Wavelets for Computer Graphics AK Computergrafik WS 2005/06 PDF
Preview Wavelets for Computer Graphics AK Computergrafik WS 2005/06
Wavelets for Computer Graphics AK Computergrafik WS 2005/06 Markus Grabner AKCG WS2005/06 1/49 Graz University of Technology Content Introduction Simple example (Haar wavelet basis) Mathematical background Image operations Other useful properties MATLAB examples AKCG WS2005/06 2/49 Graz University of Technology Introduction Large data Analyzation Visualization Manipulation Single value not meaningful Domains Time, space, ... Frequency (Fourier) Mix? AKCG WS2005/06 3/49 Graz University of Technology Fourier vs. wavelets (1) AKCG WS2005/06 4/49 Graz University of Technology Fourier vs. wavelets (2) Fourier: localized in frequency only (each coefficient captures entire signal) Wavelets: localized in time and frequency AKCG WS2005/06 5/49 Graz University of Technology History First ideas by Weierstrass (1873) Not “invented”, but used in different fields: Seismology (term coined by Ricker, 1940) Physics Signal and image processing Multiresolution analysis (Mallat, 1989) AKCG WS2005/06 6/49 Graz University of Technology Wavelet properties Hierarchical representations Linear time complexity (conversion to/from) Sparsity (compression, efficiency) Adaptibility (wide variety of functions/domains) AKCG WS2005/06 7/49 Graz University of Technology MR group @ Caltech Prof. Peter Schröder Linear elasticity and wavelets AKCG WS2005/06 8/49 Graz University of Technology Haar wavelet basis Alfred Haar, 1909 Simplest wavelet basis Example AKCG WS2005/06 9/49 Graz University of Technology Example: sequence of 4 values [ 9 3 2 6 ] AKCG WS2005/06 10/49 Graz University of Technology
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