Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression
Bibliographic record
Abstract
We study 3D point cloud attribute compression via a volumetric approach: assuming point cloud geometry is known at both encoder and decoder, parameters $\theta$ of a continuous attribute function $f: \mathbb{R}^{3} \mapsto \mathbb{R}$ are quantized to $\hat{\theta}$ and encoded, so that discrete samples $f_{\hat{\theta}}\left(\mathbf{x}_{i}\right)$ can be recovered at known 3D points $\mathbf{x}_{i} \in \mathbb{R}^{3}$ at the decoder. Specifically, we consider a nested sequences of function subspaces ${\mathcal{F}}_{l_{0}}^{(p)} \subseteq \cdots \subseteq {\mathcal{F}}_{L}^{(p)}$, where ${\mathcal{F}}_{l}^{(p)}$ is a family of functions spanned by B-spline basis functions of order $p, f_{l}^{*}$ is the projection of f on ${\mathcal{F}}_{l}^{(p)}$ represented as low-pass coefficients $F_{l}^{*}$, and $g_{l}^{*}$ is the residual function in an orthogonal subspace ${\mathcal{G}}_{l}^{(p)}$ (where ${\mathcal{G}}_{l}^{(p)} \oplus {\mathcal{F}}_{l}^{(p)}=$ $\left.{\mathcal{F}}_{l+1}^{(p)}\right)$ represented as high-pass coefficients $G_{l}^{*}$. In this paper, to improve coding performance over [1], we study predicting $f_{l+1}^{*}$ at level $l+1$ given $f_{l}^{*}$ at level l and encoding of $G_{l}^{*}$ for the $p=1$ case (RAHT (1)). For the prediction, we formalize RAHT (1) linear prediction in MPEG-PCC in a theoretical framework, and propose a new nonlinear predictor using a polynomial of bilateral filter. We derive equations to efficiently compute the critically sampled high-pass coefficients $G_{l}^{*}$ amenable to encoding. We optimize parameters in our resulting feed-forward network on a large training set of point clouds by minimizing a rate-distortion Lagrangian. Experimental results show that our improved framework outperforms the MPEG G-PCC predictor by $11 \%-12 \%$ in bit rate.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".