4DRGS: 4D Radiative Gaussian Splatting for Efficient 3D Vessel Reconstruction from Sparse-View Dynamic DSA Images

Hongdong Li; Huangxuan Zhao; Ruyi Zha; Zhentao Liu; Zhiming Cui

REVIEW 4 major objections 6 minor 1 cited by

4DRGS: 4D Radiative Gaussian Splatting for Efficient 3D Vessel Reconstruction from Sparse-View Dynamic DSA Images

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that 3D vessel reconstruction from sparse dynamic DSA images can be done in minutes with 4D radiative Gaussian splatting, a decoupling of static vessel geometry from time-varying contrast attenuation, at quality matching…

desk verdict Genuinely new and fast Gaussian-splatting pipeline for dynamic DSA reconstruction, but the 3D SOTA claim hinges on an asymmetric-threshold metric with margins inside the noise. read the letter →

arxiv 2412.12919 v2 pith:DAXAETCF submitted 2024-12-17 eess.IV cs.CV

Zhentao Liu , Ruyi Zha , Huangxuan Zhao , Hongdong Li , Zhiming Cui This is my paper · ORCID

classification eess.IVcs.CV

keywords 4DradiativeGaussiansplattingsparse-viewDSAreconstruction3Dvesseldynamicdigitalsubtractionangiographycontrast-agentflowmodelingkernelpruningX-rayrasterizationneuralattenuationfield

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that high-quality 3D vessel reconstruction from sparse-view dynamic digital subtraction angiography (DSA) images can be done in minutes rather than hours by modeling vessels as a set of 4D radiative Gaussian kernels. The key move is to split the problem: each kernel has fixed geometry (position, rotation, and scale) that encodes the static vessel structure, while a compact neural network predicts its time-dependent central attenuation to follow contrast-agent flow. The kernels are trained by differentiable X-ray rasterization against real DSA images, then voxelized into a 3D volume. On 15 patient cases with 30 to 60 input views, the method reaches state-of-the-art or comparable reconstruction and synthesis quality while training in about 13 minutes, and a fast 10k-iteration version matches the previous method's quality in about 5 minutes, a 32x speedup. If this holds, it would make 3D DSA reconstruction practical enough for clinical use with substantially lower radiation exposure.

What carries the argument

The load-bearing object is the 4D radiative Gaussian kernel $G_i(x,t) = \rho(p_i,t)\exp\left(-\frac{1}{2}(x-p_i)^\top \Sigma_i^{-1}(x-p_i)\right)$, where $\Sigma_i = R_i S_i S_i^\top R_i^\top$ encodes fixed orientation and size and $\rho(p_i,t)$ is the time-varying central attenuation predicted by a compact neural field. This single identity does two jobs: it constrains the reconstruction to static vessel geometry, which regularizes the severely ill-posed sparse-view problem, and it lets contrast-agent dynamics be represented as a scalar function of position and time rather than as a full 4D volume. X-ray rasterization from radiative Gaussian splatting integrates these kernels along rays to synthesize DSA images, and GPU voxelization converts the trained kernels into an attenuation volume. Accumulated attenuation pruning and bounded scaling activation are the two supporting mechanisms that keep the kernel set clean and compact during optimization.

What would settle it

Run 4DRGS and the previous method on a synthetic or physical phantom with known vessel centerlines, generate sparse-view dynamic DSA projections from a known ground-truth attenuation volume, and measure Chamfer and Hausdorff distances against the true geometry at identical mesh thresholds; if the gap between methods shrinks or reverses, or if the 0.025-versus-0.008 threshold choice explains the reported margin, then the paper's accuracy claim is a measurement artifact.

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Extended reading notes

Core claim

The authors claim that 4DRGS is the first Gaussian-splatting framework for 3D vessel reconstruction from sparse-view dynamic DSA images. The central discovery is that time-varying contrast-agent flow and static vessel anatomy can be decoupled in a single explicit representation: vessels are static in space, so only attenuation needs to change over time. Each 4D radiative Gaussian kernel carries time-invariant position, rotation, and scale, and a neural attenuation field predicts the kernel's central attenuation from its position and timestamp. The kernels are optimized with an L1 plus D-SSIM loss against real DSA frames under temporal perturbation, and the trained kernels are voxelized and averaged across timestamps to produce the final vessel volume. The paper further introduces accumulated attenuation pruning, which removes kernels whose attenuation averaged over training is consistently small, and bounded scaling activation, which keeps kernels within a fixed size range to avoid needle artifacts. With these components, the method reports state-of-the-art or comparable Chamfer and Hausdorff distances for 3D reconstruction and PSNR/SSIM for 2D DSA synthesis across 30, 40, 50, and 60 input views, while training in minutes.

