filtering theory: battling aliasing with antialiasing tomas akenine-möller department of computer...

Filtering theory:Filtering theory:Battling Aliasing with AntialiasingBattling Aliasing with Antialiasing

Tomas Akenine-Möller

Department of Computer Engineering

Chalmers University of Technology

Tomas Akenine-Mőller © 2003

Why care at all?Why care at all?

Quality!!Example: Final fantasy

– The movie against the game– In a broad way, and for most of the scenes, the

only difference is in the number of samples and the quality of filtering


Computer graphics is aComputer graphics is aSAMPLING & FILTERING process!SAMPLING & FILTERING process!Pixels

Texture

Time

DEMO


Sampling and reconstructionSampling and reconstruction

Sampling: from continuous signal to discrete Reconstruction recovers the original signal Care must be taken to avoid aliasing Nyquist theorem: the sampling frequency should

be at least 2 times the max frequency in the signal Often impossible to know max frequency

(bandlimited signal), or the max frequency is often infinite…


Sampling theoremSampling theorem

Nyquist theorem: the sampling frequency should be at least 2 times the max frequency in the signal

f=1 rpm

1 sample per revolution

A little more than 1 sample/revolution

2 samples per revolution

>2 samples per revolution


Sampling is simple, now turn to: Sampling is simple, now turn to: ReconstructionReconstruction

Assume we have a bandlimited signal (e.g., a texture)

Use filters for reconstruction


Reconstruction with box filter Reconstruction with box filter (nearest neighbor)(nearest neighbor)


Reconstruction with tent filterReconstruction with tent filter

32x32texture

Nearest neighbor Linear


Reconstruction with sinc filterReconstruction with sinc filter

In theory, the ideal filterNot practical (infinite extension, negative)


ResamplingResampling

Enlarging or diminishing signalsAssume samples are at unit-intervals,

i.e., 0,1,2,3,4,…Resample so that they are a apart

– a< 1 gives magnification– a>1 gives minification


ResamplingResamplingMagnificationMagnification

Assume we want to half sample distance


ResamplingResamplingMinificationMinification

Assume we want to double the distance between samples

Gives a blur effect – LP filter


Screen-basedScreen-basedAntialiasingAntialiasing

Hard case: edge has infinite frequencySupersampling: use more than one

sample per pixel


Formula and…Formula and…examples of different schemesexamples of different schemes

wi are the weights in [0,1]c(i,x,y) is the color of sample i inside pixel

),,(),(1

yxiwyxn

ii

cp


Jittered samplingJittered sampling Regular sampling cannot eliminate aliasing – only

reduce it! Why? Because edges represent infinite frequency Jittering replaces aliasing with noise Example:


The A-bufferThe A-bufferMultisampling techniqueMultisampling techniqueTakes >1 samples per pixel, and shares

compuations between samples inside a pixel

Supersampling does not share computations

Examples:– Lighting may be computed once per pixel– Texturing may be computed once per pixel

Strength: aliasing edges and properly handling transparency


The A-buffer --- cont’dThe A-buffer --- cont’dTo deal better with edges:

use a coverage mask per pixelCoverage mask, depth, & color

make up a fragmentDuring rendering fragments are

discarded when possible (depth test)When all polygons have been rendered,

the fragments are merged into a visible color– Allows for sorting transparent surfaces as well– But costs memory


Another multisampling techniqeAnother multisampling techniqeQuincunxQuincunx

Generate 2 samples per pixel at the same time w1=0.5, w2=0.125, w3=0.125, w4=0.125, w5=0.125

(2D tent filter) All samples gives the same effect on the image

(mid pixel = 0.5, corner pixels = 4*0.125=0.5) Is available on NVIDIA GeForce3 and up


Yet another scheme:Yet another scheme:FLIPQUAD multisamplingFLIPQUAD multisampling Recap, RGSS:

– One sample per row and column

Combine good stuff from RGSS and Quincunx

Weights: 0.25 per sample Performs better than Quincunx

DEMO


More on filtering More on filtering theory and practicetheory and practice

Especially important for texturing and filtering of textures

More about this in next lecture

filtering theory: battling aliasing with antialiasing tomas akenine-möller department of computer...

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