spectral compression of mesh geometry (karni and gotsman 2000)
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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 - PowerPoint PPT PresentationTRANSCRIPT
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Spectral Compression of Mesh Geometry
(Karni and Gotsman 2000)
Presenter: Eric Lorimer
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Overview• Background• Spectral Compression• Evaluation• Recent Work • Future Directions
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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
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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]
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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
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Spectral Compression
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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
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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
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Spectral Compression• Visual Metric• Center: 4.1b/v• Right: TG at 4.1b/v (lossless =
6.5b/v)
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Spectral Compression• Connectivity Shapes [Isenburg et
al. 2001]
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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
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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
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Fixed Spectral Bases
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Future Directions• Wavelets (JPEG2000, MPEG4 still
image coder)• Integration of connectivity and
geometry
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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