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Gaussian Density Splatting Network

NeurIPS 2026 · 3D vision › Gaussian splatting · approach: Compact and efficient Gaussian splatting

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Proposes GDSNet, a crowd counter that represents density as continuous 2D Gaussian primitives placed via Delaunay-triangulated control points and trained end-to-end by differentiable Gaussian splatting.

Problem

Grid-based density maps are tied to the backbone's downsampling stride and point-based methods collapse people to Dirac impulses with unstable bipartite matching; learning free-form Gaussian density fields is ill-posed and prone to degenerate solutions.

Approach

Represent the crowd density as a superposition of learnable anisotropic 2D Gaussians with mass, where centers are constrained by barycentric weights over Delaunay simplices of structure-guided control points, and features are aggregated over the simplex adjacency graph; supervision uses Bayesian rasterized density loss plus count and shape regularizers.

Key results

• GDSNet achieves MAE 48.8 on ShanghaiTech A, 5.4 on ShanghaiTech B, 52.8 on JHU-Crowd++, 75.9 on UCF-QNRF and 68.7 on NWPU, reported as state of the art across all benchmarks.
• Ablation on UCF-QNRF: full model MAE 75.86 vs 89.46 with none of CPA, SCP, TFA.
• Train/test stride robustness: models trained at stride 10 keep MAE below 80 on UCF-QNRF for test strides below 15 without finetuning.

Surprising findings

• Triangle-based mass regression (piecewise-constant basis) is only slightly worse than full Gaussian (82.21 vs 75.86 MAE on UCF-QNRF), suggesting the gain partly comes from the simplex structure itself.

Limitations

• Delaunay triangulation adds the dominant runtime overhead (about 9 ms of topology computation at 256x256).
• Relies on a structural prior from an external frozen InstantGI estimator.
• Performance degrades at very sparse test strides (15 and 16).

Experimental setup

Datasets: ShanghaiTech A ShanghaiTech B JHU-Crowd++ UCF-QNRF NWPU-Crowd

Benchmarks: ShanghaiTech A ShanghaiTech B JHU-Crowd++ UCF-QNRF NWPU-Crowd

Metrics: MAE MSE

Baselines: BL DMCount UOT GL P2PNet MAN CLTR ChfL PET APGCC Gramformer PML

Builds on: Bayesian loss 2D Gaussian splatting Image-GS P2PNet

Closest papers by meaning

• Distribution Matching for Crowd Counting (NeurIPS 2020 · similarity 0.87)
• Gaussian Graph Network: Learning Efficient and Generalizable Gaussian Representations from Multi-view Images (NeurIPS 2024 · similarity 0.86)
• 3D Student Splatting and Scooping (CVPR 2025 · similarity 0.85)
• CrowdDiff: Multi-hypothesis Crowd Density Estimation using Diffusion Models (CVPR 2024 · similarity 0.85)
• 3D Gaussian Splatting as Markov Chain Monte Carlo (NeurIPS 2024 · similarity 0.85)
• Gaussian Splatting Lucas-Kanade (ICLR 2025 · similarity 0.84)