Title: LinPrim: Linear Primitives for Differentiable Volumetric Rendering
Venue: NeurIPS 2025
Accepted: yes
Keywords: Novel View Synthesis

Real-Time Rendering

Scene Representations
Abstract: Volumetric rendering has become central to modern novel view synthesis methods, which use differentiable rendering to optimize 3D scene representations directly from observed views. While many recent works build on NeRF or 3D Gaussians, we explore an alternative volumetric scene representation. More specifically, we introduce two new scene representations based on linear primitives - octahedra and tetrahedra - both of which define homogeneous volumes bounded by triangular faces. To optimize these primitives, we present a differentiable rasterizer that runs efficiently on GPUs, allowing end-to-end gradient-based optimization while maintaining real-time rendering capabilities. Through experiments on real-world datasets, we demonstrate comparable performance to state-of-the-art volumetric methods while requiring fewer primitives to achieve similar reconstruction fidelity. Our findings deepen the understanding of 3D representations by providing insights into the fidelity and performance characteristics of transparent polyhedra and suggest that adopting novel primitives can expand the available design space.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes two new primitives to perform volumetric rendering, namely octahedra and tetrahedra, and adapt the existing 3D Gaussian Splatting (3DGS) framework to select a suitable number of primitives and to optimize the rendering process efficiently. The method is evaluated on two datasets, showing comparable performance to competitive baselines while, in some cases, reducing the number of primitives required.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n- the method is evaluated on multiple datasets and ablation studies are presented\n- visualizations aid the explanation of the method\n\n**Weaknesses:**\n- the paper is overall difficult to follow: several concepts are not introduced (e.g., primitives, alpha blending, rasterization, quaternions, Structure-from-Motion) and the method section goes into detail too quickly (e.g., octahedra and tetrahedra are not introduced in Sec. 3.1, which only presents their technical challenges for the problem at hand) \n- the contribution appears limited: the paper adapts the existing 3DGS framework to accommodate 2 new primitives, without significantly diverging from it. The numerical results also do not show a significant enough performance improvement to justify this as a relevant contribution (e.g., on ScanNet++, the performance and number of primitives is very similar to GS-MCMC)\n- the experimental section is overall not clear: the two datasets are not introduced (what do they contain, what is the specific task) and some choices appear arbitrary:\n\t- why are the baselines for the two datasets different?\n\t- what are the metrics in Table 1?\n\nQUESTIONS:\n- the population control technique seems to be potentially complex, what is the impact on the training time and stability of the overall approach?\n- the comparison between using tetrahedra and octahedra could be improved, what are the advantages and disadvantages of one compared to the other based also on the empirical evidences?\n- why are the baselines in Table 1 and 2 different? What is the performance of those not reported in one of the two tables?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-23"}

comments: SUMMARY:
This paper introduces LinPrim, a novel explicit scene representation for novel-view synthesis that replaces Gaussian kernels with transparent linear polyhedra. LinPrim achieves competitive reconstruction quality on ScanNet++ and Mip-NeRF 360, while using significantly fewer primitives than 3DGS.

STRENGTHS AND WEAKNESSES:
Strengths
1. The method provides a complete and systematic solution, including full forward and backward derivations for triangle-ray intersections, seamless integration into the 3DGS training loop, and full preservation of end-to-end differentiability.
2. This approach enables a marked decrease in attribute complexity while preserving high-fidelity rendering performance.

Weaknesses
1. Recent work like 3D Convex Splatting [CVPR 2025] also propose modifications to Gaussian primitives. A more in-depth comparison and analysis with these methods would strengthen the paper.
2. Although the method employs fewer primitives, its training and inference times are still slower than those of 3DGS. The potential reasons, including per-triangle computation costs or overdraw effects, are not thoroughly investigated.
3. Despite emphasizing a substantial reduction in primitive count, the paper omits quantitative measurements of total storage requirements, making the practical memory efficiency unclear.
4. It would be interesting to explore whether this representation provides enhanced geometric fidelity relative to 3DGS, such as in depth maps or mesh reconstruction.

QUESTIONS:
See the weaknesses.

