Download Antialiasing

CAP4730: Computational Structures in
Computer Graphics
Antialiasing
Outline
What is antialiasing?
 How do we see the affects of
antialiasing?
 What can we do about it?
 Math behind antialiasing
 Antialiasing in modern day graphics
cards
 Advanced stuff on AA
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Let’s Revisit a pixel
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A pixel is which of these things
(theoretically)?
– point
– circle/disk
– square/rectangle
– has area
– has a location
– sample
White Picket Fence
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What happens
when we back
away?
– 1: with a
camera /eye
– 2: with
OpenGL
– 3: with raytracing
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What’s the
cause of the
difference?
A pixel could
be too BIG!
A New Thought about Images
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Images are really a
2D function
Here’s an image
plotted as a height
field
Now we store this
image as an “array”
of points. What does
that mean?
We Sample the Image
Function
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Here is the sampling function. It is
called the delta function
Thus we are “sampling” a
continuous image function
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We call these samples at
this regular grid of
points, pixels.
Pixels are a sampling of
the function that
describes the image.
We store these pixels
into memory as an array
of colors.
How densely should we
sample?
What would govern this?
Samples
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Continuous - function with values at any input. Most things
in the world. Ex. sine and cosine
Discrete - function with values only at specific inputs.
Computers are discrete.
What is a 1D example? a 2D example?
To convert from a continuous function to a discrete one, we
discretize or sample
To convert form a continuous variable to a discrete one, we
quantize
When we render an image (which is a continuous function,
why?), we sample and quantize
Let’s get grounded with an
example
Similar examples?
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High frequency information, low
sampling.
– Examples?
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Train comes every 2 hours. You go every 2:15.
How long do you wait?
Audio. 44/48 Khz signal. 11 Khz Sample
– What is the result?
– Images
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8 MP vs 4 MP vs 640 x 480
A quick footnote into
frequency analysis
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A way to understand the sampling question is to
convert the function into a different “space” or
domain.
We use the Fourier Transform to convert the function
(in our case the image) into the frequency domain.
What does sampling mean?
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What happens if we don’t sample
enough?
Aliasing
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If we sample at too low a rate, the high frequencies
in the image appear as lower frequencies.
How do we fix it?
Increase sampling
Remove high frequencies
Aliasing Manifestations
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Pixels approximating
a signal
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Pixels aren’t small
enough and MISS
information
Aliasing
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Aliasing manifests itself as “jaggies” in graphics.
Thus we don’t have enough pixels to accurately
represent the underlying function. Check out what
happens when we increase our sampling.
Aliasing
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Aliasing also manifests
itself in repeating
patterns
Car wheels
Big picture:
– Continuous signal
– Discrete sampling (pixels,
frames, etc.)
– Aliasing represents
misrepresentation (hence
the name) involved
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How do we fix it?
Fixing Aliasing
Increase Resolution
 What’s wrong with this approach?
 Filtering is another possibility
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– We want to remove the high frequency
areas
– How would we do that?
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Let’s re-examine what a pixel is in
reality.
Pixels are points
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But when we display the points, what happens?
Each pixel is actually a “blob” on the CRT. This blob has
energy that falls off close to a Gaussian.
Thus the CRT has a built in “blurring” system. Think
about how this works with resolution of your monitor.
Let’s recall
(4,2)
2
1
(0,0)
(4,0)
0
0
1
2
3
4
Point Sampling
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Thus for each pixel, we are “sampling” a specific
point. In the frequency domain we get:
To convert from frequency to spatial domains, we do
an integration.
To get around point sampling we should come up
with another sampling technique
BiLinear Sampling
What we will do is use a bilinear filter.
 This reduces the high frequencies
(which cause aliasing)
 Interpolate between samples.
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BiLinear Sampling
What are we doing?
(4,2)
2
1
(0,0)
(4,0)
0
0
1
2
3
4
Blurring
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Remember, blurring removes high frequencies, which
cause aliasing.
We can do other filtering besides bilinear, and we
would like to to avoid artifacts.
http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture
11/Slide27.html
How would we blur using our traditional graphics
pipeline?
Two ways to Antialias
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Increase resolution (increase sampling)
– or
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Supersampling
Increase Rendering Resolution
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Render the image at a higher resolution and
downsample.
Really, you are letting your eye do some filtering
for you.
Supersampling
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1
For each pixel, we would like to figure
out what “percentage” is covered.
(0,0)
(4,0)
0
0
1
2
3
4
Supersampling
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For each pixel, sample at multiple
points.
– What is the distribution of these points?
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Uniform Grid
Random
Psuedo-random
How many?
How far away from center should I try?
– How would I program this?
Line Antialiasing
Full Screen Antialiasing
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Another way to do the supersampling is to do full
screen antialiasing
We want to draw the image with several camera jitter
positions and average the answers
Can you see why this would give us near similar
answers?
That’s what they mean by 2-tap, 4-tap antialiasing
What does this require?
– Memory-wise
– Computation-wise
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How would you implement this?
Full Screen Antialiasing
Example (Exaggerated)
Antialiasing in OpenGL
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To do this in OpenGL, use the
Accumulation buffer
– glAccum(GL_ACCUM, FRAMES_TO_AVERAGE);
– glAccum(GL_LOAD, 1);
– glAccum(GL_RETURN);
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VERY SLOW! What does this mean memory
wise?
Other approahces: graphics cards, quincux
Aliasing Examples
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From:
http://www.os2ezine
.com/v1n7/colorwks.
html
Hardware Antialiasing
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Don’t just
generate 1
answer to write
to a pixel
nVidia Quincunx
AA (2000 –
GeForce3)
Result
Results from
http://www.techreport.com/etc/2005q3/sl
i-aa/index.x?pg=4
Difference
OpenGL Antialiasing
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Points and Lines
– glEnable(GL_POINT_SMOOTH);
– glEnable(GL_LINE_SMOOTH);
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Triangles
– glEnable(GL_POLYGON_SMOOTH);
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Provides blend alpha at edges of a triangle