ST$^2$360D: Spatial-to-Temporal Consistency for Training-free 360 Monocular Depth Estimation
Authors: Zidong Cao
Jinjing Zhu
Hao Ai
Lutao Jiang
Yuanhuiyi Lyu
Hui Xiong
Venue: NeurIPS 2025 poster ()
Keywords: 360 camera
monocular depth estimation
Primary area: applications

Abstract: 360-degree monocular depth estimation plays a crucial role in scene understanding owing to its 180-degree by 360-degree field-of-view (FoV). To mitigate the distortions brought by equirectangular projection, existing methods typically divide 360-degree images into distortion-less perspective patches. However, since these patches are processed independently, depth inconsistencies are often introduced due to scale drift among patches. Recently, video depth estimation (VDE) models have leveraged temporal consistency for stable depth predictions across frames. Inspired by this, we propose to represent a 360-degree image as a sequence of perspective frames, mimicking the viewpoint adjustments users make when exploring a 360-degree scenario in virtual reality. Thus, the spatial consistency among perspective depth patches can be enhanced by exploiting the temporal consistency inherent in VDE models. To this end, we introduce a training-free pipeline for 360-degree monocular depth estimation, called ST²360D. Specifically, ST²360D transforms a 360-degree image into perspective video frames, predicts video depth maps using VDE models, and seamlessly merges these predictions into a complete 360-degree depth map. To generate sequenced perspective frames that align with VDE models, we propose two tailored strategies. First, a spherical-uniform sampling (SUS) strategy is proposed to facilitate uniform sampling of perspective views across the sphere, avoiding oversampling in polar regions typically with limited structural details. Second, a latitude-guided scanning (LGS) strategy is introduced to organize the frames into a coherent sequence, starting from the equator, prioritizing low-latitude slices, and progressively moving toward higher latitudes. Extensive experiments demonstrate that ST²360D achieves strong zero-shot capability on several datasets, supporting resolutions up to 4K.

ST>360D: Epatial-to-Temporrs Consistency for Training-free 360 Monocular Depth Estimation
Zidong Cao Jinjing Zhu Hao Ai
Lutao Jiang' Yuanhuiyi Lyu² Thrust of Artificial Intelligence, HKUST (Guangzhou), China
Hui Xiong 1.31
University of Birmingham, UK
Department of Computer Science and Engineering, HKUST, Hong Kong SAR, China paozidonge 1111119960mmmmmm com; jinjingzhu ma sgmail.com aihaol 9971 28 gmail com; jianglutao gmail. com; ryan. 1yu mai maaallgmmaii com; xionghui Satshuuuuuuttt.. hk
Abstract
360 monocular depth estimation plays a crucial role in scene understanding owing its 180 360 field-of-view (FoV). To mitigate the distortions brought by equirectangular projection, existing methods typically divide 360 images into distortion-less perspective patches. However, since these patches are processed independently, depth inconsistencies are often introduced due to scale drift among patches. Recently, video depth estimation (VDE) models have leveraged temporal consistency for stable depth predictions across frames. Inspired by this, we propose represent 360 image sequence of perspective frames, mimicking the viewpoint adjustments users make when exploring a 360 scenario in virtual reality. Thus. the spatial consistency among perspective depth patches can be enhanced by exploiting the temporal consistency inherent in VDE models. To this end, we introduce training-free pipeline for 360 monocular depth estimation, called ST"360D, Specifically, ST"360D transforms a 360 image into perspective video frames, predicts video depth maps using VDE models, and seamlessly merges these predictions into a complete 360 depth map. To generate sequenced perspective frames that align with VDE models, we propose two tailored strategies. First, a aeherical-unifomm sampling (SUS) strategy is proposed to facilitate uniform sampling of perspective views across the sphere, avoiding oversampling in polar regions typically with limited structural details. Second, latitude anittud-guuiee scanning (LGS) strategy is introduced to organize the frames into a coherent sequence, starting from the equator, prioritizing low-latitude slices, and progressively moving toward higher latitudes. Extensive experiments demonstrate that ST2360D achieves strong sero-shot capability several datasets, supporting resolutions up 4K.
Introduction
There has been growing interest in 360 cameras for capturing 180" 360 field-of-view (FoV). 360 monocular depth estimation is crucial for scene understanding
with a wide range of applications such autonomous driving [3 4) virtual reality (VR) 5 and visual navigation [8]. The most common representation 360 images is the equirectangular projection (ERP), which maps spherical data onto 2D plane for storage and processing. However, ERP representation introduces spherical distortions, particularly near the poles [9), stretching visual content unevenly and degrading the performance of perspective depth estimators when applied to 360 images.
"Equal contributions. Corresponding Author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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360 image
to video
Video Depth Estimation Model
Merge
Figure 1: Left: Our proposed training-free pipeline. We represent 360 image video frames, mimicking viewpoint adjustments in VR. The arrow - denotes the direction of the visual transition. The video frames are processed with the VDE model to predict video depth maps, which are merged into a 360 depth map. Right: 3T03 shows impressive zero-shot capability in outdoor scenario.
To mitigate distortions, existing methods mainly project 360 images onto distortion-less perspective patches [10] []] [2 [1), which are more compatible with standard perspective models. However, processing these perspective patches independently often leads to depth inconsistencies, causing noticeable seams and degraded performance. To address this issue. both training- -based and training- free methods have been proposed. ttaining-baset methods [10 14] fuse global features from ERP images with local features extracted from perspective patches. However, these methods heavily rely on expensive 360% depth annotations [ 16 177. and have limited zero-shot capabilities. Furthermore, due to limited computational resources, the input resolution for ERP images is constrained. In contrast, training-free -free methods [18 19] convert high-resolution ERP images into perspective patches, and estimate patch-wiss wise depths in parallel using pre-trained perspective models 21] Subsequently, the perspective depth patches are re- re-projected the ERP plane and merged into a high-resolution 360 depth map. Nevertheless, these methods still face challenges, such as dependence on time-consuming post-processing [8] or requiring additional 360 depth estimation models as references [19]
Recently, Video Depth Estimation (VDE) models [22 23 24] have demonstrated significant advance- ments, enabling stable and accurate depth predictions across video frames. Specifically, VDE models ensure depth alignment within overlapping regions of consecutive frames by leveraging temporal consistency, significantly mitigating depth flickering issues. This raises interesting question: Can the temporal consistency inherent in VDE models be leveraged to address the depth inconsistency challenges encountered by current 360 methods? To explore this, propose representing single 360 image as a sequence of perspective frames, closely mimicking the continuous viewpoint adjust- ments that occur in VR (See left of Fig. D. Within VR environments, users experience smooth visual transitions as their viewpoints gradually shift, producing coherent sequences of perspective images akin to continuous video stream. With this video representation, the spatial consistency among perspective depth patches can be enhanced by the temporal consistency in VDE models. To this end, we propose a novel training-free pipeline for 360 monocular depth estimation, named ST Specifically, 360D represents 360 image as sequence of perspective frames, then predicts video depth maps using VDE models, and finally seamlessly merges video depth maps back into the ERP plane to yield a complete 360 depth map.
To better align sequenced perspective frames with VDE models in our pipeline, we introduce two key strategies. First, we propose a spherical-unifom sampling (SUS) strategy, distributing viewpoints evenly across the sphere based on the vertices of subdivided icosahedron. Compared with conventional uniform sampling on the ERP plane, our strategy avoids oversampling polar regions with limited structural information. Second, we introduce a latitude-guided scanning (LGS) strategy that organizes the viewpoints to obtain perspective frames. Given that VDE models rely on initial frames for accurate subsequent predictions (22]. we begin scanning equatorial viewpoints with rich structural information and sequentially search subsequent viewpoints from their spherical neighborhoods. In addition, we partition the spherical surface into latitude slices. The scanning path originates from the lowest-latitude slice; after fully traversing viewpoints within one slice, the scanning path progressively shifts upward to higher latitudes. This ensures a smooth, coherent, and structurally informative sequence, enhancing the performance of VDE models (See right of Fig. [ Experiments demonstrate that ST2360D predicts consistent 360 depth maps with impressive zero- shot performance. Project page: https: https:://cazzidongg.ooo
1 STD36DD Depth/

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In summary, our contributions are fhree-fold: (I) We propose to represent 360 image sequence of perspective frames, unleashing the temporal consistency of VDE models enhance spatial consistency across perspective depth patches. (II) We present ST3360D, a training-free pipeline for 360 monocular depth estimation, along with two key strategies- -US and LGSSto better align with VDE models. (III) Extensive experiments demonstrate that 3T3360D achieves impressive zero-shot performance across diverse scenarios, supporting resolutions up to 4K.
