Active View Selection for Tomography via Perturbed Gaussian Ensemble¶

Conference: ECCV2026
arXiv: 2603.06852
Project Page: perturbed-gaussian-ensemble.cvmlgroup.web.illinois.edu
Code: None
Area: Medical Imaging
Keywords: Sparse CT Reconstruction, Active View Selection, Radiative 3D Gaussian Splatting, Uncertainty Quantification, Perturbed Ensemble

TL;DR¶

To address the challenging problem of active X-ray view selection in sparse-view CT, a perturbed Gaussian ensemble framework based on radiative 3DGS is proposed. By randomly perturbing the density parameters of low-density Gaussian primitives to construct a lightweight model ensemble, epistemic uncertainty is quantified using the structural similarity (SSIM) variance of projections under candidate views. The view that maximizes the exposure of geometric artifacts is selected as the next best acquisition angle.

Background & Motivation¶

X-ray computed tomography (CT) is an indispensable non-destructive imaging modality in medical diagnosis and industrial inspection. Sparse-view CT reduces ionizing radiation exposure to patients by significantly decreasing the number of projection acquisition angles. However, this formulates tomographic reconstruction as a highly ill-posed inverse problem. Conventional algorithms often suffer from severe streak artifacts and structural distortions under extremely sparse conditions. In recent years, the emergence of Radiative 3D Gaussian Splatting (3DGS) has brought a breakthrough to this challenge. It adapts the classic 3DGS framework to X-ray transmission imaging, modeling the 3D density field of an object using a set of explicit Gaussian primitives, enabling fast and accurate CT reconstruction via differentiable rendering (subsequent works like R2-Gaussian push radiative GS towards direct, unbiased voxel-oriented reconstruction). However, despite the significant improvement in 3D modeling capabilities, the ultimate bottleneck of reconstruction quality shifts back to the source of data—under a limited budget of views, which angles should projections be acquired from to both cover global contours and precisely capture local structural details? This is the under-explored "active view selection" problem in CT.

Existing active view selection methods are primarily designed for natural illumination scenes. Representative methods like FisherRF estimate the expected information gain of candidate views through a diagonal approximation of the Fisher Information Matrix (FIM). However, the physical properties of X-rays differ fundamentally from those of natural light. X-rays follow the Beer-Lambert law, where projections are pure linear integrals of the density field along ray paths, presenting no occlusion and surface reflection. Meanwhile, X-ray attenuation is isotropic, meaning Gaussian primitives do not have view-dependent spherical harmonics coefficients. Consequently, the assumption of "front-surface dominant rendering + view-dependent gradients" that natural light methods rely on completely fails in CT. All Gaussians along a ray path are highly coupled, and the diagonal approximation of FIM leads to severe bias. This renders the methods unable to distinguish between needle-like artifacts and true high-density structures, often selecting redundant views rather than those that truly eliminate geometric ambiguity.

The core insight of this paper is that under sparse-view constraints, geometric ambiguity usually manifests as fragile structures—uncertain boundaries, needle-like artifacts formed by overfitting, etc.—whose projections exhibit extreme instability under different viewing angles. An effective next best view should maximally expose such latent structural fragility. Core Idea: By using low-density Gaussian primitives as proxies for uncertain regions and applying random perturbations to their density parameters to build a model ensemble, the structural variance (SSIM variance) of the rendered projections from the ensemble is calculated under candidate views. The view with the maximum variance is selected as the best view that can maximally expose geometric artifacts.

Method¶

Overall Architecture¶

The proposed method is built upon the R2-Gaussian radiative Gaussian splatting framework, and the core pipeline is an iterative closed loop. In the initial stage, given a small set of sparse projections (e.g., 2 initial views), a radiative GS model is trained to model the 3D density field. Subsequently, the active selection loop begins: first, a batch of Gaussian primitives with the lowest densities are identified from the trained model as uncertain primitives, and their density parameters are randomly scaled to generate $N$ perturbed models, forming the Perturbed Gaussian Ensemble. Next, for each view in the candidate view pool, a projection is rendered using the unperturbed base model and each of the $N$ perturbed models. $N$ SSIM scores are computed, and their variance is taken as the uncertainty score for that view. The view with the highest score is selected as the next best view. Its ground-truth projection is acquired and added to the training set. After re-optimizing the GS model, the pipeline proceeds to the next iteration until the total number of views reaches the target budget.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Initial Sparse Projection Set<br/>N_init views"] --> B["Train Radiative GS Model<br/>R2-Gaussian"]
    B --> C["Identify Low-Density Gaussians<br/>Lowest α = 10% by density"]
    C --> D["Random Scale Perturbation of Density<br/>→ Generate N = 10 perturbed models"]
    D --> E["For each candidate view v:<br/>Render N+1 projections<br/>→ Compute SSIM variance u(v)"]
    E --> F["Select v* = argmax u(v)<br/>Acquire GT projection → Add to training set"]
    F --> B

