Efficient Compression of Structured and Unstructured Volumes via Learned 3D Gaussian Representation

1 INTRODUCTION

• Prior unstructured INRs compress scalar fields but omit mesh geometry, so downstream sampling still requires storing some uncompressed geometry.The paper notes that traditional compression can reduce data size but requires decompression before use, adding latency and memory usage.Source: §1 · p. 1
• Directly sampled Gaussian primitives represent the volume’s scalar field by averaging the values of Gaussians intersecting each sample location.Using fewer Gaussians than ground-truth data points reduces memory while preserving direct sampling.Source: §1 · p. 2
• The explicit Gaussian model encodes unstructured volume geometry, avoiding the mesh storage required by prior approaches and removing their hard cap on compression ratios.The model can represent data with arbitrarily small compressed models by allowing some lossiness in domain representation.Source: §1 · pp. 1–2
• 1.52× faster training than the fastest INR on average, with reconstruction quality equivalent to models that take much longer to train.The model uses CUDA-accelerated sampling for structured and unstructured data.Source: §1 · p. 2
• 1.60× higher PSNR and 6.97× faster training than unstructured INRs across compression ratios and datasets.The paper attributes improved reconstruction quality, particularly for unstructured volumes, to sampling-error based densification.Source: §1 · p. 2

2.1 Neural Representations for Volume Data

• Neural representations estimate a volume’s scalar field, and unstructured extensions cluster data points into separate networks; these approaches do not encode mesh geometry.The paper’s explicit model instead allows adaptive Gaussian allocation and can encode mesh geometry, while skipping the clustering steps used by UGINR and MCINR.Source: §2.1 · p. 2

2.2 Novel View Synthesis for Volume Visualization

• Novel-view-synthesis methods train on rendered images to produce renderings from unseen viewpoints and other rendering parameters, rather than compressing volume data directly.Prior work includes 3D Gaussian methods, with VEG replacing per-Gaussian color and opacity with scalar values that learn the volume more directly.Source: §2.2 · p. 2
• The paper applies VEG to volume compression, enabling use for tasks supported by the original data rather than only rendering in a specific configuration.The original VEG benchmarks took 10–20 minutes on Chameleon, RBL, and Mito, compared with less than a minute for this method.Source: §2.2 · pp. 2–3

2 RELATED WORK

• Structured volumes define scalar fields on regular grids, whereas unstructured volumes require explicit geometry.Figure 2 contrasts their sampling setups.Source: Figure 2 · p. 3

3 PRELIMINARIES

• The preliminaries frame the paper’s focus as adapting volume encoding Gaussians for volume sampling after reviewing data types and the representation.They also introduce image-space I-VEG as a model family to test for volume reconstruction.Source: §3 · p. 3

3.1 Volume Types

• Structured volumes define scalar values on a regular grid with implicit geometry, whereas unstructured volumes require explicit geometry and cell lookup for sampling.Unstructured domains can have arbitrary geometry and nonuniform spatial complexity.Source: §3.1 · p. 3

3.2 Volume Encoding Gaussians

• W-VEG represents a scalar field with 3D Gaussians whose parameters include mean, covariance, scalar value, and weight.Unlike traditional 3D Gaussians, these use trainable scalar values and weights rather than colors and opacities.Source: §3.2 · p. 3
• The method estimates volume samples in 3D by normalized weighted aggregation of intersecting Gaussians, rather than rendering images.Gaussian weights let training increase or reduce each Gaussian’s influence.Source: §3.2 · p. 3

3.3 Testing Image-Trained VEG

• Image-trained I-VEG models yield volumetric PSNRs of 19.8 for Chameleon and 23.0 for Vortex when sampled onto a 512^3 grid.Scaling Gaussian extents and weights did not improve reconstruction quality.Source: §3.3 · p. 3

4 STRUCTURED VOLUME RECONSTRUCTION

• The structured-volume method adapts a tile-based 2D rasterizer to test Gaussian-sample intersections with CUDA-accelerated sampling.The section also introduces a training pipeline and techniques for optimizing W-VEG models.Source: §4 · pp. 3–4
• The forward pass finds Gaussian bounding boxes, organizes Gaussian-block intersections, and estimates samples; the backward pass computes loss and accumulates Gaussian gradients.Figure 4 illustrates these steps on a 10×12 dataset using blocks of 2×2 cells.Source: Figure 4 · p. 4
• The illustration treats 0-valued cells as empty space while showing how gradients could improve the Gaussians in the next iteration.Source: Figure 4 · p. 4

