REVIEW 3 major objections 7 minor 1 cited by
RaySplats: Ray Tracing based Gaussian Splatting
T0 review · 3 major / 7 minor · reviewed 2026-08-09 · deepseek-v4-flash
Pith's one-line read RaySplats replaces rasterization in 3D Gaussian Splatting with ray tracing directly on Gaussian primitives, making shadows, transparency, mirrors, glass, and mesh integration part of the same differentiable pipeline.
desk verdict A real incremental step for ray-traced 3DGS, but Proposition 3.2's alpha proof is wrong for half-rays and the lighting claims lack quantitative evidence. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the Gaussian confidence ellipsoid, the set of points at Mahalanobis distance $Q$ from the Gaussian mean, where $Q$ is a configurable quantile of the chi-square distribution with three degrees of freedom. The first identity is the closed-form closest intersection of a ray with this ellipsoid (Proposition 3.1), obtained by whitening coordinates $o' = S^{-1}R^T(o-\mu)$ and $d' = S^{-1}R^T d$ so that the ellipsoid becomes a sphere and the intersection reduces to solving a quadratic with a numerically stable root. The second identity is the per-Gaussian $\alpha$ rule (Proposition 3.2): $\alpha_i = \hat{\alpha}_i \exp\left(-\tfrac{1}{2}\left\| o' - \frac{d'}{\|d'\|}\left\langle \frac{d'}{\|d'\|}, o' \right\rangle \right\|^2\right)$, which is the peak of the Gaussian density along the ray rather than an integral over the ray segment. A supporting mechanism is the two-phase traversal with ray-termination thresholds, plus an index buffer that records all hit Gaussians, allowing the backward pass to reuse forward traversal data and to compute the gradient of the last meaningful Gaussian.
What would settle it
Render a single strongly elongated Gaussian viewed edge-on, first with RaySplats' closed-form alpha rule and again by numerically integrating the same Gaussian density along the ray in the volumetric formula of Eq. (4); if the two pixel values diverge substantially as the confidence parameter $Q$ changes, the peak-density approximation is not capturing the primitive's contribution.
Extended reading notes
Core claim
On the paper's own terms, the discovery is that the central operation of 3D Gaussian Splatting—projecting each Gaussian to the screen—is not what makes the representation work; the same primitive can be evaluated along true camera rays. RaySplats represents each Gaussian by its confidence ellipsoid $E_{\mu,\Sigma,Q}$ defined by a Mahalanobis distance equal to a quantile of the chi-square distribution with three degrees of freedom, and assigns to a ray the first intersection point given by Proposition 3.1. Each Gaussian's $\alpha$ contribution is then the learned opacity times the maximum of the Gaussian's normalized density along the ray (Proposition 3.2), and colors are combined by ordinary $\alpha$ blending. Because the ray–ellipsoid intersection is analytic and the $\alpha$ rule is closed form, both forward and backward passes are differentiable, and an index buffer stores intersected Gaussians so gradients can be computed without re-traversing rays. The authors report quantitative results in the same range as rasterized 3DGS and 3DGRT on standard scene-collection tests, and qualitative results with glass, shadows, mirror reflections, and Gaussian splats placed inside mesh scenes.
Load-bearing premise
The model assumes that how much a Gaussian contributes to a pixel depends only on how close the ray passes to its center and on a fixed cut-off for including it, not on how long the ray spends inside the Gaussian or how the Gaussian's fuzziness is spread along the ray.
Editorial extensions
If this is right
- A scene represented as Gaussians can be rendered either by rasterization or by ray tracing, so splats can be composited directly into path-traced mesh scenes without converting them to triangles.
- Shadows, transparency, mirror reflections, and glass-like refraction become trainable features of the same optimization rather than post-processing effects.
- Storing intersected Gaussians in an index buffer during the forward pass lets the backward pass reuse the same ray intersections, roughly halving the number of ray–Gaussian intersection computations.
- The switch from spherical harmonics to plain RGB colors is reported to be sufficient in the ray-tracing setting, simplifying the per-Gaussian parameters.
- On the tested datasets, adopting ray tracing does not appear to cost fidelity relative to rasterized baselines, making the richer rendering model usable where 3DGS already works.
Reading between the lines
- Extension: because the alpha rule uses the density peak rather than an integral over the ray segment, physically based volumetric effects such as absorption, scattering, or participating media would likely need a segment-length correction or per-sample integration to remain accurate for elongated or overlapping Gaussians.
- Extension: the same closed-form ellipsoid intersection can be reused for shadow rays and light rays, not only camera rays, which suggests a direct path to soft shadows and one-bounce global illumination that the paper's examples only begin to demonstrate.
