cgt is one of the most important properties of...

CGT 511(Anti)aliasing(Anti)aliasing

dři h š hBedřich Beneš, Ph.D.

Purdue University

Department of Computer Graphics Technology

Aliasing• Aliasing is one of the most important properties of

sampling

C i f i f( ) i• Continuous function f(x) is discretized into I(i) by sampling

We loose some information• We loose some information

• How is this fact presented in the discrete image?

Wh i h diff b f( ) d I(i)?• What is the difference between f(x) and I(i)?

© Bedrich Benes

Aliasing

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continuous function sampling space result

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AliasingHaving originally continuous function

We get something else after its reconstructionWe get something else after its reconstruction

original

reconstructed

samples

© Bedrich Benes

Aliasing

the new (low frequency) information is called alias

Original function

liA sample

alias

© Bedrich Benes

Aliasing• Alias is ubiquitous for Computer Graphics

• Examples are• jaggies

• crowlies(animation)

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© Bedrich Benes

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Aliasing• Examples

• New patterns(moire)

© Gomez and Wehlo

• wagon wheel effect (aliasing in time domain)

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Aliasing• Alias is a loss of information caused by

transition from continuous to discrete space.

• Aliasing artifacts are caused by high‐frequency information aliasing as a low‐frequency one.

• Can we avoid this? Practically no!yCan we decrease the error? Yes!

© Bedrich Benes

Antialiasing• (partial) elimination of alias is called

antialiasing

We have to add some information, so we have to sample better.… we need additional effort,… we have to compute more,… it takes longer time

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Antialiasing• Antialiasing is a partial elimination of alias

• Can be done in two ways• Object antialiasing

(only one object is antialiased)

• Screen‐based antialiasingg(the entire image is antialiased)

© Bedrich Benes

Object Antialiasing

© Bedrich Benes© Bedrich Benes

11

Object Antialiasing

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Scene Antialiasing

© Bedrich Benes

Sampling• Let’s have a close look at sampling

Sampling frequency 1Sampling frequency (i.e., how often we take the sample)

xf

1

point samplingpoint sampling takes exactly one value (usually in the middle)

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(usually in the middle)

Sampling• area sampling

measures an average of the sampled area

xx

dttfxI )(1)( xx

• But the integral is hard to evaluate

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SamplingLet’s use numerical methods! (i.e., n<)

nxx 11

n

ii

nx ndttf

xxI

1

1)(1)( lim

Where:n ‐ # of the samplesn # of the samples ‐ is a sample i.e., =f(t) is somewhere

© Bedrich Benes

f(t) is somewhere in the sampling area t<x, x+x>

SamplingThere are some special cases:

for n=1 we have point sampling method, for n‐> we have area sampling,

So the antialiasing picks something in the middle…

© Bedrich Benes

SupersamplingLet’s take n samples from the area

corresponding to a pixel over the originally continuous function

Estimate the value from the sampelsEstimate the value from the sampels.

This is an approximating the function.

Taking more samples from the <x, x+x>is called supersampling.

© Bedrich Benes

is called supersampling.

Supersampling• Depending on the way we take it

Regular (uniform)

R l i ki l i l i l

Random (stochastic)

Regular is taking samples in regular intervals and it shifts alias to higher frequencies

Stochastic involves random numbers changes alias to noise (noise is nicer for human visual

© Bedrich Benes

( fperception system)

Regular Supersampling• Digitalize the image in higher resolution

• Scale it down

• Use the average as the new colororiginal supersampling average scale downoriginal supersampling average scale down

© Bedrich Benes

Regular Supersampling

© Bedrich Benes


original 3x3 uniform supersamplingg p p g

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Regular Supersampling ‐ FSAA

