Gaussian Stippling: Efficient Sorting-Free 3D Gaussian Rendering through Hybrid Sampling and Spatiotemporal Reconstruction

1 Introduction

• 3DGS requires depth sorting and ordered compositing of overlapping primitives, limiting practicality for large scenes and resource-constrained devices (Kerbl et al. 2023).Existing alternatives are not always directly applicable to unmodified 3DGS assets.Source: §1 · p. 1
• Gaussian stippling converts continuous Gaussian splats into discrete, opaque stochastic visibility samples that compete through a standard depth test.Stochastic transparency preserves the underlying Gaussian representation while enabling sorting-free visibility sampling.Source: §1 · pp. 1–2
• The hybrid renderer routes Gaussians by opacity and projected footprint between fragment-based and primitive-based stippling, whose complementary cost profiles are combined with a shared depth test.Fragment-based cost grows with rasterized coverage, while primitive-based cost grows with the number of generated samples.Source: §1 · p. 2
• A lightweight reconstruction network uses Gaussian attributes and current-frame plus reprojected historical observations to suppress noise from sparse stochastic samples.The attributes include opacity, covariance, and depth; additional samples can mitigate artifacts but erode sorting-free performance gains.Source: §1 · p. 2
• A cross-scene-trained reconstruction network applies to evaluated unseen scenes without scene-specific network training or Gaussian-asset modification, and the framework demonstrates interactive mobile rendering.With scene-specific training, higher sampling and a larger network offer a quality-oriented operating point at higher computational cost.Source: §1 · p. 2

2.1 Accelerating 3D Gaussian Splatting

• Some acceleration methods modify the Gaussian representation or its optimization, whereas this renderer operates on fixed 3DGS assets.Related approaches include order-independent transparency approximations, depth peeling, and newly optimized Gaussian variants.Source: §2.1 · p. 2
• StochasticSplats (Kheradmand et al. 2025) and Gaussian Point Splatting preserve assets and eliminate sorting, but their low-spp outputs have high variance.Temporal filtering and increased sampling budgets can mitigate the noise.Source: §2.1 · pp. 2–3

2.2 Neural Reconstruction from Stochastic Samples

• Neural point-based and deferred rendering methods reconstruct dense images from sparse point features, while this setting also involves stochastic visibility changes and overlapping semi-transparent Gaussians.The method retains Gaussian-local footprint, opacity, and depth descriptors because a single surface description may not capture overlapping splat contributions.Source: §2.2 · p. 3
• Forward reprojection supplies historical observations because changing visible Gaussians complicates conventional backward alignment based on stable surface motion vectors.The network receives current and reprojected historical observations as separate inputs and learns to combine their evidence.Source: §2.2 · p. 3

3.2 Spatiotemporal Gaussian Observations

• The network input combines the current observation map with maps from K = 3 preceding frames after forward reprojection.Historical observations are reprojected into the target frame before concatenation.Source: §3 · p. 3, §3.2 · p. 5

3.1 Hybrid Stochastic Observation Generation

• Routing uses opacity and projected footprint in a fitted time-cost rule to assign each Gaussian to the faster sampling stream.The two streams have complementary costs: fragment rendering benefits from large footprints, while primitive sampling is more efficient for tiny footprints.Source: §3.1 · p. 4
• Primitive sampling draws opacity-corrected Poisson points, while fragment sampling rasterizes a finite footprint; the nearest-depth accepted candidate supplies pixel color.The renderer’s unbiasedness claim requires one stream per primitive, matched effective alpha and support, and independent acceptance events.Source: §3.1 · p. 4

3.2 Spatiotemporal Gaussian Observations

• Selected Gaussians contribute 10-channel descriptors carrying opacity, covariance, and depth cues; M observations are averaged into a fixed-dimensional map.Opacity and Mahalanobis distance help distinguish sampling variation from footprint boundaries, while covariance and depth provide anisotropy and visibility cues.Source: §3.2 · pp. 4–5

3.3 Neural Reconstruction

• Reconstruction uses a pixel-wise MLP bypass and a multiscale U-Net context branch, whose outputs are fused to regress final color.Scene-specific training combines a Charbonnier reconstruction penalty with a first-order gradient consistency term to encourage robust reconstruction and preserve local structures and boundaries.Source: §3.3 · p. 5

4.1 Experimental Setup

• The evaluation uses 11 scenes from three datasets, with separate scene-specific network training on held-out views unless otherwise stated; Gaussian representations remain fixed.The setup also compares against StochasticSplats, Gaussian Point Splatting, and MobileGS; Ours-S and Ours-L use U-Net-style architectures with different capacities.Source: §4.1 · p. 5

