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Hausdorff -Near-Optimal Point Cloud Compression

Andrew Waters Richard Baraniuk Rice University. Hausdorff -Near-Optimal Point Cloud Compression. 2-sided Hausdorff metric natural for evaluating and fitting representations to LIDAR point clouds … but NP-Hard to compute

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Hausdorff -Near-Optimal Point Cloud Compression

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  1. Andrew WatersRichard Baraniuk Rice University Hausdorff-Near-Optimal Point Cloud Compression • 2-sided Hausdorff metric natural for evaluatingand fitting representations to LIDAR point clouds … but NP-Hard to compute • Progress this year:near-optimal fit based on 1-sided Hausdorffmetric • Sample Theorem: Let d2 be the 2-sided Hausdorff metric and let d1 be the 1-sided Hausdorff metric; then where ds is the cloud inter-point spacing target 0.07 bits/point

  2. Hausdorff Error Metric • Recall definition of Hausdorff distance: • Hausdorff-optimal fit: NP hard • Instead: One-sided optimal fit, bound error Two-sided metric

  3. One-side Optimal Planar Fit Set of normals Set of offsets Dictionary Convex hull of local point cloud: Compute distances for all normals Compute best (quantized) offsets Compute worst distance for each normal/offset pair, choose minimizer Return the best pair

  4. Relation to Two-sided Optimal Fit One-sided fit easy to obtain, but how good is it? Let be the one-sided distance and be inter-point spacing. Bound on (two-sided optimal distance) is: Within factor of inter-point spacing!

  5. Dictionary Construction Spherical coordinates: • Unit normal vector (two numbers) • Constant offset (one number) Want to allocate bits, , to minimize maximum distortion for each term

  6. Dictionary Results For Hausdorff distortion, occurs when i.e., equal bits for each term Not Intuitive: L2 optimal fitting result states that resolution for offset should be double that of the linear terms (see Chandrasekaran et al 2009)

  7. Example Results Original point cloud (21,120 points) DH = 0.085 0.07 bpp(bits per point) DH = 0.05 0.2 bpp DH = 0.04 0.3 bpp DH = 0.03 0.45 bpp

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