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Differentiable Voxel-based X-ray Rendering Improves Sparse-View 3D CBCT Reconstruction

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read DiffVox claims that directly optimizing a regularized voxel grid with an exact differentiable Beer-Lambert X-ray renderer reconstructs higher-fidelity cone-beam CT volumes from fewer views than iterative algorithms and neural fields…

desk verdict A clean within-framework comparison of Siddon vs trilinear rendering on real CBCT data, but the headline advantage over classical algorithms is mostly TV regularization, not the renderer. read the letter →

arxiv 2411.19224 v2 pith:UAU5QEHU submitted 2024-11-28 eess.IV cs.CVphysics.med-ph

Mohammadhossein Momeni , Vivek Gopalakrishnan , Neel Dey , Polina Golland , Sarah Frisken This is my paper · ORCID
classification eess.IVcs.CVphysics.med-ph
keywords cone-beamCTsparse-viewreconstructiondifferentiableX-rayrenderingvoxelgridoptimizationBeer-LambertlawSiddon'smethodtotalvariationregularizationrealdataset
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

DiffVox is a self-supervised framework that reconstructs cone-beam CT (CBCT) volumes by directly optimizing a voxel grid of linear attenuation coefficients, using a differentiable X-ray renderer as the forward model. The central claim is that using an exact implementation of the discrete Beer-Lambert law (Siddon's method) in the renderer produces higher-fidelity 3D reconstructions and novel 2D views than widely used iterative algorithms such as SIRT and Nesterov, and than modern neural-field approaches, in the sparse-view regime of 5 to 60 input X-rays. The appeal is practical: if true, the same diagnostic quality can be obtained from fewer X-rays, reducing radiation exposure, and the voxel representation is fast enough (tens of minutes) to be used on real clinical-resolution data, unlike neural fields that take hours to days. The paper evaluates on a dataset of 42 walnuts with 3,600 real X-ray images per walnut, reconstructing from sparse subsets and comparing against several classical and neural baselines.

What carries the argument

The central object is the differentiable X-ray renderer implementing Siddon's method: an exact discretization of the Beer-Lambert law in which each detector pixel's negative log intensity equals the sum, over all ray-voxel intersections, of the linear attenuation coefficient (LAC) times the intersection segment length. The renderer is contrasted with a faster approximation that samples evenly spaced points along the ray and uses trilinear interpolation of the LAC volume. Both renderers are embedded in a photometric L1 loss plus total-variation regularization, optimized with Adam directly on a zero-initialized voxel grid whose values are passed through a softplus activation to enforce nonnegativity. Siddon's exact line integrals carry the argument by giving the optimizer physically accurate gradients from sparse X-ray measurements.

What would settle it

Take a phantom with a known ground-truth attenuation volume, render sparse X-ray views with the same acquisition geometry used for the walnuts, and reconstruct with DiffVox and the baselines; if DiffVox's advantage over SIRT and Nesterov shrinks or disappears on this exact ground truth, the real-data result depends on the undisclosed reference reconstruction rather than on the forward model.

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Extended reading notes

Core claim

The paper's discovery is that the numerical integration scheme inside the differentiable renderer is the decisive factor for sparse-view CBCT reconstruction quality. Siddon's method, which exactly integrates the Beer-Lambert attenuation along each ray by weighting each intersected voxel's attenuation coefficient by the geometric intersection length, consistently produces sharper reconstructions and more accurate novel views than trilinear-interpolation quadrature, with the largest gains in the 5–20 view regime. On 15-view reconstructions of held-out walnuts, DiffVox with Siddon's method reaches SSIM 0.923 and PSNR 37.69, outperforming the best neural-field baseline (SSIM 0.835, PSNR 33.43) and all classical algorithms. The paper further shows that total-variation regularization is essential to both renderers, and that removing it degrades Siddon's method more than trilinear interpolation because the exact line integral confines each pixel's gradient to voxels on the ray, while trilinear interpolation lets supervision leak to neighboring voxels, acting as a crude scattering approximation.

Load-bearing premise

The paper's quality metrics are computed against high-resolution reference volumes reconstructed from all 3,600 X-ray images per walnut, but the paper does not state which algorithm produced those references; if those references contain artifacts or forward-model bias, the measured advantage of DiffVox could be inflated.