Key Designs¶

1. Density-guided random perturbation: Low-density Gaussian primitives as uncertainty probes

In radiative GS, the density parameter $\rho$ of each Gaussian primitive determines its contribution to X-ray attenuation. High-density primitives correspond to well-defined structures like bones—even with sparse views, their projection constraints along multiple rays are sufficient, and the model is highly confident in these parameters. Low-density primitives are the exact opposite: they are typically distributed near tissue boundaries, interfaces between soft tissues and air, or the "tails" of needle-like artifacts derived from overfitting. Due to the extremely limited training views, the geometry of these regions exhibits severe ambiguity—the model can stretch a long string of low-density Gaussians along the ray direction to fit known projections, which manifests as obvious artifacts under unobserved views.

Based on this observation, the authors select the lowest $\alpha\%$ (in experiments, $\alpha = 10\%$) primitives as the fragile subset, and perform random scaling on the density of each primitive in this subset: $$\rho_{i,j} = \begin{cases} \rho_j \cdot (1 + \epsilon_{i,j}), & \text{if } G_j \in \mathcal{G}_{\text{low}} \\ \rho_j, & \text{otherwise} \end{cases}, \quad \epsilon_{i,j} \sim \text{Uniform}(-\beta, \beta)$$ High-density primitives remain completely unchanged. Each perturbed model essentially represents a plausible but different hypothesis—what the reconstructed structure would look like if the density of those uncertain regions changed slightly. The ensemble of $N = 10$ perturbed models naturally exhibits different interpretations of geometric ambiguity in the projection space, and to distinguish which interpretation is more correct, one needs to view it from a new angle—which is exactly the information needed for active selection.

2. Projection-space structural variance: Quantifying epistemic uncertainty with SSIM variance

Given the perturbed ensemble, how is the "information content" of a candidate view defined? The core idea is that if a view can amplify the projection structure discrepancy among different density hypotheses, it can provide information to distinguish these hypotheses. Specifically, for a candidate view $v$, a reference projection $I$ is rendered using the unperturbed base model, and another projection $I_i$ is rendered using each of the $N$ perturbed models. The SSIM score between each perturbed projection and the reference projection is calculated as $s_i = \text{SSIM}(I, I_i)$. The uncertainty score of the candidate view is defined as the sample variance of these $N$ SSIM scores: $u(v) = \text{Var}[s_1, \dots, s_N]$.

Why choose SSIM over L1 error or PSNR? This is a subtle yet crucial engineering insight. The linear integration property of X-ray projections dictates that perturbing Gaussian densities inevitably causes a shift in the overall brightness of the projection, as the contributions of all primitives along the ray are accumulated. L1 and PSNR are absolute or mean squared errors calculated pixel-by-pixel, which are extremely sensitive to such global brightness drifts. Low-frequency brightness variations would easily drown out the structural change signals arising from geometric ambiguity. In contrast, SSIM has built-in luminance and contrast normalization, effectively decoupling absolute brightness shifts from genuine structural information. Ablation studies clearly demonstrate that replacing the uncertainty metric with L1 variance or PSNR variance leads to a decrease in reconstruction PSNR by $0.43\text{dB}$ and $0.69\text{dB}$, respectively, fully proving that the structural awareness of SSIM is key to the success of this method.