2 Related Work
2.1 360 Monocular Depth Estimation
To mitigate spherical distortions, existing 360 monocular depth estimation approaches typically di- vide 360" images into perspective patches, categorized into training-based and training-free methods.
Training- based methods. With publicly available 360 depth datasets [ 16 17 training-based methods have been developed and achieved promising performance. Besides ERP-based methods [25] perspective patches as input, including cubemaps (CP) [10] [2] and tangent patches (TP) [13] [4]. However, these perspective patches sacrifice the global continuity in ERP, often leading to ambiguous depth scales and shifts among different patches. To address this, OmniFusion 13 introduces a geometry-aware fusion mechanism that integrates 3D geometric cues with patch features, while HRDFuse [14 collaboratively learns holistic contextual features from ERP images and regional structural details from TPs. Nevertheless, these methods heavily rely on labeled 360 depth datasets, which have limited number of samples and are primarily composed of indoor scenes. Consequently, these training-based methods have limited zero-shot capabilities, particularly for outdoor scenarios. To address it, recent approaches, including PanDA [25] and Depth Anywhere [1I, have leveraged the perspective depth foundation models [32 33 to generate pseudo depth labels for unlabeled 360 images. However, taking ERP images as input constrains them for high-resolution 360 depth estimation due to limited GPU memory. Instead. our ST 360D is training-free and can be flexibly extended 4K resolutions.
26 27 28
29 30), several methods adopt distortion-
Training-free methods. Recently, several training-free pipelines 18 19 have been proposed. The general pipeline is to project single 360 image into multiple perspective patches, leverage pre- trained models [20] to predict perspective depth patches in parallel, and subsequently re-project these patches onto the ERP plane to form a complete 360 depth map. 360MonoDepth [88] proposes deformable multi-scale alignment to recombine the individual depth patches. However, such post- processing is computationally expensive, particularly at high resolutions. A subsequent method [T9] introduces a pre-traine are-trained 360 depth estimator to generate an initial ERP depth map as reference, which is utilized for perspective depth patches to register to. Nevertheless, this referenced estimator still requires annotated 360 depth data for supervised training. In contrast, our ST 360D addresses the depth inconsistencies among patches by exploiting the temporal consistency in VDE models.
2.2 Video Depth Estimation
36), VDE methods aim to maintain temporal consistency, specifically by minimizing flickering effects between consecutive frames. Cur- rent VDE methods fall into two main categories: test-time optimization and feed-forward prediction. Test-time optimization approaches [37 23 38) fine-tune a pre-trained image-based depth estimation model on testing videos, typically requiring auxiliary information like camera poses or optical flow during inference. And
Unlike image-based depth estimation methods
prediction methods [39 40 41 are trained directly on video datasets, leveraging both spatial and temporal supervision. Recent advancements, including Chron- oDepth [42], DepthCrafter [43] and DepthAny Video (24). employ pre-trained video diffusion models (e.g., Stable Video Diffusion (44) to improve both stability and accuracy in video depth predictions. Furthermore, methods such as Video Depth Anything (VDA) (22 and BufferAnytime [45] extend the capabilities the vision foundation models (32) while ensuring temporal stability over long video sequences. To the best of our knowledge, ST2 360D is the first enhance the spatial consistency across perspective patches by leveraging the temporal consistency in VDE models.
3 Methodology
Our ST2360D a training-free pipeline for effective 360 depth estimation, leveraging the inherent temporal consistency in VDE models. We first briefly introduce the concepts of perspective patch
3

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1=0
1=1
=
ERP-uniform sample
Spherical-unifome sample
(a) Different levels of icosahedra
(b) Comparison between two sampling strategies
Figure 2: (a) Different levels of icosahedra, whose vertices are utilized for sampling viewpoints. (b) Compared with ERP plane sampling, the proposed spherical-uniform sampling strategy prevents oversampling near poles. vertices are the spherical neighbors of the vertice.
projection Sec. 3.1 To compile these perspective patches into video frames that align with VDE models, we propose two tailored strategies; spherical-unifee sampling (SUS) in Sec. 3.2 and latitude-guided scanning (LGS) in Sec. 3.3 The SUS strategy distributes the perspective patches evenly on the spherical surface, preventing oversampling near the poles with limited structural details. Moreover, the LGS strategy prioritizes perspective patches in the low-latitude slices and gradually progresses toward high-latitude slices. Finally, in Sec. Sec.[.4] we utilize VDE models predict video depth maps from the video frames and merge the video depth maps into complete 360 depth map.
3.1 Preliminary of Perspective Patch Projection
Given 360 image in ERP format I E Hxxx3 we extract N perspective patches P = (P,,..., Pv) based N viewpoints
(Vi,-... VN) } the spherical surface, each with spatial resolution S x S. The perspective projection from I to P involves three primary steps. Firstly, we determine parameters for N virtual cameras, including intrinsic and extrinsie matrices. The intrinsic matrix K is defined by the focal length f which is derived from the FoV a: f 2tan(o/2]
with the center point set to C₁ = C. = 2 Note that all virtual cameras share this intrinsic matrix. For the extrinsic matrix of the i-th virtual camera, denoted E; = [R,,,, t,). the rotation matrix R. transforms coordinates from the world coordinate system to camera coordinate system, determined construct pixel coor-
primarily by the viewpoint V;. The translation matrix t, is zero. Secondly, dinate map X E IR xxXWxx containing normalized image coordinates (u, v) E (0, 1). We project X from the image coordinates to the world coordinate system based K. The world coordinate system then transformed to the virtual camera coordinate system based on E;: [z, y, =]² = E, (u, V. 1)²". Finally, these virtual camera coordinates are projected onto spherical coordinates (0, Φ) using the following formula: [0, 6) aarcsin(2), (g/ Using the calculated spherical coordinates as indices, pixels from the original ERP image are sampled to generate the perspective patches. The entire process for generating patches P can be formulated as: P, = P(I, v,, S,a), 1.
3.2 Unnirieal-Uniform Sampling (SUS) Strategy
To obtain viewpoints v for perspective patch projection, straightforward method is to uniformly sample viewpoints on the ERP plane, as illustrated in Fig. (b). These sampled viewpoints are arranged from top to bottom to form video sequence. However, this planar sampling strategy leads suboptimal results (See Fig. 6). primarily due redundant sampling in polar regions, which typically contain limited structural details (e.g., ceilings, floors, or sky), depicted in Fig. Furthermore, since VDE models process fixed-length video frame segments, the initial segments may be dominated by less informative polar regions. As result, although denser sampling potentially enhances video stability, excessive sampling near the poles can degrade the overall performance.
To address this, we propose novel spherical-unifone sampling (SUS) strategy by leveraging icosahedron projection (ICOSAP) to evenly distribute viewpoints across the sphere (See Fig 2 a)). An icosahedron approximates spherical surface with significantly reduced distortion, especially as the subdivision level increases [46]] 47). At subdivision level the underlying icosahedral grid comprises 20 4 triangular faces and 10 x 4' + 2 vertices. Practically. we utilize these vertices as candidate viewpoints for generating perspective patches. To prevent redundant sampling in regions of limited structural detail, vertices located excessively close to the poles (with absolute latitude exceeding 899) are excluded. The SUS strategy provides two specific benefits our pipeline: (1) reduces redundant sampling in polar regions, reallocating viewpoints towards low- latitude regions that

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90
0
0
8
02
Spherical neighbor viewpoint searching. Based on the SUS strategy, directly searching for the next viewpoint along the horizontal or vertical directions on the ERP plane does not guarantee that the next viewpoint a spherical neighbor of the current one, depicted in Fig. (b). To ensure coherent video sequence, we propose searching for the next viewpoint among the spherical neighbors of the current viewpoint. From these neighbors, we select the viewpoint with the lowest absolute latitude, in accordance with the latitude-aware traversing strategy. The spherical neighbor relationships are constructed using ICOSAP, where neighbors are defined as vertices within the same triangular face (See Fig. a))). In practice, the searching process may encounter dead ends. In such cases, Traversing latitude in [-0,,01 0,]
90
Traversing latitude in
Traversing latitude in
[-0,, 10,y0,110 0,110 [0,,0.]