Load-bearing premise

The reported 3D accuracy rests on the scanner's inbuilt FDK volumes being accurate enough to serve as reference geometry, even though the paper says they are 'not entirely accurate,' and on comparing surfaces that were meshed at different attenuation thresholds for reference versus reconstruction.

Editorial extensions

If this is right

A full 3D vessel reconstruction from 30 to 60 DSA views converges in about 13 minutes on a single GPU, and a fast 10k-iteration version reaches the previous method's quality in about 5 minutes, a 12x to 32x speedup.
The method reports the best or second-best Chamfer and Hausdorff distances against scanner-volume references and the best PSNR/SSIM on held-out DSA frames in most tested view counts.
Because kernels only cover vascular structures rather than the whole scan volume, training and rendering time scale with vessel sparsity instead of scene size.
Accumulated attenuation pruning preserves vessels that are not yet opacified at a given timestamp, which random or instantaneous-threshold pruning removes.
Bounded scaling activation removes the needle-like elongated Gaussians that unbounded exponential scaling produces in DSA reconstruction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the reported 3D accuracy is measured against scanner-inbuilt FDK volumes that the paper itself calls 'not entirely accurate,' and reference meshes are extracted at a higher attenuation threshold (0.025) than reconstructed meshes (0.008); an independent ground-truth phantom study would determine how much of the Chamfer/Hausdorff margin is real geometry fidelity.
Editorial inference: the static-geometry assumption means the approach would likely degrade with patient motion or cardiac-driven vessel displacement; extending the kernels with per-kernel temporal displacement or motion compensation is the natural next test.
Editorial inference: the same 'static structure, time-varying attenuation' decomposition should transfer to other dynamic tomographic problems, such as contrast-enhanced cone-beam CT or 4D CT, where a compact Gaussian-plus-MLP representation could replace full 4D volume optimization.
Editorial inference: because the neural attenuation field is compact and rasterization is differentiable, the trained 4DRGS model could be used for near-real-time re-rendering of DSA frames at arbitrary angles, which would help interventional navigation; the paper does not demonstrate this but the representation supports it.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The short version: this is a real new application — radiative Gaussian splatting moved from static CT to dynamic DSA — and the speedup is the headline number that holds up. The paper deserves a serious referee, but the 3D SOTA claim is conditional, not proven, because the metric is noisy and the reference has a known bias.

What is actually new: the decomposition into time-invariant geometry plus a compact neural attenuation field over time is sensible and matches the physics of contrast flow. Accumulated attenuation pruning is a clean fix for the dynamic setting, where instantaneous attenuation would wrongly prune kernels that are merely unfilled at that timestamp. Bounded scaling activation is a small but useful correction for needle artifacts. The 12-32x speedup over VPAL on the same RTX 3090 is robust and not in dispute, and the held-out 2D PSNR/SSIM gains are consistent across view counts. That is meaningful engineering progress.

Where I would push back: the 3D comparison uses the inbuilt FDK volumes as references, although Sec. 4.1 admits they are "not entirely accurate." The meshing thresholds are asymmetric — 0.025 for the reference, 0.008 for all algorithms — without a calibration argument. For a Gaussian kernel, the extracted iso-surface radius depends on the ratio between peak attenuation and threshold, so a lower threshold systematically thickens reconstructed vessels. If the learned volumes sit at a different absolute attenuation scale than the FDK reference, the CD/HD numbers measure calibration more than geometry. The margins over VPAL are also small relative to the spread: at 30 views CD is 1.72±0.29 vs 1.79±0.51, and at 50 views VPAL wins CD outright. A 15-case sample with overlapping error bars does not support "SOTA in most scenarios" as a statistical statement. The TOGS baseline, forced through 720-view rendering plus FDK, also likely understates what TOGS could do. None of this kills the contribution — the speed and the 2D synthesis are enough — but it means the 3D claim should be softened to "comparable to VPAL" until verified on public data or with released code.

This paper is for the medical imaging and 3D reconstruction crowd. I would send it to a serious referee with a request to fix the evaluation protocol, not desk reject it. The core idea is sound, the engineering is honest, and the limitations section candidly notes patient motion and the small private dataset.