Editorial extensions

If this is right

  • At 15 input views, DiffVox with Siddon's method achieves SSIM 0.923 and PSNR 37.69 on real clinical-resolution walnut data, above all classical and neural baselines tested.
  • Reconstruction with Siddon's method takes roughly 11 minutes at 15 views and 45 minutes at 60 views, an order of magnitude faster than neural-field baselines that require hours to days.
  • Siddon's method yields the most accurate novel 2D X-ray views in the 5–20 view regime, which is the range most relevant for reducing patient radiation dose.
  • Total-variation regularization is necessary for both renderers, and its removal hurts the exact Siddon renderer more than the trilinear approximation.
  • The only regime where a baseline (SAX-NeRF) beats DiffVox is PSNR at 30 and 60 views for 3D reconstruction; DiffVox wins all other view counts and metrics.

Reading between the lines

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

  • It is a plausible but untested extension that the same exact Beer-Lambert renderer could improve neural-field reconstructions, since the paper's ablation isolates the forward model as the main driver rather than the voxel representation itself.
  • Because the renderer is differentiable with respect to geometry as well as the volume, the framework could jointly refine unknown X-ray source poses during reconstruction; the authors mention this as future work but do not demonstrate it.
  • The observation that trilinear interpolation behaves as a mild scatter-like regularizer suggests a tunable hybrid: weighting the exact Siddon gradient and the interpolated gradient could trade off sharpness and robustness in ultra-sparse settings.
  • The reported runtimes assume a large-batch GPU setting (up to 1.8 million rays per batch for trilinear); clinical adoption at higher resolution may require gradient checkpointing or streamed optimization.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes DiffVox, a self-supervised CBCT reconstruction method that directly optimizes a voxelgrid using a differentiable X-ray renderer. It compares two forward models: Siddon's exact ray-voxel intersection method and trilinear-interpolation quadrature, trained with an L1 photometric loss plus total-variation regularization (Eq. 4). Experiments on the open walnut dataset use 40 held-out subjects, with Table 1 reporting 15-view results and Figure 3 showing 5-60 views, against classical ASTRA solvers (FDK, CGLS, SIRT, Nesterov) and two neural field baselines (NAF, SAX-NeRF). The paper reports that DiffVox, especially with Siddon's method, achieves the best 3D reconstruction and novel-view metrics in the sparse-view regime while being an order of magnitude faster than neural field approaches.

Significance. If confirmed, the central claim would be valuable: a simple differentiable voxelgrid with an exact ray-tracing forward model could outperform both classical iterative solvers and modern neural fields on real clinical-resolution CBCT data, with large speedups over neural fields. The paper has genuine strengths: it evaluates on real X-ray images rather than synthetic renderings, uses 40 held-out scans, reports standard errors across multiple metrics, includes an ablation, and releases code. However, the headline attribution of the gains to the exact Beer-Lambert renderer is not currently supported by the experimental design. The reported margin over classical baselines is dominated by the TV regularizer, and the ground-truth reconstruction protocol is unspecified; both issues are load-bearing for the paper's main empirical claim.

