Perturbed Gaussian Ensemble

Abstract

Sparse-view computed tomography (CT) is critical for reducing radiation exposure to patients. Recent advances in radiative 3D Gaussian Splatting (3DGS) have enabled fast and accurate sparse-view CT reconstruction. Despite these algorithmic advancements, practical reconstruction fidelity remains fundamentally bounded by the quality of the captured data, raising the crucial yet underexplored problem of X-ray active view selection. Existing active view selection methods are primarily designed for natural-light scenes and fail to capture the unique geometric ambiguities and physical attenuation properties inherent in X-ray imaging.

In this paper, we present Perturbed Gaussian Ensemble, an active view selection framework that integrates uncertainty modeling with sequential decision-making, tailored for X-ray Gaussian Splatting. Specifically, we identify low-density Gaussian primitives that are likely to be uncertain and apply stochastic density scaling to construct an ensemble of plausible Gaussian density fields. For each candidate projection, we measure the structural variance of the ensemble predictions and select the one with the highest variance as the next best view. Extensive experimental results on arbitrary-trajectory CT benchmarks demonstrate that our density-guided perturbation strategy effectively eliminates geometric artifacts and consistently outperforms existing baselines in progressive tomographic reconstruction under unified view selection protocols.

Method

Given a few initial X-ray projections, the goal is to iteratively pick the next best view from a pool of candidate scanner poses on a hemisphere, acquire it, and keep training a radiative Gaussian Splatting model until the view budget is spent. Our core intuition: under sparse-view constraints, geometric ambiguities show up as fragile structures, such as uncertain boundaries and needle-like artifacts, whose projections change dramatically when observed from an informative, unseen angle. The best next view is the one that exposes this structural instability the most.

Comparison of active view selection paradigms for X-ray Gaussian Splatting: gradient-based, ensemble-based, and our Perturbed Gaussian Ensemble. — **Active view selection paradigms for X-ray Gaussian Splatting.** **(a)** Gradient-based methods such as FisherRF estimate expected information gain with a diagonal Fisher Information Matrix, but suffer from gradient coupling along transmissive rays and the absence of view-dependent parameters. **(b)** Ensemble-based methods measure rendering disagreement across several models trained from different seeds, at a prohibitive computational cost. **(c)** Our **Perturbed Gaussian Ensemble** builds the ensemble from a single trained model by density-guided perturbation and scores each candidate view by the structural variance of its rendered projections.

Density-guided perturbation

High-density Gaussians (bones, dense organs) are well constrained even from few views. Low-density ones sit on soft boundaries, background noise, or over-fitted needle-like tails, and are where the uncertainty lives. We take the fraction \(\alpha\) of Gaussians with the lowest densities and stochastically rescale them:

\(\rho_{i,j} = \rho_j\,(1+\epsilon_{i,j}),\quad \epsilon_{i,j}\sim\mathcal{U}(-\beta,\beta)\)

Repeating this \(N\) times yields an ensemble of plausible density fields with no extra training.

Render the ensemble

For every candidate pose \(\mathbf{v}\) we render the unperturbed projection \(\mathbf{I}(\mathbf{v})\) and the \(N\) perturbed projections \(\mathbf{I}_i(\mathbf{v})\). Because X-ray projection is a linear integral of the density field (Beer-Lambert law), perturbing coupled Gaussians along a ray directly reveals how fragile that view's structure is.

Select by structural variance

We compare each perturbed rendering with the original using SSIM, \(s_i(\mathbf{v}) = \mathrm{SSIM}(\mathbf{I}(\mathbf{v}), \mathbf{I}_i(\mathbf{v}))\), and score the view by the variance of these scores:

\(u(\mathbf{v}) = \tfrac{1}{N-1}\sum_{i=1}^{N}\big(s_i(\mathbf{v})-\bar{s}(\mathbf{v})\big)^2\)

\(\mathbf{v}^{*} = \arg\max_{\mathbf{v}\in\mathcal{V}_{\text{cand}}} u(\mathbf{v})\)

SSIM normalizes luminance and contrast, so global intensity shifts caused by density scaling do not drown out genuine geometric disagreement.