Recommendation: engage; require better 3D evaluation before accepting.

Referee Report

4 major / 6 minor

Summary. The paper introduces 4DRGS, a 4D radiative Gaussian splatting framework for reconstructing 3D vessel structures from sparse-view dynamic DSA images. Vessels are represented by Gaussian kernels with static geometry (position, rotation, scale) and a time-varying central attenuation predicted by a compact hash-encoded MLP (DNAF). The model is trained by differentiable X-ray rasterization against captured DSA images, with an accumulated-attenuation pruning criterion and a bounded scaling activation to improve quality. The final volume is obtained by voxelizing and averaging the trained kernels over time. Experiments on 15 real patient cases at 30, 40, 50, and 60 views compare against FDK, R2-Gaussian, TOGS, and VPAL using Chamfer/Hausdorff distances, PSNR/SSIM on held-out views, and training time. The paper claims state-of-the-art or comparable reconstruction quality in most scenarios with a 12x-32x speedup over VPAL. The 2D synthesis results are based on held-out views and appear internally consistent, but the 3D comparison relies on an admittedly inaccurate FDK reference meshed at a different attenuation threshold than the reconstructed volumes, which undermines the central 3D-quality claim as currently presented.

Significance. If the 3D-quality claim were substantiated, this would be a practically important contribution: it is the first Gaussian-splatting method for sparse-view dynamic DSA reconstruction, and the reported training times (about 13 minutes for the full version and 5 minutes for the fast version) are dramatically lower than the roughly 2.6 hours reported for VPAL. The core representation is well motivated: static vessel geometry with time-varying attenuation is a natural fit for DSA, and the two proposed components, accumulated attenuation pruning and bounded scaling activation, are clearly explained and ablated. The use of 15 real clinical cases and multiple view settings is a strength relative to many medical-imaging papers. However, the paper does not release code or data, and the main quantitative evidence for 3D superiority depends on a threshold-sensitive comparison against a reference that the paper itself describes as inaccurate. Because the 3D metric is load-bearing for the headline claim, the current evidence does not yet support the stated level of certainty.

major comments (4)

[Sec. 4.1] The 3D evaluation against the FDK reference is not yet convincing. The paper states that "the provided volumes are not entirely accurate" and then uses them as reference geometry; it also meshes the reference at attenuation threshold 0.025 while meshing all reconstructed volumes at 0.008. Since the iso-surface of a thresholded Gaussian attenuation field depends strongly on the chosen threshold, a 3.1x asymmetry can systematically favor methods whose reconstructed attenuation scale is lower than the reference. CD and HD may therefore be measuring attenuation calibration rather than geometric accuracy. I ask for a threshold-sweep analysis (e.g., varying both thresholds and reporting CD/HD curves), a calibration procedure for attenuation scales across methods, or validation against a trustworthy ground-truth geometry (e.g., a phantom or a high-quality 3D-DSA volume) before the 3D superiority claim can be accepted.
[Sec. 4.2, Table 2] The claim of "SOTA or comparable" performance in most scenarios is not statistically supported by the reported numbers. At 30 views the Chamfer distance is 1.72 +/- 0.29 for 4DRGS versus 1.79 +/- 0.51 for VPAL; at 50 views VPAL wins CD (1.58 +/- 0.19 versus 1.67 +/- 0.29); and most PSNR and HD differences are within one standard deviation over 15 cases. The paper should report paired significance tests (e.g., Wilcoxon signed-rank) and effect sizes, and should identify explicitly at which view settings the differences are statistically significant. Without this, the abstract's "SOTA" phrasing overstates what the data show.
[Sec. 3.1 and Sec. 3.2] The method depends on several manually set quantities, including the FDK initialization threshold delta = 0.016, the scale bounds smin = 0.1 and smax = 10 times voxel spacing, and the pruning threshold epsilon = 1e-6, yet no sensitivity analysis is provided. Since the central claim is that the method works robustly for sparse-view clinical data, the paper should show how CD, HD, PSNR, and SSIM vary with these parameters over reasonable ranges, or otherwise justify that the reported results are not a tuned operating point.
[Sec. 4.1, competing methods] The efficiency comparison would be more complete if the paper reported convergence criteria and loss curves for VPAL and for 4DRGS. The current table reports final iteration counts for 4DRGS (10k and 30k) but does not state whether VPAL was run to its own convergence or was stopped at a fixed schedule. If VPAL was stopped early or was not tuned, the "12x-32x speedup" could partly reflect implementation choices. Reporting training loss over time for all methods would make the efficiency claim more robust.

