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Spectral Compression of Mesh Geometry (Karni and Gotsman 2000)

Spectral Compression of Mesh Geometry (Karni and Gotsman 2000). Presenter: Eric Lorimer. Overview. Background Spectral Compression Evaluation Recent Work Future Directions. Background. Mesh geometry compressed separately from mesh connectivity

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Spectral Compression of Mesh Geometry (Karni and Gotsman 2000)

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  1. Spectral Compression of Mesh Geometry(Karni and Gotsman 2000) Presenter: Eric Lorimer

  2. Overview • Background • Spectral Compression • Evaluation • Recent Work • Future Directions

  3. Background • Mesh geometry compressed separately from mesh connectivity • Geometry data contains more information than the connectivity data (15 bpv vs 3 bpv) • Most techniques are lossless

  4. Background • Standard techniques use quantization and predictive entropy coding • Quantization: 10-14 bpv visually indistinguishable from the original (“lossless”) • Prediction rule • Parallelogram rule [Touma, Gotsman 1998]

  5. Spectral Compression • Consider now an implicit global prediction rule: Each vertex is the average of all its neighbors • Laplacian: • Eigenvalues are “frequencies” • Eigenvectors form orthogonal basis

  6. Spectral Compression

  7. Spectral Compression • Encoder • Compute eigenvectors of L • Project geometry onto the basis vectors (dot product) to generate coefficients • Quantize these coefficients and entropy code them • Decoder • Compute eigenvectors of L • Unpack coefficients • Sum coefficients * eigenvectors to reproduce the signals

  8. Spectral Compression • Computing eigenvectors prohibitively expensive for large matrices • Partition the mesh • MeTiS partitions mesh into balanced partitions with minimal edge cuts. • Average submesh ~ 500 vertices

  9. Spectral Compression • Visual Metric • Center: 4.1b/v • Right: TG at 4.1b/v (lossless = 6.5b/v)

  10. Spectral Compression • Connectivity Shapes [Isenburg et al. 2001]

  11. Evaluation • Pros • Progressive compression/transmission • Capable of compressing more than traditional methods • Cons • Expensive • Eigenvectors computed by decoder • Each mesh requires computing new eigenvectors • Limited to smooth meshes • Edge effects from partitioning

  12. Recent Work • Fixed spectral basis [Gotsman 2001] • Don’t compute eigenvector basis vectors for each mesh • Instead, map mesh to another mesh (e.g. 6-regular mesh) for which you have basis functions • Good results, but small, expected loss of quality

  13. Fixed Spectral Bases

  14. Future Directions • Wavelets (JPEG2000, MPEG4 still image coder) • Integration of connectivity and geometry

  15. References • Z. Karni and C. Gotsman. Spectral Compression of Mesh Geometry. In Proceedings of SIGGRAPH 2000, pp. 279-286, July 2000. • M. Ben-Chen and C. Gotsman. On the Optimality of Spectral Compression of Mesh Geometry. To appear in ACM transactions on Graphics 2004 • Z. Karni and C.Gotsman. 3D Mesh Compression Using Fixed Spectral Bases. Proceedings of Graphics Interface, Ottawa, June 2001. • M. Isenburg., S. Gumhold and C. Gotsman. Connectivity Shapes. Proceedings of Visualization, San Diego, October 2001

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