Antialiasing

1
Antialiasing
CAP4730 Computational Structures in Computer
Graphics
2
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

3
Lets Revisit a pixel

• A pixel is which of these things (theoretically)?
• point
• circle/disk
• square/rectangle
• has area
• has a location
• sample

4
White Picket Fence

• What happens when we back away?
• 1 with a camera /eye
• 2 with OpenGL
• 3 with ray-tracing
• Whats the cause of the difference?
• A pixel could be too BIG!

5
A New Thought about Images

• Images are really a 2D function
• Heres an image plotted as a height field
• Now we store this image as an array of points.
  What does that mean?

6
We Sample the Image Function

• Here is the sampling function. It is called the
  delta function

7
Thus we are sampling a continuous image function

• 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?

8
Samples

• 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

9
Lets get grounded with an example
10
Similar examples?

• High frequency information, low sampling.
• Examples?
• Train comes every 2 hours. You go every 215.
  How long do you wait?
• Audio. 44/48 Khz signal. 11 Khz Sample
• What is the result?
• Images
• 8 MP vs 4 MP vs 640 x 480

11
A quick footnote into frequency analysis

• 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.

12
What does sampling mean?

• What happens if we dont sample enough?

13
Aliasing

• 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

14
Aliasing Manifestations

• Pixels approximating a signal
• Pixels arent small enough and MISS information

15
Aliasing

• Aliasing manifests itself as jaggies in
  graphics. Thus we dont have enough pixels to
  accurately represent the underlying function.
  Check out what happens when we increase our
  sampling.

16
Aliasing

• 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
• How do we fix it?

17
Fixing Aliasing

• Increase Resolution
• Whats wrong with this approach?
• Filtering is another possibility
• We want to remove the high frequency areas
• How would we do that?
• Lets re-examine what a pixel is in reality.

18
Pixels are points

• 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.

19
Lets recall
(4,2)
2
1
(0,0)
(4,0)
0
2
1
0
3
4
20
Point Sampling

• 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

21
BiLinear Sampling

• What we will do is use a bilinear filter.
• This reduces the high frequencies (which cause
  aliasing)
• Interpolate between samples.

22
BiLinear Sampling
23
What are we doing?
(4,2)
2
1
(0,0)
(4,0)
0
2
1
0
3
4
24
Blurring

• 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/Lect
  ure11/Slide27.html
• How would we blur using our traditional graphics
  pipeline?

25
Two ways to Antialias

• Increase resolution (increase sampling)
• or
• Supersampling

26
Increase Rendering Resolution

• Render the image at a higher resolution and
  downsample.
• Really, you are letting your eye do some
  filtering for you.

27
Supersampling

• For each pixel, we would like to figure out what
  percentage is covered.

1
(0,0)
(4,0)
0
2
1
0
3
4
28
Supersampling

• For each pixel, sample at multiple points.
• What is the distribution of these points?
• Uniform Grid
• Random
• Psuedo-random
• How many?
• How far away from center should I try?
• How would I program this?

29
Line Antialiasing
30
Full Screen Antialiasing

• 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?
• Thats what they mean by 2-tap, 4-tap
  antialiasing
• What does this require?
• Memory-wise
• Computation-wise
• How would you implement this?

31
Full Screen Antialiasing Example (Exaggerated)
32
Antialiasing in OpenGL

• To do this in OpenGL, use the Accumulation buffer
• glAccum(GL_ACCUM, FRAMES_TO_AVERAGE)
• glAccum(GL_LOAD, 1)
• glAccum(GL_RETURN)
• VERY SLOW! What does this mean memory wise?
• Other approahces graphics cards, quincux

33
Aliasing Examples

• From http//www.os2ezine.com/v1n7/colorwks.html

34
(No Transcript)
35
Hardware Antialiasing

• Dont just generate 1 answer to write to a pixel
• nVidia Quincunx AA (2000 GeForce3)
• Result

36
Results from http//www.techreport.com/etc/2005q3/
sli-aa/index.x?pg4
37
Difference
38
OpenGL Antialiasing

• Points and Lines
• glEnable(GL_POINT_SMOOTH)
• glEnable(GL_LINE_SMOOTH)
• Triangles
• glEnable(GL_POLYGON_SMOOTH)
• Provides blend alpha at edges of a triangle