minor comments (6)

[Sec. 4.1, Table 1] The row labeled "Others" is ambiguous; please list the cases it covers or give per-case configuration details in supplementary material.
[Eq. (7)] The summation notation in Eq. (7) is typeset as "P iter" without a subscript; it should be a sum over iterations between neighboring pruning operations.
[Eq. (6)] Please clarify whether the temporal perturbation tau is sampled once per image or per pixel/ray, since this affects the interpretation of the loss and the temporal-consistency claim.
[Sec. 3.1] In Eq. (3), s_i denotes the activated scale vector while earlier s_i is used as a scale parameter; the notation should be made consistent, for example by writing s_i as a vector and sigma as elementwise sigmoid.
[Sec. 4.1, TOGS baseline] The TOGS volume baseline is reconstructed by rendering 720 views in a full circle and applying FDK; please justify the choice of a full circle rather than the original 198-degree arc, since this may affect the comparison.
[General] The paper does not state whether code or data will be made available; given the overlap of the authors with the VPAL and R2-Gaussian baselines, releasing source code or detailed baseline configurations would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: optimization is image-driven and evaluated on held-out views against an external (if imperfect) FDK reference; overlapping baselines are code-reproduced and not load-bearing.

full rationale

4DRGS's derivation is self-contained. Geometry and attenuation parameters are optimized exclusively against real DSA images via the L1 + D-SSIM loss in Eq. (6); 2D evaluation is performed on held-out frames not used in training, and the 3D volume is obtained by voxelizing the trained Gaussian kernels (Sec. 3.3) rather than by copying the FDK initialization or the Siemens reference. The CD/HD comparison uses the system FDK volumes as an external reference, and the paper explicitly discloses their imperfection ('the provided volumes are not entirely accurate'), which is a metric-validity limitation rather than a circular step. Self-citations to VPAL [15], R2-Gaussian [30], and TOGS [32] are used as baselines or as borrowed software modules; these are code-reproduced comparisons, not unverified premises that force the result. The meshing-threshold asymmetry (0.025 vs 0.008) and FDK-based initialization are potential experimental confounds, but no equation in the paper makes the reported prediction equal to an input by construction. Therefore no circular step is identified.

Assumptions & free parameters 6 free parameters · 5 assumptions · 3 invented entities

The method's central claim is empirical and rests on standard Beer-Lambert radiography, the static-vessel/dynamic-attenuation decomposition, a Gaussian kernel approximation, and the use of system FDK volumes as ground truth. The main hand-set parameters are scale bounds, pruning threshold, initialization threshold, and loss and hash hyperparameters; none of these are fitted constants in a physical derivation, but several directly affect the final vessel thickness and kernel count.

free parameters (6)

Scale bounds s_min, s_max = 0.1 x voxel size, 10 x voxel size
Chosen by hand to keep kernels small; bounding activation uses them (Eq. 3), and they directly control vessel thickness and needle artifacts.
FDK initialization threshold delta = 0.016
Selects M=30k non-empty voxels from the FDK volume to seed kernels; affects coverage and final geometry.
Accumulated attenuation pruning threshold epsilon = 1e-6
Hand-set criterion for deciding which kernels are background; changes the final kernel set.
Loss weight lambda_ssim = 0.2
Hand-set balance between L1 and D-SSIM in Eq. 6.
Hash encoding capacity = 2^19 entries, 2D features, 12 levels (3D), similar 4D configuration
Network architecture hyperparameters chosen by hand; determine expressiveness of the DNAF.
Number of kernels M = 30,000
Initial kernel count, hand-set; adaptive control changes it during training.

assumptions (5)

standard math X-ray attenuation follows the Beer-Lambert law, and DSA images are log-subtracted line integrals of attenuation
Invoked in Eq. 5 and in the DSA formation model in Sec. 2; underpins the whole rasterization and optimization.
domain assumption Vessels remain static during scanning while only attenuation changes over time
Sec. 3.1 key observation; the entire 4D kernel design assumes static geometry. The paper admits this fails under patient or cardiac motion in the Discussion.
domain assumption Contrast-agent attenuation can be approximated by a sum of Gaussian kernel responses
Eqs. 1-2 define the scene representation; this is a modeling choice, not derived from physics beyond Beer-Lambert.
domain assumption The FDK reconstructed volume from the system, though 'not entirely accurate', is a valid reference for ranking methods
Sec. 4.1 evaluation; used for mesh comparison via Chamfer and Hausdorff distances. If the reference is biased, the quantitative ranking may not reflect true vessel geometry.
ad hoc to paper The sparse-view FDK volume provides a good-enough initialization for kernel positions
Sec. 3.1 Model Initialization; this specific choice is not compared against random initialization, so the contribution of the prior is not isolated in ablations.

