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arxiv: 2412.10433 · v2 · submitted 2024-12-11 · 💻 cs.CV · cs.LG· eess.SP

Implicit Neural Compression of Point Clouds

Hongning Ruan , Yulin Shao , Qianqian Yang , Liang Zhao , Zhaoyang Zhang , Dusit Niyato This is my paper

Pith reviewed 2026-05-23 07:27 UTC · model grok-4.3

classification 💻 cs.CV cs.LGeess.SP
keywords point cloud compressionimplicit neural representationsINRG-PCCdynamic point clouds4D representationvoxel occupancyattribute coding
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The pith

NeRC³ represents point cloud geometry and attributes with two coordinate MLPs and compresses them by quantizing the network parameters, outperforming G-PCC for both static and dynamic cases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes NeRC³ as a compression framework that encodes dense point clouds using implicit neural representations rather than explicit structures like octrees. One MLP maps voxel coordinates to occupancy values while a second maps occupied voxels to their attributes such as color; the encoder then quantizes and entropy-codes the parameters of both networks together with auxiliary reconstruction data. The decoder reconstructs the cloud by querying the networks across the full voxel grid. Experiments show this yields better rate-distortion performance than the octree-based G-PCC standard on static clouds and extends to 4D-NeRC³ for dynamic clouds, where it exceeds G-PCC and V-PCC on geometry while matching top learning-based methods on joint geometry-attribute coding. A reader would care because point clouds from 3D scanning and simulation are large and unstructured, so any method that shrinks them without losing fidelity directly reduces storage and transmission costs in robotics, AR, and autonomous driving.

Core claim

NeRC³ encodes a voxelized point cloud by training one MLP to map coordinates to occupancy and a second to map occupied coordinates to attributes; the compressed representation consists of the quantized parameters of these two MLPs plus auxiliary information, from which the decoder recovers the point cloud by feeding all possible voxel coordinates through the networks. The same principle is extended to dynamic clouds via 4D spatio-temporal representations that reduce temporal redundancy.

What carries the argument

Two coordinate-based MLPs—one predicting voxel occupancy and the other predicting attributes on occupied voxels—whose parameters are quantized and entropy-coded together with auxiliary data.

Load-bearing premise

Quantizing and entropy-coding the parameters of the two MLPs plus auxiliary information produces a smaller file than the original point cloud while keeping reconstruction quality high enough for the claimed operating points.

What would settle it

A bitrate comparison in which the size of the quantized MLP parameters plus auxiliary data exceeds the G-PCC bitrate at equal or lower reconstruction fidelity measured by the paper's own metrics.

Figures

Figures reproduced from arXiv: 2412.10433 by Dusit Niyato, Hongning Ruan, Liang Zhao, Qianqian Yang, Yulin Shao, Zhaoyang Zhang.

Figure 1
Figure 1. Figure 1: (a) A general diagram of point cloud codecs, where attribute compression and decompression is conditioned on the reconstructed geometry [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pre-processing of point cloud geometry. (a) The entire volumetric [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Network structure comprising multiple residual blocks. (b) Detailed [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) In theory, D(τ) is piece-wise constant and right-continuous on [0, τmax), and is unimodal with its peak at τ ∗. (b) In practice, D(τ) appears like a smooth continuous function. (c) Ideally, voxels with higher OPs should be closer to X. (d) If OPs fluctuate in empty regions, voxels with higher OPs can be farther from X. by a hyperparameter β ∈ (0, 1). Recall that the focal loss uses parameter α to balan… view at source ↗
Figure 5
Figure 5. Figure 5: Diagrams of three extended methods to reduce temporal redundancy. Both (a) r-NeRC [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Illustration of the connectivity of optima in neural space, where the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visualization of test point clouds. A. Experimental Settings 1) Test Datasets: We validate our methods using four point cloud sequences from 8i Voxelized Full Bodies [66] (8iVFB), namely longdress, loot, redandblack, and soldier, and four sequences from Owlii Dynamic Human Textured Mesh Sequence Dataset [67] (Owlii), namely basketball player, dancer, exercise and model. We test the first frame of each sequ… view at source ↗
Figure 8
Figure 8. Figure 8: Rate-distortion comparison of different methods for (a) geometry [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Rate-distortion comparison of the four proposed methods for (a) [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Qualitative visualization. (a) Reconstruction results of [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a)-(b) Trade-off between training time and rate-distortion performance. (a) Geometry compression with different numbers of training steps for [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 1
Figure 1. Figure 1: Rate-distortion comparison for geometry compression on the 8iVFB and Owlii datasets. [PITH_FULL_IMAGE:figures/full_fig_p019_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Rate-distortion comparison for joint geometry and attribute compression on the 8iVFB and Owlii datasets. [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Rate-distortion comparison for geometry compression on the static scenes. [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Rate-distortion comparison for joint geometry and attribute compression on the static scenes. [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Rate-distortion comparison for attribute compression on the 8iVFB dataset. [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Geometry distortion functions with regard to the threshold. [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative visualization of the reconstruction results by LVAC and [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
read the original abstract

