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PLEDGE: Progressive Lossy Error-Bounded Compression of 3D Gaussian Splatting
Mingze Xia, Yuxiao Li, Baixi Sun, Wenbo Li, Pu Jiao, Sheng Di, Franck Cappello, Hanqi Guo, Xin Liang
TL;DR
Existing 3DGS codecs provide aggregate reconstruction quality but little control over individual primitives or intermediate reconstructions. PLEDGE translates four tolerances into per-primitive bounds and progressively codes residuals; across thirteen scenes it achieves 15–30× compression ratios.
Problem
Existing 3DGS codecs report aggregate reconstruction quality, and progressive codecs provide no error guarantee for intermediate reconstructions at different download budgets.
Source: §1 · p. 1Method
Results
15–30× compression ratios across thirteen scenes; including the off-axis factor costs 1.7% of the rate on average and omitting it violates the footprint bound on off-axis primitives.
Source: §5.2 · p. 8, §5.3 · p. 9Takeaways & Limitations
At tight color tolerance, degree 1–3 SH coefficients account for 48% of the bitstream, compared with 14% for position, reflecting different rate costs across tolerances.
Source: §1 · p. 1The guarantee is relative to the pruned model and declared camera domain, covers the rasterized footprint rather than the exact perspective silhouette, and bounds composited color only at fixed geometry and opacity.
Source: §4.1 · p. 6, §6 · p. 9
Abstract
from arXiv · showhide
Existing 3D Gaussian Splatting (3DGS) codecs report reconstruction quality after compression, and give users little control over the distortion of individual primitives. We present PLEDGE, a training-free, progressive, error-bounded codec that translates four user-declared tolerances into per-primitive quantization bounds: screen-space position, footprint deformation due to rotation and scale, view-dependent color, and opacity. The bounds apply throughout a declared camera domain, including previously unseen viewpoints. Position and opacity are bounded directly; footprint deformation is bounded under the rasterizer's affine projection model, and color is bounded over all viewing directions. PLEDGE organizes quantized residuals into a progressive bitstream with explicit error bounds for every valid prefix. Experiments across thirteen scenes verify all declared per-mechanism bounds and demonstrate competitive rate-distortion performance. The four tolerances incur substantially different rate costs, so users can spend rate where their application needs it.
1. Introduction
Existing 3DGS codecs emphasize aggregate reconstruction quality, leaving users little control over individual primitives or intermediate download budgets. PLEDGE maps four user-declared tolerances to per-primitive quantization bounds and codes them progressively so every valid prefix has a bound.
1. Introduction
- Existing codecs report aggregate reconstruction quality, while users may need different control over position, geometry, or color for tasks such as occlusion masking, measurement, or streaming previews.At tight color tolerance, degree 1–3 SH coefficients account for 48% of the bitstream, compared with 14% for position.Source: §1 · p. 1
- Existing progressive codecs provide no predictable error guarantee for intermediate reconstructions at different download budgets.Source: §1 · p. 1
- The four tolerances and camera domain determine per-primitive quantization steps, with subsequent coding stages affecting rate but not the guarantee.Source: Figure 1 · p. 2, §1 · p. 2
- PLEDGE converts four user-declared tolerances into per-primitive quantization bounds, then codes residuals so every valid bitstream prefix carries an error bound.It needs a trained 3DGS model and its camera calibration.Source: §1 · p. 2
2. Related work
3DGS codecs divide between retraining methods that need training images and training-free methods that post-process trained models. PLEDGE applies error-bounded compression to 3DGS and bounds every valid stream prefix, unlike approaches that bound only the complete file.
2. Related work
- Retraining codecs reach the best rates but require training data, while training-free approaches post-process a trained model; PLEDGE is training-free and, to the authors’ knowledge, no prior codec bounds error.FlexGaussian comes closest with a 1 dB target, but its scene average does not bound individual primitives or unseen viewpoints.Source: §2 · p. 2
- PLEDGE adapts error-bounded scientific compression to embedded coding and bounds every valid stream prefix, not only the complete file.Source: §2 · p. 2
3. Declared bounds and their inversion
Section 3 maps four declared tolerances to per-primitive quantization bounds over a camera domain D, distinguishing pixel displacement, footprint motion, radiance, and opacity error. The guarantees cover cameras satisfying D’s imaging-parameter limits, including cameras not supplied to the encoder.
3.1 The contract
- Per-primitive, per-channel half-steps are derived from the four targets, quantized downward, and keep decoded channel errors within their bounds for any predictor.The camera domain D is set by a near plane, maximum focal length, and half-angle.Source: §3.1 · p. 3
- Center coordinates bounded by εµ keep projected displacement within τpx on each image axis for primitives whose centers project inside the frustum.The center-position guarantee does not extend to out-of-frustum centers.Source: §3.1 · p. 3
- Rotation and log-scale changes are bounded using primitive-specific limits based on smax,i; at a fixed center, their combined footprint displacement is at most 2τsh.The footprint is the 1σ ellipse of the projected covariance under the rasterizer’s clamped projection model.Source: §3.1 · p. 4
- Per-coefficient SH bounds enforce radiance error τC in every viewing direction, while opacity is bounded directly by τα.With geometry and alphas fixed, the primitive color contracts also bound composited pixel color by τC.Source: §3.4 · p. 5
- 2.3× larger εk and 1.2 bits per coefficient result when optimizing the maximum summed color error instead of bounding each SH coefficient separately.The encoder alternates a worst-direction search with water-filling; correctness requires feasible bounds, not an optimal search.Source: §3.4 · p. 5
- 0.7% rate overhead accompanies a Lipschitz correction equal to 2.4% of τC; the covering radius η is asserted and confirmed by sampling, not computed exactly.The correction extends sampled-direction checks toward a whole-sphere color guarantee.Source: §3.4 · p. 5
4. The codec
The codec builds a hierarchy of retained primitives and encodes predicted quantization residuals progressively. Its progression order and truncation ladder determine what a prefix contains and the error bound it carries.
