antialiasing - Antialiasing A ti li i Chapter 4 Ch Intro....

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Antialiasing Chapter 4 Intro. to Computer Graphics pring 2009 Y G Shin Spring 2009, Y.G. Shin
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A Simple Image Model ± Image: a 2-D light- tensity function intensity function f(x,y) ± The value of f at (x,y) Æ the intensity (brightness) of the image at that point ± 0 < f(x,y) <
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Digital Image Acquisition
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Sampling & Quantization ± Sampling: partitioning xy plane into a grid ± the coordinate of the center of each grid is a pair gp of elements from the Cartesian product Z x Z (Z 2 ), Z: set of real integers ± Where Does Sampling Occur? ± Almost all data we are dealing with is discrete ± Evaluation of sampled functions at arbitrary sites ± Volume rendering ± Isosurface extraction ± Ray tracing
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Sampling & Quantization ± Quantization: once the signal has been sampled, it needs to be quantized to turn the samples into numbers which we can process. Quantization means that we break e full positive and negative range the full positive and negative range of the sample value into N sections and then code it in log 2 N bits.
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Digital Image
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Sampling & Quantization
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Sampling & Quantization ± The digitization process requires decisions about: ± Values for N,M (where N x M: the image array) ± AND, the number of discrete gray levels, G, allowed for each pixel. sually these quantities are integer powers of ± Usually, these quantities are integer powers of two: N=2 n , M=2 m and G=2 k nother assumption is that the discrete levels ± Another assumption is that the discrete levels are equally spaced between 0 and L-1 in the gray scale.
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Examples
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Examples
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Sampling & Quantization ± If b is the number of bits required to store a digitized image then: ± b = N x M x k (if M=N, then b=N 2 k) ± Storage for various values of N and k
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Sampling & Reconstruction ± Reconstruction ± Given a set of digitized samples, how to approximate the original signal? sampling Filtering Aliasing reconstruction Frequency Under sampling Super sampling Niquist rate
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Continuous Luminosity signal Slide © Rosalee Nerheim-Wolfe
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Sampled Luminosity Slide © Rosalee Nerheim-Wolfe
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Reconstructed luminosity Slide © Rosalee Nerheim-Wolfe
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Reconstruction artefact Slide © Rosalee Nerheim-Wolfe
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Staircasingor Jaggies The raster aliasing effect – removal is called antialiasing b D M i t h l l Images by Don Mitchell
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Can be a serious problem lide © Rosalee Nerheim olfe Slide © Rosalee Nerheim-Wolfe
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Artifacts - Disintegrating textures isintegrating textures Disintegrating textures
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Blurring does not work well. emoved the but also all the detail ! Removed the jaggies, but also all the detail ! Reduction in resolution
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Aliasing PROBLEM ' /2) 2 1/( s ss f ft = = Δ s t Δ 1/ s s Sampling rate:
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How is antialiasing done? ± We need some mathematical tools to ± analyse the sampling and reconstruction ± find an optimum solution ± Process of sampling and reconstruction is best nderstood in frequency domain understood in frequency domain ± Use Fourier transform to switch between time and frequency domains ± Function in time domain: signal ± Function in frequency domain:
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This note was uploaded on 04/29/2010 for the course CSE 4190.411 taught by Professor Shinyeonggil during the Fall '08 term at Seoul National.

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antialiasing - Antialiasing A ti li i Chapter 4 Ch Intro....

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