major comments (3)
  1. [Section 3 (Dataset)] The manuscript states that 'Ground truth CBCT volumes were reconstructed using all images to produce high-resolution 501 x 501 x 501 volumes' but does not specify which algorithm, regularizer, or software produced these reference volumes. Since every SSIM, PSNR, MSE, and PCC value in the paper is computed against these volumes, unknown artifacts or forward-model bias in the reference reconstruction could systematically favor or penalize particular methods. The authors should report the reconstruction algorithm and its settings, and ideally evaluate sensitivity of the main comparisons to an alternative reference reconstruction.
  2. [Table 1 and Eq. (4)] The ablation rows in Table 1 show that removing the TV regularizer from DiffVox lowers PSNR from 37.23/37.69 to 29.25/27.41 and SSIM from 0.912/0.923 to 0.827/0.812, putting both variants below the unregularized classical baselines SIRT (PSNR 33.0, SSIM 0.809) and Nesterov (PSNR 34.4, SSIM 0.834). This indicates that the large advantage over classical baselines in Table 1 is carried primarily by the TV term in Eq. (4), not by the differentiable renderer or the voxel-based learning framework. Because the classical baselines are run without TV, the comparison conflates regularization with renderer/framework choice. I request TV-regularized versions of SIRT, CGLS, and Nesterov, with matched or tuned regularization strength and comparable iteration budgets, before the abstract's claim can be accepted.
  3. [Table 1 and Fig. 3A] The renderer-specific comparison, which is the cleanest test of the paper's secondary claim, shows only a modest difference between DiffVox-Siddon and DiffVox-Trilinear at 15 views (PSNR 37.69 vs 37.23; SSIM 0.923 vs 0.912), and Figure 3A shows that SAX-NeRF achieves higher PSNR at 30 and 60 views. The paper's claim that the exact Beer-Lambert implementation 'outperforms' other methods should therefore be scoped to the sparse-view regime and to the specific metrics. In addition, paired significance tests or confidence intervals for the Siddon-versus-trilinear difference would strengthen the claim, since the reported standard errors are non-negligible relative to the observed gap.
minor comments (5)
  1. [Figure 2 caption] The caption states that 'Novel views were rendered using the forward model implemented in each method'; this means the novel-view comparison partly reflects forward-model differences rather than purely reconstruction quality. Please clarify whether a common forward model was used for any of the comparisons, and discuss how this choice affects the ranking.
  2. [Section 3 (Dataset)] Please clarify the number of X-ray images per orbit: the text says 3,600 images were acquired 'across three circular orbits,' and sparse subsets are taken 'from only the middle orbit,' but the per-orbit count is not stated explicitly.
  3. [Section 2 (Methods)] The sentence describing trilinear interpolation as 'an approximation of second-order effects such as X-ray scatter' is speculative; the manuscript should label this as a hypothesis rather than a demonstrated property of the model.
  4. [Table 1] The 'DiffVox – Trilinear w/o TV' and 'DiffVox – Siddon's w/o TV' rows are reported only at 15 views; reporting the same ablation across the full view range would clarify whether the regularizer's contribution persists in less sparse settings.
  5. [Throughout] There are minor typographical issues, such as 'returns of the LAC' in the description of Eq. (2), and the inconsistent use of 'DiffV ox' with a space in the compiled text; these should be corrected in a revision.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: DiffVox's central claims rest on external benchmarks and held-out evaluation, not on self-referential definitions.

full rationale

The paper's central claim is an empirical comparison. DiffVox optimizes a voxelgrid against measured projection intensities using the photometric loss in Eq. (4), and quality is evaluated against held-out 3D reference volumes and unseen real X-ray views from 40 test walnuts. Hyperparameters were tuned on two subjects and applied to the remaining 40, so no reported metric is defined in terms of a fitted parameter on the test set. The differentiable Siddon renderer is imported from the authors' prior work [10], but that is a tooling citation: the underlying Siddon path model is externally due to Siddon [13], and the comparison between Siddon's method and trilinear interpolation is performed within the same DiffVox framework, so the renderer comparison is not forced by construction. The unspecified algorithm used to create the reference volumes and the fact that classical baselines are not TV-regularized are evaluation-validity concerns, not circularity: they do not make any predicted quantity equivalent to its input by definition. The Table 1 ablation shows that TV regularization carries much of the headline gain, but that is a baseline-fairness confound rather than a circular derivation. No circular step can be exhibited from the paper's own equations or citations.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central empirical claim rests on a physics-based forward model, known acquisition geometry, a reference reconstruction treated as ground truth, a TV prior, and fair baseline tuning. The most fragile items are the unspecified ground-truth reconstruction algorithm, the absence of a TV-regularized classical baseline, and the unstated training details for neural-field baselines. No new physical entities are introduced.