4.1 Structured Volume Implementation

• The implementation extends 3DGS to voxel rasterization on a regular 3D grid, with a differentiable sampling process and custom backward pass.Source: §4.1 · p. 4

4.1.1 Finding Gaussian Bounding Boxes

• Gaussian influence cutoffs define ellipsoids that are converted to grid-block AABBs, while precomputed inverse covariance matrices reduce sampling work.The evaluation uses τ1 = 0.01 as a tradeoff between fewer unnecessary intersections and maintained accuracy.Source: §4.1.1 · p. 4

4.1.2 Writing Gaussian-Block Intersections

• The intersection pipeline organizes Gaussian-block pairs by block ID and parallelizes work over intersections to improve workload balance.The authors report that atomically counting and writing intersections performed worse than the sort-based method.Source: §4.1.2 · p. 4

4.1.3 Estimating Samples

• Each cell accumulates Gaussian influence and weighted values from its block’s intersection list, with blocks cooperatively loading Gaussian data.Source: §4.1.3 · p. 4

4.1.4 Accumulating Gaussian Gradients

• Grouped Gaussian-block intersections let each Gaussian sum cell gradients before a global atomic update, reducing atomic operations by a factor of the volume block size.The figure contrasts sample-error densification, which places new Gaussians at high-error samples, with gradient duplication and low-weight relocation.Source: §4.1.4 · pp. 4–5, Figure 5 · p. 5

4.2 Structured Volume Training

• Training repeatedly samples W-VEG, computes L1 reconstruction loss against ground truth, and backpropagates gradients to Gaussian parameters.Sigmoid activations constrain values and weights to [0,1), while a soft scale cap reduces workload imbalance.Source: §4.2 · p. 5

4.2.1 Densification

• Densification adapts 3DGS world-space positional gradients, MCMC relocation, and sample-error selection; pruning removes Gaussians below a weight threshold of 0.005.MCMC relocation divides the target weight among the Gaussians at that position to preserve Equation 2's output.Source: §4.2.1 · p. 5
• Sample-error densification adds Gaussians at the k highest-error samples, prioritizes false negatives, and is limited to the target compression ratio as pruning frees slots.Densification is applied every 100 iterations after iteration 500.Source: §4.2.1 · p. 5, §4.2.2 · p. 6

4.2.2 Preventing False Negatives

• False negatives are source-defined positions with no influencing Gaussian, so ordinary reconstruction loss cannot directly correct them.The loss operates on samples contributed to by Gaussians; at false-negative positions, none contribute.Source: §4.2.2 · p. 5
• In the unstructured sampling illustration, a Gaussian’s AABB traverses a sample-position BVH, accumulates weighted values at intersecting positions, and normalizes by accumulated influence.The illustrated example samples at each cell center.Source: Figure 7 · p. 6
• Random positions within each cell discourage overfitting to cell centers, while a false-negative loss discourages influence from falling below the cutoff.With a proper λFN, the loss prevents Gaussian influence from dropping when that would create a false negative.Source: §4.2.2 · p. 6

5 UNSTRUCTURED VOLUME RECONSTRUCTION

• Unstructured volumes require variable-density sampling and inside-volume tests, and model sampling can produce false positives outside the original geometry.Earlier approaches assume samples are inside the volume and require storing its exterior surface for arbitrary sampling or intersection testing.Source: §5 · p. 6, §5.2 · p. 6

5.1 Unstructured Volume Implementation

• A Gaussian-side BVH is less performant when Gaussian overlap is high and sample counts greatly exceed Gaussian counts.The implementation instead builds a BVH over sample positions and queries it with each Gaussian.Source: §5.1 · p. 6

5.1.1 Creating BVH

• The implementation builds a BVH over sample positions with adaptive spatial-median splits; 256 primitives per leaf are used in the evaluation.Larger leaves improve BVH build time and parallelism, despite potentially increasing unnecessary intersection checks.Source: §5.1.1 · p. 6