Why not reuse natural-light methods? X-ray imaging has no occlusion and no view-dependent appearance, so radiative Gaussians carry no spherical-harmonic parameters. Along a transmissive ray, many Gaussians are strongly coupled, which breaks the diagonal Fisher-information approximation that gradient-based selectors rely on. Our forward, sampling-based approach explores that coupled uncertainty directly. Default setting: \(N=10\), \(\alpha=10\%\), \(\beta=0.5\).

Results

We follow the R2-Gaussian setting: a synthetic benchmark of 15 CT volumes and three real-world cases from the FIPS dataset (pseudo ground truth via FDK). Views are selected from a candidate pool of 448 poses on two concentric hemispheres, starting from two initial views, under 24-view and 36-view budgets. All baselines (rule-based heuristics, 2D no-reference IQA selectors, and 3D uncertainty-based FisherRF) are re-implemented on the same radiative Gaussian Splatting framework. Metrics: 3D PSNR / SSIM on the reconstructed volume, and 2D PSNR / SSIM for novel view synthesis.

Tomographic reconstruction and novel view synthesis

Table 1. Quantitative comparison under the 24-view and 36-view protocols. PSNR₃ / SSIM₃ are computed on the 3D volume, PSNR / SSIM on 2D novel views. Best in bold.

Category	Method	24-view				36-view
Category	Method	PSNR₃ ↑	SSIM₃ ↑	PSNR ↑	SSIM ↑	PSNR₃ ↑	SSIM₃ ↑	PSNR ↑	SSIM ↑
Synthetic dataset
Rule-based	Random	32.629	0.881	41.862	0.954	34.823	0.915	44.552	0.961
	Uniform	33.562	0.890	43.260	0.961	35.877	0.921	46.053	0.968
	FPS	33.508	0.891	43.081	0.957	35.367	0.919	45.386	0.964
2D-based	TOPIQ	33.000	0.882	42.898	0.961	34.951	0.912	45.483	0.967
	MANIQA	32.319	0.882	41.482	0.953	34.543	0.913	44.516	0.962
	MUSIQ	33.083	0.886	42.675	0.957	35.030	0.916	45.133	0.965
3D-based	FisherRF	33.347	0.887	43.289	0.962	35.551	0.919	46.212	0.969
3D-based	Ours	34.078	0.896	44.069	0.966	36.226	0.926	46.849	0.971
Real-world dataset
Rule-based	Random	36.112	0.903	42.992	0.985	36.765	0.921	44.965	0.989
	FPS	36.134	0.905	43.073	0.985	36.898	0.925	45.171	0.989
2D-based	TOPIQ	36.208	0.906	43.121	0.986	37.167	0.928	45.644	0.990
	MANIQA	36.222	0.906	43.476	0.986	37.187	0.929	45.644	0.990
	MUSIQ	36.257	0.906	43.293	0.985	37.119	0.925	45.494	0.990
3D-based	FisherRF	36.205	0.902	43.179	0.985	37.258	0.926	46.022	0.990
3D-based	Ours	36.399	0.909	43.546	0.986	37.480	0.932	46.046	0.991

Visual comparisons of reconstructed 3D volumes for Random, MUSIQ, FisherRF, Ours, and ground truth on synthetic and real scenes. — **Reconstructed 3D volumes** under different view selection strategies. The 3D PSNR (dB) of each scene is shown at the top-left corner. Ours consistently reaches the highest quality, suppresses boundary artifacts and background noise, and better preserves fine structures.

Visual comparisons of novel view synthesis for Random, MUSIQ, FisherRF, Ours, and ground truth. — **Novel view synthesis** on the synthetic dataset (24-view). The PSNR (dB) of each rendering is shown at the top-left corner. More informative views mitigate the needle-like artifacts and noise that usually appear along rays through dense regions such as bones.

Sparser view budgets

Table 2. 3D reconstruction quality on the synthetic dataset under 6 / 8 / 12 / 16-view protocols. Best in bold.

Method	6-view		8-view		12-view		16-view
Method	PSNR₃ ↑	SSIM₃ ↑	PSNR₃ ↑	SSIM₃ ↑	PSNR₃ ↑	SSIM₃ ↑	PSNR₃ ↑	SSIM₃ ↑
Random	24.58	0.711	25.14	0.729	28.54	0.805	29.98	0.836
FPS	25.29	0.742	26.85	0.780	29.10	0.822	30.50	0.846
Uniform	23.77	0.697	26.84	0.772	28.95	0.811	31.16	0.851
MUSIQ	25.54	0.741	27.04	0.767	29.86	0.824	31.03	0.847
FisherRF	25.80	0.748	27.43	0.779	29.87	0.823	30.79	0.846
Ours	25.93	0.758	27.90	0.786	30.29	0.830	31.30	0.855

Ablation studies (24-view, synthetic)

Table 3. Uncertainty metric, ensemble size \(N\), perturbed ratio \(\alpha\), and scaling amplitude \(\beta\). † marks the default setting.

