth sampling and obtain a more accurate geometric prior for the spherical radiance fields. Experiments on multiple datasets verify that PanoGRF can render high-quality novel views given wide-baseline panoramas.
Limitations Similar to other generalizable radiance fields, PanoGRF suffers from the issue of rendering speed. Additionally, since we only train PanoGRF on indoor data due to the lack of large-scale outdoor  $360^{\circ}$  datasets, its generalization performance can be limited when applied to outdoor scenes with significantly different depth scales.
Societal impact This method may be used to synthesize fake or deceptive panoramas, combined with generative methods.
Figure 5: Qualitative results of ablation studies for depth estimation on Matterport3D. Mono only and MVS only respectively refer to the results obtained when using only  $360^{\circ}$  monocular depth and  $360^{\circ}$  multi-view stereo. The use of  $360^{\circ}$  monocular depth alone does not ensure multi-view consistency, resulting in potential discrepancies between the predicted scale and the ground truth in certain regions. Due to the occlusion problem, using only  $360^{\circ}$  MVS results in inaccurate and less detailed depth predictions, especially at the boundaries of objects.
This work was supported by the Natural Science Foundation of China (Project Number 62132012) and Tsinghua-Tencent Joint Laboratory for Internet Innovation Technology.
w/o MVS
w/o Mono
Figure 6: Qualitative results of ablation studies for novel view synthesis on Replica.
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Table 4: Additional ablation studies on Matterport3D
Dataset	Matterport3D (1.0m)
method	PSNR↑	WS-PSNR↑	SSIM↑	LPIPS↓
w/o appearance	5.44	5.24	0.001	0.707
w/o geometry	26.25	25.25	0.839	0.263
full	28.10	27.10	0.876	0.195
A More Results of Qualitative Comparisons
Qualitative comparisons with baseline methods on Replica and Matterport3D can be seen in Fig. 7 and Fig. 8, respectively.
Figure 7: Qualitative comparisons with baseline methods on Replica.
OmniSyn
IBRNet
NeuRay
Figure 8: Qualitative comparisons with baseline methods on Matterport3D.
OmniSyn
IBRNet
NeuRay
PanoGRF
Ground Truth
Table 5: Ablation studies for depth estimation on Matterport3D
setting	L1↓	L2↓	RMSE↓	WS-L1↓	WS-L2↓	WS-RMSE↓
MVS only	0.1731	0.5048	0.5831	0.1984	0.2806	0.4731
Mono only	0.2452	0.3175	0.4731	0.2445	0.2729	0.4522
full	0.1441	0.2047	0.3877	0.1502	0.1624	0.3546
Table 6: The impact of different backbones for depth estimation on Matterport3D
setting backbone)	L1↓	L2↓	RMSE↓	WS-L1↓	WS-L2↓	WS-RMSE↓	parameters(M)
MVS(resnet-18)	0.1731	0.5048	0.5831	0.1984	0.2806	0.4731	29.75
MVS(resnet-34)	0.1654	0.4820	0.5676	0.1844	0.2577	0.4493	39.39
MVS(resnet-50)	0.1598	0.4725	0.5630	0.1822	0.2446	0.4442	47.10
MVS(resnet-101)	0.1642	0.4994	0.5717	0.1835	0.2519	0.4441	65.22
MVS(resnet-18)+Mono	0.1441	0.2047	0.3877	0.1502	0.1624	0.3546	58.95
MVS(resnet-34)+Mono	0.1549	0.2231	0.4120	0.1684	0.1878	0.3844	68.59
MVS(resnet-50)+Mono	0.1519	0.2379	0.4188	0.1675	0.1955	0.3887	76.30
MVS(resnet-101)+Mono	0.1735	0.2673	0.4452	0.1831	0.2129	0.4023	94.42
Table 7: The impact of different numbers of depth candidates  ${N}_{mono}$  for depth estimation on Matterport3D
Nmono	L1↓	L2↓	RMSE↓	WS-L1↓	WS-L2↓	WS-RMSE↓
1	0.1586	0.2498	0.4317	0.1745	0.1971	0.3937
3	0.1432	0.1993	0.3865	0.1529	0.1649	0.3580
5	0.1441	0.2047	0.3877	0.1502	0.1624	0.3546
7	0.1496	0.2252	0.4104	0.1640	0.1896	0.3832
9	0.1645	0.2912	0.4511	0.1752	0.2215	0.4059
16	0.1596	0.2379	0.4188	0.1675	0.1955	0.3887
32	0.1735	0.2673	0.4452	0.1831	0.2129	0.4023
48	0.1689	0.2618	0.4333	0.1776	0.2047	0.3941
64	0.1604	0.2432	0.4162	0.1669	0.2004	0.3853
Table 8: The impact of different values of  $\sigma$  for depth estimation on Matterport3D
σ	L1↓	L2↓	RMSE↓	WS-L1↓	WS-L2↓	WS-RMSE↓
0.1	0.1544	0.2515	0.4261	0.1672	0.1915	0.3830
0.5	0.1441	0.2047	0.3877	0.1502	0.1624	0.3546
1.0	0.1689	0.2686	0.4424	0.1803	0.2124	0.4029
1.5	0.1426	0.2457	0.4254	0.1563	0.1759	0.3723
B Spherical Projection
Equirectangular-to-spherical The transformation from the equirectangular image coordinate system to the polar coordinate system is defined as:
$$
\phi = v / H * \pi
$$
$$
\theta = u / W * 2 \pi - 0. 5 \pi , \tag {6}
$$
where  $\phi, \theta$  represent the latitude and longitude of the sphere,  $u, v$  represent the rows and columns of the panorama,  $H$  and  $W$  represent the height and width of the panorama respectively.
