LINR-PCGC: Lossless Implicit Neural Representations for Point Cloud Geometry Compression

Conference: ICCV 2025 arXiv: 2507.15686 Code: https://huangwenjie2023.github.io/LINR-PCGC/ Area: 3D Vision / Point Cloud Compression Keywords: Lossless point cloud compression, implicit neural representations, multi-scale sparse convolution, GoP coding, model compression

TL;DR

LINR-PCGC proposes the first implicit neural representation (INR)-based method for lossless point cloud geometry compression. By designing a lightweight multi-scale SparseConv network with Scale Context Extraction (SCE) and Child Node Prediction (CNP) modules, combined with a GoP-level shared decoder and initialization strategy, the method achieves a 21.21% bitrate reduction over G-PCC TMC13v23 and a 21.95% reduction over SparsePCGC on the MVUB dataset, without relying on any specific training data distribution.

Background & Motivation

Background: Point cloud compression methods fall into two categories: traditional approaches (G-PCC, V-PCC) and AI-driven approaches (PCGCv2, SparsePCGC). Traditional methods rely on hand-crafted tools and parameters, while AI-based methods exploit neural networks to model spatial correlations and achieve state-of-the-art compression performance.

Limitations of Prior Work: - AI-based methods are heavily dependent on training data distributions; distribution shift leads to significant performance degradation (e.g., SparsePCGC underperforms G-PCC on MVUB). - INR methods address the distribution dependency issue by overfitting to target data, but face two challenges: (1) the decoder network parameters must be encoded into the bitstream, constraining network size and fitting capacity; (2) overfitting is time-consuming. - Existing INR methods are limited to lossy compression; no INR solution for lossless compression exists.

Key Challenge: A fundamental tension exists between compression efficiency and distribution generalizability in AI-based methods, and between generalizability and network capacity/coding efficiency in INR methods.

Goal: How to achieve lossless point cloud geometry compression within an INR framework while controlling decoder size and encoding time?

Key Insight: The paper draws inspiration from the Group of Pictures (GoP) concept in video coding — adjacent frames share a single lightweight decoder network to amortize parameter overhead; the overfitted network from the previous GoP initializes the next GoP to accelerate convergence.

Core Idea: Reduce parameter overhead via GoP-level network sharing + achieve efficient lossless compression via multi-scale SparseConv child node prediction + save approximately 65% of encoding time through an initialization strategy.

Method

Overall Architecture

The input is a point cloud sequence \(S = \{x_1, ..., x_M\}\), grouped and encoded by GoP (GoP size T=32 frames). Encoding each GoP consists of three steps: 1. Initialization: Initialize the current GoP's network parameters using the overfitted parameters from the previous GoP. 2. Encoding: Overfit the network parameters → separate into pc-encoder and pc-decoder → encode the point cloud + quantize and compress pc-decoder parameters. 3. Decoding: Decompress pc-decoder parameters → decode the point cloud scale by scale.

The final bitstream comprises: lowest-scale point cloud coordinates + decoder network parameters + occupancy coding information at each scale.

Key Designs

1. Multi-Scale SparseConv Network:

   • Function: Progressively downsamples the point cloud until only tens to hundreds of points remain, then predicts occupancy probabilities from low to high scales.
   • Mechanism: MaxPooling is used for downsampling \(x_t^{i+1} = DS(x_t^i)\); at each scale, occupancy probabilities of child nodes are predicted and compressed via arithmetic coding.
   • Design Motivation: The multi-scale architecture allows high-scale details to leverage structural priors from lower scales, enabling progressively refined predictions.

2. Scale Context Extraction (SCE):

   • Function: Provides discriminative information for point clouds at different spatial scales.
   • Mechanism: A scale embedding (SEMB, 8-channel implicit feature expanding scale index \(i\)) serves as global information and is concatenated with neighborhood occupancy (occupancy states of 7 positions: front/back/left/right/up/down/self), then fused via MLP to generate the scale context feature \(l_t^{i+1}\).
   • Formula: \(l_t^{i+1} = MLP_i(Concat(Nb^{i+1}, SEMB(i)))\)
   • Design Motivation: Since all scales share the same set of network parameters, a mechanism is needed to inform the network of the current scale; otherwise, scale-specific spatial features cannot be extracted.

