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REVIEW 4 major objections 4 minor 5 cited by

3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Smooth convexes replace Gaussian blobs for sharper 3D views

desk verdict New primitive for splatting that works well empirically, but the '3D' in the title is doing more work than the math supports. read the letter →

arxiv 2411.14974 v3 pith:33RZUOQP submitted 2024-11-22 cs.CV

Jan Held , Renaud Vandeghen , Abdullah Hamdi , Adrien Deliege , Anthony Cioppa , Silvio Giancola , Andrea Vedaldi , Bernard Ghanem
show 1 more author
Marc Van Droogenbroeck
This is my paper · ORCID
classification cs.CV
keywords novelviewsynthesis3DGaussianSplattingsmoothconvexesdifferentiablerenderingradiancefieldsconvexhullrasterizationreal-timescenereconstruction
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 argues that the standard primitive of real-time radiance field rendering, the 3D Gaussian, is the wrong shape for many scenes, and replaces it with a 3D smooth convex, a point-set convex hull with soft edges. The authors claim that smooth convexes capture hard edges, flat surfaces, and dense volumes more faithfully than Gaussians, so a scene needs fewer primitives and less memory for the same or better image quality. On the Mip-NeRF360, Tanks and Temples, and Deep Blending benchmarks, the method reports gains over 3D Gaussian Splatting of up to 0.81 dB PSNR and 0.026 LPIPS, while rendering in real time. The practical stake is that a primitive with an explicit geometric boundary could give sharp, editable, compact 3D reconstructions instead of a cloud of soft blobs.

What carries the argument

The load-bearing object is the 3D smooth convex primitive: a convex hull of $K$ 3D points whose boundary is softened by a log-sum-exp signed-distance function with smoothness $\delta$ and sharpness $\sigma$. The rendering machinery skips an explicit 3D hull: it projects the $K$ points to 2D, builds the 2D convex hull with a standard planar hull algorithm, evaluates the same smooth indicator per pixel on the hull's delimiting lines, scales $\delta$ and $\sigma$ by the depth $d$, and composites the resulting opacities by depth-ordered $\alpha$-blending. All steps, including point projection, hull construction, line-distance evaluation, and backpropagation, run in custom GPU kernels, which is what keeps rendering real-time.

What would settle it

Render a synthetic scene of a single tilted rectangular slab both with 3DCS and with a ray-marched ground truth of the same 3D smooth convex; if the predicted images diverge substantially at grazing camera angles, or if pulling the projected points nearly collinear changes the image far more than the true 3D shape would, the 2D proxy is falsified.

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Extended reading notes

Core claim

3D Convex Splatting (3DCS) treats a scene as a collection of 3D smooth convexes, each defined by a set of $K$ freely moving 3D points. To render one convex, the points are projected onto the camera plane, their 2D convex hull is computed, and the per-pixel opacity is set by a smooth indicator function $I(q)=\mathrm{Sigmoid}(-d\,\sigma\,\phi(q))$, where $\phi(q)=\log\sum_t \exp(d\,\delta\, L_t(q))$ accumulates signed distances $L_t(q)$ to the hull's delimiting lines, with smoothness $\delta$, sharpness $\sigma$, and depth scale $d$ inherited from the underlying 3D shape. The authors claim that this differentiable splatting, together with a densification step that splits each convex into $K$ smaller copies when its sharpness loss is high, lets convexes represent hard-edged and flat geometry more compactly than Gaussians. They report consistent quality gains over 3DGS on structured indoor and human-made scenes, with the largest margin on Tanks and Temples, and a roughly 30% memory reduction in the full model.

Load-bearing premise

The argument assumes that a 2D soft projection of a convex hull is a faithful stand-in for the true 3D volume's appearance; unlike a 3D Gaussian, whose 2D projection is the exact ray integral, no such equivalence is established for convexes, so the proxy could diverge at oblique angles or when projected points become nearly collinear.

Editorial extensions

If this is right

  • On structured indoor scenes, 3DCS reports gains of 0.9 PSNR, 0.007 SSIM, and 0.023 LPIPS over 3DGS, indicating the primitive's advantage is largest where walls, edges, and furniture dominate.
  • The full model uses roughly 70% of 3DGS memory on the same benchmark while reporting better or equal quality; the lightweight variant uses under 15% of 3DGS memory and still beats it on Tanks and Temples and Deep Blending.
  • Because each primitive has a geometric boundary, the method produces visibly sharper renderings in qualitative comparisons, with the paper attributing PSNR's tendency to favor blur to pixel-level sensitivity.
  • Training remains practical at roughly one hour for the full model, versus 48 hours for the NeRF baseline, while rendering stays in real time.