[-90',
[0.. 90*
Latitude slices
Scanning direction
Viewpoints
Structurally-eess Structurally-richer
Figure Illustration of the proposed latitude-aware traversing strategy, with set to 2 as an example.
contain richer structural details; and (2) captures spherical neighhorhood relationships, facilitating the generation of more continuous video sequences, as discussed in Sec. 3.3
3.3 Latitude-Guided Scanning (LGS) Strategy
After obtaining N viewpoints using the SUS strategy, our objective is organize these viewpoints obtain video frames 1F,....,PP. FN) that can be effectively compatible with VDE models.
Effect of starting latitude. The conventional scanning path of viewpoints starts from the north pole and progresses toward the south pole. Consequently, the initial viewpoints predominantly cover polar regions with less structural details. However, VDE models rely heavily initial frames to ensure accurate predictions in subsequent frames [22]. Therefore, as depicted in Fig. we investigate how the starting latitude of the scanning path influences performance. As demonstrated at the bottom of Fig. 4 performance improves significantly as the absolute value of the starting latitude decreases. This finding underscores the importance of prioritizing viewpoints from low-latitude regions early in the video sequence. Notably, for a given absolute latitude, initiating the scan in the upper hemisphere (negative latitudes) generally yields superior performance compared to starting in the lower hemisphere (positive latitudes). This phenomenon may be attributed the earlier placement of information-rich equator regions in the sequence when starting from the upper hemisphere. These insights motivate our subsequent designs.
Latitude-aware traversing. To organize information- rich regions early in the video sequence, we propose the latitude-aware traversing strategy to fully utilize the struc- tural information in ERP images. Specifically, we define K key latitudes 0 < 01 <
90'
0K S 90". As illustrated in Fig. 3 the scamning proceeds multiple traversals: First, viewpoints whose latitude satisties (0) <. 01 are arranged at the beginning of the video sequence. This ensures that viewpoints near the equator are prioritized and placed early. After traversing the low- slice, we move to higher- latitude slices. Viewpoints whose latitude falls within the range 0, < |0| < O2 are then added to the sequence. The traversal continues progressively, from to 0x, until viewpoints are incorporated into the sequence. In this way, we provide the VDE model with a sequence of frames that more accurately reflect the geometric structure of 360 image.
RAISE (m)
0.58
0.54
0.53
0.52
-72
-54
-36
-18
18
36
54
72
Lariiude
Figure 4: Top: Vertically shift the ERP image. Bottom: The influence of perfor- mance by varying starting latitude.
5

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Table 1: Zero-shot comparison on Matterport3D and Stanford2D3D datasets with 504 x 1008 input
resolution, following 25
Numbers are excerpted from [25]. Highlighting: best, second-best.
Matterport3D
15
Stanford2D3D
[6
Methods
AbsRel
RMSE
61 1
62 f
6% f
AbsRel
RMSE +
81 t
82 f
0g t
Marigold
0.2103
0.5745
65.46
91.36
98.19
0.2533
0.5069
58.78
87.60
96.57
DAv2-Small
0.2113
0.6063
65.44
91.58
98.00
0.2343
0.5041
62.25
89.37
96.90
PanDA-
25
0.1206
0,4915
86.89
96.57
98.60
0.1250
0.3462
83.60
97.05
99.46
Ours (VDA-Small)
0.1408
0.4670
84.17
96.08
98.66
0.1288
0.3529
86.76
96.60
98.89
DAv2-Large
0.1962
0.5522
68.37
93.03
98.28
0.2363
0.4884
60.57
88.77
96.89
PanDA-Large 25
0.1122
0.4690
88.65
97.00
98.77
0.1026
0.3260
88.98
96.84
99.36
Ours (VDg-Large)
0.1153
0.4284
89.23
96.38
98.49
0.1005
0.2986
91.16
97.99
99.29
Replica360-28
Input ERP
360MomoDepth-Meun
360MonoDDpth- Poisssn
Depth GT
ST'360D-Mean
11'360D-Poisson
Replica360-4k
Input ERP
360MonoDepth-Menn
360MonoDepth-Poisee
Depth GT
ST336DD-Meen
ST:360D-Poisson
Figure 5: Qualitative results on Replica360-2K (top) and Replica360-4K (bottom) datasets.
manually include all unexplored viewpoints neighbors of the current viewpoint. This spherical searching ensures the construction of a coherent video sequence.
3.4 Video Depth Estimation and Blending
Video depth map estimation. We consider VDA 12 as representative example of VDE models. During the pre-processing phase, VDA divides the input video frames into overlapping segments. The final frame of the last segment is optionally repeated to make it compatible with the temporal dimension. Each segment of video frames is processed by VDA to generate the corresponding disparity maps. In the post-processing stage, adjacent segments are aligned based on shared scale and shift, determined by two common key frames. The segments are then seamlessly integrated to maintain the original length of the video sequence. In implementation, the disparity maps are converted into depth maps before being re- projeccted to the ERP plane. Our empirical findings indicate that merging perspective video predictions in depth space yields better quantitative results.
Video depth map blending. After re-projecting video depth maps onto the ERP plane, we use mean blending efficiently recombine them. For each pixel the ERP plane, its depth value is calculated

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Table 2: Quantitative comparison on high-resolution datasets. is "Mean Blending"; P is "Poisson Blending". Numbers are excerpted from [9] Highlighting: best, second-best.
Datasct
Method
RMSEL
MAEL
AbsRell RMSE-logU)
511
52t
HoHoNet
49
0,4707
0.2620
0.0967
0.0629
90.50
97.27
97.09
SliceNet
50
0.4463
0.2153
0.0665
0.0513
95.17
98.07
99.54
UniFuse
0.6040
0,3309
0.1110
0.0728
87.79
95.70
98.38
PanDA-Small
25
0,4868
0.2770
0.1311
0,0771
85,03
96.18
98.47
PanDA-Base
0.4813
0.2747
0.1288
0.0755
85.34
96.13
98.54
PanDA-Large
2
0,4658
0.2584
0.1190
0.0713
87.27
96.55
98.59
Matterport3D-2K
360MonoDepth
18
0.7729
0.5106
0.2653
0.1253
60.38
85,55
94.70
360MonoDepth
(DAv2)
0.7968
0.4401
0.1822
0.1076
71.99
91.86
96.78
Peng et al. 19
0.4791
0.2655
0.1004
0.0662
90.23
97.09
98.93
Ours (VDA-Small))
0.6055
0,4033
0.2138
0.1069
71.07
90.86
96.75
Ours (VDA-lLarge) M
0.5110
0.3317
0.1718
0.0907
79.60
94.10
97.59
Ours (VDA-Small) P
0,4964
0.3044
O. 0.1624
0.0870
81.30
93.93
97.65
Ours (VDA--Large)
0.4460
0.2568
0.1264
0.0732
87.41
95.01
97.80
HoHoNet 49
0.0300
0,0193
0.1116
0.0671
90.31
95.90
98.11
SliceNet
50
0,0403
0.0279
0.1590
0.0896
85.15
93.88
96.44
UniFuse 12
0.0362
0.0248
0.1336
0.0774
86.87
95.94
97.72
PanDA-Small
25
0.0215
0,0140
0.0751
0.0447
95.20
99.25
99.74
PanDA-Base
25
0.0195
0.0127
0.0692
0.0415
96.26
99.38
99.79
PanDA-Large
0.0187
0.0119
0.0648
0.0393
96.80
99.41
99.83
Replica360-2K
360MonoDepth
0.0706
0.0456
0.1813
0.0865
78.48
93.56
98.34
360MonoDepth (DAv2)
0.0497
0,0317
0.1407
0.0763
81.68
96.59
99.35
Peng al. 19
0.0272
0.0182
0.1074
0.0643
90.98
96.07
98.28
Ours (VDA-Small)*
0.0241
0.0181
0.1099
0.0581
90.17
98.47
99.79
Ours (VDA-Large)) M
0.0201
0.0153
0.0882
0.0472
94.41
99.55
99.96
Ours (VDA-Small)
0.0163
0.0116
0.0669
0.0385
96.60
99.57
99.90
Ours (VDA-Large)
0.0144
0.0097
0.0503
0.0296
99.07
99.84
99.97
HoHoNet 49
0.0357
0.0249
0.1359
0.0744
85.17
94.63
96.61
SliceNet 50
0.0473
0.0341
0.1891
0.0994
78.31
93.17
96.77
UniFuse
12
0.0394
0.0289
0.1480
0.0818
82.20
96.26
98.54
PanDA-Small
0.0213
0.0141
0.0739
0.0429
96.16
99.52
99.85
PanDA-Base
25
0.0194
0.0128
0.0676
0.0402
96.77
99.51
99.86
PanDA-Large 25
0.0183
0.0118
0.0612
0.0365
97.52
99.71
99.92
Replica360-4K
360MonoDepth [18
0.0611
0.0400
0.1667
0.0815
80.04
95.25
98.47
360MonoDepth (DAv2)
0.0448
0.0288
0.1264
0.0689
84.98
97.54
99.69
Peng et al. [9
0,0332
0,0239
0.1309
0,0709
86.07
94.98
96.76
Ours (VDA-Small)*
0.0231
0.0167
0.0954
0.0510
92.20
99.15
99.96
Ours (VDA-Larree) M
0.0190
0,0140
0.0774
0.0422
96.61
99.81
99.96
Ours (VDA-Small)*
0.0157
0.0110
0.0602
0.0341
98.19
99.83
99.97
Ours (VDA-Large)*
0.0144
0.0096
0.0492
0.0292
99.16
99.84
99.96
by averaging the values from all re-projected video depth maps covering that pixel. Although 36D significantly improves spatial consistency in overlapping regions, minor visible seams may still persist in texture-less areas (See Fig.5). To mitigate this, we further incorporate Poisson blending [48), which utilizes both first-order (gradient) and second-order (Laplacian) derivatives from the re-projected depth maps, ensuring smoothness of the final 360 depth map.
