Recent years have witnessed the growing potential of panoramic salient object detection in robotic vision, virtual reality, and related applications. However, projecting spherical scenes onto 2D planes inevitably introduces geometric distortions, which fundamentally limit the effectiveness of existing projection-based methods. Specifically, Equirectangular Projection (ERP) suffers from severe polar stretching distortions, while cube map projection introduces discontinuities across cube-face boundaries, resulting in degraded feature discriminability and compromised geometric consistency. To address these limitations, we propose TDFNet, the first Tri-projection Deformable Fusion Network for panoramic salient object detection, exploiting complementary projection representations to alleviate geometric distortions and improve detection performance.Specifically, we design a cross-projection deformable attention (CDA) module that leverages spatial correspondences between different projections to construct geometry-aware sampling locations, guiding deformable attention for cross-projection contextual aggregation and enhancing robustness against projection-induced deformations. Furthermore, we introduce a latitude-guided fusion module, which utilizes spherical latitude priors to construct geometric confidence weights for adaptively balancing ERP and CMP features. Meanwhile, LGF incorporates distortion-reduced semantic references from Tangent Projection to achieve cross-projection feature refinement and spatial alignment.By constructing a three-branch encoding architecture based on ERP, CMP, and Tangent Projection, TDFNet simultaneously preserves global spatial continuity, local geometric details, and fine-grained boundary information.
Figures & tables
Figure 1. Comparison of projection representations used in PSOD. (a) ERP maintains complete spherical topology but suffers from polar stretching distortion. (b) CMP reduces polar deformation through hexahedral decomposition but introduces semantic discontinuities at cube-face boundaries. (c) Tangent Projection, introduced in this work, provides distortion-reduced local perspective views through discrete viewport mapping, complementing ERP and CMP with high-fidelity geometric details. projection
Figure 2. Overall architecture of the proposed TDFNet. The network incorporates three core components: (i) a multi-view tangent projection branch for distortion-free local feature extraction, (ii) the cross-projection deformable attention (CDA) deployed in both ERP and cubemap branches to enhance robustness against projection distortions, and (iii) the latitude-guided fusion (LGF) module that progressively integrates tri-branch features under spherical geometric guidance for cross-projection alignment. our method
Figure 3. The structure of the deformable Transformer block in the CDA module. Deformable Transformer block in CDA.
Figure 4. The structure of the LGF module. LGF module
Model
Sm↑
MAE↓
meE↑
maxE↑
meF↑
maxF↑
FA ( Huang et al., 2020 )
.826
.021
.885
.900
.748
.770
DDS ( Li et al., 2019 )
.799
.023
.865
.904
.695
.722
DT ( Zhao et al., 2023 )
.849
.017
.907
.919
.774
.793
GFI ( Zhu et al., 2021 )
.831
.021
.894
.900
.753
.769
SCW ( Yu et al., 2021 )
.830
.021
.886
.887
.754
.759
BIPG ( Yao and Wang, 2021 )
.811
.024
.885
.890
.727
.740
Table 1. Quantitative comparison results on 360-SOD dataset. “Ours” adopts the Geometry Only strategy in the LGF module. ↑ and ↓ indicate that the larger scores and the smaller ones are better, respectively. The best scores are highlighted in bold .
Model
Sm↑
MAE↓
meE↑
maxE↑
meF↑
maxF↑
LD ( Huang et al., 2023 )
.756
.034
.845
.863
.492
.511
FA ( Huang et al., 2020 )
.717
.039
.727
.735
.520
.532
HVP ( Liu et al., 2020 )
.773
.143
.800
.854
.500
.529
DT ( Zhao et al., 2023 )
.770
.026
.832
.865
.644
.657
GFI ( Zhu et al., 2021 )
.767
.034
.829
.848
.526
.536
SCW ( Yu et al., 2021 )
.760
.029
.813
.854
.511
.518
Table 2. Quantitative comparison results on 360-SSOD dataset. “Ours” adopts the Mixed strategy in the LGF module. ↑ and ↓ indicate that the larger scores and the smaller ones are better, respectively. The best scores are highlighted in bold .
Model
Sm↑
MAE↓
meE↑
maxE↑
meF↑
maxF↑
View ( Wu et al., 2022 )
.831
.035
—
—
—
.822
FA ( Huang et al., 2020 )
.730
.050
.771
.790
.610
.632
DDS ( Li et al., 2019 )
.791
.045
—
—
—
.761
HVP ( Liu et al., 2020 )
.732
.061
.787
.795
.616
.627
DC ( Zhu et al., 2023 )
.659
.120
.685
.691
.520
.530
MDSAM ( Gao et al., 2024 )
.706
.084
.744
.748
.597
.603
Table 3. Quantitative comparison results on ODI-SOD dataset. “Ours” adopts the Mixed strategy in the LGF module. ↑ and ↓ indicate that the larger scores and the smaller ones are better, respectively. The best scores are highlighted in bold .
Model
Sm↑
MAE↓
meE↑
meF↑
FA ( Huang et al., 2020 )
.621
.056
.700
.345
DDS ( Li et al., 2019 )
.612
.057
.700
.325
ACCo ( Li et al., 2022 )
.613
.060
.694
.334
MPFR ( Cong et al., 2023 )
.617
.052
.742
.370
DT ( Zhao et al., 2023 )
.611
.058
.652
.310
CPNet ( Wen et al., 2025 )
.651
.051
.729
.382
Table 4. Quantitative comparison results on F-360iSOD dataset. “Ours” adopts the Geometry Only strategy in LGF. ↑ and ↓ indicate that the larger scores and the smaller ones are better, respectively. The best scores are highlighted in bold .