invented entities (3)

4D radiative Gaussian kernel independent evidence
purpose: Primary scene representation: static Gaussian geometry modulated by time-varying central attenuation to mimic contrast-agent flow
The kernel parameters are optimized to reproduce held-out DSA frames and voxelized volumes, so they are falsifiable through image synthesis, though they are not independently measured physical entities.
Dynamic neural attenuation field (DNAF) independent evidence
purpose: Compact MLP with 3D and 4D hash encodings that predicts kernel attenuation from position and time
Its outputs are directly constrained by real DSA images during training and by test-frame synthesis, giving an external handle.
Accumulated attenuation A_i
purpose: Pruning statistic averaging per-kernel attenuation over iterations to identify background kernels
Defined in Eq. 7 purely as an algorithmic criterion; no independent physical meaning or test outside the method's own pruning rule.

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Cite this review

Pith. "Pith review of 4DRGS: 4D Radiative Gaussian Splatting for Efficient 3D Vessel Reconstruction from Sparse-View Dynamic DSA Images." pith.science (2026). https://pith.science/paper/DAXAETCF

@misc{pith2026241212919,
  author       = {Pith},
  title        = {Pith review of: 4DRGS: 4D Radiative Gaussian Splatting for Efficient 3D Vessel Reconstruction from Sparse-View Dynamic DSA Images},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DAXAETCF}},
  note         = {Machine review of arXiv:2412.12919}
}

read the original abstract

Reconstructing 3D vessel structures from sparse-view dynamic digital subtraction angiography (DSA) images enables accurate medical assessment while reducing radiation exposure. Existing methods often produce suboptimal results or require excessive computation time. In this work, we propose 4D radiative Gaussian splatting (4DRGS) to achieve high-quality reconstruction efficiently. In detail, we represent the vessels with 4D radiative Gaussian kernels. Each kernel has time-invariant geometry parameters, including position, rotation, and scale, to model static vessel structures. The time-dependent central attenuation of each kernel is predicted from a compact neural network to capture the temporal varying response of contrast agent flow. We splat these Gaussian kernels to synthesize DSA images via X-ray rasterization and optimize the model with real captured ones. The final 3D vessel volume is voxelized from the well-trained kernels. Moreover, we introduce accumulated attenuation pruning and bounded scaling activation to improve reconstruction quality. Extensive experiments on real-world patient data demonstrate that 4DRGS achieves impressive results in 5 minutes training, which is 32x faster than the state-of-the-art method. This underscores the potential of 4DRGS for real-world clinics.

Figures

Figures reproduced from arXiv: 2412.12919 by the authors.

**Figure 1.** Overview of DSA imaging and vessel reconstruction. (a) DSA images are generated by subtracting fill-run X-ray images from their mask-run counterparts. (b) We model vessels as a set of 4D radiative Gaussians. (c) The final 3D vessel volume is reconstructed via attenuation voxelization. injection. Subtracting X-ray images in the fill run from those in the mask run yields 2D DSA images, which highlight blood flow marke… view at source ↗

**Figure 2.** The overall pipeline of 4DRGS. We model vessels as a set of 4D radiative Gaussian kernels (Sec. 3.1) and optimize them with image losses (Sec. 3.2). 3D vessel volume is reconstructed via attenuation voxelization (Sec. 3.3). Radiative Gaussian Splatting R2 -Gaussian [30] is the first work to leverage 3DGS for static CT reconstruction. It represents the scanned scene using 3D radiative Gaussian kernels, each defined b… view at source ↗

**Figure 3.** 3D vessel reconstruction of different methods with CD(mm)/HD(mm) values shown at the top right of each image [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: 2D DSA image synthesis of different methods at test frames. PSNR(dB)/SSIM values averaged over the test set are shown at the top right of each image [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: Qualitative results of ablation study. (a) 3D vessel reconstruction. Top row: 3D visualization with CD(mm)/HD(mm) values shown at the top right of each image. Bottom row: sagittal slice of reconstructed volume. (b) 2D DSA image synthesis at test frame. PSNR(dB)/SSIM va…

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