Spherical-to-cartesian The transformation from the polar coordinate system to the 3D Cartesian coordinate system is:
$$
x = \sin (\phi) * \cos (\theta)
$$
$$
y = \cos (\phi) \tag {7}
$$
$$
z = \sin (\phi) * \sin (\theta).
$$
Cartesian-to-spherical The camera cartesian coordinate  $(x,y,z)$  is transformed into the polar coordinate  $(\theta ,\phi ,t)$ $(t\in \mathbb{R}^{+}$  denotes its spherical depth in view  $I_{j})$  by:
$$
t = \sqrt {x ^ {2} + y ^ {2} + z ^ {2}}
$$
$$
\theta = \arctan \left(\frac {z}{x}\right) \tag {8}
$$
$$
\phi = \operatorname {a r c c o s} (\frac {y}{t}).
$$
Table 9: Quantitative comparison with Cross Attention Renderer [7] on Matterport3D and Replica
Dataset	Matterport3D (1.0m)	Replica(1.0m)
method	PSNR↑	SSIM↑	LPIPS↓	PSNR↑	SSIM↑	LPIPS↓
CAR [7]	22.87	0.7679	0.3108	23.60	0.8594	0.2515
PanoGRF	27.78	0.8158	0.2444	29.87	0.9046	0.1604
Table 10: Comparisons with NeuRay [20] given multi-view inputs on Matterport3D
Dataset	Matterport3D (1.0m)
method	PSNR↑	WS-PSNR↑	SSIM↑	LPIPS↓
NeuRay [20]	27.82	26.74	0.8614	0.2312
PanoGRF	28.99	27.91	0.8762	0.2071
Figure 9: Qualitative comparisons between PanoGRF and NeuRay on Matterport3D with multi-view panoramic inputs.
Spherical-to-equirectangular The spherical polar coordinate  $(\theta, \phi, t)$  is turned into the equirectangular image coordinate  $(u, v)$  by the inverse process of Eq. 6.
C More Ablation Studies for  $360^{\circ}$  View Synthesis
We conducted ablation studies on Matterport3D, and the results are shown in Table. 4. In the "w/o appearance feature" ablation study, we replaced the appearance feature vector with a zero vector to disable the appearance feature while keeping other modules unchanged. We found that the model without appearance features loses its ability to infer the color of novel views entirely, as the generalizable renderer heavily relies on appearance cues from input views. In the "w/o geometry feature" ablation study, we replaced the geometry feature vector with a zero vector to disable the geometry feature while keeping other modules unchanged. We observed that although the model can still infer normal results, its performance is significantly worse than the original (full) model.
D Comparisons with NeuRay [20] Given Multi-view Inputs
Our method is not limited to two panoramas. For instance, when rendering a test view in the renderer module, we use  $N$  input panoramas as reference images, and the renderer does not need to be modified. In the  $360^{\circ}$  spherical depth estimator module, for each reference image, we use the other  $N - 1$  input panoramas as source images. We average the multiple cost-volumes obtained during  $360^{\circ}$  multi-view matching process between the reference image and each source image. The rest is unchanged. In this way, our method can be applied to the multi-view panoramic inputs.
To further verify the effectiveness of our method, we conducted comparative experiments with NeuRay using multiple panoramic image as inputs. We placed the four input viewpoints at the
Figure 10: Qualitative comparisons with NeuRay beyond the camera baseline on Matterport3D. We synthesized novel views at positions 0.25 meters above the middle point between two input viewpoints. The input viewpoints are 1.0 meters apart. Our method can achieve better results than NeuRay beyond the camera baseline.
PanoGRF
Figure 11: Failure case. The carpet area behind the bed was not visible in the input viewpoints, but it becomes visible in higher viewpoints. NeuRay and PanoGRF tend to produce different and blurry results compared to the ground truth because they lack generative power. Combining existing diffusion generative models could potentially address this issue. We leave this as future work.
corners of a horizontal square and tested the rendering performance at the center viewpoint and other viewpoints located at -0.4, -0.2, -0.1, -0.05, 0.05, 0.1, 0.2, and 0.4 meters in the vertical direction from the center viewpoint. The diagonal length of the square is 1.0 meters. Table. 10 and Fig. 9 present the quantitative and qualitative comparison results between PanoGRF and NeuRay. As shown, PanoGRF still largely outperforms NeuRay with multiple panoramic inputs.
