spectral processing of point-sampled geometry mark pauly markus gross eth zürich
Post on 21-Dec-2015
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Spectral Processing of Point-sampled GeometrySpectral Processing of
Point-sampled Geometry
Mark Pauly Markus Gross
ETH Zürich
Spectral Methods
IntroductionIntroduction
Model Acquisition
Range scans Depth images …
Point Rendering
QSplat Surfels …
Introduction
Point-based Geometry Processing
•Extend Fourier transform to 2-manifold surfaces
Spectral representation of point-based objectsPowerful methods for digital geometry processing
Introduction
Spectral TransformSpectral Transform
•Spectral filtering:
•Noise removal
•Microstructure analysis
•Enhancement
•Adaptive resampling:
• Complexity reduction
• Continuous LOD
Introduction
ApplicationsApplications
•Benefits:
•Sound concept of frequency
•Extensive theory
•Fast algorithms
•Limitations:
•Euclidean domain, global parameterization
•Regular sampling
•Lack of local control
Fourier TransformFourier Transform
Introduction
Clustering Optimization
Samples Clusters Patches
Spectral Processing Pipeline
Patch Layout GenerationPatch Layout Generation
• Iterative, local optimization method
•Quality metric:
Spectral Processing Pipeline
Patch Merging OptimizationPatch Merging Optimization
curvature
patch Size
patch boundary
spring energy regularization
Scattered Data ApproximationScattered Data Approximation
Spectral Processing Pipeline
Hierarchical Push-Pull Filter:
•2D Discrete Fourier Transform (DFT) Direct manipulation of spectral coefficients
•Filtering as convolution:
Convolution: O(N2) Multiplication: O(N)
• Inverse Fourier Transform Filtered patch surface
)()()( yFxFyxF
Spectral Processing Pipeline
Spectral AnalysisSpectral Analysis
Spectral Processing Pipeline
Spectral AnalysisSpectral Analysis
Gaussian low-passIdeal low-pass
EnhancementBand-stop
Original
Spectral Processing Pipeline
ResamplingResampling
•Low-pass filtering
Band-limitation
•Regular Resampling
Optimal sampling rate (Sampling Theorem)
Error control (Parseval’s Theorem)
Power Spectrum
Spectral Processing Pipeline
ReconstructionReconstruction
• Filtering can lead to discontinuities at patch boundaries
Create patch overlap, blend adjacent patches
region of overlap
Sampling rates
Point positions
Normals
Original Gaussian Wiener Patch
noise+blur Filter Filter Layout
Results
Surface RestorationSurface Restoration
Results
TimingsTimings
HeadHeadSt. St.
MatthewMatthew DavidDavid
#points#patches
460,800256
3,382,866595
4,128,614
2,966
Preprocess
10.9 117.2 128.3
Total Total 15.815.8 153.0153.0 189.6189.6
Conclusions
•Versatile spectral decomposition of point-based models
•Effective filtering
•Adaptive resampling
•Efficient processing of large point-sampled models
SummarySummary
Conclusions
•Compression Scalar Representation + Spectral
Compression
•Hierarchical Representation Modeling and Animation
•Feature Detection & Extraction Robust Computation of Laplacian
Future WorkFuture Work