4.2 Hybrid Stochastic Rendering

• At 1080p, the hybrid renderer is 7.2–9.2× faster than vanilla 3DGS and outperforms both single-stream sampling baselines.Figure 4 also shows lower view-dependent latency fluctuations than the primitive-based stream on the evaluated trajectory.Source: Table 1 · p. 6, §4.2 · p. 6

4.3 End-to-End Reconstruction

• At 1 spp, Ours-S reaches 283.17–305.32 FPS and a 2.3–2.7× speedup over 3DGS; 16-spp Ours-L has higher average PSNR than 3DGS on three benchmarks at higher cost.Reconstruction takes 1.78 ms for Ours-S and 11.31 ms for Ours-L; Figures 5 and 6 show the respective operating points.Source: Table 1 · p. 6, §4.3 · pp. 6–7, Figure 5 · p. 6
• Removing historical observations or keeping only RGB lowers average reconstruction PSNR, while individual descriptor removals have smaller, scene-dependent effects.The ablations use 1-spp Ours-S on three representative scenes.Source: Table 2 · p. 7, §4.3 · p. 7
• On five DL3DV target scenes, the cross-scene Ours-S outputs exceed the raw stochastic baselines in PSNR but remain below standard 3DGS on average.The comparison is against 4-spp StochasticSplats and Gaussian Point Splatting.Source: Table 3 · p. 7, §4.3 · p. 7

4.4 Application: Mobile Deployment and Simultaneous Graphics and Compute

• At 540p on the evaluated mobile platform, the renderer averages 92.6 FPS versus 53.3 FPS for StochasticSplats and 49.0 FPS for Gaussian Point Splatting; compact-network inference reaches 73.2 FPS.Ours-S uses the device’s NPU for inference, and the interactive implementation also applies reprojected temporal accumulation.Source: Table 4 · p. 7, §4.4 · p. 7

5 Conclusion

• The framework combines primitive- and fragment-driven sampling without modifying 3DGS assets, then uses current and historical stochastic evidence to suppress noise.It supports both a fixed cross-scene model and scene-specific reconstruction aimed at higher quality.Source: §5 · p. 7
• Sparse stochastic observations can over-smooth high-frequency appearance, especially around thin structures, sharp visibility transitions, and view-dependent details.Unified per-scene optimization is proposed as a quality-oriented direction, but requires additional scene-specific optimization beyond fixed-asset deployment.Source: §5 · p. 7

A Mobile Baseline and Deployment

• The mobile evaluation ports sorting-free methods and tests a GPU-NPU parallel framework on a Vivo device, reporting throughput for the tested methods.The mobile baseline section says MobileGS uses unsorted per-tile lists and order-independent weighted color and transmittance accumulation; its MLP runs on the NPU while rasterization runs on the GPU with overlapped frames.Source: A Mobile Baseline and Deployment · p. 9, §A.1 · p. 9

A.1 MobileGS Reproduction

• The MobileGS reproduction preserves its preprocessing, culling, weighting, and compositing equations, with FP16 MLP inference on the NPU and Vulkan-compute rasterization on the GPU.It uses zero-copy buffers and overlaps NPU inference for one frame with GPU rendering of the preceding frame.Source: §A.1 · p. 9

A.2 SortFreeGS Reproduction

• The SortFreeGS mobile port preserves learned visibility and depth weighting, sorting removal, weighted-sum compositing, and signed background normalization.Its mobile optimizations include GPU-resident culling and indirect drawing; only spherical-harmonic storage uses FP16, while projection, rasterization, and accumulation remain FP32.Source: §A.2 · p. 9

A.3 Future Work

• On iPhone 13 Pro, overlapping rasterization and neural reconstruction yields approximately 30 FPS at 720p; on iPhone 17 Pro, NPU inference takes about one-third as long while GPU rasterization stays relatively stable.The authors identify platform-specific implementation and evaluation as necessary for extending the pipeline to other device classes.Source: §A.3 · pp. 9–10

B Stochastic Gaussian Stippling

• The sampling construction’s ordered-compositing expectation requires independent Bernoulli acceptance, a common effective alpha function and support, and consistent finite-support handling across streams.The continuous point construction uses a pixel-center approximation and does not alone establish exact equivalence after discretization or unequal truncation.Source: B Stochastic Gaussian Stippling · pp. 10–11
• The appendix calls the radius-sampling procedure an opacity-corrected Box–Muller transform, using inverse transform sampling after drawing a uniform random variable.Sampling the point count from a Poisson distribution and then sampling point locations constructs an inhomogeneous Poisson point process; pixel occupancy approximates alpha under the stated pixel-center approximation.Source: B Stochastic Gaussian Stippling · p. 11