4 Experiment
4.1 Experiment Setup
Datasets. We evaluate on five 360" depth datasets with varying resolutions. We use Matterport3D 15]
and Stanford2D3D [16] 512 1024 resolution (504 x 1008 in Tab. [T: Matterpor3D-2KK (15] and
Replica360-21 [5]] 1024 2048; and Replica360-4K [51] at the highest resolution of 2048 x 4096.
7

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Table 3: Ablation on the effectiveness of temporal consistency in VDE models.
Matterport3D
Replica360-2K
Replica360-4K
Methods
AbsRel
RMSE
51t
AbsRRl
RMSE +
AbsRel + RMSE +
Per frame input
0.1634
0,5003
79.42
0.0985
0.0208
91.42
0.0909
0.0202
92.47
Video frames input
0.1403
0.4664
84.31
0.0669
0.0163
96.60
0.0602
0.0157
98.19
A
14.14%
6.78%
4.89%
32.08%
21.63%
5.18%
33.77%
22.28%
5.72%
Implementation details. By default, we use VDA 22 with ViT-Small as the backhone, which is of feed-forward architecture. Since our pipeline is saining-frree, the parameters of VDE models are kept frozen during inference. All experiments are conducted on single NVIDIA A40 GPU.
Evaluation metries. Following [8] 12,
we utilize standard metrics for depth estimation: Absolute Relative Error (AbsRel), Root Mean Squared Error (RMSE). Mean Absolute Error (MAE), Root Mean Squared Logarithmic Error (RMSE-log), and three threshold percentage metries ó; for we apply scale-and-shh alignment in the depth space.
{1.25', 1.25², 1.25 Similar to [8 25
4.2 Qualitative and Quantitative Evaluation
Matterport3D and Stanford2D3D. As shown in Tab. ST*360D consistently outperforms the perspective methods DAv2 [33] and Marigold [34] highlighting its strong zero-shot capability on 360% images. Notably, without any 360 depth annotations for training. ST achieves results comparable to PanDA (25), which fine-tunes DAv2 [33 using synthetic 360 depth datasets [2]
Mat In Tab. 2 ST2360D performs slightly worse than previous data-specific methods 49 50 This is mainly due to that these methods are specifically trained on the Matterport3D dataset at resolution of 512 1024, allowing them leverage dataset-specific characteristics. Additionally, Peng et al. [1] outperform our ST2360D by employing a pre-trained 360 depth estimation model [49]. However, when compared with 360MonoDepth (18], which requires no 360 depth annotation, our ST"360D achieves superior performance. Furthermore, we have also replaced the perspective depth estimator used in 360MonoDepth with the recent DAv2. In this case, our 360D still surpasses 360MonoDepth. We ascribe it to the temporal consistency in VDE models, which reduces depth inconsistency during inference and benefits the overall performance. To compare with the recent method PanDA [25]. we first downsample input 360 images to a resolution of 504x 1008. The resulting depth predictions are then upsampled to the original image resolution using bilinear interpolation, following a similar pre-processing strategy of 360MonoDepth [18] Our 360D outperforms PanDA in most metries.
Rep2ica360-2K and Replica360-4K. In Tab. 2 the results demonstrate that our ST"360D, employing ViT-Small as the backbone with mean blending, already outperforms existing methods across most metrics (12 out of 14) on the Replica360-28 and Replica360-44 datasets. These findings underscore the effectiveness of our method for high-resolution 360 depth estimation, particularly highlighting its robust zero-shot capability. Furthermore, as illustrated in Fig. 5 our ST2360D exhibits more precise structural details compared to 360MonoDepth [18), such the chairs. Moreover, even when employing only mean blending, our 3603 significantly reduces visible seams in depth predictions. Our ST outperforms PanDA, which is specifically fine-tuned on synthetic 360 depth datasets.
4.3 Ablation Studies
By default, we employ VDA with ViT-Small as the backbone, with 252 x 252 patch resolution.
Effectiveness of temporal consistency. We conduct an ablation study presented in Tab. examining the influence of temporal consistency. Specifically, we feed each frame individually into the VDE model, degrading it into single-image depth estimation model. The results three datasets consistently demonstrate that temporal consistency significantly enhances overall performance.
Effectiveness of SUS strategy. In Fig. 6 using similar number of video frames, the SUS strategy obtains better results than ERP-plane uniform sampling. It because SUS strategy distributes viewpoints evenly on the spherical surface, avoiding oversampling at the polar regions.

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Table 5: Ablation the com- ponents LGS strategy on the Matterport3D dataset.
Table 6: Ablation on the choice of key latitudes in the LGS strategy on the Matterport3D dataset.
Table 4: Ablation on the scanning directions on the Matterport3D dataset.
Neigh. Traverse AbsRel & RMSE
Methods
AbsRel RMSE +
Choice
AbsRel
RMSE +
0.1776
0.5603
Horizontal
0.1776
0.5603
0.1586
0.5307
[18]
0,1544
0.5246
Vertical
0.1945
0.6128
/
0.1580
0,5291
[36)
0.1542
0.5236
Ours
0.1530
0.5216
0.1530
0.5216
(18, 36)
0.1530
0.5216
Table Ablation on the spatial resolution of perspective patches various datasets, We report the RMSE metric.
Table 7: Ablation on the FoV of perspective patches the Mat- terport3D dataset.
Datasets
252 252 378 x 378 518 x 518 756 x 756
Matterport3D
0.5216
0.4664
0.4661
0.4746
FoV
AbsRel
RMSE 4
Matterpor33D-2K
0.5497
0.5044
0.4964
0.5016
60
0.1687
0.5276
Replica360-2K
0.0245
0.0170
0.0163
0.0188
90
0.1530
0.5216
120
0.1796
0.6028
Replica360-4K
0.0240
0.0167
0.0157
0.0175
Scanning directions. Tab. presents an ablation study on scanning directions, Horizontal scanning arranges viewpoints horizontally, while vertical scanning arranges viewpoints vertically. Results show horizontal scanning performs better due to smoother transitions. Furthermore, our LGS strategy outperforms both horizontal and vertical strategies, showing the importance of prioritizing structurally-rich regions early in the sequence.
The LGS strategy. From Tab. 5 incorporating spherical neighbor viewpoint search improves performance by ensuring continuous scanning on the spherical surface. Employing latitude-aware traversing also enhances performance by prioritizing lat-tut regions. Crucially, integrating both components achieves optimal results. Furthermore, as shown in Fig. 6 the LGS strategy consistently improves overall performance on various frame counts. With both the SUS and LGS strategies, notable performance gain is observed when increasing the number of video frames from 40 to 160.