free parameters (5)
  • Total variation weight lambda_TV for Siddon's method = 25
    Tuned via grid search over two subjects; controls the strength of the piecewise-constant prior and is central to reported performance.
  • Total variation weight lambda_TV for trilinear interpolation = 15
    Tuned separately from Siddon's method; the different value complicates a clean comparison of forward models.
  • Trilinear quadrature sample count M = 500 points per ray
    Chosen as a trade-off between quadrature accuracy and speed; affects the trilinear renderer's approximation quality.
  • Softplus slope beta = 20
    Chosen for the nonnegativity mapping of the voxel grid; shapes gradient magnitudes and optimization behavior.
  • Learning rate schedule = initial lr 1, linear decay to 0 over 50 iterations
    Chosen via hyperparameter tuning; an aggressive schedule that is important for the reported convergence in 50 iterations.
assumptions (7)
  • domain assumption The Beer-Lambert law with line integrals of linear attenuation coefficients is the correct model for the projection images.
    Eq. (1) in Section 2; ignores scatter, beam hardening, detector noise, and polychromatic effects, though the paper notes trilinear interpolation approximates second-order scatter effects.
  • domain assumption The unknown volume is exactly representable on a finite-resolution voxelgrid with piecewise-constant LACs.
    Section 2 discretizes mu onto a voxelgrid; the reconstruction resolution is 501^3, so discretization error is assumed acceptable.
  • domain assumption The acquisition geometry is known exactly for all X-ray images.
    Rays r(alpha) in Section 2 are defined from known source and pixel positions; no pose optimization is performed.
  • domain assumption The 501^3 volumes reconstructed from all 3,600 images are valid ground truth for evaluating sparse-view reconstructions.
    Section 3 Dataset; the reconstruction algorithm used to produce these references is not specified, so the reference quality is taken on faith.
  • domain assumption Total variation regularization is an appropriate prior for CBCT volumes.
    Loss in Eq. (4) adds lambda_TV TV(mu_hat); this modeling choice assumes piecewise-constant structure and can suppress texture.
  • standard math Automatic differentiation through Siddon's ray-voxel intersection sum yields usable gradients.
    The paper cites [10] for a fully differentiable implementation of Eq. (2); this is not re-derived or formally verified in the preprint.
  • domain assumption The neural-field baselines were trained and tuned fairly on the same real walnut data.
    Section 3 Baselines lists NAF and SAX-NeRF without training or validation details, so the comparison assumes representative hyperparameters and fair evaluation.

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Cite this review

Pith. "Pith review of Differentiable Voxel-based X-ray Rendering Improves Sparse-View 3D CBCT Reconstruction." pith.science (2026). https://pith.science/paper/UAU5QEHU

@misc{pith2026241119224,
  author       = {Pith},
  title        = {Pith review of: Differentiable Voxel-based X-ray Rendering Improves Sparse-View 3D CBCT Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UAU5QEHU}},
  note         = {Machine review of arXiv:2411.19224}
}
read the original abstract

We present DiffVox, a self-supervised framework for Cone-Beam Computed Tomography (CBCT) reconstruction by directly optimizing a voxelgrid representation using physics-based differentiable X-ray rendering. Further, we investigate how the different implementations of the X-ray image formation model in the renderer affect the quality of 3D reconstruction and novel view synthesis. When combined with our regularized voxel-based learning framework, we find that using an exact implementation of the discrete Beer-Lambert law for X-ray attenuation in the renderer outperforms both widely used iterative CBCT reconstruction algorithms and modern neural field approaches, particularly when given only a few input views. As a result, we reconstruct high-fidelity 3D CBCT volumes from fewer X-rays, potentially reducing ionizing radiation exposure and improving diagnostic utility. Our implementation is available at https://github.com/hossein-momeni/DiffVox.

Figures

Figures reproduced from arXiv: 2411.19224 by the authors.

Figure 1
Figure 1. (A) In sparse-view CBCT reconstruction, a small number of X-ray images are acquired in a circular orbit about a subject. We compare two implementations of the X-ray image formation model for reconstruction via differentiable rendering: (B) Siddon’s method and (C) trilinear interpolation. 2 Methods Image Formation Model ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (A) CBCT reconstructions of an exemplar walnut from the test set using 15 input views. The Structural Similarity Index Measure (SSIM) for each 3D reconstruction is annotated. Blue insets highlight where our methods outperform the baselines, with sharper boundaries and fewer artifacts. Red insets indicate areas where all methods struggle, particularly in reconstructing thin structures. (B) Novel views rendered from t… view at source ↗
Figure 3
Figure 3. Quality of (A) reconstructed 3D volumes and (B) novel 2D views rendered from these volumes, and (C) reconstruction runtimes over a range of input views. DiffVox, using either Siddon’s method or trilinear interpolation as the forward model, achieves the highest quality reconstructions and renderings, with particularly appreciable gains in the sparsest-view settings. Error bars are plotted using the standard error (se… view at source ↗

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

17 extracted references · 15 canonical work pages · cited by 1 Pith paper

  1. [1]

    Practical cone-beam algorithm

    Lee A Feldkamp, Lloyd C Davis, and James W Kress. Practical cone-beam algorithm. Journal of the Optical Society of America A, 1(6):612–619, 1984

    work page 1984

  2. [2]

    On Krylov methods for large-scale CBCT reconstruction

    Malena Sabaté Landman, Ander Biguri, Sepideh Hatamikia, Richard Boardman, John Aston, and Carola-Bibiane Schönlieb. On Krylov methods for large-scale CBCT reconstruction. Physics in Medicine & Biology, 68(15):155008, 2023

    work page 2023

  3. [3]