- Extension: the confidence quantile $Q$ is a smooth quality-versus-speed dial; one could schedule it during training, starting broad to catch sparse coverage and tightening it later, instead of fixing it per dataset.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes RaySplats, a differentiable ray-tracing renderer for 3D Gaussian Splatting that replaces the standard splatting projection with explicit ray-Gaussian intersections computed on confidence ellipsoids. The color of each pixel is obtained by front-to-back alpha blending, where the alpha of a Gaussian is the product of a learned opacity and the maximum of its normalized Gaussian density along the ray. The method is implemented in C/C++ with OptiX and includes hand-derived gradient formulas for all trainable parameters. The experimental section reports novel-view synthesis results on Mip-NeRF360, Tanks and Temples, and Deep Blending, together with qualitative demonstrations of shadows, reflections, and transparency, and an ablation study of three hyperparameters.
Significance. If the proposed rendering procedure is correct, it would provide a useful alternative to polytope-based 3DGRT and enable secondary-ray effects such as reflections and shadows within a Gaussian Splatting framework. The paper includes detailed analytic gradient derivations in the appendices and a full from-scratch CUDA implementation, which is a substantial engineering effort. However, the central alpha computation in Proposition 3.2 contains a genuine mathematical error for rays whose perpendicular foot lies behind the ray origin, and the claimed lighting capabilities are not evaluated quantitatively. These issues currently prevent the paper from being a reliable foundation for the stated claims.
major comments (3)
- [Appendix A.2, Eq. (11)] The closed form for alpha_i in Proposition 3.2 is derived by replacing the constrained maximum over t>=0 with the unconstrained distance from the point o' to the full line {td' : t in R}. This replacement is valid only when the orthogonal projection parameter t* = -<o',d'>/<d',d'> is nonnegative. When <o',d'> > 0, the constrained maximum over t>=0 occurs at t=0, giving alpha_i = sigmoid(alpha_hat_i) * exp(-1/2 ||o'||^2), whereas Eq. (11) reports exp(-1/2(||o'||^2 - <o',d'>^2/||d'||^2)), which is larger by the factor exp(+1/2 <o',d'>^2/||d'||^2). The proof's step 'min_{t>=0}||td'+o'|| = min_{t>=0}||td'-o'||' is false because the ray is a half-line, not a full line; only the full line is symmetric about the origin. Since this alpha value is used both in training and inference, and since secondary rays for reflections, transparency, and shadows may start on surfaces or inside ellipsoids, this error is load-bearing and must be corrected by clamping t* at zero and re-deriving the gradient formulas accordingly.
- [Section 3, Proposition 3.1 and ray-ellipsoid intersection rule] The ray-Gaussian intersection procedure discards a Gaussian whenever the smaller root of the quadratic is negative, even if the larger root is positive. This is inconsistent with the definition of the intersection set {t>=0 : ||o'+td'||^2 <= Q} and causes rays whose origin lies inside a confidence ellipsoid (for example, secondary rays originating at a mesh surface or inside a Gaussian) to be incorrectly classified as having no intersection. The paper's own description in Section 3 states that a ray is treated as missing if the closest intersection point 'is negative and does not belong to the ray,' which is exactly the situation in which the ray starts inside the ellipsoid and exits through the positive root. Given that the central claim includes mesh integration and secondary-ray effects, the intersection rule must accept the positive root when it exists, and the implementation in OptiX should be checked against this case.
- [Section 4, Table 1] The experimental section validates RaySplats only on standard novel-view synthesis metrics. The central claim of the paper—that ray tracing enables the incorporation of meshes, lights, shadows, and transparency—is supported only by qualitative figures (Figs. 3-6), with no quantitative evaluation of relighting, shadow, or reflection accuracy. Moreover, Table 1 shows that on Tanks and Temples RaySplats achieves PSNR 22.20 dB, which is 1.00 dB below 3DGRT (23.20 dB) and 0.94 dB below 3DGS-30K (23.14 dB); the statement that RaySplats attains 'outcomes that are analogous' to classical 3DGS is therefore not supported by the reported numbers. The authors should add a dedicated lighting-effects benchmark and compare with IRGS and EnvGS, which are discussed in the related work but not evaluated.
minor comments (7)
- [Section 4, first paragraph] The phrase 'ourRaySplats' is missing a space and should read 'our RaySplats'.
- [Section 3, Eq. (11)] The variables o' and d' are used in Eq. (11) before they are defined in Appendix A.1; define them in the main text for readability.