3. One training, multiple perturbations: Lightweight ensemble simulation instead of brute-force ensembling

The most intuitive way to estimate uncertainty is to train $N$ independent GS models with different random seeds and compare their rendering differences. However, the cost of this brute-force ensembling scales linearly with $N$. Training a single GS already requires tens of thousands of iterations, making training $N$ models impractical in reality. The key innovation of this paper is the realization that the source of uncertainty lies primarily in the parameter variation of low-density primitives. Therefore, only one base model needs to be trained, and during evaluation, the fragile subset is repeatedly perturbed to simulate multi-model divergence through $N$ forward passes. This is mathematically equivalent to a Monte Carlo approximation of the posterior distribution $p(I(v)|\mathcal{D})$—where the perturbations sample $N$ plausible posterior locations in the parameter space. The cost of a single forward pass is far lower than a full optimization, allowing the entire active selection pipeline to run efficiently on a single A40. Ablation studies show that $N = 10$ is the optimal choice: $N = 5$ suffers from insufficient sampling and unstable uncertainty estimation, while $N = 40$ dilutes the contribution of extreme structural failures, reducing the contrast of the uncertainty scores.

Loss & Training¶

The optimization objective of the base model includes projection-level L1 loss, D-SSIM loss, and a 3D total variation regularization loss. Active selection and model optimization are executed alternately: whenever a best view is selected, the ground-truth projection of that view is added to the training set for incremental optimization of the GS model. The selection trigger time follows the configuration of FisherRF—occurring before the end of the densification phase of GS to ensure the model parameters are sufficiently stable.

Key Experimental Results¶

Main Results¶

Evaluations are performed on a synthetic dataset (15 volumes from multiple public CT datasets) and a real dataset (3 cases from FIPS, with FDK full sampling used as pseudo-GT), adopting a hemispherical scanning trajectory. The candidate view pool contains 448 uniformly sampled scanning poses. Baselines include regular baselines (Random/Uniform/FPS), 2D no-reference IQA methods (MUSIQ/MANIQA/TOPIQ), and 3D uncertainty methods (FisherRF).

Dataset	Protocol	Metric	Random	Uniform	FPS	FisherRF	Ours
Synthetic	24-view	PSNR3↑	32.629	33.562	33.508	33.347	34.078
Synthetic	24-view	SSIM3↑	0.881	0.890	0.891	0.887	0.896
Synthetic	36-view	PSNR3↑	34.823	35.877	35.367	35.551	36.226
Synthetic	36-view	SSIM3↑	0.915	0.921	0.919	0.919	0.926
Real	24-view	PSNR3↑	36.112	—	36.134	36.205	36.399
Real	36-view	PSNR3↑	36.765	—	36.898	37.258	37.480

The proposed method consistently outperforms all baselines in sparser settings (6/8/12/16-view) as well. At the minimum of 6-view, the PSNR reaches 25.93 (vs. 25.80 of the runner-up FisherRF), validating the applicability of the framework under extremely sparse sampling conditions.

Ablation Study¶

Configuration	24-view PSNR3	Explanation
Full (SSIM Variance)	34.078	Default configuration
Replaced with L1 variance	33.644	↓0.43dB, brightness shift contaminates structural signal
Replaced with PSNR variance	33.390	↓0.69dB, also dominated by global brightness changes
$N=5$	33.952	Ensemble size too small, unstable uncertainty estimation
$N=10$	34.078	Optimal trade-off
$N=40$	33.670	Too many samples smooth out the contrast of extreme structural failures
$\alpha=5\%$	33.680	Perturbation range too small, missing primitives that form artifacts
$\alpha=10\%$	34.078	Optimal
$\alpha=20\%$	33.589	Perturbation affects highly confident structures, introducing non-informative variations
$\beta=0.1$	34.040	Perturbation too weak, insufficient to disrupt the balance of artifacts
$\beta=0.5$	34.078	Optimal
$\beta=1.0$	33.338	Perturbation too strong, structures completely distorted, variance loses discriminative power

Key Findings¶

SSIM variance vs L1/PSNR variance is the most critical ablation finding of this work. It not only verifies the necessity of SSIM's brightness normalization in X-ray scenarios but also reveals a design principle for active view selection in CT: one must isolate the global brightness shifts caused by X-ray linear integration and focus on structural-level change signals.
Density-guided perturbation outperforms sparse Dropout and position jittering: Directly removing low-density Gaussians via Dropout completely discards the signals of these regions rather than detecting their sensitivity; position jittering alters geometric locations rather than density parameters, failing to align with the physical model of Beer-Lambert attenuation.
FisherRF underperforms even FPS heuristics in the synthetic 24-view setting, indicating that the mathematical bias of its diagonal approximation in highly coupled X-ray scenarios does not produce gains and may instead introduce misleading information estimation.
Although the gap between methods narrows on real data compared to synthetic data, the proposed method still maintains its lead, showing that the framework possesses robustness against different noise levels.

