Compression-Oriented Voxelization Network

• The paper introduces a unified framework that treats voxelization as an integral part of coding, using learnable components to optimize bitrate and reconstruction fidelity.
• It details multiple strategies including block-based TSDF autoencoders, octree-conditioned context models, and codec-aware preprocessing for efficient 3D data compression.
• Empirical results demonstrate significant gains, with bitrate reductions up to 66% and enhanced PSNR outcomes through targeted entropy modeling and adaptive voxelization.

A compression-oriented voxelization network is a voxel-domain representation and prediction system whose voxelization strategy, feature hierarchy, and entropy model are selected to reduce coding rate for a prescribed reconstruction fidelity. In the recent literature, the term covers both explicitly neural models and algorithmic modules that can be interpreted as learnable voxelization components: block-based TSDF autoencoders, octree-conditioned voxel context models, coordinate-based implicit fields over voxelized point clouds, adaptive voxelization for 3D Gaussian splatting, and learned preprocessors placed in front of legacy codecs such as G-PCC (Tang et al., 2020, Ruan et al., 2024, Wang et al., 30 May 2025, Ma et al., 3 Aug 2025).

1. Conceptual scope

Within contemporary 3D compression research, the defining property of a compression-oriented voxelization network is not merely that it uses voxels, but that voxelization itself is treated as part of the coding problem. Some systems directly learn a compact representation from voxel blocks, as in TSDF compression with a 3D convolutional encoder–decoder and explicit entropy modeling (Tang et al., 2020). Others retain a voxelized or octree-voxel domain but learn the occupancy or attribute field implicitly through network parameters, so that the parameters become the compressed representation (Ruan et al., 2024). A different line of work uses voxelization as a preprocessing transform for an existing codec, making the point cloud easier for that codec to encode while leaving the decoder unchanged (Ma et al., 3 Aug 2025).

The concept also extends beyond strict voxel occupancy coding. In adaptive voxelization for 3D Gaussian splatting, voxelization is designed as a pre-transform for coding rather than as a rendering representation, with octree depth chosen by compression-relevant criteria such as Gaussian volume, density, and distance to the voxel center (Wang et al., 30 May 2025). This suggests that the central idea is better understood as a design objective—optimizing discretization for bitrate and distortion—than as a single network topology.

2. Representational substrates and voxelization strategies

Compression-oriented voxelization has been instantiated over several 3D substrates. In volumetric capture, the substrate is a truncated signed distance field on a uniform grid. "Deep Implicit Volume Compression" operates on non-overlapping TSDF blocks $x \in \mathbb{R}^{k \times k \times k}$, with only occupied blocks—those containing a zero crossing—being processed and transmitted; the reported operating point uses $k=8$ (Tang et al., 2020). In point cloud compression, voxelization is usually tied to octree levels, so that a node at depth $r$ corresponds to a voxel at resolution $r$; this is the basis of local voxel contexts in VoxelContext-Net and of hybrid octree-voxel coding in VoxelDNN-style systems (Que et al., 2021, Nguyen et al., 2020).

A second strategy is to retain a regular voxel domain but restrict computation to spatially relevant regions. The implicit neural representation framework of "Point Cloud Compression with Implicit Neural Representations: A Unified Framework" voxelizes the point cloud at $N$-bit resolution, partitions the space into $2^T \times 2^T \times 2^T$ cubes, and processes only voxels within non-empty cubes $\mathcal{W}$ (Ruan et al., 2024). This removes the need to evaluate networks over the full $2^N \times 2^N \times 2^N$ grid.

A third strategy is adaptive voxelization. For 3D Gaussian splatting, uniform voxelization is described as inefficient because Gaussian distributions are highly non-uniform and Gaussians have unequal rendering impact. The adaptive octree in (Wang et al., 30 May 2025) refines to $J_{\text{high}}$ for the largest $v\%$ Gaussians, initializes other regions at $k=8$0, and further subdivides according to thresholds on local count $k=8$1 and distance to the voxel center $k=8$2. For sparse LiDAR compression, the stage-wise and level-wise Space-to-Channel models preserve a multilevel voxelization, but replace fine spatial refinement with channel-domain refinement and, at high levels, with Geometry Residual Coding on a fixed lower-resolution grid (Liu et al., 24 Mar 2025).

Hybridization across representations is another recurrent pattern. PIVOT-Net explicitly allocates coarse bits to a tree representation, middle bits to voxel-domain processing, and fine bits to point-based networks, arguing that the optimal representation changes with bit depth and point density (Pang et al., 2024). A plausible implication is that compression-oriented voxelization is often most effective as one component of a heterogeneous hierarchy rather than as a universal representation for all geometric scales.

