Submitted:
12 June 2025
Posted:
13 June 2025
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Abstract
Keywords:
1. Introduction
- 1
- We propose a new architecture, FusionFormer-X, designed explicitly for fusing high-dimensional spectral and geometric cues from HSI and LiDAR data.
- 2
- We develop a novel Hierarchical Multi-Scale Multi-Head Self-Attention module that enables progressive cross-modal feature integration with spatial and spectral consistency.
- 3
- We integrate convolutional inductive biases into the tokenization stage, enhancing local feature modeling and preserving fine-grained spatial structures.
- 4
- We conduct extensive experiments on Trento and MUUFL benchmarks, showing that FusionFormer-X significantly outperforms existing state-of-the-art methods across various evaluation metrics.
2. Related Work and Preliminary Studies

3. Methodology
3.1. Hierarchical FusionFormer-X Framework
3.2. Multi-Scale Self-Attention via Spatial Pyramids
Head-wise Partitioning.
Self-Attention within Each Scale.
Hierarchical Aggregation.
Positional Bias Injection.
3.3. Cross-Modality Gated Fusion Layer
3.4. Feedforward Projection with Dual-Scale Normalization
3.5. Objective Function and Regularization
3.6. MLP Classifier Head
4. Experiments
4.1. Benchmark Datasets and Evaluation Protocols
- Trento Dataset. This dataset captures a rural zone located south of Trento, Italy. It comprises a hyperspectral image with 63 spectral bands and a corresponding single-band LiDAR-derived digital surface model (DSM). The spatial resolution is 1 meter, and the image spans pixels. There are six labeled landcover categories, including buildings, trees, and terrain classes such as grass and agricultural land. The simplicity in background but complexity in class overlap makes Trento ideal for analyzing cross-modal synergy.
- MUUFL Dataset. The MUUFL Gulfport dataset was acquired over the University of Southern Mississippi campus. After noise band removal, 64 effective hyperspectral bands remain, and the LiDAR modality contains 2 elevation-related channels. With a spatial size of pixels, this dataset features 11 fine-grained landcover types including road markings, curbs, trees, and man-made structures. MUUFL is more challenging due to narrow classes, urban clutter, and spectral ambiguities.
- Training Configuration. All models are implemented in PyTorch 1.12.1 and trained on a CentOS 7.9 workstation equipped with a single NVIDIA RTX 3090 GPU (24 GB). The batch size is fixed to 64 for all models to ensure comparability. Optimization is performed using the Adam optimizer with an initial learning rate of , decayed by every 50 epochs using a step-based scheduler. A weight decay of is used for regularization. Each model is trained for 500 epochs and evaluated across 3 independent seeds, reporting the mean and standard deviation.
- Evaluation Metrics. We adopt three standard metrics for classification: Overall Accuracy (OA), Average Accuracy (AA), and Cohen’s Kappa coefficient (). OA reflects pixel-wise global accuracy. AA measures the average per-class accuracy, accounting for class imbalance. Kappa provides a chance-corrected agreement:where is the observed agreement and is the expected agreement. These metrics collectively ensure both absolute and balanced performance evaluation.
4.2. Performance Comparison on Trento and MUUFL
4.3. Ablation Studies on Trento
- Multimodal Fusion Effectiveness. In Table 1, we compare the performance of FusionFormer-X trained with only HSI, only LiDAR, and both modalities. While HSI alone provides rich spectral cues, and LiDAR contributes spatial geometry, their fusion achieves the best results in every metric. Specifically, multimodal fusion improves OA by +2.62% over HSI-only and +8.89% over LiDAR-only, with similar improvements in AA and Kappa. This demonstrates the complementary nature of elevation and spectral information.
- Multi-Scale Self-Attention Variants.Table 2 evaluates the MSMHSA module under various scale settings. We observe that using a coarse-to-fine hierarchy (e.g., , , ) yields the best results. Adding too many scales may slightly degrade performance due to over-fragmentation, while using only one scale fails to capture both local and global interactions. This validates our hypothesis that hierarchical attention enhances fine-grained segmentation boundaries and maintains scene context.