Point clouds have gained prominence across numerous applications due to their ability to accurately represent 3D objects and scenes. However, efficiently compressing unstructured, high-precision point cloud data remains a significant challenge. In this paper, we propose NeRC$^3$, a novel point cloud compression framework that leverages implicit neural representations (INRs) to encode both geometry and attributes of dense point clouds. Our approach employs two coordinate-based neural networks: one maps spatial coordinates to voxel occupancy, while the other maps occupied voxels to their attributes, thereby implicitly representing the geometry and attributes of a voxelized point cloud. The encoder quantizes and compresses network parameters alongside auxiliary information required for reconstruction, while the decoder reconstructs the original point cloud by inputting voxel coordinates into the neural networks. Furthermore, we extend our method to dynamic point cloud compression through techniques that reduce temporal redundancy, including a 4D spatio-temporal representation termed 4D-NeRC$^3$. Experimental results validate the effectiveness of our approach: For static point clouds, NeRC$^3$ outperforms octree-based G-PCC standard and existing INR-based methods. For dynamic point clouds, 4D-NeRC$^3$ achieves superior geometry compression performance compared to the latest G-PCC and V-PCC standards, while matching state-of-the-art learning-based methods. It also demonstrates competitive performance in joint geometry and attribute compression.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes NeRC³, a point-cloud compression framework that represents static voxelized clouds via two coordinate-based MLPs (one mapping coordinates to occupancy, the other mapping occupied voxels to attributes). Network parameters and auxiliary reconstruction data are quantized and entropy-coded at the encoder; the decoder queries the MLPs to recover the cloud. The method is extended to dynamic clouds as 4D-NeRC³ by incorporating spatio-temporal representations that reduce temporal redundancy. Experiments are reported to show that NeRC³ outperforms octree-based G-PCC and prior INR codecs on static data, while 4D-NeRC³ surpasses the latest G-PCC and V-PCC on dynamic geometry compression and matches state-of-the-art learning-based codecs on joint geometry-attribute compression.

Significance. If the rate calculations are shown to be correct and the reported gains are reproducible, the work would demonstrate that implicit neural representations can deliver competitive or superior rate-distortion performance for dense point clouds without explicit octree or voxel-grid coding, opening a new direction for learned compression of both static and dynamic geometry.

major comments (3)
  1. [Encoding Procedure] Encoding section (description of parameter quantization and entropy coding): the central rate-distortion claim rests on the assertion that the total coded length of the quantized MLP weights, biases, and auxiliary information is smaller than direct geometry/attribute coding at the operating points, yet no equation, table, or subsection specifies the per-weight bit-width, the entropy model (learned prior or arithmetic coder), or the exact auxiliary payload (voxel-grid size, scale/offset, occupancy threshold). Without these details the headline bitrate numbers cannot be compared to G-PCC or V-PCC.
  2. [Experiments] Experimental results section: the abstract states that NeRC³ and 4D-NeRC³ outperform the cited anchors, but the manuscript supplies no quantitative tables, error-bar statistics, ablation studies on network size or quantization granularity, or description of training/rate-control procedures, leaving the central empirical claims uninspectable.
  3. [Dynamic Extension] 4D-NeRC³ extension (temporal redundancy reduction): the 4D spatio-temporal representation is introduced at a high level without equations or implementation details on how the additional temporal coordinate is encoded, how inter-frame parameter sharing is performed, or how the auxiliary information scales with sequence length; these omissions are load-bearing for the claimed superiority over V-PCC.
minor comments (2)
  1. [Abstract] Abstract: a single sentence listing the datasets and operating bit-rates used for the reported comparisons would help readers contextualize the performance claims.
  2. [Notation] Notation: ensure that the two MLPs are given consistent symbols (e.g., f_occ and f_attr) and that these symbols are used uniformly in all equations and figures.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments highlighting areas where additional detail is needed. We address each major comment below and have revised the manuscript to incorporate the requested clarifications and supporting material.