3. Architectural families

One major family is the block-based neural transform codec. In TSDF compression, the encoder is a 3D convolutional network with three stride-2 convolutional layers, the decoder mirrors it with three transposed-convolution layers, and the decoder has two heads: one for TSDF magnitudes and one for sign probabilities (Tang et al., 2020). The reconstruction is

$k=8$3

where the sign field $k=8$4 is decoded losslessly from a separate bitstream. The block factorization keeps the model under approximately $k=8$5 MB and supports independent block coding and streaming (Tang et al., 2020).

A second family is the voxel-context entropy model. VoxelContext-Net extracts a binary local voxel neighborhood $k=8$6 around each octree node, uses 3D convolutions to derive a feature, concatenates the node coordinate and depth, and predicts a categorical distribution over the 256 possible 8-bit child occupancy patterns (Que et al., 2021). Related octree-context systems include NNOC and fNNOC, which encode candidate voxel occupancies with an MLP conditioned on a $k=8$7 template, and sequence-optimized CNN models that code 2-by-2 voxel groups as 16-way symbols in four phases (Kaya et al., 2021, Kaya et al., 2022). In these systems, voxelization is local and causal: the neighborhood is defined so that the decoder can reconstruct the same context during arithmetic decoding.

A third family represents voxelized geometry implicitly. The unified implicit framework uses two coordinate-based MLPs, $k=8$8 for occupancy and $k=8$9 for attributes, both fed by positional-encoded voxel coordinates and trained per point cloud; the quantized parameters are entropy-coded with DeepCABAC (Ruan et al., 2024). Here the network parameters themselves form the compressed object representation.

A fourth family uses sparse convolutional feature hierarchies whose purpose is to reshape geometry before or during coding. PIVOT-Net places sparse CNNs and an Enhanced Voxel Transformer on the middle bit range of a point cloud, using context-aware upsampling to reconstruct finer voxel occupancy from compressed features (Pang et al., 2024). The Space-to-Channel model goes further by folding sub-voxel occupancy into channels and decoding those channels autoregressively, thereby avoiding repeated spatial upsampling and preserving a larger world-space receptive field at high levels (Liu et al., 24 Mar 2025).

A fifth family learns voxelization as codec-aware preprocessing. In (Ma et al., 3 Aug 2025), a sparse CNN based on SConvBlock and SInceptionResNet performs global scaling, fine-grained pruning, and point-level editing before standard G-PCC coding. A differentiable surrogate of G-PCC supplies gradients, but only the lightweight voxelization network is used at inference; the decoder remains the standard G-PCC decoder (Ma et al., 3 Aug 2025).

4. Optimization objectives, entropy models, and error control

Most compression-oriented voxelization networks are trained under an explicit or implicit rate objective. In TSDF compression, the joint objective is

$r$0

with a masked distortion term that emphasizes voxels near zero crossings, a learned prior over quantized latents, and a cross-entropy proxy for sign bitrate (Tang et al., 2020). The lossless sign stream is not an auxiliary detail: it preserves the sign configuration used by marching cubes and therefore preserves surface topology while bounding the reconstruction error by the voxel size (Tang et al., 2020).

In implicit voxelized point cloud coding, rate is often approximated through parameter sparsity rather than an explicit latent entropy model. The occupancy and attribute networks in (Ruan et al., 2024) are trained with reconstruction terms plus $r$1-regularization on network parameters, and the quantized weights are later entropy-coded with DeepCABAC. This formulation is explicitly described as conceptually similar to a rate–distortion objective, with $r$2 acting as a surrogate for rate (Ruan et al., 2024).

Codec-aware preprocessing returns to a classical Lagrangian form. The differentiable G-PCC surrogate of (Ma et al., 3 Aug 2025) uses

$r$3

where $r$4 is an occupancy-domain distortion between the original and preprocessed geometry, and $r$5 is a surrogate cross-entropy term approximating G-PCC coding cost. Hard voxel decisions are implemented with a straight-through rounding operator, so occupancy is binary in the forward pass but differentiable in training (Ma et al., 3 Aug 2025).

High-bit-depth sparse geometry introduces another variant. In Geometry Residual Coding for LiDAR, the residual child index $r$6 at each fine level is predicted by the Residual Probability Approximation module, and training minimizes cross-entropy over the residual symbol distribution (Liu et al., 24 Mar 2025). This reformulates late octree refinement as residual classification at fixed spatial resolution, which addresses the receptive-field collapse of ordinary voxel upsampling (Liu et al., 24 Mar 2025).

5. Empirical behavior across domains

In TSDF-based dynamic human capture, the block-based neural codec of (Tang et al., 2020) reports a bitrate reduction of $r$7 for the same distortion, or a distortion reduction of $r$8 for the same bitrate, relative to the stated state of the art. The same work reports that conditional sign coding reduces sign data to approximately $r$9 KB per volume, compared with approximately $r$0 KB raw and approximately $r$1 KB under a naive global-probability sign model (Tang et al., 2020).