Reading between the lines

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

  • A natural extension the authors do not develop is surface extraction: because convexes have explicit hull boundaries, one could read off depths, normals, or meshes directly from the primitives, something Gaussian clouds make ill-posed.
  • The depth-scaling of $\delta$ and $\sigma$ is introduced empirically; a tighter derivation from perspective projection might predict when the 2D proxy breaks and suggest a corrective term for grazing views.
  • The split-into-$K$ densification rule is an unusual target for future work: coupling it to a learned importance signal could further cut primitive counts without retraining the rasterizer.
  • Since convexes are closed shapes, they invite semantic or object-level decomposition, potentially turning a renderer into a parseable scene representation.
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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

4 major / 4 minor

Summary. The paper proposes 3D Convex Splatting (3DCS), a primitive-based radiance field renderer that replaces 3D Gaussians with smooth convex shapes. The method defines a 3D convex by a point set, projects the points to the camera plane, computes a 2D convex hull, and evaluates a smooth 2D indicator function that is composited with alpha blending. The authors report improved PSNR/LPIPS over 3DGS on Tanks and Temples and Deep Blending, comparable results on Mip-NeRF360, reduced primitive counts, and real-time rendering via a custom CUDA rasterizer. The paper also includes synthetic shape experiments, ablations of the number of points per convex, densification strategies, and perspective scaling.

Significance. If the central claims held, 3DCS would be a meaningful step toward primitive-based radiance fields with more geometrically expressive primitives than Gaussians. The empirical results on Tanks and Temples and Deep Blending are promising, and the paper provides useful engineering contributions: a differentiable CUDA rasterizer, an adaptive split-into-K densification scheme, and a parameter-efficiency analysis. The ablations for K, densification, and perspective scaling are valuable. However, the core conceptual claim that the method renders 3D smooth convexes is not supported by the actual rendering equations, which operate on a 2D convex hull of projected points. As a result, the claimed geometric interpretability and physical meaningfulness of the representation are not established. The paper would be significantly stronger if it were reframed as a 2D convex-kernel splatting method or if a genuine equivalence to 3D volume rendering were derived.

major comments (4)
  1. [Sec. 2.2 and Supplementary Eqs. (7)-(8)] The rendering pipeline never evaluates the 3D signed-distance function of Eqs. (2)-(3); after projecting the K points to 2D, it computes a 2D convex hull and evaluates a 2D LogSumExp/sigmoid over 2D line distances. No derivation shows that this 2D indicator equals the integral of the 3D smooth-convex density along a camera ray, in contrast to 3DGS, where the 2D Gaussian is the exact ray integral of the 3D Gaussian. The distance scaling of δ and σ in Eqs. (7)-(8), whose sensitivity is shown in Table 4, is a heuristic correction rather than a consequence of perspective projection. The abstract's claim of modeling '3D smooth convexes' and the 'geometrically-meaningful 3D representation' language in Sec. 3.4 are therefore not supported by the method as defined; the primitive is, as implemented, a 2D convex splat. The authors should either derive the relation to 3D volume rendering or re-state the contribution as 2D convex-kernel splatting and soften the 3D-interpretability claims.
  2. [Sec. 3.2 and Supplementary Sec. 5] The best-performing 3DCS model uses hyperparameters fine-tuned separately for indoor and outdoor scenes, including different densification thresholds, different split scaling factors (0.7 indoor vs. 0.6 outdoor), and different treatment of σ after splitting. This makes the headline comparison against 3DGS and other baselines a comparison that includes per-scene-type model selection, rather than a single method with fixed hyperparameters. Moreover, no error bars or multiple-run statistics are reported. Given these issues, the claim in Table 1 of consistent superiority over 3DGS on Mip-NeRF360 is not robust: the SSIM is lower (0.802 vs. 0.815) and the PSNR gain is only 0.08 dB. The paper should present the unified-hyperparameter light model as the primary comparison and report variance or at least acknowledge the model-selection issue explicitly.
  3. [Tables 8-10 (Supplementary)] The per-scene results for Mip-NeRF360 show that 3DCS underperforms 3DGS on several scenes, including Bicycle (PSNR 24.72 vs. 25.24, SSIM 0.737 vs. 0.771) and Treehill (PSNR 21.77 vs. 22.49, SSIM 0.595 vs. 0.638), in addition to the aggregate SSIM deficit. The statement in Sec. 3.3 that 3DCS 'consistently matches or surpasses existing methods' is therefore too strong. The scene-level variability should be discussed, especially since the indoor/outdoor split in Table 2 is exactly where the method's advantage concentrates.
  4. [Sec. 3.4 and Fig. 11] The claim that 3DCS yields 'physically meaningful 3D representations' and decomposes objects into meaningful convex shapes is supported only by qualitative examples with a small number of primitives. No evidence is provided that the inferred convexes are consistent across views, that they correspond to actual scene surfaces, or that the decomposition is semantically meaningful. Since the rendered quantity is a 2D convex-hull indicator, the view-dependent masks do not by themselves establish a 3D volumetric decomposition. This section should be substantially toned down or backed by quantitative multi-view consistency or geometry metrics.
minor comments (4)
  1. [Eq. (5)] The opacity factor in Eq. (5) is not clearly defined in the text: the sentence refers to 'on the opacity' but does not state that the symbol o_n denotes opacity, nor is the product term typeset unambiguously.
  2. [Sec. 3.3] The text says '3DCS light outperforms 3DGS and GES on the T&T and DP dataset'; 'DP' should be 'DB' (Deep Blending).
  3. [Reference [14]] The title of [14] contains a typo: 'algorith' should be 'algorithm'.
  4. [Sec. 1] The sentence 'by representing scenes with millions of 3D Gaussian' should read 'millions of 3D Gaussians'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: 3DCS is an empirical primitive-rendering method whose benchmark claims are measured results and whose design choices are ablated, not derived from the target.