3. Child Node Prediction (CNP):

   • Function: Upsamples the point cloud from lower to higher scales, i.e., predicts octree child node occupancy.
   • Mechanism: The upsampling problem is formulated as octree child node occupancy prediction (8 channels corresponding to 8 child nodes). A channel-wise 8-stage prediction scheme is adopted — already-decoded child nodes serve as context for subsequent stages. Two modules are employed: GDFE (Global Deep Feature Extraction) for global features and LDFE (Local Deep Feature Extraction) for local features from decoded child nodes; their fusion drives occupancy probability prediction.
   • vs. Transposed Convolution: Transposed convolutions incur high memory and time complexity; CNP operates directly on the octree structure and is more efficient.
   • Design Motivation: Channel-wise sequential prediction resembles an autoregressive approach, where already-decoded child nodes provide additional context for those yet to be decoded, improving prediction accuracy.

4. Adaptive Quantization (AQ) and Model Compression (MC):

   • AQ: Normalizes decoder parameters to [0,1] and quantizes to B=8 bits.
   • MC: Adds L2 regularization during training to encourage parameters to follow a Laplacian distribution, then encodes them via arithmetic coding using the Laplacian distribution parameters (mean \(\mu\) and scale \(b\)).

Loss & Training

\[\mathcal{L} = \sum_{i=0}^{N} \sum_{j=0}^{7} L_{BCE}^{i,j} + \lambda \|\boldsymbol{\theta}\|_2^2\]

• \(L_{BCE}^{i,j}\) is the binary cross-entropy at scale \(i\), stage \(j\), estimating the bitstream size at the current stage.
• \(\lambda \|\boldsymbol{\theta}\|_2^2\) is L2 regularization, concentrating the parameter distribution for easier compression.
• Adam optimizer is used with learning rate decayed from 0.01 to 0.0004.
• The first GoP is trained for 6 epochs; subsequent GoPs are trained for 1–6 epochs.
• A single RTX 3090 GPU is used.

Key Experimental Results

Main Results

8iVFB Dataset (Tab. 1):

Method	bpp (avg)	Relative bpp	Enc. Time (s)	Dec. Time (s)
G-PCC v23	0.743	100%	2.72	0.923
SparsePCGC	0.625	84.0%	2.202	1.048
V-PCC v23	1.415	190.4%	194.261	2.304
Ours	0.616	82.9%	2.464	0.501
Ours 2	0.564	75.9%	16.423	0.459

MVUB Dataset (Tab. 3) — Distribution Shift Scenario:

Method	bpp (avg)	Relative bpp	Enc. Time (s)	Dec. Time (s)
G-PCC v23	0.921	100%	3.951	1.284
SparsePCGC	0.930	100.9%	3.06	1.456
V-PCC v23	1.543	167.6%	213.192	3.071
Ours	0.806	87.5%	2.712	0.554
Ours 2	0.725	78.8%	18.564	0.544

Note that on the MVUB dataset, SparsePCGC (trained on ShapeNet) even underperforms G-PCC (100.9%), whereas LINR-PCGC maintains a strong 78.8% relative bitrate, demonstrating the distribution-agnostic nature of INR-based methods.

Ablation Study

Initialization Strategy Ablation (Tab. 5):

Initialization	Relative Time (8iVFB)	Relative Time (Owlii)	Relative Time (MVUB)	Average
Random init. (rand.)	100%	100%	100%	100%
Prev. GoP init. (ini.)	36.0%	34.4%	33.7%	34.7%
Similar-sequence init. (fur. ini.)	22.9%	29.2%	20.0%	24.0%

The initialization strategy saves an average of 65.3% encoding time (ini.) and 76.0% (fur. ini.).

Module Ablation (Tab. 6):

Configuration	Relative bpp ↓
CNP only	100.0%
CNP + AQ&MC	91.9%
CNP + AQ&MC + SCE (full)	88.8%

AQ&MC reduces bpp by 8.1%; SCE provides an additional 3.1% reduction.