In standardized point cloud coding, learned voxelization as preprocessing produces particularly large gains. The G-PCC surrogate framework of (Ma et al., 3 Aug 2025) reports an average BD-rate reduction of $r$2 over G-PCC in D1 PSNR and $r$3 in D2 PSNR, while requiring no decoder modification. The average voxelization time is reported as approximately $r$4 s on CPU or $r$5 s on GPU per frame, and the decoder cost remains that of vanilla G-PCC (Ma et al., 3 Aug 2025).

For 3D Gaussian splatting, adaptive voxelization yields more moderate but still explicit rate–distortion gains. On Playroom and Truck, (Wang et al., 30 May 2025) reports Bjontegaard bitrate savings of approximately $r$6 with negligible PSNR gains of $r$7 dB, and states that the simplified voxelization criteria reduce runtime by approximately $r$8 relative to explicit Wasserstein barycenter computation. The same work reports that with its initialization, about $r$9K iterations suffice to reach near ground-truth PSNR, compared with $N$0K iterations without the special initialization (Wang et al., 30 May 2025).

Lossless point cloud geometry coding has produced a broad range of voxel-based gains over G-PCC. VoxelDNN reports average rate savings of $N$1 over MPEG G-PCC on MVUB and MPEG datasets (Nguyen et al., 2020). MSVoxelDNN reports average rate savings over G-PCC of $N$2 while significantly reducing encoding and decoding times relative to VoxelDNN through multiscale grouped prediction (Nguyen et al., 2021). VoxelContext-Net reports BDBR reductions of $N$3 on ScanNet and $N$4 on Semantic KITTI for static compression, and $N$5 for dynamic compression on Semantic KITTI when temporal voxel context is added (Que et al., 2021). Sequence-optimized CNN coding reports average sequence bitrates of about $N$6 bpp on MVUB and about $N$7 bpp on 8i, compared with approximately $N$8 bpp and $N$9 bpp for TMC13, respectively (Kaya et al., 2022).

For dense and sparse voxel codecs built around Space-to-Channel modeling, (Liu et al., 24 Mar 2025) reports $2^T \times 2^T \times 2^T$0 bpp on average for dense point clouds, compared with $2^T \times 2^T \times 2^T$1 bpp for SparsePCGC and $2^T \times 2^T \times 2^T$2 bpp for G-PCC. On KITTI and Ford at high bit rates, the same work reports bit savings of about $2^T \times 2^T \times 2^T$3 and $2^T \times 2^T \times 2^T$4 over SparsePCGC, together with encoding-time reductions of $2^T \times 2^T \times 2^T$5 (Liu et al., 24 Mar 2025).

6. Misconceptions, limitations, and open directions

A common misconception is that compression-oriented voxelization is synonymous with dense global voxel grids. The literature repeatedly avoids that formulation: TSDF coding transmits only occupied blocks (Tang et al., 2020), implicit occupancy networks evaluate only voxels inside non-empty cubes (Ruan et al., 2024), octree methods use local voxel neighborhoods around existing nodes (Que et al., 2021), and G-PCC preprocessing operates on sparse tensors aligned with occupied octree nodes (Ma et al., 3 Aug 2025). This suggests that the “voxelization” in the term is often sparse, blockwise, or hierarchical rather than globally volumetric.

A second misconception is that uniform voxelization is always a neutral preprocessing step. The 3DGS study (Wang et al., 30 May 2025) explicitly argues that uniform voxelization is inefficient for highly non-uniform Gaussian distributions, because it overspends bits in dense regions of small Gaussians and can under-resolve large high-impact Gaussians. The high-bit-depth S2C work reaches a similar conclusion from a different angle: ordinary voxel upsampling causes receptive-field collapse at fine levels, especially on sparse LiDAR data (Liu et al., 24 Mar 2025).

A third point of tension concerns where learning should reside. Some methods push learning into the core codec, which can yield strong rate gains but may increase decoder complexity or require per-instance optimization; (Ruan et al., 2024) trains networks per point cloud, and (Kaya et al., 2022) trains a CNN as part of sequence encoding. Others deliberately keep the decoder classical and deterministic, using learning only on the encoder side; (Ma et al., 3 Aug 2025) is explicit about this choice. This suggests a persistent trade-off between end-to-end optimality and deployment constraints such as interoperability, reproducibility, and decoder simplicity.

Several limitations recur across the literature. TSDF compression in (Tang et al., 2020) processes each frame independently and does not exploit temporal redundancy. Adaptive voxelization for 3DGS in (Wang et al., 30 May 2025) still relies on hand-crafted heuristics and encoder-side fine-tuning. Implicit voxelized point cloud coding in (Ruan et al., 2024) incurs heavy per-instance training cost. S2C and GRC models improve receptive field, but their receptive field remains finite and their coordinate-system choices are domain-specific (Liu et al., 24 Mar 2025). A plausible implication is that future work will continue to couple adaptive voxelization, stronger entropy surrogates, and heterogeneous representations rather than converging on a single canonical architecture.