Graph-based Scalable Sampling of 3D Point Cloud Attributes

TL;DR

This paper tackles scalable sampling of 3D point cloud color attributes when full geometry is available, by formulating reconstruction-aware graph-based samplers. It introduces two methods: Reconstruction-Aware Global Sampling (RAGS) and Reconstruction-Aware Block Sampling (RABS), which rely on a vertex-domain interpolation operator $Q(p)$ built from a local graph filter $Z$ and a localization parameter $p$ that adapts to the sampling rate $\alpha$. The authors derive efficient greedy selection criteria, provide strategies to choose $p$, and show that block-based sampling with self-loops achieves near-global performance with substantially reduced complexity. Empirical results on two large PC datasets show up to 2 dB PSNR gains over fast subsampling methods and up to 50x faster runtimes than existing graph-sampling approaches, with additional benefits in PC attribute compression yielding up to 11% bitrate savings in chroma subsampling.

Abstract

3D Point clouds (PCs) are commonly used to represent 3D scenes. They can have millions of points, making subsequent downstream tasks such as compression and streaming computationally expensive. PC sampling (selecting a subset of points) can be used to reduce complexity. Existing PC sampling algorithms focus on preserving geometry features and often do not scale to handle large PCs. In this work, we develop scalable graph-based sampling algorithms for PC color attributes, assuming the full geometry is available. Our sampling algorithms are optimized for a signal reconstruction method that minimizes the graph Laplacian quadratic form. We first develop a global sampling algorithm that can be applied to PCs with millions of points by exploiting sparsity and sampling rate adaptive parameter selection. Further, we propose a block-based sampling strategy where each block is sampled independently. We show that sampling the corresponding sub-graphs with optimally chosen self-loop weights (node weights) will produce a sampling set that approximates the results of global sampling while reducing complexity by an order of magnitude. Our empirical results on two large PC datasets show that our algorithms outperform the existing fast PC subsampling techniques (uniform and geometry feature preserving random sampling) by 2dB. Our algorithm is up to 50 times faster than existing graph signal sampling algorithms while providing better reconstruction accuracy. Finally, we illustrate the efficacy of PC attribute sampling within a compression scenario, showing that pre-compression sampling of PC attributes can lower the bitrate by 11% while having minimal effect on reconstruction.

Figures (10)

• Figure 1: Summary of the proposed reconstruction aware block sampling (RABS) algorithm. RABS first divides the PC into blocks, then self-loops are added to sub-graphs, followed by sub-graph sampling.
• Figure 2: Illustration of self-loop for the boundary node as a consequence of boundary condition using a line graph
• Figure 3: (a) Normalized spectral response of the proposed interpolator - $g_{p}(\lambda_{i}) = \frac{1}{p} \sum_{l=1}^{p} (1 - \frac{1}{2} \lambda_{i})^{l}$.(b) Vertex domain interpretation of the interpolator $\mathbf{Q}(p)$.
• Figure 4: Illustration of interpolation when samples are selected uniformly on a line graph at rates $50\%$, $33\%$ (left) and uniform sampling on 3D grid graph at $50\%$ sampling rate (right)
• Figure 5: Proposed $p$ values from \ref{['eqn:p_estimate_uni']} and \ref{['eqn:p_estimate_rand']}.

Theorems & Definitions (10)

• Lemma 3.1
• Lemma 3.2
• Theorem 3.1
• Remark 1
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof