Introduction

Signal Processing

 

• Raster Image is a sampling of a continuous function
• If samples spaced too far apart, then don't get true representation of scene:

• In graphics, a variety of bad things happen:
  • Stairstep or ``jaggies''
  • Moire Patterns
  • Loss of small objects
  • Temporal
    • Sampled too far apart in time

      Backwards rotating wheels

    • Crawling jaggies
    • Appearing/dissappearing objects, flashing objects

Image as a signal

: 

• Signal processing signal is function of time
• Scene is a function of space

  Spatial domain: f(u)

• Raster image is a sampling of this signal
• Can represent sinal as sum of sine waves

  Frequency domain: F(u)

• Regular sampling restricts frequencies at which we sample

Nyquist Limit

 

• Theory tells us that we must sample at twice the highest frequency in the image to avoid aliasing.
• This sampling rate is known as the Nyquist Limit

• Problem: Man made objects have distinct edges

  Distinct edges have infinite frequency

What to do?

 

• After we get image, run through low pass filter

  This helps, but not a full solution

• Get a Higher Resolution Monitor

  This helps, but...

  • Not usually feasible
  • Alleviates jaggies but
    • Moire patterns merely shifted
    • Small objects still vanish
  • Increased CPU spent on extra pixels can be put to better use.
• Smarter sampling

Area Sampling

 

Rather than sample, we could integrate.

For lines, this means treating them as boxes

• Colour shades of gray based on fraction of pixel covered
• Gives better looking images at a sufficiently far distance

  Look close ant it looks blurry

Weighted Sampling

 

• Unweighted sampling is a box filter

  

  • No contribution outside of pixel
  • All contributions are equal
• Weighted sampling
  • Give different weights depending on position in pixel

  • Filter may extend outside of pixel

    Avoids certain temporal aliasing problems

    ``Correct'' filter is infinite

Anti-aliasing in Ray Tracing

 

• Can't always integrate area under pixel
• For ray tracing, we want to point sample the image
• Super Sampling

  Take more samples and weight with filter

  If sampling pattern regular, we still get aliasing

• Stocastic Sampling
  • Idea: Eye easily detects coherent errors (aliasing)

    Eye is poor at detecting incoherent errors (noise)

  • Rather than regular supersampling, we ``jitter'' the samples in one of several ways:
    • Choose random location within pixel
    • Displace small, random distances from regular grid