C Route Criterion Estimation

• Across layer counts 1–8, the opacity-area crossover boundaries nearly overlap, indicating that depth complexity has minimal impact on the streams’ relative execution time in the synthetic benchmark.This supports using a unified routing criterion across the tested occlusion conditions.Source: C Route Criterion Estimation · p. 11

D.1 Dataset

• Custom names for DL3DV scenes are provided for clarity, with their corresponding dataset hash identifiers listed in Table A6.The table caption identifies the mapping as scene names and dataset hash values.Source: §D.1 · p. 11

D.2 Compare with Gaussian Point Splatting

• A hard cap of 2.5×10^8 sampling points can trigger forced culling and rendering failures, while preallocating for arbitrary scenes and viewpoints is difficult.At that cap, preallocation consumes approximately 1 GB of memory.Source: §D.2 · p. 11
• The GPS runtime comparison follows its original implementation except that the upper limit on single-Gaussian sampling is disabled.The authors report that capping this limit causes severe artifacts from certain viewpoints.Source: §D.2 · p. 11
• The Fragment Stream locates Gaussian IDs by binary search over a prefix-sum array, unlike GPS’s pre-allocated fixed array, but the observed runtime difference is negligible.The authors attribute the negligible difference to a compute-bound rather than memory-I/O-bound rendering pipeline.Source: §D.2 · p. 11

D.3 Network Architecture

• Each pixel contributes 10 channels per frame, combining RGB, alpha, squared Mahalanobis distance, Gaussian opacity, projected covariance coefficients, and inverse depth; current and three history frames yield 40 input channels.The history frames are reprojected observations.Source: §D.3 · pp. 11–12
• Ours-S uses three downsampling stages and 16-channel features, while Ours-L uses four stages with encoder widths 64, 96, 128, 192, and 256.Both are encoder–decoder U-Nets without normalization; they directly predict RGB, with linear output for Ours-S and ReLU output for Ours-L.Source: §D.3 · p. 12
• The renderer-supervised generalization model uses the same Ours-S architecture and loss as the scene-specific model.Source: §D.3 · p. 12

D.4 Temporal Accumulation

• The GUI forward-reprojects the previous accumulated result, keeps the closest history sample by depth, and incrementally averages valid history with the current denoised frame.History length is capped at 12 for a stationary camera and 2 during camera motion; invalid history is replaced by the current denoised frame.Source: §D.4 · p. 13
• Figure A2 reports a loss when rendering with GPS source code at 1024 spp is compared with Gaussian rendering.The caption notes that the only modification to Gaussian Point Splatting was removing its upper limit on individual Gaussian sampling.Source: Figure A2 · p. 13

E.1 Temporal Ablations

• Forward nearest-neighbor reprojection achieves the highest mean PSNR among the evaluated variants, and outperforms either backward variant at the evaluated network capacity.Table A5 compares transport variants under stochastic visibility.Source: §E.1 · pp. 13–14
• Forward reprojection can leave unfilled pixels, while backward reprojection can introduce structured artifacts in the stochastic-input setting.Figure A4 illustrates the reported temporal artifacts.Source: §E.1 · pp. 13–14, Figure A4 · p. 14
• With forward reprojection, nearest-neighbor sampling yields higher PSNR than bilinear sampling on the three evaluated scenes.The authors suggest nearest-neighbor assignment may avoid mixing descriptor values from neighboring observations.Source: §E.1 · p. 14

E.2 Observation Budget and Network Size Ablations

• Across scenes, rendering quality is evaluated at 1, 4, and 16 spp using two network capacities: Ours-S reduces stochastic noise, while Ours-L provides additional capacity.Source: §E.2 · p. 14
• Figure A5 presents qualitative neural-reconstruction results for additional scenes at 16 spp with the Large network.Qualitative examples are also provided in the main text and Section F.Source: Figure A5 · p. 15, §E.2 · p. 15
• The interactive GUI pipeline applies TAA after neural denoising, so its temporal appearance reflects both reconstruction and the additional TAA stage.The supplementary video shows this combined pipeline for the 1-spp + Ours-S configuration.Source: §E.2 · p. 15

• Large networks reconstruct complex lighting and local details, as shown in Figure A5.Source: F Additional Qualitative Results · p. 15