LIMITATIONS:
yes.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-26

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis manuscript proposes to use linear primitives for 3D scene reconstruction and novel view synthesis. Inspired by 3D Gaussian Splatting, this work designs a differentiable rasterization pipeline and a population control strategy for the linear primitives, enabling gradient-based optimization. Compared to vanilla 3D Gaussian Splatting, the proposed method achieves comparable rendering quality with fewer primitives, while exhibiting qualitatively superior fidelity in some challenging cases, such as sharper geometric edges and mitigation of over-densification (e.g., the table edge and carpet in Fig.4).\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1.\tThe proposed method can achieve close rendering quality with significantly fewer primitives. In some challenging cases, as shown in the qualitative comparisons, it exhibits unique advantages over previous arts.\n\n2.\tThe proposed linear primitive holds strong potential to inspire future exploration. Compared to 3DGS, it allows for more precise define of ray-primitive intersection, while easier to equipping topological structuring, and more like the triangle meshes commonly used in graphics pipelines.\n\nWeaknesses：\n\n1.\tAs shown in Table 4, the advantage of using fewer primitives does not transform into rendering efficiency (although it can already achieve interactive frame rates on standard benchmarks). In addition, since L321 claims the advantage of low memory footprint, it is suggested to compare the memory usage quantitatively to better illustrate the compactness of the representation.\n\n2.\tThe benefits of the proposed linear primitives over the vanilla 3D Gaussians are not convincingly described. Now its potential is far from fully unleashed, and the demonstrated advantages appear circumstantial rather than fundamental or indispensable.\n\nQUESTIONS:\n1.\tThe manuscript does not clearly explain how and why EWA splatting is applied on linear primitives. L149 mentions a trade-off between approximation error and computational overhead, it is better to provide a quantitative comparison.\n\n2.\tWhy is opacity maintained by each primitive and use it to derive density, rather than directly learning a density attribute?\n\n3.\tAlthough 3DGS also have a truncated range, its AABB is somewhat over-estimated. However, the proposed linear primitive seems incapable of receiving gradients from non-intersecting pixels. Could this property impose stricter requirements on initialization?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces LinPrim, a differentiable 3D representation for volumetric-rendering-based reconstruction that replaces Gaussian kernels with bounded, linear polyhedral primitives: axis-aligned octahedra and tetrahedra.\n\nEach primitive is described by 11–12 floats for geometry + 48 SH coefficients for color and is rasterized with a custom GPU kernel that (i) projects the polyhedron into the ray space used by EWA splatting, (ii) computes differentiable ray-triangle intersections, and (iii) composites in front-to-back order (with simple anti-aliasing heuristics).\n\nAs evaluated on ScanNet++ and Mip-NeRF 360 dataset, the proposed method achieves comparable (slightly off) quality while using 4x fewer primitives compared with 3DGS.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- It is always interesting and worth exploring to bring polyhedra-based primitives into differentiable rendering with splatting. \n- The representation is compact with efficiency improvement over 3DGS. Octahedra need only 11 float params (same budget as a Gaussian) yet deliver comparable PSNR/SSIM with one quarter the primitive count on ScanNet++.\n- Fully differentiable rasterizer introduced by analytical ray-triangle gradients (derived in the appendix) enable end-to-end training without resorting to volumetric sampling.\n- The paper compares octahedra vs. tetrahedra, tests anti-aliasing filters, and re-uses publicly available 3DGS/Mip-Splatting code with identical training schedules for fair comparisons.\n\nWeaknesses:\n- Runtime still heavier than 3DGS. Octahedra render at ~14.6 ms per 1 K×1 K view vs. 5.7 ms for 3DGS on the same hardware; the face count largely offsets the smaller population.\n- It is always a downside for polygon-based primitives to represent hard edges when coverage is sparse, whereas Gaussians fade gracefully.\n- Limited evaluation scope. It would be great and more comprehensive to have more evaluations especially on the success and failure cases of the proposed representation, which would unveil unique characteristics brought by this representation compared with 3DGS. Testing on more different scenes would be beneficial, such as large-scale scenes, indoor scenes with lots of surfaces with Manhattan assumptions, and scenes with reflections, etc. \n- Anti-aliasing is heuristic. The 2D bbox inflation filter is an ad-hoc substitute for Mip-Splatting’s analytic filter and might not generalize to zoom-out scenarios.\n\nQUESTIONS:\n- Complexity trade-off. Given octahedra are slower but fewer than Gaussians, where is the break-even point in primitive count vs. faces for equal FPS?\n- Surface extraction. Is this representation friendly for surface extraction? If so, how does accuracy and performance looks like? I also assume there is better algorithm for iso-surface extraction compared with marching cubes on this representation.\n- SH bandwidth. Did you experiment with degree-1 or learned MLP colour decoders? How sensitive is quality to SH order?\n- Dynamic scenes. Your rasterizer is well suited to convex, bounded volumes—does it extend to per-frame primitive motion (e.g. for dynamic NeRFs) without severe overhead?\n- Edge-case failures. Besides ceilings, which scene structures (thin wires, foliage, specular objects) break most often, and can hybrid primitives (polyhedra + Gaussians) alleviate that?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}