UCSD CSE 168 - Lecture (56 pages)

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Lecture



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Lecture

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Lecture Notes


Pages:
56
School:
University of California, San Diego
Course:
Cse 168 - Computer Graphics II: Rendering
Computer Graphics II: Rendering Documents

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CSE168 Computer Graphics II Rendering Spring 2006 Matthias Zwicker Last time Sampling and aliasing Aliasing Moire patterns Aliasing Sufficiently sampled Insufficiently sampled R Cook Fourier analysis Periodic signals can be expressed as a summation of sinusoidal waves The Fourier transform computes the complex amplitude at each frequency Spatial domain Frequency domain power spectrum Convolution Spatial domain Convolution Frequency domain Multiplication Sampling Spatial domain multiply signal with impulse train Frequency domain convolve signal with Fourier transform of impulse train Spatial domain Sampling Theorem Shannon 1949 A signal can be reconstructed exactly if it is sampled at least at twice its maximum frequency The minimum sampling frequency is called the Nyquist frequency Anti aliasing in graphics Image signals are not band limited to half the pixel frequency in general Prefiltering Band limit Sample Sample Reconstruct Supersampling Supersampling Sampling patterns Reconstruction filters Poisson Disk Sampling Hanrahan Spatial domain Hanrahan Frequency domain Random sampling with minimum distance constraint Dart throwing algorithm Poisson Disk Sampling 2x2 Poisson sampling Dippe 85 2x2 uniform sampling Dippe 85 Today Reconstruction filtering Realistic camera models High dynamic range imaging Reconstruction Reconstruction filters are weighting functions to compute a weighted average of the samples Continuous pixel Sample Sampled pixel Reconstruct Box Filter Pretending pixels are little squares Take the average of samples in each pixel spatial frequency Box filter Pixels are not little squares Original highresolution image Horizontal banding artifacts Down sampled with a 5x5 box filter uniform weights The Ideal Reconstruction Filter Unfortunately it has infinite spatial extent Every sample contributes to every interpolated point Expensive impossible to compute Ringing Gibbs phenomenon spatial frequency Sampled signal Ideal reconstruction filter frequency



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