- [Section 3, paragraph 'Color Aggregation'] The term '2.5D approach' is introduced without explanation; please define it or replace it with a more standard description.
- [Section 4, Figure 7] The ablation study is presented as a small plot without exact numeric values; replace it with a table reporting the mean and standard deviation of PSNR for each hyperparameter setting.
- [Section 4, Implementation Details] The paper does not report training time or rendering frames-per-second, despite the introduction claiming efficiency advantages; such numbers are needed for comparison with 3DGRT.
- [Section 3, Eq. (1) and Eq. (3)] The symbol N is used both for the normal distribution N(m, Sigma) and for the number of Gaussians; this notation clash should be resolved.
- [Appendix A.1, line after Eq. (7)] The derivation of the discriminant contains a typesetting artifact with repeated 'A4' fragments; please clean up the appendix display math.
Circularity Check
No significant circularity: the ray-Gaussian intersection and alpha formulas are externally cited or explicitly defined, and the empirical evaluation is benchmark-based.
full rationale
The derivation chain in RaySplats is not circular. The ray-Gaussian intersection (Proposition 3.1) is credited to Hearn et al., and the alpha aggregation formula (Proposition 3.2) is explicitly attributed to 3DGRT; neither is a self-citation, and neither is used to "predict" a fitted quantity. The model's alpha is defined by Eq. 10 and then computed via Eq. 11; this is a rendering definition rather than a prediction from fitted parameters. The only self-citations (Kasymov et al. 2024; Waczyńska et al. 2024) appear in related-work remarks and are not load-bearing. Hyperparameters Q, epsilon1, epsilon2, and the maximum number of Gaussians are configurable thresholds, not fitted constants relabeled as predictions. The skeptic's observation that Eq. 11 may overestimate Eq. 10 when the perpendicular foot lies behind the ray origin is a mathematical correctness concern about the cited formula; it is not a case where the output is equivalent to the input by construction. The paper is evaluated against external benchmarks (Mip-NeRF360, Tanks and Temples, Deep Blending), so its central comparisons are independent.
Assumptions & free parameters
free parameters (5)
- Q (chi-squared quantile) =
set individually per dataset (not given numerically)
- epsilon1 (first transmittance threshold) =
set individually per dataset
- epsilon2 (second transmittance threshold) =
not specified
- max Gaussians per ray =
set individually per dataset
- lambda (SSIM weight) =
not specified
assumptions (4)
- domain assumption A 3D scene can be represented by a set of 3D Gaussian primitives with means, covariances, opacities, and colors.
- ad hoc to paper The color of a pixel is computed by front-to-back alpha blending with the alpha of each Gaussian being the product of learned opacity and the peak of its probability density along the ray.
- ad hoc to paper Gaussians whose confidence ellipsoid does not intersect the ray contribute zero color, so the ray-Gaussian intersection can be safely computed using the ellipsoid defined by quantile Q.
- domain assumption OptiX-provided ray traversal correctly handles the ray-ellipsoid intersections and mesh intersections used in training and inference.
Cite this review
Pith. "Pith review of RaySplats: Ray Tracing based Gaussian Splatting." pith.science (2026). https://pith.science/paper/QVQZAUFZ
@misc{pith2026250119196,
author = {Pith},
title = {Pith review of: RaySplats: Ray Tracing based Gaussian Splatting},
year = {2026},
howpublished = {\url{https://pith.science/paper/QVQZAUFZ}},
note = {Machine review of arXiv:2501.19196}
}
read the original abstract
3D Gaussian Splatting (3DGS) is a process that enables the direct creation of 3D objects from 2D images. This representation offers numerous advantages, including rapid training and rendering. However, a significant limitation of 3DGS is the challenge of incorporating light and shadow reflections, primarily due to the utilization of rasterization rather than ray tracing for rendering. This paper introduces RaySplats, a model that employs ray-tracing based Gaussian Splatting. Rather than utilizing the projection of Gaussians, our method employs a ray-tracing mechanism, operating directly on Gaussian primitives represented by confidence ellipses with RGB colors. In practice, we compute the intersection between ellipses and rays to construct ray-tracing algorithms, facilitating the incorporation of meshes with Gaussian Splatting models and the addition of lights, shadows, and other related effects.
Figures
Figures from the paper (5 more)
Forward citations
Cited by 1 Pith paper
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Floating Radiance Networks
FlaRe combines per-primitive latent radiance descriptors on planar Gaussians with a shared decoder and hardware ray tracing, making rendering, secondary rays, editing, and mesh extraction work in one scene model.
Reference graph
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" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...
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Reviewed August 9, 2026 · model on record in the stance chip above.
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