Highlights & Insights¶

巧妙地将不确定性估计从不可行的暴力集成转化为"一次训练+多次扰动"，利用辐射GS密度参数的显式物理解释直接定位不确定区域。$N$次前向渲染替代$N$次完整优化，使整套方案的算力成本降低了一个数量级。
SSIM方差替代L1/PSNR方差是一个非常细致的洞察——认识到X射线线性积分导致的亮度漂移会污染逐点指标，SSIM的亮度对比度归一化恰好避开了这个陷阱。这个选择不是凭经验的，而是由底层的透射成像物理模型直接推导得出的。
"低密度=高不确定性"这个启发式简洁且有力，不需要复杂的贝叶斯网络或MC Dropout，直接利用了辐射GS密度参数的语义含义。这种将模型自身参数语义与不确定性代理联系起来的设计思路在基于显式粒子/体素的渲染框架中具有通用借鉴价值。
论文将FisherRF等基线统一适配到辐射GS框架下重新实现并对比，为CT主动视角选择研究建立了标准化的评估协议和benchmark。

Limitations & Future Work¶

The experiments only evaluated on hemispherical scanning trajectories (simulating C-arm CT) without validation under geometric constraints like conventional medical CT circular orbits or helical scanning. The geometric distribution of candidate views differs significantly across trajectories, potentially affecting the efficacy of the selection strategy.
The "low-density = high-uncertainty" assumption holds in most cases, but extreme counterexamples may exist—such as thin but structurally well-defined membrane materials, which have low density but no geometric ambiguity. The boundaries of this assumption require more systematic stress-testing.
The ensemble perturbation only acts on density parameters, neglecting the randomness of location and covariance. Although ablations show position jittering is less effective than density scaling, whether joint randomization of position and covariance yields extra gains remains an open question.
Real-data experiments are based on pseudo-GT reconstructed from FDK full-sampling rather than real clinical CT data. Performance under real noise environments (quantum noise, scatter, beam hardening) awaits clinical validation.

vs FisherRF: FisherRF estimates information gain based on the diagonal approximation of FIM, which works in natural-light front-surface-dominated rendering but fails in X-ray scenarios due to strong coupling along the ray path. This work starts from forward perturbation paths and directly simulates the impact of parameter changes on projections, avoiding gradient approximation bias while maintaining real-time capability.
vs ActiveNeRF / NAF and other NeRF-like methods: NeRF uses implicit MLPs to model the density field, resulting in much slower training and rendering speeds than 3DGS, and lacks the specialized adaptation to physical X-ray transmission modeling (such as covariance scaling factor correction) found in R2-Gaussian. Thus, it cannot easily satisfy the requirements of fast reconstruction and real-time active selection simultaneously.
vs 2D no-reference IQA methods (MUSIQ/MANIQA/TOPIQ): These methods rely directly on projection quality for view selection but lack the ability to model 3D structural uncertainty. The views they select tend to have "clear projections themselves" rather than "reflecting the uncertainty of the 3D structure."

Rating¶

Novelty: ⭐⭐⭐⭐ The design of combining perturbed ensembles with the physical characteristics of X-ray 3DGS is highly original, and using SSIM variance as an uncertainty metric is a clever fine-grained contribution.
Experimental Thoroughness: ⭐⭐⭐⭐ The ablation study is comprehensive (covering uncertainty metrics, perturbation ratios, ensemble sizes, and alternative strategies), though real data was evaluated using pseudo-GT rather than actual clinical CT.
Writing Quality: ⭐⭐⭐⭐ The motivation is clearly articulated, the logical chain across method sections is complete, and the figures and tables are of high quality.
Value: ⭐⭐⭐⭐ Provides a feasible technical solution for intelligent scan planning in low-dose CT, with clear potential for clinical translation.