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Spectral Compression of Mesh Geometry (Karni and Gotsman 2000)

This presentation by Eric Lorimer provides an overview of the background, techniques, evaluation, recent work, and future directions in the field of spectral compression of mesh geometry. The presentation discusses how mesh geometry can be compressed separately from mesh connectivity, and explores the use of spectral compression techniques that involve quantization, predictive entropy coding, and computing eigenvectors of laplacian matrices.

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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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