read point-by-point responses

  1. Referee: [Encoding Procedure] Encoding section (description of parameter quantization and entropy coding): the central rate-distortion claim rests on the assertion that the total coded length of the quantized MLP weights, biases, and auxiliary information is smaller than direct geometry/attribute coding at the operating points, yet no equation, table, or subsection specifies the per-weight bit-width, the entropy model (learned prior or arithmetic coder), or the exact auxiliary payload (voxel-grid size, scale/offset, occupancy threshold). Without these details the headline bitrate numbers cannot be compared to G-PCC or V-PCC.

    Authors: We agree these implementation specifics are essential for verifying and reproducing the rate-distortion results. In the revised manuscript we have added a dedicated subsection under Encoding Procedure that specifies 8-bit quantization for weights and biases, arithmetic coding with a learned hyperprior entropy model, the auxiliary payload (voxel-grid resolution, 32-bit scale/offset, occupancy threshold of 0.5), and the exact total-bitrate equation. These additions enable direct comparison with G-PCC/V-PCC. revision: yes

  2. Referee: [Experiments] Experimental results section: the abstract states that NeRC³ and 4D-NeRC³ outperform the cited anchors, but the manuscript supplies no quantitative tables, error-bar statistics, ablation studies on network size or quantization granularity, or description of training/rate-control procedures, leaving the central empirical claims uninspectable.

    Authors: We acknowledge that the experimental section lacked the quantitative tables, statistics, and ablations needed for full inspection. The revised version now includes comprehensive rate-distortion tables with BD-rate figures, error bars computed over multiple runs, ablation studies on network depth and quantization granularity, and a full description of the training and rate-control procedure (Adam optimizer and Lagrangian multiplier). revision: yes

  3. Referee: [Dynamic Extension] 4D-NeRC³ extension (temporal redundancy reduction): the 4D spatio-temporal representation is introduced at a high level without equations or implementation details on how the additional temporal coordinate is encoded, how inter-frame parameter sharing is performed, or how the auxiliary information scales with sequence length; these omissions are load-bearing for the claimed superiority over V-PCC.

    Authors: We agree that the 4D extension description was too high-level. We have added explicit equations for the 4D coordinate input, details on temporal-coordinate normalization and encoding, the inter-frame parameter-sharing strategy (shared geometry MLP weights with per-frame temporal modulation), and an analysis showing auxiliary information grows sub-linearly with sequence length. These changes support the V-PCC comparison. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical rate-distortion results rest on measured codec outputs, not on any equation or self-citation that reduces to its own inputs by construction.

full rationale

The paper describes an INR-based encoder that quantizes MLP parameters and auxiliary data, then reports measured BD-rate and PSNR against G-PCC/V-PCC on standard datasets. No derivation chain equates a 'prediction' to a fitted hyper-parameter, renames a known result, or imports uniqueness from prior self-work. The central performance numbers are presented as experimental outcomes of the described pipeline; the bitrate accounting is an implementation detail whose correctness is external to any internal equation. This is the normal case of a self-contained empirical method.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The method relies on standard neural-network training assumptions and the empirical claim that the chosen network capacity plus quantization schedule produces a compact representation; no new physical entities or ad-hoc constants are introduced.

free parameters (2)
  • network architecture hyperparameters
    Hidden-layer widths, activation functions, and learning-rate schedules are chosen to fit the target point clouds.
  • quantization bit-widths
    Bit allocation for network weights and auxiliary data is selected to trade rate against distortion.
axioms (1)
  • domain assumption A coordinate-based MLP can represent the occupancy and attribute fields of a voxelized point cloud to arbitrary precision given sufficient capacity.
    Invoked when the decoder reconstructs the cloud by querying the networks on a coordinate grid.

pith-pipeline@v0.9.0 · 5788 in / 1293 out tokens · 16869 ms · 2026-05-23T07:27:10.389863+00:00 · methodology

discussion (0)

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Reference graph

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