Setting	PSNR₃ ↑	SSIM₃ ↑
L1 variance	33.644	0.894
PSNR variance	33.390	0.889
SSIM variance †	34.078	0.896
\(N=5\)	33.952	0.895
\(N=10\) †	34.078	0.896
\(N=15\)	34.034	0.896
\(N=20\)	33.865	0.895
\(N=40\)	33.670	0.893

Setting	PSNR₃ ↑	SSIM₃ ↑
\(\alpha=5\%\)	33.680	0.893
\(\alpha=10\%\) †	34.078	0.896
\(\alpha=15\%\)	33.938	0.896
\(\alpha=20\%\)	33.589	0.892
\(\beta=0.1\)	34.040	0.896
\(\beta=0.3\)	34.057	0.897
\(\beta=0.5\) †	34.078	0.896
\(\beta=1.0\)	33.338	0.890

Table 4. Alternative perturbation strategies. † is our stochastic density scaling.

Views	Dropout		Position jittering		Jittering + scaling		Stochastic scaling †
Views	PSNR₃ ↑	SSIM₃ ↑	PSNR₃ ↑	SSIM₃ ↑	PSNR₃ ↑	SSIM₃ ↑	PSNR₃ ↑	SSIM₃ ↑
24	32.718	0.883	34.061	0.895	33.886	0.896	34.078	0.896
36	34.607	0.924	36.112	0.925	36.200	0.925	36.226	0.926

Pixel-wise metrics (L1, PSNR) are dominated by the global intensity shifts that density scaling induces in a linear-integral image, whereas SSIM isolates structural disagreement. A moderate ensemble size keeps the uncertainty landscape sharp; too many samples smooth away the catastrophic failures that mark informative views. Perturbing too few Gaussians misses the degenerate primitives, and perturbing too many pollutes well-constrained anatomy.

Code

The implementation is built on R2-Gaussian and released at github.com/yulunwu0108/Perturbed-Gaussian-Ensemble. Data are available on Google Drive.

# Install
git clone https://github.com/yulunwu0108/Perturbed-Gaussian-Ensemble.git --recursive
cd Perturbed-Gaussian-Ensemble
conda env create --file environment.yml
conda activate perturbed-gaussian-ensemble

# Active view selection + progressive reconstruction (24 views, 2 initial)
CUDA_VISIBLE_DEVICES=0 python active_train.py \
    -s data/<scene_name> \
    -m output/<scene_name> \
    --method ensemble \
    --schema v24init2

# Evaluate
CUDA_VISIBLE_DEVICES=0 python test.py -m output/<scene_name>

--method: ensemble for our selector, rand for random selection.
--schema v<N>init<K>: select N views in total starting from K initial views.
--ensemble_num_trials (\(N\), default 10), --ensemble_low_density_ratio (\(\alpha\), default 0.1), --ensemble_scale (\(\beta\), default 0.5).

BibTeX

@inproceedings{wu2026active,
  title     = {Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstruction},
  author    = {Wu, Yulun and Zha, Ruyi and Cao, Wei and Li, Yingying and Cai, Yuanhao and Liu, Yaoyao},
  booktitle = {European Conference on Computer Vision (ECCV)},
  pages     = {405--424},
  year      = {2026},
  organization = {Springer}
}

Acknowledgements

This research is supported by the National Artificial Intelligence Research Resource (NAIRR) Pilot Awards NAIRR250199, NAIRR260019, and NAIRR260077, the AMD University Program's AI & HPC Cluster, NVIDIA Academic Grant Program, and Lambda's Research Grant. Computational resources are also provided by Delta and DeltaAI at the National Center for Supercomputing Applications (NCSA) through ACCESS allocations CIS250012, CIS250816, and CIS251188. This project has benefited from 3D Gaussian Splatting, R2-Gaussian, FisherRF, and DiffDRR.