    Computational analysis and improvement of SIRT

    Jens Gregor and Thomas Benson. Computational analysis and improvement of SIRT. IEEE Transactions on Medical Imaging, 27(7):918–924, 2008

    work page 2008

  4. [4]

    NAF: neural attenuation fields for sparse-view CBCT reconstruction

    Ruyi Zha, Yanhao Zhang, and Hongdong Li. NAF: neural attenuation fields for sparse-view CBCT reconstruction. In International Conference on Medical Image Computing and Computer- Assisted Intervention, pages 442–452. Springer, 2022

    work page 2022

  5. [5]

    NeAT: Neural adaptive tomography

    Darius Rückert, Yuanhao Wang, Rui Li, Ramzi Idoughi, and Wolfgang Heidrich. NeAT: Neural adaptive tomography. ACM Transactions on Graphics (TOG), 41(4):1–13, 2022

    work page 2022

  6. [6]

    Learning deep intensity field for extremely sparse-view CBCT reconstruction

    Yiqun Lin, Zhongjin Luo, Wei Zhao, and Xiaomeng Li. Learning deep intensity field for extremely sparse-view CBCT reconstruction. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 13–23. Springer, 2023

    work page 2023

  7. [7]

    Instant neural graphics primitives with a multiresolution hash encoding

    Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with a multiresolution hash encoding. ACM Transactions on Graphics (TOG), 41(4): 1–15, 2022

    work page 2022

  8. [8]

    Structure-aware sparse-view X-ray 3D reconstruction

    Yuanhao Cai, Jiahao Wang, Alan Yuille, Zongwei Zhou, and Angtian Wang. Structure-aware sparse-view X-ray 3D reconstruction. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11174–11183, 2024

    work page 2024

Show all 17 references
  1. [9]

    Direct voxel grid optimization: Super-fast convergence for radiance fields reconstruction

    Cheng Sun, Min Sun, and Hwann-Tzong Chen. Direct voxel grid optimization: Super-fast convergence for radiance fields reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5459–5469, 2022

    2022

  2. [10]

    Fast auto-differentiable digitally reconstructed radiographs for solving inverse problems in intraoperative imaging

    Vivek Gopalakrishnan and Polina Golland. Fast auto-differentiable digitally reconstructed radiographs for solving inverse problems in intraoperative imaging. In Workshop on Clinical Image-Based Procedures, pages 1–11. Springer, 2022

    2022

  3. [11]

    Nonlinear total variation based noise removal algorithms

    Leonid I Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 60(1-4):259–268, 1992

    1992

  4. [12]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015

    2015

  5. [13]

    Fast calculation of the exact radiological path for a three-dimensional CT array

    Robert L Siddon. Fast calculation of the exact radiological path for a three-dimensional CT array. Medical Physics, 12(2):252–255, 1985

    1985

  6. [14]

    A cone-beam X-ray computed tomography data collection designed for machine learning

    Henri Der Sarkissian, Felix Lucka, Maureen van Eijnatten, Giulia Colacicco, Sophia Bethany Coban, and Kees Joost Batenburg. A cone-beam X-ray computed tomography data collection designed for machine learning. Scientific Data, 6(1):215, 2019

    2019

  7. [15]

    Fast and flexible X-ray tomography using the ASTRA toolbox

    Wim Van Aarle, Willem Jan Palenstijn, Jeroen Cant, Eline Janssens, Folkert Bleichrodt, Andrei Dabravolski, Jan De Beenhouwer, K Joost Batenburg, and Jan Sijbers. Fast and flexible X-ray tomography using the ASTRA toolbox. Optics Express, 24(22):25129–25147, 2016

    2016

  8. [16]

    Multiscale vessel enhancement filtering

    Alejandro F Frangi, Wiro J Niessen, Koen L Vincken, and Max A Viergever. Multiscale vessel enhancement filtering. In Medical Image Computing and Computer-Assisted Interven- tion—MICCAI’98: First International Conference Cambridge, MA, USA, October 11–13, 1998 Proceedings 1, pa...

    1998

  9. [17]

    Intraoperative 2D/3D image registration via differentiable X-ray rendering

    Vivek Gopalakrishnan, Neel Dey, and Polina Golland. Intraoperative 2D/3D image registration via differentiable X-ray rendering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11662–11672, 2024. 6

    2024

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