5.1.2 Estimating Samples

• A warp per Gaussian cooperatively traverses the sample-position BVH, accumulates contributions at intersecting samples, then normalizes by accumulated influence.The backward pass reuses the BVH and computes per-Gaussian gradients through cooperative traversal and warpwide reduction.Source: §5.1.2 · p. 6

5.2 Preventing False Positives

• Gaussian influence directly defines the represented domain, eliminating the need to store unstructured-volume geometry; matching the domain more precisely can require more Gaussians for the same reconstruction quality.False-positive penalties reduce influence outside the original volume but can increase false negatives; the tradeoff supports high compression when surface storage is costly.Source: §5.2 · pp. 6–7

6 EVALUATION

• The evaluation compares reconstruction quality and training time across structured and unstructured datasets at multiple compression ratios, plus densification strategies.Training used an NVIDIA A100 GPU, and reported model sizes exclude file compression.Source: §6 · p. 7

6.1 Structured Volume Evaluation

• 37.76, 38.04, and 38.08 average PSNR for IVNR 200k, AMGSRN, and W-VEG respectively; W-VEG is 14.91× and 17.48× faster than IVNR 200k and AMGSRN.W-VEG took 1.52× less time than IVNR 20k on average, but did not train faster on every structured benchmark.Source: §6.1 · p. 7
• W-VEG outperformed IVNR 200k on Richtmyer, where complexity clusters on the mixing surface, but lost on Miranda, where complexity is uniform.AMGSRN also performed well on Richtmyer, likely because its adaptive feature grids fit high-error regions.Source: §6.1 · pp. 7–8, Figure 8 · p. 7

6.2 Unstructured Volume Evaluation

• W-VEG achieved the best reconstruction quality and training time against UGINR on every studied dataset when encoding only scalar fields.Its average PSNR gain was 33.81 on smaller datasets and 3.13 on Valley and Earthquake; UGINR could not run on Impact.Source: §6.2 · p. 8, Table 2 · p. 8
• W-VEG+S raised real compression ratios by an average of 18× and up to 135×, with marginally worse reconstruction quality and training time than W-VEG.Its training time beat UGINR except on RBL, and its PSNR was higher except on Earthquake at 1024× compression.Source: §6.2 · p. 8, Table 2 · p. 8
• Only W-VEG+S produced reasonable 1024× Mito and Earthquake renderings without exterior-surface testing, demonstrating sampling without mesh storage.The comparison includes UGINR, W-VEG, and W-VEG+S, with and without intersection testing.Source: §6.2 · p. 9, Figure 9 · p. 9

6.3 Densification

• Error-based densification gave the highest reconstruction quality on all four tested datasets, with larger gaps over alternatives on unstructured data.3DGS ranked second in accuracy, while 3DGS and MCMC added training overhead from synchronization or sampling operations.Source: §6.3 · p. 9, Table 3 · p. 9

• The method trains explicit 3D Gaussian models with efficient sampling, domain-encoding losses, and error-based densification for volume compression.The representation encodes mesh geometry and removes the prior hard cap on compression ratios imposed by mesh storage.Source: §7 · p. 9
• The authors report competitive reconstruction quality with faster training than state-of-the-art neural methods, and stronger quality and training-time results on unstructured volumes.The conclusion states that geometry encoding permits model sizes smaller than previously possible.Source: §7 · p. 9
• The evaluation of accuracy for specific visualization operations remains future work, and the method does not implement existing 3DGS disk-compression techniques.Time-varying and multivariate datasets, SDF-based domain losses, and a dedicated rendering engine are also identified as future directions.Source: §7 · p. 9

• Tables 4 and 5 list the evaluation datasets, with Table 4 sorted by total size and Table 5 reporting unstructured-volume and exterior-surface sizes.Table 5 gives counts in millions and sizes in megabytes; the appendix also identifies these dataset details as evaluation information.Source: Table 4 · p. 11, Table 5 · p. 11, A DATASET INFORMATION · p. 11

• Tables 6 and 7 provide the AMGSRN and InstantVNR configurations used in the structured-dataset comparisons.The configurations are associated with the models discussed in Section 6.1.Source: B MODEL CONFIGURATIONS · p. 11, Table 6 · p. 11, Table 7 · p. 11