4.1 Pruning
- Pruning keeps the top 60% of primitives by an image-free significance score; guarantees are relative to that pruned model, which costs 0.082 dB on Mip-NeRF 360.Pruning uses camera poses and intrinsics without pixels or subsequent fine-tuning.Source: §4.1 · p. 6
4.2 Hierarchy and ordering
- Retained primitives are split into five hierarchy levels, with early levels selected for spatial coverage and high importance; later-level children are sorted contiguously by parent.Each later-level primitive uses its nearest earlier-level neighbor as parent, allowing prediction by array offset rather than explicit child indices.Source: §4.2 · p. 6
4.3 Prediction and quantization
- Prediction uses a transmitted global mean for level 0 and earlier-level neighbors thereafter; rotation is represented in the parent’s tangent space, while quantization bounds the error.The decoder reproduces the encoder’s prediction from the base-precision reconstruction, which is 32× coarser than the final value.Source: §4.3 · p. 6
4.4 Bit-plane coding
- Integer residuals are coded most-significant-bit first, with coefficients ordered by attribute and significance before refinement within each bit-plane.Grouping bits with similar statistics improves entropy adaptation, while coding each plane as one stream avoids per-plane length metadata.Source: §4.4 · p. 6
4.5 Progression order and the container
- The default progression completes levels before refining precision; with G ≥ B, prefixes land on level boundaries, while G = 3 provides precision rungs at 9% more rate.The header carries tolerances, camera-domain parameters, and quantization-bound tables; Figure 2 depicts rate–distortion and byte-budgeted prefixes.Source: §4.5 · pp. 6–7, Figure 2 · p. 7
4.6 The truncation ladder
- At base precision, each delivered level has a tight per-primitive prefix bound; three-scene measurements match it to four decimals, while below-base prefixes have no claimed bound.Undelivered levels are absent rather than erroneous.Source: §4.6 · p. 7
5. Experiments
Across thirteen scenes, experiments report 15–30× compression, verify declared bounds, and test byte-budgeted progressive decoding. The results also show that rate costs vary across tolerances and attributes.
5.1 Protocol
- The evaluation uses official INRIA 3DGS-30K models for nine Mip-NeRF 360 scenes, two Tanks and Temples scenes, and two Deep Blending scenes, with methods re-rendered under one metric implementation.Nothing is trained; bound inversion and the residual loop take 0.4–1.2 seconds per scene on one A100 for the nine Mip-NeRF 360 scenes.Source: §5.1 · pp. 7–8
5.2 Rate–distortion
- PLEDGE achieves 15–30× compression across thirteen scenes and produces smaller files at 11 of 19 comparable training-free baseline operating points.The comparison is at matched quality.Source: §5.2 · p. 8
- Over four scenes, relaxing τsh cuts file size by 21% with less than 0.05 dB PSNR loss, versus 13% for τpx and 5% for τα.Degree 1–3 SH accounts for 48% of the file at τC = 0.05 but 11% at τC = 0.4, while position rises from 14% to 26%.Source: §5.2 · p. 8
5.3 Verifying the declared bounds
- All 585 parameter-space checks met their declared bounds; image-space center displacement and footprint deformation reached at most 0.77τpx and 0.35·2τsh, respectively.The image-space measurements compare rasterized projected covariances for reference and decoded primitives.Source: §5.3 · p. 9
- Omitting the off-axis factor violates the footprint bound; including it costs 1.7% of the rate on average.The factor sec ϕJ ranges from 1.13 on bonsai to 1.61 on train.Source: §5.3 · p. 9
5.4 Progressive decoding
- Across nine Mip-NeRF 360 scenes, test-split PSNR rises monotonically at ten sampled budgets, from 14.7 dB at 10% of the stream to 26.9 dB at full size.At 50% of the file, the mean gap to full decode is 2.0 dB and the worst gap is 3.9 dB.Source: §5.4 · p. 9
6. Limitations and conclusion
PLEDGE's guarantees have a defined scope: they are relative to the pruned model and declared camera domain, with distinct boundaries for footprint and color. Within that scope, its per-primitive bounds hold throughout valid progressive decoding.
Limitations and conclusion
- Guarantees are relative to the pruned model and declared camera domain; footprint bounds cover rasterized footprints, not exact perspective silhouettes.Composited color is bounded only at fixed geometry and opacity.Source: §6 · p. 9
- Within its stated scope, PLEDGE provides interpretable per-primitive bounds across a camera domain and throughout valid progressive decoding.Source: §6 · p. 9
- Improved residual coders can be incorporated without changing the bound derivation because the bounds are independent of prediction and entropy coding.Source: §6 · p. 9