Regular Supersampling also called

Full Screen Antialiasing (FSAA)Full Screen Antialiasing (FSAA)

is today’s state of the art

ti li i d iantialiasing used in games

© Bedrich Benes



© Bedrich Benes



© Bedrich Benes

Regular Supersampling• Antialiasing with regular SS

1) Digitalize image in 3x higher resolution

2) For each pixel of the small image doa) get the corresponding superpixels) g p g p pb) calculate average of their colorsc) apply the color) pp y

© Bedrich Benes

Regular Supersampling• Pros

• easy to do

• Can be done in HW

• Cons• image must be calculated in a higher resolution

(but who cares today…)

• blurs the image

• alias is shifted to higher frequencies

© Bedrich Benes

g q

Other Regular Supersampling• 1x2 or 2x1 supersampling

• more samples at one screen axis

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Other Regular Supersampling• Rotated Grid Super Sampling (RGSS)

• samples in a rotated grid

• good for nearly horizontal edges

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Other Regular Supersampling• Quincunx (NVIDIA)

High Resolution AA (HRAA)• four samples in corners, one in the center

• corners 1/8 weight, center ½

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Supersampling• Depending on the way we take it

Regular (uniform)

R l i ki l i l i l

Random (stochastic)

Regular is taking samples in regular intervals and it shifts alias to higher frequencies

Stochastic involves random numbers changes alias to noise (noise is nicer for human visual

© Bedrich Benes

( fperception system)

Stochastic supersamplingcover the pixel by n random samples

assure well‐proportioned point distributionassure well proportioned point distribution

if the stochastic sampling is really random

this can happen inside one pixelthis can happen inside one pixel

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and the image will be heavily noisy!

Stochastic supersamplingThe best covering is assured by

Poisson disc random number distributionPoisson disc random number distribution

Each sample is at least in distance dfar from the others

dd

d

|[xk,yk|‐[x,y]|>2dd

d

© Bedrich Benes

Poisson disc generatorSet list of points to empty

for (i=0;i<n;i++){repeat{repeat{generate a random point with uniform distribution A=[xk,yk]

}until there is NO point Slow!

|[xk,yk|-[x,y]|<2d add A to the list}// end of for

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}// end of for

Jitteringan approximation of the

Poisson disc random numbers distribution

Uniform samples are jittered

the worst case that can happen:

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Jittering

jittering

l jitt dregular supersampling

jitteredsupersampling

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Jittering

original 3x3 jittered supersampling

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Jittering

original 5x5 jittered supersampling

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Jitteringjitt dl jittered

supersampling 3x3regular

supersampling 3x3

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N‐rooks distributionApproximation of Poisson disc

Supersampling in superresolution n x nSupersampling in superresolution n x n

Put n samples as a spatial permutation of the diagonal

We have these matrices stored in memory andWe have these matrices stored in memory and we are taking them randomly.It is cheaper variant of jittering.

© Bedrich Benes

It is cheaper variant of jittering.

N‐rooks distribution

etc.

• Matrices are stored and taken randomly.

• It is cheaper variant of jittering.

© Bedrich Benes

Adaptive SupersamplingImagine the following continuous function:

sampling in 2x2 one partially covered pixel

there is no need to sample the others better!

© Bedrich Benes

Adaptive Supersampling• Idea – sample only when necessary

step 1 step 2 step 3 etc…

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Adaptive Supersampling• The color value is then

B CB C

AE F

AD G

GFED

44)(

GFEDCBAxI

© Bedrich Benes

Summary• alias, examples

• sampling ‐ point areasampling point, area

• supersampling ‐ uniform, stochastic

• Poisson disc, Jittering, N‐rooks

• Adaptive supersampling

© Bedrich Benes

ReadingsReal‐time rendering, Tomas Akeine Mollner, Eric

Haines, AKPeters Ltd, 2002, pp.84‐101

Advanced Rendering and Animation Techniques, Watt Watt Addison‐Wesley Reading 1992Watt, Watt, Addison Wesley, Reading, 1992, pp.XX‐XX

© Bedrich Benes

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