This experiment is added during the rebuttal period. Due to the limited time, we trained PanoGRF only for 20k iterations and NeuRay for 80k iterations. The learning decay strategies are similar to the setting of two views.
E Comparisons with NeuRay [20] beyond Camera Baseline and Failure Case
We conducted an additional experiment where novel views were generated at positions 0.25 and 0.5 meters above the middle point between two input viewpoints. The input viewpoints are 2.0 meters apart. We compared the quantitative and qualitative results of our method with NeuRay's as shown in Table. 11 and Fig. 10. PanoGRF consistently surpassed NeuRay's performance, indicating its capacity to yield superior results beyond the camera baseline.
We also present the failure case of PanoGRF under such condition in Fig. 11. In some viewpoints, a previously occluded area may be visible and since this area has not been seen in either of the two
Table 11: Comparisons with NeuRay [20] beyond Camera Baseline on Matterport3D
Dataset	Matterport3D (1.0m)
distance	method	PSNR↑	WS-PSNR↑	SSIM↑	LPIPS↓
0.25m	NeuRay	20.66	20.05	0.714	0.409
0.25m	PanoGRF	21.98	21.30	0.763	0.348
0.5m	NeuRay	20.39	19.94	0.711	0.420
0.5m	PanoGRF	21.99	21.42	0.769	0.349
existing viewpoints, the synthesis of this area is not effective. The area, which has not been seen in either of the existing viewpoints may be able to be filled in by combining with the existing diffusion generative approach. This is the next direction we plan to investigate.
F Experiments for Mono-guided Spherical Depth Estimator
F.1 Ablation Studies for Mono-guided Spherical Depth Estimator
To further validate the effectiveness of the key components, namely  $360^{\circ}$  multi-view stereos and  $360^{\circ}$  monocular depth, we conducted ablation studies specifically focused on spherical depth estimation. For evaluation purposes, we selected three commonly used metrics:  $L_{1}, L_{2}$ , and RMSE. Additionally, we also used  $\mathrm{WS - }L_{1}$ ,  $\mathrm{WS - }L_{2}$ , and  $\mathrm{WS - RMSE}$  as metrics, which incorporate weighted latitudes of equirectangular images to simulate WS-PSNR [29]. This approach aims to mitigate the impact of equirectangular projection distortion. We selected the first 1000 panorama pairs from Matterport3D as our test data, with a camera baseline of 1 meter. For the evaluation, we considered depth values within the range of [0.1, 10] as valid.
The quantitative results of our ablation studies are presented in Table 5, while the qualitative results can be observed in Fig. 12. The experiments clearly demonstrate the importance of each module in achieving accurate depth estimation. Removing either the  $360^{\circ}$  multi-view stereo or the  $360^{\circ}$  monocular depth significantly reduces the depth accuracy. Using only  $360^{\circ}$  monocular depth does not guarantee multi-view consistency, resulting in potential discrepancies between the predicted scale and the ground truth in certain regions. The occlusion problem poses a challenge for using only  $360^{\circ}$  MVS, particularly at the boundaries of objects. Consequently, the depth predictions in these regions are inaccurate and lack detail.
F.2 Different Backbones for  $360^{\circ}$  Multi-view Stereo
Introducing  $360^{\circ}$  monocular depth to  $360^{\circ}$  multi-view stereo does result in an increase in the number of model parameters. However, it is important to note that the improvement in depth accuracy is not attributed to the increase in parameters. In our experiments, we increased the model size of  $360^{\circ}$  MVsNet by using larger backbones, specifically ResNet [9].
From Table. 6, we found that  $L_{2}$  and RMSE of  $360^{\circ}$  MVSNet(ResNet-101) are still far inferior to those of  $360^{\circ}$  MVSNet(ResNet-18) together with the  $360^{\circ}$  monocular depth network [13]. This observation suggests that simply increasing the model size does not effectively address the view inconsistency problem in the wide-baseline setting. On the other hand, the introduction of  $360^{\circ}$  monocular depth provides a qualitative improvement to the accuracy of  $360^{\circ}$  multi-view stereo. By incorporating monocular depth information, the model gains additional cues that help mitigate the view inconsistency issue and improve depth estimation performance. Furthermore, when larger backbones were used as replacements, it was found that the performances of  $360^{\circ}$  MVS+Mono deteriorated. This could be attributed to the excessive model parameters leading to overfitting.
F.3 Different Hyperparameters for Mono-guided Spherical Depth Estimator
We conducted evaluations to assess the impact of different values for  $\sigma$  (standard deviation) and  $N_{mono}$  (number of monocular depth candidates) on mono-guided spherical depth sampling. The results are presented in Table 7 and Table 8.
Mono only