full rationale

Walking the derivation chain, the 3D smooth-convex definition (Eqs. 1-3) is inherited from CvxNet [9], and the rendering pipeline then projects the 3D point set to 2D and builds a 2D convex-hull indicator (Eqs. 7-8). These are distinct constructions; the paper explicitly says it 'substitute[s] the 3D point p with the 2D point q and replace[s] the planes delimiting the 3D convex hull with the lines that delimit the resulting 2D convex hull.' It does not claim that the 2D indicator is the exact ray integral of the 3D density, so the skeptical objection about physical fidelity is a validity/approximation concern, not a circular one. The perspective scaling of delta and sigma by distance d is a manual design choice validated by the ablation in Table 4, not a parameter fitted to the reported test metrics and then renamed as a prediction. The densification rule based on sigma loss is an optimization heuristic, analogous to 3DGS's positional-gradient heuristic, and is itself ablated in Sec. 3.4. The loss (Eq. 6) is a standard photometric-plus-mask objective with stated weights. No result reduces to its inputs by construction. On self-citation: GES [18] shares authors with this paper but appears only as a baseline comparison, not as load-bearing justification; CvxNet [9] and 3DGS [25] are external prior works, and no uniqueness theorem is invoked. Hyperparameters are disclosed and ablated, and the central claims are empirical benchmark numbers rather than consequences of a self-referential premise. Hence the paper is self-contained against external benchmarks and merits a circularity score of 0.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a substantial set of hand-tuned hyperparameters and on the assumption that the 2D projected soft convex is a valid rendering primitive. These are listed below.

free parameters (9)
  • Initial smoothness δ = 0.1
    Hand-set in Sec. 5 (supplementary); chosen empirically to start with diffuse shapes.
  • Initial sharpness σ = 0.00095
    Hand-set in Sec. 5 (supplementary).
  • Densification criterion threshold = 0.000004 (loss of σ)
    Split when the loss with respect to σ exceeds this value; ad hoc (Sec. 5).
  • Prune opacity threshold = 0.03
    Convexes with lower opacity are removed (Sec. 5).
  • Prune size threshold = 0.3 × scene size
    Overly large convexes are removed (Sec. 5).
  • Split scale factors = 0.7 (indoor), 0.6 (outdoor)
    Downscaling for new convexes; tuned per dataset (Sec. 5).
  • Loss weight β for mask loss = 0.0005
    From [29]; hand-set (Sec. 2.3).
  • Number of points per convex K = 6
    Ablated in Table 3; K=6 selected as best trade-off.
  • Perspective scaling exponent = 1 (scale by d)
    Chosen from ablation in Table 4 (supplementary); d gave best PSNR.
assumptions (5)
  • standard math The projection of a convex hull equals the convex hull of the projected points.
    Relied on in Sec. 2.2 to render the 2D footprint of the 3D convex by computing the 2D hull of projected points.
  • standard math The LogSumExp function with smoothness δ approximates the max of signed distances, and the sigmoid with sharpness σ yields a valid occupancy indicator.
    Used in Eqs. (2) and (3) from CvxNet; assumed to be a good surrogate for hard edges.
  • domain assumption Rendering the 2D projected soft polygon with alpha blending approximates the appearance of the 3D primitive.
    The paper does not derive this from a volumetric integral; it is an assumption adopted from Gaussian splatting (Sec. 2.2, Eq. 5).
  • domain assumption The mask loss L_m from [29] encourages compactness and does not harm fidelity.
    Used in Eq. (6); not detailed in this paper.
  • ad hoc to paper The densification criterion based on the loss of σ identifies under/over-reconstructed regions.
    The authors state that positional gradients are unreliable and instead use σ loss, but provide no theoretical justification (Sec. 2.3).