Key latitude in LGS. We check the effectiveness of key latitude settings within the LGS strategy Tab. [6] Us- ing larger key latitude slightly enhances performance by prioritizing more low-latitude slices earlier the se- quence. Moreover, incorporating two key latitudes further improves performance by gradually arranging structurally rich perspective patches the sequence.
sampling
SUS
0..00
RMSE (e))
0.58
0.56
Impact of FoV. As shown in Tab. 7 the FoV significantly influences the overall performance. Setting the FoV to 90% achieves optimal performance, whereas increasing it to 120 degrades the performance, likely due redundant structural information from excessively large views.
0.54
200
600
Number Samples
Figure 6: Results using SUS and LGS with varying numbers of frames.
Impact of spatial resolution of patches. Tab. 8 shows that an intermediate patch resolution 518 518, aligned
with the training resolution of VDA [22]. consistently yields the best performance. Increasing patch resolution from 252 x 252 to 378 x 378 notably improves performance, but further increases yield minimal benefits and even degrade the performance at resolution of 756 x 756.
4.4 Discussion
Different VDE models. Our training-free pipeline agnostic to specific VDE models. To illustrate this, we evaluate our ST2360D using several VDE models: ChronoDepth 42). DepthCrafter [3] and Depth Any Video (4). As presented Tab. our ST2360D consistently outperforms 360Mon- Deeph [18 with DAv2 as the depth estimator both Replica360-24 and Replica360-4K datasets.

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Table 9: Discussion about employing different VDE models in ST 360D. We take 360MonoDepth with DAv2 as the reference and report RMSE metric.
Table 10: Discussion about time consumption (sec-
onds). is "Mean Blending"; is "Poisson Blending".
Methods
Input Num.
Pre proc.
Inf.
Post proc.
Total
18
20
0.6
5.4
7.8
13.8
Methods
2K [S]
4K
[5]
ST 360D
12
0.3
0.7
0.1
1.1
3eph (DAv2)
0.0497
0.0488
3T0
40
0.7
1.0
0.1
1.8
3T03
160
2.4
3.0
0.5
5.9
ChronoDepth 42
0.0278
0.0279
DepthCrafter
0.0260
0.0247
18
20
0.6
5.4
27.7
33.7
Depth Any Vidco
0.0399
0.0413
ST 360D
160
2.4
3.0
21.5
26.9
ST2360D
360MonoDepth
Figure 7: Depth-controlled generation results. First prompt: "cyberpunk style". The second is empty.
Inference time. Tab. T0 compares the inference time of method against 360MonoDepth on the Replica360-2K dataset. Our ST#360D significantly reduces inference time compared to 360Mon- oeephh. Although adding more video frames increases inference time, our method remains more efficient than 360MonoDepth, which requires additional alignment during post-processing.
Depth-controlled generation. In Fig. we showcase depth-controlled generation using 360 depth predictions from our ST23600 and 360MonoDepthh. We utilize the ControlNet [53 branch of the adopt
FLUX model [54] which takes depth map guide the synthesis process. Specifically, the baack-ffrret-lab/FLLUN 1-1.1th-ephter variant, which supports the use of a referenced depth map input for conditioning. Due the stronger zero-shot capability of ST"360D, our generated results consistently surpass those obtained using 360MonoDepth on various prompts.
Conclusion and Limitation
Conclusion. In this work, we propose to represent a 360 image as sequence of video frames. Accordingly, we introduce 3T*360D, novel training- frining-free pipeline to leverage the inherent temporal consistency of VDE models to enhance spatial consistency across perspective depth patches. align the perspective frames with VDE models, we further propose two strategies: the spherical-unifomm sampling strategy and the latitude-guin guidded scanning strategy. Comprehensive experimental evaluations demonstrate the impressive effectiveness and zero-shot capability of 3T03 in diverse scenarios.
Broader impacts. Our 3T2360D can provide effective structural priors support various scene understanding tasks, such as 360 visual navigation, and has the potential to benefit embodied Al.
Limitation and future work: Currently, the pipeline of 3T2360D is limited to the task of 360 depth estimation. Encouraged by the promising results, future research can extend our 3T2360D by incorporating video foundation models in other tasks, such semantic segmentation.
Acknowledgments and Disclosure of Funding
This work was supported in part by the National Key R&D Program of China (Grant No. No.2023YFFO725001, in part by the National Natural Science Foundation of China (Grant
No. No.92370204), in part by the guangdong Basic and Applied Basic Research Foundation (Grant No. (023315515120057) in part by the Education Bureau of Guangzhou.
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Reviews:
[{"review_id": "ZVJTT3rqsV", "reviewer": "Reviewer_YR1d", "summary": "The paper presents a training-free method for depth estimation from 360-degree images by leveraging video depth estimation models on undistorted image patches. The approach employs spherical uniform sampling and latitude-guided scanning to achieve efficient sampling, avoiding oversampling at polar regions and prioritizing the equator to enhance temporal consistency in depth predictions. Resulting in state-of-the-art performance on Stanford2D3D and Replica360 datasets.", "questions": "* How robust is the LGS method when applied to outdoor 360-degree datasets, where high-latitude regions may contain significant information?\n\n* Why does the LGS method incorporate randomness rather than a deterministic scanning strategy? What specific measures could be implemented to ensure more consistent results?\n\n* Table 10 indicates that the proposed method has a significantly shorter inference time compared to 360MonoDepth, despite requiring sequential inference. What factors contribute to this efficiency, given that 360MonoDepth does not rely on sequential processing?", "limitations": "yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n* The method is innovative in its ability to directly utilize established foundational models without requiring additional training, enhancing its practical applicability.\n* The use of spherical uniform sampling and latitude-guided scanning effectively ensures temporal consistency, with experimental results demonstrating superior performance compared to existing methods.\n* The paper provides thorough experimental evidence to support the novelty and significance of the proposed method, strengthening its contributions.\n* The paper is well-structured and accessible, making the methodology and results easy to follow for readers.\n\nWeaknesses\n* The latitude-guided scanning method assumes that information near the equator (zero latitude) is dominant and serves as an optimal starting point for achieving temporal consistency. This assumption may not hold for outdoor 360-degree datasets, where regions near 90-degree latitudes could contain critical information, potentially limiting the method’s generalizability.\n* The latitude-guided scanning approach introduces randomness (noted in line 209, particularly that the algorithm could encounter a \"dead end\" during scanning), which may lead to instability or inconsistent results.", "was_revised": true, "final_justification": "My concerns have been sufficiently addressed in the rebuttal; therefore, I maintain my recommendation.", "rebuttal": "We sincerely thank you for your positive review and thoughtful questions. \"W/Q\" numbers the weakness or question, followed by our response.\n\n**W1/Q1: About the robustness of the LGS strategy in outdoor datasets.**\n\nThank you for your valuable suggestions. Based on additional experiments, we confirm that the proposed LGS strategy demonstrates robustness in outdoor scenarios. Below we describe the details of these additional experiments.\n\n**[Outdoor datasets:]** We utilize two datasets containing outdoor scenes. The first one is the Deep360 dataset [1], including outdoor driving scenes generated via the CARLA simulator. Its testing set contains 600 samples. The second dataset is derived from the Matterport3D dataset. We employ SegFormer [2] to detect sky regions in each sample of the Matterport3D dataset and collect samples where the detected sky regions constitute more than 10% of the entire ERP images. Subsequently, we manually select 100 samples by further filtering out wrongly detected samples.\n\n**[Structural Information Across Latitudes in Outdoor Scenes:]** We quantitatively assess the distribution of structural information across latitudes. Specifically, we utilize the Sobel operator to detect edges of 360 ground-truth depth maps, and normalize edge maps to the range [0, 255]. Subsequently, we average all edge maps within each dataset and summarize the edge values within four distinct latitude slices: $[-90^\\circ, -45^\\circ)$, $[-45^\\circ, 0^\\circ)$, $[0^\\circ, 45^\\circ)$\n, and $[45^\\circ, 90^\\circ]$. The **summarized edge values** are normalized and presented in the following table. The results indicate that equator regions consistently exhibit rich structural information across both outdoor datasets. Furthermore, high-latitude regions can also contain significant structural information, particularly in the Deep360 dataset.