Bitstream Allocation and Time Breakdown (Tab. 4, MVUB):

Component	Bitstream %	Enc. Time %	Dec. Time %
Decoder parameters	0.73%	0.47%	0.00%
Lowest-scale point cloud	0.17%	8.58%	—
High scales (scale 2–6)	5.83%	30.47%	31.60%
Mid scale (scale 1)	18.10%	14.92%	16.25%
Highest scale (scale 0)	75.17%	45.56%	51.63%

Key Findings

• The key advantage of INR methods is distribution agnosticism: On the MVUB dataset, SparsePCGC (trained on ShapeNet) underperforms G-PCC, whereas LINR-PCGC independently overfits to each sequence and is unaffected by training data distribution.
• Decoder parameter overhead is negligible: Accounting for only 0.73% of total bitstream (owing to GoP-level sharing), it does not become a bottleneck.
• Trade-off between encoding time and compression ratio: Encoding for 1 epoch (~2.5 s/frame) already matches SparsePCGC in compression ratio; encoding for 6 epochs (~16 s/frame) further reduces bitrate by 15–20%.
• Fast decoding: Approximately half the decoding time of G-PCC or SparsePCGC, owing to the lightweight network design.

Highlights & Insights

• GoP-level INR framework — Adapting the GoP concept from video coding to INR-based point cloud compression simultaneously addresses parameter overhead and encoding speed, a design choice that is transferable to other INR compression scenarios (e.g., NeRF scene compression).
• Child node prediction as a substitute for transposed convolution — Formulating octree upsampling as staged child node occupancy prediction is both memory-efficient and exploits already-decoded nodes as context, representing an elegant engineering design.
• L2 regularization → Laplacian distribution → efficient parameter coding — A simple training technique that shapes the parameter distribution for easier compression, reflecting a deep understanding of INR parameter characteristics.

Limitations & Future Work

• Inter-frame prediction is not exploited; frames within a GoP are compressed independently, leaving temporal redundancy unaddressed.
• Encoding time remains substantial (approximately 16 s/frame for full encoding), precluding real-time applications.
• Only geometry is addressed; the method has not been extended to attribute (color) compression.
• No comparison with the latest Unicorn-Part I is provided, though a reasonable justification is given.
• The network architecture is fixed; neural architecture search or adaptive architecture selection is not explored.

Related Work & Insights

• vs. G-PCC: The traditional method performs robustly across all datasets but offers limited compression ratio; LINR-PCGC reduces bitrate by 21–28% with sufficient encoding time.
• vs. SparsePCGC: SparsePCGC performs well within its training distribution but degrades sharply under distribution shift (even underperforming G-PCC on MVUB); LINR-PCGC is inherently distribution-agnostic due to the INR paradigm.
• vs. V-PCC: V-PCC yields the highest bitrate and is extremely slow to encode (194–213 s), making it unsuitable for sparse point clouds.
• vs. INR compression methods (Hu & Wang 2022, etc.): Prior INR methods address only lossy compression; LINR-PCGC extends the paradigm to the lossless setting for the first time.

Rating

• Novelty: ⭐⭐⭐⭐ First INR-based lossless point cloud compression method; the GoP framework and CNP module are novel.
• Experimental Thoroughness: ⭐⭐⭐⭐ Comprehensive comparisons on three datasets, including encoding-time vs. bitrate curves and detailed ablations.
• Writing Quality: ⭐⭐⭐⭐ Well-structured, though notation-heavy in places.
• Value: ⭐⭐⭐⭐ Fills the gap in lossless INR-based point cloud compression; distribution-agnostic property has practical deployment value.

Related Papers

• [ICCV 2025] Neural Compression for 3D Geometry Sets
• [ICCV 2025] SL2A-INR: Single-Layer Learnable Activation for Implicit Neural Representation
• [ICCV 2025] Efficient Spiking Point Mamba for Point Cloud Analysis
• [ICCV 2025] UPP: Unified Point-Level Prompting for Robust Point Cloud Analysis
• [ICCV 2025] TurboReg: TurboClique for Robust and Efficient Point Cloud Registration