Advanced Computer Graphics Antialiasing

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Advanced Computer GraphicsAntialiasing

• David Luebke
• cs551dl_at_cs.virginia.edu
• http//www.cs.virginia.edu/cs551dl

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Administrivia

• Assignment 1 sample scenes

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Recap

• Prefiltering
• Before sampling the image, use a low-pass filter
  to eliminate frequencies above the Nyquist limit
• This blurs the image
• But ensures that no high frequencies will be
  misrepresented as low frequencies

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Recap

• Supersampling
• Sample image at higher resolution than final
  image, then average down
• Average down means multiply by low-pass
  function in frequency domain
• Which means convolving by that functions FT in
  space domain
• Which equates to a weighted average of nearby
  samples at each pixel

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Recap

• Supersampling cons
• Doesnt eliminate aliasing, just shifts the
  Nyquist limit higher
• Cant fix some scenes (e.g., checkerboard)
• Badly inflates storage requirements
• Supersampling pros
• Relatively easy
• Often works all right in practice
• Can be added to a standard renderer

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Antialiasing in the Continuous Domain

• Problem with prefiltering
• Sampling and image generation inextricably linked
  in most renderers
• Z-buffer algorithm
• Ray tracing
• Why?
• Still, some approaches try to approximate effect
  of convolution in the continuous domain

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Antialiasing in the Continuous Domain
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Antialiasing in the Continuous Domain

• The good news
• Exact polygon coverage of the filter kernel can
  be evaluated
• What does this entail?
• Clipping
• Hidden surface determination

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Antialiasing in the Continuous Domain

• The bad news
• Evaluating coverage is very expensive
• The intensity variation is too complex to
  integrate over the area of the filter
• Q Why does intensity make it harder?
• A Because polygons might not be flat- shaded
• Q How bad a problem is this?
• A Intensity varies slowly within a pixel, so
  shape changes are more important

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Catmulls Algorithm
A2
A1

• Find fragment areas
• Multiply by fragment colors
• Sum for final pixel color

AB
A3
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Catmulls Algorithm

• First real attempt to filter in continuous domain
• Very expensive
• Clipping polygons to fragments
• Sorting polygon fragments by depth (Whats wrong
  with this as a hidden surface algorithm?)
• Equates to box filter (Is that good?)

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The A-Buffer

• Idea approximate continuous filtering by
  subpixel sampling
• Summing areas now becomes simple

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The A-Buffer

• Advantages
• Incorporating into scanline renderer reduces
  storage costs dramatically
• Processing per pixel depends only on number of
  visible fragments
• Can be implemented efficiently using bitwise
  logical ops on subpixel masks

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The A-Buffer

• Disadvantages
• Still basically a supersampling algorithm
• Not a hardware-friendly algorithm
• Lists of potentially visible polygons can grow
  without limit
• Work per-pixel non-deterministic

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The A-Buffer

• Comments
• Book claims this is most common algorithm for
  high-quality rendering
• Im not so sure, anymore
• Book gives much gory detail
• I wont test you on it

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Stochastic Sampling

• Sampling theory tells us that with a regular
  sampling grid, frequencies higher than the
  Nyquist limit will alias
• Q What about irregular sampling?
• A High frequencies appear as noise, not aliases
• This turns out to bother our visual system less!

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Stochastic Sampling

• An intuitive argument
• In stochastic sampling, every region of the image
  has a finite probability of being sampled
• Thus small features that fall between uniform
  sample points tend to be detected by non-uniform
  samples

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Stochastic Sampling

• Integrating with different renderers
• Ray tracing
• It is just as easy to fire a ray one direction as
  another
• Z-buffer hard, but possible
• Notable example REYES system (?)
• Using Image jittering is easier (more later)
• A-buffer nope
• Totally built around square pixel filter and
  primitive-to-sample coherence

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Stochastic Sampling

• Idea randomizing distribution of samples
  scatters aliases into noise
• Problem what type of random distribution to
  adopt?
• Reason type of randomness used affects spectral
  characteristics of noise into which high
  frequencies are converted

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Stochastic Sampling

• Problem given a pixel, how to distribute points
  (samples) within it?

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Stochastic Sampling

• Poisson distribution
• Completely random
• Add points at random until area is full.
• Uniform distribution some neighboring samples
  close together, some distant

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Stochastic Sampling

• Poisson disc distribution
• Poisson distribution, with minimum-distance
  constraint between samples
• Add points at random, removing again if they are
  too close to any previous points
• Very even-looking distribution

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Stochastic Sampling

• Jittered distribution
• Start with regular grid of samples
• Perturb each sample slightly in a random
  direction
• More clumpy or granular in appearance

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Stochastic Sampling

• Spectral characteristics of these distributions
• Poisson completely uniform (white noise). High
  and low frequencies equally present
• Poisson disc Pulse at origin (DC component of
  image), surrounded by empty ring (no low
  frequencies), surrounded by white noise
• Jitter Approximates Poisson disc spectrum, but
  with a smaller empty disc.

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Stochastic Sampling

• Watt Watt, p. 134

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