Figure 5. Qualitative comparisons of various PSOD methods under several challenging scenarios. The all-black images marked with yellow boxes indicate that the corresponding saliency maps cannot be obtained. Qualitative comparisons
360-SOD
Settings
Sm↑
MAE↓
meE↑
meF↑
360-SSOD
Sm↑
MAE↓
meE↑
meF↑
ERP
.824
.026
.889
.742
.748
.039
.827
.595
ERP-CMP
.858
.018
.918
.812
.793
.028
.862
.677
ERP-CMP-TAN
.878
.016
.925
.822
.796
.027
.872
.689
Table 5. Ablation study on different branch combinations in the proposed model.
Figure 6. Visualization of three variants, ERP, ERP-CMP and ERP-CMP-TAN. Visualization of three variants
Figure 7. Visualization of multi-projection features extracted by the tri-branch encoder. Visualization of different modules.
Figure 8. Visualization results of ablation studies in different modules. Visualization of different modules.
360-SOD
Settings
Sm↑
MAE↓
meE↑
meF↑
360-SSOD
Sm↑
MAE↓
meE↑
meF↑
w/o CDA
.869
.017
.923
.807
.795
.027
.865
.677
w/o LGF
.878
.016
.925
.822
.796
.027
.872
.689
Ours
.883
.015
.927
.835
.804
.026
.877
.697
Table 6. Ablation experiment of each module in the model.
Strategy
360-SOD
360-SSOD
Complexity
Sm↑
MAE↓
meE↑
meF↑
Sm↑
MAE↓
meE↑
meF↑
Params (M)
FLOPs (G)
Geometry Only
0.883
0.015
0.927
0.835
0.789
0.029
0.863
0.678
0.000
∼ 0
Mixed
0.860
0.019
0.917
0.802
0.804
0.026
0.877
0.697
0.084
0.086
Table 7. Ablation study on the fusion strategies of the LGF module.
Figure 9. Visualization of feature enhancement by the proposed CDA module.
Figure 10. Visualization of the LGF fusion process and final predictions.
360° salient object detection (SOD) aims to accurately segment salient regions across a full field of view. However, equirectangular projection (ERP) introduces severe spatial distortion when mapping the spherical domain onto a planar representation. Existing methods mainly focus on compensating projection distortion while overlooking the interaction between panoramic geometry and salient object structure during feature perception and prediction refinement. To this end, we propose SphereSOD, an ERP-native framework that couples panoramic geometry with evolving salient structures. Specifically, spherical geometry governs feature sampling and spatial weighting, while coarse-grained saliency and contour prediction influence context aggregation during the progressive decoding process. SphereSOD first initializes deformable sampling based on spherical projection geometry and then employs bounded, content-adaptive offsets, yielding features that are better aligned with the underlying panoramic geometry. Subsequently, the decoder performs structure-guided context aggregation and progressive refinement to recover complete salient regions and accurate boundaries. Extensive experiments on three public 360° SOD benchmarks demonstrate state-of-the-art performance and a favorable accuracy-efficiency trade-off, supporting structurepreserving inference directly in ERP space as a promising alternative to projection-heavy panoramic pipelines.
Panoramic cameras provide a 360° field of view and are widely used in panoramic vision, immersive visual computing, and robotic perception. However, changes in camera orientation can produce non-upright panoramas, introducing geometric variations that can complicate downstream visual analysis. Existing vision-based rectification methods usually operate within a single projection domain, limiting their ability to jointly exploit local geometric structures and global contextual information. To address this, we formulate 360° image rectification as a projection-aware representation learning problem and propose a dual-projection framework for upright panoramic rectification. A convolutional neural network branch captures local geometric structures from equirectangular projection (ERP) inputs, while a vision transformer branch models global contextual cues from cubemap projections. Cross-projection feature transformation and multi-level feature fusion enable effective interaction between these complementary representations. The learned representation supports collaborative inclination estimation and upright panorama generation, with the two tasks providing complementary geometric and appearance supervision. Experiments on SUN360 and M3D show consistent improvements over existing methods, achieving accuracies within a 1° error threshold of 65.9% and 85.2% and Fréchet Inception Distance scores of 5.87 and 3.26, respectively. Ablation studies verify the contributions of dual-projection representation, cross-projection feature transformation and fusion, and collaborative multi-task learning. The proposed framework provides a projection-aware visual computing approach for panoramic rectification. Code, pretrained models, and training/testing scripts are available at https://github.com/YuhaoShine/DualProjectionFusion.
Yuhao Shan, Qianyi Yuan, Jingguo Liu +3
college of electronic and information engineering, Southwest University, Chongqing 400700, China
Panoptic scene graph generation (PSGG) represents scene entities with segmentation masks and directed relations. Equirectangular projection (ERP) panoramas challenge PSGG through distortion, latitude-dependent pixel areas, and an artificial seam. We propose a two-stage spherical geometry-aware framework that fuses overlapping perspective-view predictions using observation reliability, spherical overlap, and angular proximity. Relation reasoning combines spherical-area-aware aggregation, weighted no-relation supervision, and dual-longitude score fusion. We also construct a dataset of 340 high-resolution panoramas with 10,571 nodes and 6,632 directed relations. Against corresponding baselines, spherical fusion improves PQ by 36.03% under matched views, while relation reasoning improves mR@50 by 11.20% under PredCls with ground-truth masks and object labels. The full framework improves mR@50 by 52.99% under SGDet with predicted panoptic segments. These results demonstrate the value of spherical geometry for panoramic PSGG.
Zhe Wu, Xiaoyan Fei, Xinyi Jiang +4
Shanghai DianJi University, Shanghai, China · University of Minnesota Twin Cities, Minneapolis, MN, USA