4.4. Extended Quantitative Insights
4.5. Visual Quality Assessment
4.6. Inference Robustness and Repeatability
4.7. Summary and Takeaways
5. Conclusion and Future Directions
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| Class No. | RF | CNN2D | ViT | SpectralFormer | MFT | FusionFormer-X |
|---|---|---|---|---|---|---|
| 1 | 83.73 ± 0.06 | 96.98 ± 0.21 | 90.87 ± 0.77 | 96.76 ± 1.71 | 98.23 ± 0.38 | 99.71 ± 0.25 |
| 2 | 96.30 ± 0.06 | 97.56 ± 0.14 | 99.32 ± 0.77 | 97.25 ± 0.66 | 99.34 ± 0.02 | 98.06 ± 0.80 |
| 3 | 70.94 ± 1.55 | 55.35 ± 0.00 | 92.69 ± 1.53 | 58.47 ± 11.54 | 89.84 ± 9.00 | 94.47 ± 1.77 |
| 4 | 99.73 ± 0.07 | 99.66 ± 0.03 | 100.0 ± 0.00 | 99.24 ± 0.21 | 99.82 ± 0.26 | 99.96 ± 0.02 |
| 5 | 95.35 ± 0.25 | 99.56 ± 0.07 | 97.77 ± 0.86 | 93.52 ± 1.75 | 99.93 ± 0.05 | 99.90 ± 0.07 |
| 6 | 72.63 ± 0.90 | 76.91 ± 0.15 | 86.72 ± 2.02 | 73.39 ± 6.78 | 88.72 ± 0.94 | 95.34 ± 1.32 |
| OA | 92.57 ± 0.07 | 96.14 ± 0.03 | 96.47 ± 0.49 | 93.51 ± 1.27 | 98.32 ± 0.25 | 99.18 ± 0.02 |
| AA | 86.45 ± 0.32 | 87.67 ± 0.04 | 94.56 ± 0.57 | 86.44 ± 2.96 | 95.98 ± 1.64 | 97.91 ± 0.25 |
| 90.11 ± 0.09 | 94.83 ± 0.04 | 95.28 ± 0.65 | 91.36 ± 1.67 | 97.75 ± 0.00 | 98.90 ± 0.02 |
| Class No. | RF | CNN2D | ViT | SpectralFormer | MFT | FusionFormer-X |
|---|---|---|---|---|---|---|
| 1 | 95.42 | 95.79 | 97.85 | 97.30 | 97.90 | 98.88 |
| 2 | 74.03 | 72.76 | 76.06 | 69.35 | 92.11 | 88.84 |
| 3 | 75.81 | 78.92 | 87.58 | 78.48 | 91.80 | 90.00 |
| 4 | 68.59 | 83.59 | 92.05 | 82.63 | 91.59 | 95.19 |
| 5 | 88.17 | 78.29 | 94.73 | 87.91 | 95.60 | 95.28 |
| 6 | 77.28 | 50.34 | 82.02 | 58.77 | 88.19 | 88.48 |
| 7 | 64.83 | 79.70 | 87.11 | 85.87 | 90.27 | 92.94 |
| 8 | 93.29 | 71.95 | 97.60 | 95.60 | 97.26 | 97.84 |
| 9 | 19.15 | 43.92 | 57.83 | 53.52 | 61.35 | 65.02 |
| 10 | 4.41 | 12.45 | 31.99 | 8.43 | 17.43 | 36.97 |
| 11 | 71.88 | 26.82 | 58.72 | 35.29 | 72.79 | 80.85 |
| OA | 85.32 | 83.40 | 92.15 | 88.25 | 94.34 | 94.73 |
| AA | 66.62 | 63.14 | 78.50 | 68.47 | 81.48 | 84.57 |
| 80.39 | 77.94 | 89.56 | 84.40 | 92.51 | 93.02 |
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