\n\n| Dataset       | Samples | $[-90^\\circ, -45^\\circ)$   | $[-45^\\circ, 0^\\circ)$   | $[0^\\circ, 45^\\circ)$   | $[45^\\circ, 90^\\circ]$   |\n|---------------|:---------:|:------------:|:------------:|:------------:|:------------:|\n| Deep360       | 600     | 38%  | **41%**  | 19%   | 2%    |\n| Matterport3D  | 100     | 13%   | 35%  | **37%**  | 15%   |\n\n**[Ablation studies of LGS strategy in outdoor scenes:]** To evaluate the robustness of the proposed LGS strategy, we conduct ablation studies on the two outdoor datasets. The results are presented in the table below. These results demonstrate that the LGS strategy consistently improves performance in outdoor scenes.\n\n| Dataset        || AbsRel $\\downarrow$  | RMSE $\\downarrow$ |\n|-----------------|----|:--------:|:------------:|\n| Matterport3D        | w/o LGS | 0.2725  | 0.9498  |\n|          |w/ LGS | **0.2512**  | **0.8977**  |\n| Deep360        | w/o LGS | 2.3860  | 1.5312  |\n|          |w/ LGS | **2.0369**  | **1.3986**  |\n\n**[Conclusion:]** **(1)** From the results of *structural information*, it can be found that equator regions contain rich structural information in most cases. Thus, starting from equator viewpoints is generally suitable. **(2)** Furthermore, our proposed LGS strategy is still effective in outdoor scenes. Notably, the LGS strategy rearranges perspective views rather than discarding high-latitude views entirely. The high-latitude views can also be aligned with the previous equator views. **(3)** Finally, a promising direction for future work involves designing an adaptive LGS strategy that automatically identifies the most salient region as the starting point.\n\n**W2/Q2: About the randomness of the scanning strategy.**\n\nSorry for the confusion. In the proposed LGS strategy, given **(1)** the viewpoints determined by the SUS strategy, **(2)** the starting viewpoint, and **(3)** key latitudes, the scanning path becomes entirely deterministic. Notably, we have presented the scanning path using viewpoint indices in Fig. 1 of the supplementary material, including different subdivision levels. A viewpoint might encounter the dead-end case, where no unexplored spherical neighbors remain within the current latitude slice. In this case, all remaining unexplored viewpoints in this latitude slice are collected as the neighbor set for the current viewpoint, allowing the scanning process to continue. From this expanded neighbor set, we select the viewpoint with the minimum latitude as the subsequent viewpoint. \n\nAlthough such dead-end cases could potentially introduce variability, **they consistently arise at specific viewpoints, and the selection of the next viewpoints remains uniform across implementations**. Moreover, we have verified our experimental results multiple times and across diverse GPU environments to confirm reproducibility and robustness of the scanning process.\n\n**Q3: About the efficiency compared to 360MonoDepth.**\n\nThe primary reason for the improved efficiency of our method compared to 360MonoDepth lies in **the avoidance of time-consuming depth map alignment in the post-processing.** In 360MonoDepth, depth alignment involves multi-scale operations and incorporates several optimization terms, such as smoothness and scale consistency, which significantly increase time consumption. \n\nIn contrast, our pipeline does not require such alignment, as it leverages the temporal consistency inherent in video depth estimation models during inference. Moreover, our SUS and LGS strategies efficiently organize the perspective views into a coherent video sequence. \n\nFurthermore, The Video Depth Anything (VDA) model used in our pipeline can process 32 frames simultaneously within each sequential step. As the number of input views increases from 12 to 160, the number of sequential processing steps increases from 1 to 8, with a 12-frame overlap between adjacent sequences. This design ensures efficiency even with large number of  input views.\n\n[1] Li, Ming, et al. \"MODE: Multi-view omnidirectional depth estimation with 360 cameras.\" European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022.\n\n[2] Xie, Enze, et al. \"SegFormer: Simple and efficient design for semantic segmentation with transformers.\" Advances in neural information processing systems 34 (2021): 12077-12090."}, {"review_id": "x48OGCn8py", "reviewer": "Reviewer_NpNi", "summary": "This paper proposes a training-free method for 360 monocular depth estimation. Existing training-based methods rely on expensive 360 depth estimation and have limited zero-shot capability. Existing training-free methods are time-consuming or rely on 360 depth models. The proposed method addresses these limitations through sequentializing the input equirectangular projection (ERP) image into a sequence of patches and processing the sequence via a pre-trained large zero-shot video depth estimation model. A Spherical-Uniform Sampling (SUS) Strategy and a Latitude-Guided Scanning (LGS) Strategy are proposed to sequentialize the ERP image. Experiment results show that the proposed method possesses comparable zero-shot capability to SOTA training-based methods, and outperforms existing training-free methods by a large margin.", "questions": "1. Table 10 shows that 360monodepth takes 20 views as input, which is far less than the proposed method. How will it perform if more views are used?\n2. Can you compare the inference time efficiency of your method with more baselines and include GPU memory consumption?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strength**\n+ The idea of using video depth estimation models to solve the 360 monocular depth estimation task is interesting and novel.\n+ The experiment results are impressive, compared to both training-based and training-free methods.\n+ Substantial designs of sequentializing strategies are tested.\n\n**Weakness**\n+ The illustration of latitude-aware traversing is not clear enough. It is better presented using an algorithm block or in equations. \n+ The inference efficiency of the proposed method is only compared with one baseline method. More methods should be included. Furthermore, GPU memory consumption, which is also important, is not given.", "was_revised": true, "final_justification": "The proposed method has good motivation and performance. The rebuttal shows efficiency comparison results with more baseline methods. And the rebuttal also shows that the proposed method has better scaling property with number of views compared to the baseline method 360monodepth. In all, this is a solid paper and should be accepted.", "rebuttal": "We sincerely thank you for your positive review and thoughtful questions. \"W/Q\" numbers the weakness or question, followed by our response.\n\n**W1: About the illustration of latitude-aware traversing.**\n\nThanks for your suggestion. To make the latitude-aware traversing clear enough, we present it with an algorithm block as follows:\n\n**Algorithm 1: Latitude-aware Traversing**\n\n1. **Input:** A set of $N$ Viewpoints $\\mathbf{v} = \\\\{\\mathbf{v}\\_{1},..., \\mathbf{v}\\_{N}\\\\}$\n\n  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $K$ key latitudes $0 < \\theta_1 < \\dots < \\theta_K \\le 90^{\\circ}$\n\n2. **Latitude computation**: For each viewpoint $\\mathbf{v}_i$, obtain the  $\\Theta(\\mathbf{v}_i)$\n\n3. **Slice partitioning**: Partition viewpoints into latitude slices based on $K$ key latitudes:  \n\n    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$ \\mathbf{v}\\_{\\text{slice}\\_{0}} = \\\\{\\mathbf{v}\\_i \\mid \\mathbf{v}\\_i \\in \\mathbf{v}, |\\Theta(\\mathbf{v}\\_i)| \\leq \\theta\\_{1}\\\\} $  \n\n    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$ \\mathbf{v}\\_{\\text{slice}\\_{k}} = \\\\{\\mathbf{v}\\_i \\mid \\mathbf{v}\\_i \\in \\mathbf{v}, \\theta\\_{k} < |\\Theta(\\mathbf{v}\\_i)| \\leq \\theta\\_{k+1}\\\\} $, for $ k = 1,\\ldots,K-1 $ \n \n    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$ \\mathbf{v}\\_{\\text{slice}\\_{K}} = \\\\{\\mathbf{v}\\_i \\mid \\mathbf{v}\\_i \\in \\mathbf{v}, \\theta\\_{K} < |\\Theta(\\mathbf{v}\\_i)| \\leq 90^{\\circ}\\\\} $  \n4. **Slice ordering**: Arrange the slices in ascending latitude to form the list $ \\mathbf{v}\\_{\\text{slices}} \\leftarrow [\\mathbf{v}\\_{\\text{slice}\\_{0}},\\ldots,\\mathbf{v}\\_{\\text{slice}\\_{K}}] $  \n5. **Output**: The ordered slices $\\mathbf{v}_{\\text{slices}}$ \n\n\nBased on the latitude slices, we utilize **the spherical neighbor viewpoint searching** to generate the video frame sequence $\\\\{\\mathbf{F}_1, \\dots, \\mathbf{F}_N\\\\}$.\n\n**W2/Q2: About the inference time and GPU consumption.**\n\nThanks for your suggestion. We have extended our evaluation to include inference time and GPU memory consumption across additional baseline methods. All experiments are conducted on a single A40 GPU. The input resolution of UniFuse and ACDNet is 512x1024, while the input resolution of PanDA (Small, Base, and Large variants) is 504x1008. We report the results of our $\\text{ST}^2\\text{360D}$ with 160 input views and perspective resolution 378x378.