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Cite this review

Pith. "Pith review of 3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes." pith.science (2026). https://pith.science/paper/33RZUOQP

@misc{pith2026241114974,
  author       = {Pith},
  title        = {Pith review of: 3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/33RZUOQP}},
  note         = {Machine review of arXiv:2411.14974}
}
read the original abstract

Recent advances in radiance field reconstruction, such as 3D Gaussian Splatting (3DGS), have achieved high-quality novel view synthesis and fast rendering by representing scenes with compositions of Gaussian primitives. However, 3D Gaussians present several limitations for scene reconstruction. Accurately capturing hard edges is challenging without significantly increasing the number of Gaussians, creating a large memory footprint. Moreover, they struggle to represent flat surfaces, as they are diffused in space. Without hand-crafted regularizers, they tend to disperse irregularly around the actual surface. To circumvent these issues, we introduce a novel method, named 3D Convex Splatting (3DCS), which leverages 3D smooth convexes as primitives for modeling geometrically-meaningful radiance fields from multi-view images. Smooth convex shapes offer greater flexibility than Gaussians, allowing for a better representation of 3D scenes with hard edges and dense volumes using fewer primitives. Powered by our efficient CUDA-based rasterizer, 3DCS achieves superior performance over 3DGS on benchmarks such as Mip-NeRF360, Tanks and Temples, and Deep Blending. Specifically, our method attains an improvement of up to 0.81 in PSNR and 0.026 in LPIPS compared to 3DGS while maintaining high rendering speeds and reducing the number of required primitives. Our results highlight the potential of 3D Convex Splatting to become the new standard for high-quality scene reconstruction and novel view synthesis. Project page: convexsplatting.github.io.

Figures

Figures reproduced from arXiv: 2411.14974 by the authors.

Figure 1
Figure 1. 3D Convex Splatting for Novel View Synthesis. We introduce a novel primitive-based pipeline for novel view synthe￾sis with 3D smooth convexes. Our 3D smooth convexes share the rendering speed of 3D Gaussians [25] and the flexible represen￾tation of smooth convexes [9]. As a result, 3D Convex Splatting better reconstructs scenes with fewer primitives. which are optimized to render novel views at high-quality. However… view at source ↗
Figure 2
Figure 2. Toy Experiment of Modeling a Chair. For the chair input image, we use Gaussians and smooth 6-point convexes to fit the chair with an increasing number of primitives. Note how the convexes efficiently represent the chair with fewer parameters. Neural radiance fields (NeRF). Recovering the 3D struc￾ture of a scene from images captured from multiple view￾points is a fundamental problem in computer vision [1, 12]. The i… view at source ↗
Figure 3
Figure 3. Convex Splatting Pipeline. The 3D smooth convex is represented with a point set that is projected in the 2D camera plane. We extract the line-delimited convex hull of the projected points and define the signed distance function for each line. The lines are combined to define an indicator function for each pixel based on smoothness δ and sharpness σ of the 3D convex. The pipeline is differentiable end-to-end, which a… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Effects of δ and σ on Splatting. The smoothness δ char￾acterizes vertices and edges, from soft to hard, while the sharpness σ characterizes radiance field transitions, from diffuse to dense. 0.5. More details about smooth convexes can be found in [9] [PITH_FULL_IMAGE:…
Figure 5
Figure 5. Figure 5: Adaptive Convex Densification Scheme. We divide each convex, here exemplified with K = 8 points, into as many scaled-down occurrences of the convex, centered at the initial points, each with reduced opacity. Following the approach used in 3DGS, we apply a standard expo…
Figure 7
Figure 7. Figure 7: Qualitative Comparison between 3DCS, 3DGS and 2DGS. Our 3DCS captures finer details and provides a more accurate approximation of real-world scenes compared to Gaussian splatting methods, which often produce blurrier results [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Visual Comparison Between our Light Model and 3DGS. The light model (right) shows high visual quality compared to 3DGS (left), using less than 15% of the memory. ments. In fact, for indoor scenes, it can be seen that 3DCS significantly outperforms 3DGS with an improvem…
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 10
Figure 10. Figure 10: # Parameters vs. LP IP S↓ (Truck scene). The num￾ber of primitives is indicated for each point. 3DCS achieves a better regime than 3DGS for a comparable number of parameters. Number of points per shape. Increasing K provides greater flexibility in representing convex …
Figure 12
Figure 12. Figure 12: Smooth convexes can represent a wide variety of shapes, whether hard or soft, dense or diffuse. They effectively approximate [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: Qualitative Comparison between 3DCS, 3DGS and 2DGS. 3D Convex Splatting achieves high-quality novel view synthesis and fast rendering by representing scenes with 3D smooth convexes. In contrast, the softness of Gaussian primitives often results in blurring and loss of…

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Forward citations

Cited by 5 Pith papers

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.