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This paper discusses the challenges of handling massive point cloud data sets and presents a novel approach for efficient representation and compression using multiscale representations and predictive encoding. The method outperforms existing techniques in terms of compression ratio and error metric. The paper also proposes open questions for further research.
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Multiscale Representations for Point Cloud Data Andrew Waters Manjari Narayan Richard Baraniuk Luke Owens Ron DeVore
3D Surface Scanning Explosion in data and applications • Terrain visualization • Mobile robot navigation
Data Deluge • The Challenge: Massive data sets • Millions of points • Costly to store/transmit/manipulate • Goal: Find efficient algorithms for representation and compression
Selected Related Work • Point Cloud Compression [Schnabel, Klein 2006] • Geometric Mesh Compression [Huang, Peng, Kuo, Gopi 2006] • Surflets [Chandrasekaran, Wakin, Baron, Baraniuk 2004] • Multiscale tiling of piecewise surface polynomials
Optimality Properties • Surflet encoding for L2 error metric for piecewise constant/smooth functions • Polynomial order determined by smoothness of the image • Optimal asymptotic approximation rate for this function class • Optimal rate-distortion performance for this function class • Our innovation: • More physically relevant error metric • Extension to point cloud data Smoothness Dimension Rate
Error Metric • From L2 error • Computationally simple • Suppress thin structures • To Hausdorff error • Measures maximum deviation
Our Approach • Octree decomposition of point cloud • Fit a surflet at each node • Polynomial order determined by the image smoothness • Encode polynomial coefficients • Rate-distortion coder • multiscale quantization • predictive encoding
Step 1: Tree Decomposition (2D) -- data in square i Assume surflet dictionary with finite elements Stop refining a branch once node falls below threshold
Octree Hallmarks • Multiscale representation • Enable transmission of incremental details • Prune tree for coarser representation • Grow tree for finer representation
Step 2: Encode Polynomial Coeffs • Must encode polynomial coefficients and configuration of tree • Uniform quantization suboptimal • Key: Allocate bits nonuniformly • multiscale quantization adapted to octree scale • variable quantization according to polynomial order
Multiscale Quantization • Allocate more bits at finer scales: • Allocate more bits to lower order coefficients • Taylor series : Scale Smoothness Order
Step 3: Predictive Encoding “Likely” • Insight: Smooth images small innovation at finer scale • Coding Model: Favor small innovations over large ones • Encode according to distribution: “Less likely” • Encode with –log(p) bits: Fewer bits More bits
Experiment: Building 22,000 points piecewise planar surflets Octree: 150 nodes 1100 bits “1400:1” compression 0.05 bpp
Experiment: Mountain 263,000 points piecewise planar surflets Octree: 2000 Nodes 21000 Bits “1500:1” Compression 0.08 bpp
Summary • Multiscale, lossy compression for large point clouds • Error metric: Hausdorff distance, not L2 distance • Surflets offer excellent encodingfor piecewise smooth surfaces • Multiscale surface polynomial tiling • Multiscale quantization • Predictive Encoding • Open Question: Asymptotic optimality for Hausdorff metric