\n\n| Method  |Inference Time (s)| GPU memory (G) |\n|-----------------|:----:|:--------:|\n| PanoFormer         | 0.1 |  2.4 |\n| EGFormer         | 0.1 |  2.2 |\n| ACDNet       | 0.07 | 1.7  |\n| PanDA-Small        | 0.06 |  1.2 |\n| PanDA-Base        | 0.1 | 2.3  |\n| PanDA-Large        | 0.3 | 4.4 |\n| 360MonoDepth        | 13.8 | 0.9 |\n| Ours (VDA-Small)     | 5.9 |  1.5 | \n\n**Q1: About more views of 360MonoDepth.**\n\nAs suggested, we conduct an extended comparison with 360MonoDepth using increased numbers of input views. In 360MonoDepth, viewpoints are derived from the triangular faces of an icosahedron. A triangular face can be divided into four sub-faces, thus increasing the input views accordingly. *However, the original codebase supports only an unsubdivided icosahedron, and this limitation applies to its input processing, depth estimation, post-processing, and output processing.*\n\nTo enable additional input views, we incorporate subdivision functions into the input projection and output re-projection processes by adapting code from SpherePHD [1]. Due to the time constraints of the rebuttal period, we omit the depth alignment module in the post-processing for this evaluation.\n\nWe test 360MonoDepth under various subdivision levels: level 0 (20 views), level 1 (80 views), and level 2 (320 views). We utilize the Mean blending, and test on the Replica360-2K dataset. All hyperparameters are set according to the recommended configurations. Our results show that increasing the number of input views degrades the overall performance. *Since each input view is processed independently using an image-based depth estimation model, simply increasing the number of views does not enrich structural information but instead introduces depth inconsistency across views.*\n\n| Input Views     | AbsRel $\\downarrow$  | RMSE $\\downarrow$ |\n|:--:|:----:|:--------:|\n| 20       | **0.2124** |  **0.0665** |\n| 80        | 0.3805 | 0.0991 |\n| 320     | 0.3699 |  0.1083 | \n\nMoreover, in Fig. 6 of the main paper, we have presented the results of our $\\text{ST}^2\\text{360D}$ in different input views, ranging from 12 views to 628 views. The results demonstrate the effectiveness of our proposed SUS and LGS strategy, especially when increasing input views from 40 to 160. \n\n[1] Lee, Yeonkun, et al. \"Spherephd: Applying cnns on a spherical polyhedron representation of 360deg images.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019."}, {"review_id": "4w9oaFCZFb", "reviewer": "Reviewer_qKmK", "summary": "This paper proposes a novel 360 depth estimation pipeline called ST^2360D. To cover the nature of 360 images that usually contain high-resolution spatial information, the proposed method treats a single 360 image as a sequence of perspective images and successfully utilizes existing video depth estimation methods. The authors suggest two strategies (SUS and LGS) for the seamless adaptation of the video depth estimation model into the 360 image domain. The comprehensive experimental results demonstrate that the proposed pipeline outperforms the previous monocular 360 depth estimation methods and shows the effectiveness of its design choices with two proposed modules.", "questions": "- More details about depth-controlled generation experiments are not described in the supplementary material (refer to L310 in the main paper). I wonder how the authors obtained the results in Fig. 7.\n- Could you describe the dead-end cases in the viewpoint searching procedure?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "### Strengths\n- Problem formulation: The authors newly reformulate the 360 depth estimation task as a video depth estimation task and successfully improve the depth quality, especially in terms of depth consistency, where the previous methods suffer from seamless aggregation.\n\n- Training-free pipeline: The proposed pipeline is training-free, and it shows fast inference speed compared to the previous method. Moreover, thanks to its training-free pipeline, the proposed method can easily be expanded to other tasks by utilizing various 4D perception models.\n\n- Well-constructed writing: The paper is well-written and easy to follow. Experimental results are helpful to understand the design choices and effectiveness of each proposed module.\n\n\n### Weaknesses\n- Lack of its technical novelty: Although the proposed pipeline is novel and practical, the technical contribution of the paper is insufficient. Specifically, spherical-uniform sampling (SUS) is already commonly used in 360 3D perception fields (SpherePHD [CVPR’19], PanoFormer [ECCV’22], Elite360D [CVPR’24]).\n\n- Comparison methods: In Table 2, data-specific methods (HoHoNet, SliceNet, UniFuse) are pretty outdated. To validate the effectiveness of the proposed method, it is recommended to compare it with recent 360 depth estimation methods (e.g., HRDFuse [CVPR’23], Elite360D [CVPR’24], PanDA [CVPR’25], etc.).", "was_revised": true, "final_justification": "The authors have provided thoughtful and appropriate responses to the concerns raised by the reviewers. However, one remaining issue is the novelty of SUS, which I still find unclear. In particular, the sampling strategy based on icosahedral grids does not appear to differ significantly from the method employed in Elite360D.\n\nDespite this, I believe the overall motivation and research direction of the paper are meaningful and have the potential to make a substantial impact. Considering the novelty of the proposed framework and its relevance to the field, I maintain a positive rating for this submission.", "rebuttal": "We sincerely thank you for your positive review and thoughtful questions. \"W/Q\" numbers the weakness or question, followed by our response.\n\n**W1: About the novelty of the SUS module.**\n\nThank you for your valuable suggestion. We acknowledge the significance of prior work in this domain. Regarding spherical uniform sampling (SUS), please note that it is a sampling mechanism used to represent a sphere. For the previous methods, SpherePHD projects a 360 image onto a spherical polyhedron with triangular faces to minimize spherical distortion; Elite360D maps a 360 image to an icosahedron point set to extract global spherical features; PanoFormer uniformly samples spherical neighbors for pixel-wise self-attention calculation, thereby mitigating distortion.\n\nSharing a different intuition, the novelty of incorporating SUS in our $\\text{ST}^2\\text{360D}$ stems from the following: \n\n**1.** The SUS strategy is specifically employed to obtain viewpoints for perspective patch projection, according to the vertices of icosahedral grids at different subdivision levels. This approach reduces redundant sampling in polar regions, which typically contain limited structural information.\n\n**2.** It constructs the spherical relationships among spherical viewpoints, facilitating the spherical neighbor searching in the proposed LGS strategy.\n\n**3.** As demonstrated in Fig. 6 of the main paper, SUS significantly outperforms ERP-plane uniform sampling, showing its effectiveness in aligning 360 images with existing video depth estimation models.\n\n**W2: About the Comparison methods.**\n\nFor the mentioned recent 360 depth estimation methods, *HRDFuse* and *Elite360D* have not released their model checkpoints. Therefore, we report the performance of *PanDA* (including its Small, Base, and Large versions) on three high-resolution datasets, as shown in the table below. Following a similar pre-processing strategy of 360MonoDepth, we first downsample input 360 images to a resolution of 504×1008—the training resolution of *PanDA*. The resulting depth predictions are then upsampled to the original image resolution using bilinear interpolation. Our $\\text{ST}^2\\text{360D}$ outperforms *PanDA* in most metrics.\n\n| Datasets        |Methods| AbsRel $\\downarrow$  | RMSE $\\downarrow$ |\n|-----------------|----|:--------:|:------------:|\n| Matterport3D-2K        | PanDA-Small | 0.1311  | 0.4868  |\n|          |PanDA-Base |  0.1288 | 0.4813 |\n|          |PanDA-Large | **0.1190** | 0.4658  |\n|          |Ours (VDA-Large)$^\\text{P}$ | 0.1264  | **0.4460**  |\n| Replica360-2K        | PanDA-Small | 0.0751  | 0.0215  |\n|          |PanDA-Base | 0.0692  | 0.0195 |\n|          |PanDA-Large | 0.0648 |  0.0187 |\n|          |Ours (VDA-Large)$^\\text{P}$ |  **0.0503** | **0.0144**  |\n| Replica360-4K        | PanDA-Small | 0.0739  | 0.0213  |\n|          |PanDA-Base |  0.0676 | 0.0194 |\n|          |PanDA-Large | 0.0612 | 0.0183  |\n|          |Ours (VDA-Large)$^\\text{P}$ |  **0.0492** |  **0.0144** |\n\n**Q1: About depth-controlled generation experiments.**\n\nSorry for the missing explanations. For the depth-controlled generation, we utilize the ControlNet branch of the FLUX model, which takes a depth map to guide the synthesis process. Specifically, we adopt the *black-forest-labs/FLUX.1-Depth-dev* variant, which supports the use of a referenced depth map as input for conditioning. As illustrated in Fig. 7, the generated images preserve consistent spatial relationships across varying text prompts. Specifically, in the third column of Fig. 7, we input the text prompt \"cyberpunk style\", while in the fourth column, we input the empty text prompt \"\".\n\n**Q2: About the dead-end cases in the viewpoint searching process.**\n\nWe take the case of 160 sampled viewpoints as an example. Each viewpoint is associated with 5 or 6 spherical neighbors. At each stage, the scanning procedure traverses specific horizontal slices of the sphere. For a given viewpoint, if all of its spherical neighbors within the current slice have already been visited, the procedure  may encounter a *dead-end*. In such cases, we expand the neighbor set of the current viewpoint to include all unexplored viewpoints, allowing the scanning procedure to resume. *In Fig. 1 of the supplementary material, we visualize the actual scanning paths with viewpoint indices.* Several dead-end examples can be found in Fig. 1, such as viewpoint transitions 24 $\\rightarrow$ 25, 42 $\\rightarrow$ 43, and 129 $\\rightarrow$ 130. We will clarify the dead-end cases in the revision."}, {"review_id": "irPRRDIGNH", "reviewer": "Reviewer_zFQ2", "summary": "ST²360D aims for monocular depth estimation from 360° images by incorporating the video depth estimation model (VDE). The authors first reproject an equirectangular image into perspective patches at sampled regions. Given a sequence of sampled perspective patches, VDE estimates depth with temporal consistency across patches. The estimated patch depths are reprojected to the equirectangular image and mean-/Poisson-blended to get a final 360° depth map. Authors proposed spherical uniform sampling and latitude-guided scanning strategy to reduce redundant sampling at polar region and feed richful information in the initial frame into VDE. These strategies enhance the depth estimation performances of the suggested approach. As a result, ST²360D achieves high zero-shot performance on high resolution images without additional training or fine-tuning.", "questions": "1. I suggest including figures that compare depth maps for each comparison method with an error map. This will better depict the geometrical accuracy of ST²360D.\n2. I am curious about the depth quality of ST²360D at edge regions. Does temporal consistency and Poisson blending guarantee the sharpness of depth maps then fine-tuning the network with synthetic 360° datasets?\n3. In Figure 6, is there an expected reason for degrading accuracy even with SUS and LGS as the number of samples increases? In my sense, temporal consistency across the 360° images should be strengthened thereby reducing the RMSE.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strength\n+ ST²360D investigated the first-time approach of incorporating a video depth estimation model to 360° monocular depth estimation. The authors have suggested simple but effective strategies to enhance 360° depth estimation with existing foundation models. The proposed contributions also improved the depth estimation accuracies.\n+ Authors show that temporal consistency by VDE across patches on 360° images is as effective as additional fine-tuning with 360° synthetic datasets (Table 1). Moreover, this method is generalizable since it does not need training or fine-tuning.\n+Authors have conducted thorough evaluations and ablation on the method. Experiments show the strength of ST²360D on the zero-shot performance and high-quality results in high-resolution images. Ablation shows the importance of temporal consistency and suggested strategies in the final performance while searching for the best variable sets for achieving the best performance.\n\nWeakness\n\n+ Evaluation is focused on quantitative evaluation, while qualitative comparison is insufficient. Figures mostly show the depth map result of ST²360D variations without visualizing comparisons methods’ depth maps.", "was_revised": true, "final_justification": "I am satisfied with the clear motivation and the quality the authors have achieved. The authors’ rebuttal and the discussions from other reviewers have further convinced me of the effectiveness of the contribution. I am changing my final score to Accept.", "rebuttal": "We sincerely thank you for your positive review and thoughtful questions. \"W/Q\" numbers the weakness or question, followed by our response.\n\n**W1/Q1: About the qualitative results.**\n\nThanks for your valuable advice. We will include additional qualitative results for the compared methods, including error maps, to more clearly illustrate the performance differences between our $\\text{ST}^2\\text{360D}$ and the baselines.\n\n**Q2: About the depth quality at edge regions.**\n\nThanks for the suggestion. To evaluate the sharpness of estimated depth maps at edge regions, we employ the \"*Boundary F1 score*\" proposed in Depth Pro [1]. We conduct experiments on the Replica360-2K dataset. \n\nOur method is *training-free* and achieves accurate boundaries by leveraging *temporal consistency and Poisson blending*. We compare our method with PanDA, which *fine-tunes* Depth Anything v2 on *synthetic 360 depth datasets* (Structured3D[2] and Deep360[3]). Note that our method does not support direct fine-tuning as the implementation of Poisson blending is not differentiable.\n\nGiven the significant influence of input resolution on boundary accuracy, we compare our method with PanDA at two input resolutions (training resolution of PanDA is 504x1008). Our method takes perspective frames with 518x518 resolution. The results, shown below, demonstrate that our $\\text{ST}^2\\text{360D}$ with mean blending outperforms PanDA even when using a higher input resolution of 1008×2016. Employing Poisson Blending can further improve the boundary accuracy of our $\\text{ST}^2\\text{360D}$. We ascribe it as our training-free pipeline is capable of preserving the high depth precision inherent in video depth estimation models, which have been trained on a diverse set of high-quality perspective depth datasets.\n\n| Method        |Input Resolution| Boundary F1 $\\uparrow$ |\n|-----------------|:----:|:--------:|\n| PanDA-Small        | 504x1008 | 0.0833  |\n| PanDA-Small        | 1008x2016 | 0.1911  |\n|     Ours (VDA-Small)$^\\text{M}$     |518x518 |  0.2134 | \n|     Ours (VDA-Small)$^\\text{P}$     |518x518 |  **0.2380** | \n\n**Q3: About the degraded performance with more input views.**\n\nSorry for the confusion. As shown in Fig. 6, even when applying the SUS and LGS strategies, increasing the number of viewpoints—from 160 to 628—can lead to degraded performance. There are three potential reasons to explain it. \n\n**[1. Limited Visual Transition.]** As the subdivision level increases, the visual difference between adjacent viewpoints becomes minimal. The Video Depth Anything (VDA) model processes 32 frames at a time, and its temporal attention calculation relies on effective motions across frames. When visual transitions are insignificant, it becomes challenging for the model to effectively capture temporal cues.\n\n**[2. Oversampling at Polar Regions.]** Although the SUS strategy has proven effective in reducing oversampling in polar areas, higher subdivision levels inevitably introduce more viewpoints in those regions. This increased sampling density in polar regions may degrade the overall performance.\n\n**[3. Temporal Distance in Long Sequences.]** While the VDA model can handle super-long video sequences, using 628 viewpoints results in a significant temporal gap between the first and last views. This temporal distance may make it challenging to construct coherent spatial relationships between temporally distant viewpoints.\n\n[1] Bochkovskii, Aleksei, et al. \"Depth pro: Sharp monocular metric depth in less than a second.\" ICLR 2025.\n\n[2] Zheng, Jia, et al. \"Structured3d: A large photo-realistic dataset for structured 3d modeling.\" European Conference on Computer Vision. Cham: Springer International Publishing, 2020.\n\n[3] Li, Ming, et al. \"MODE: Multi-view omnidirectional depth estimation with 360 cameras.\" European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022."}]

Author rebuttal:

Meta-review: The paper proposes a training-free method that reformulates 360-degree depth estimation as a video depth estimation problem, supported by two sampling and scanning strategies. Reviewers appreciated the strong empirical performance, clear writing, and practical advantages of leveraging foundation video depth models without retraining. Main concerns were about the limited novelty of the sampling strategy, incomplete comparisons with the very latest baselines, and initially insufficient qualitative analysis. The rebuttal convincingly addressed these points with new experiments on outdoor datasets, additional efficiency and boundary-sharpness evaluations, and clarifications on determinism and novelty. Overall, despite minor reservations, the consensus is that the work is solid, impactful, and should be accepted.
Decision: Accept (poster)