This document discusses various anti-aliasing techniques used to minimize aliasing artifacts when representing high-resolution images and signals at lower resolutions. It describes spatial anti-aliasing, super sampling, Nyquist frequency, pixel weighting masks, pixel phasing, compensating for line intensity differences, and anti-aliasing area boundaries. The key techniques are spatial anti-aliasing which removes high frequency signal components before resampling, super sampling which takes multiple samples inside each pixel and averages for smoother edges, and pixel weighting masks which assign different weights to pixel subsections.

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nti-aliasing is any of a number of techniques to combat the problems of aliasing in
a sampled signal such as a digital image or digital audio recording.
 In digital signal processing, anti- aliasing is the technique of minimizing aliasing
(jagged or blocky patterns) when representing a high resolution signal at a lower
resolution.
 In most cases, anti- aliasing means removing this part data at too high a frequency to
represent. When sampling is performed without removing this part of the signal, it
causes undesirable artifacts such as the black – and- white noise near the top of
figure.
Effects caused by Aliasing:
The errors caused by aliasing are called artefacts. Common aliasing artefacts include jagged
profiles, disappearing or improperly rendered fine detail, and disintegrating textures.
 Jagged Profiles:
The picture on the left shows the sampling grid super imposed on the original scene. The
picture on the right is the rendered image. A jagged profile is quite evident in the rendered
image. Also known as “Jaggies”, jagged silhouettes are probably the most familiar effect
caused by aliasing. Jaggies are especially noticeable where there is a high contrast between
the interior and the exterior of the silhouette.
A

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 Improperly Rendered Detail:
The original scene on the left shows a group of small polygons. In the rendered scene, one
of the two red rectangles disappears entirely, and the other doubles in width. Two of the
orange triangles disappear. Although the two yellow triangles are identical in size, one is
larger than the other in the rendered image.
 Disintegrating textures:
This is a checkered texture on a plane. The checkers should become smaller as the distance
from the viewer increases. However, the checkers become larger or irregularly shaped
when their distance from the viewer becomes too great. Simply increasing the resolution
will not remove this artefact. Increasing the resolution will only move the artefact closer
the horizon.

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Filtering Techniques:
 A more accurate method for antialiasing lines
 Similar to those for applying a weighting mask, but now we integrate over the pixel
surface to obtain the weighted average intensity
There are different anti aliasing techniques defined as follows:
 Spatial Anti-aliasing:
In digital signal processing, spatial anti-aliasing is the technique of minimizing the
distortion artifacts known as aliasing when representing a high-resolution image at a lower
resolution. Anti-aliasing is used in digital photography, computer graphics, digital audio,
and many other applications.
Anti-aliasing means removing signal components that have a higher frequency than is able
to be properly resolved by the recording (or sampling) device. This removal is done before
(re)sampling at a lower resolution.
 Super sampling:
Super sampling is a spatial anti-aliasing method, i.e. a method used to
remove aliasing (jagged and pixilated edges, colloquially known as "jaggies") from
images rendered in computer games or other computer programs that generate imagery.
Aliasing occurs because unlike real-world objects, which have continuous smooth curves
and lines, monitors, can display only discrete points of light called pixels. Since pixels are
uniformly colored and always of the same shape, lines become jagged. With super
sampling, samples are taken at several instances inside the pixel (not just at the center as
would be done by default) and an average color value is calculated. This is achieved by
rendering the image at a much higher resolution than the one being displayed, then
shrinking it to the desired size, using the extra pixels for calculation. The result is a down

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sampled image with smoother transitions from one line of pixels to another along the edges
of objects.
The number of samples determines the quality of the output.
 Nyquist Frequency:
Theoretically, in order to adequately reconstruct a signal of frequency x, the original
signal must be sampled with a frequency of greater than 2x. This is known as the
Nyquist Sampling Frequency or Nyquist Limit
 However, this is assuming that we are doing a somewhat idealized sampling
and reconstruction
 In practice, it’s probably a better idea to sample signals at a minimum of 4x
 Nyquist Sampling Frequency:
To avoid losing information from such periodic objects, we need to set
the sampling frequency to at least twice that of the highest frequency
occurring in the object
fs = 2 fmax
 Nyquist Sampling Interval:
The sampling interval should be no larger than one-half the cycle
interval

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 Pixel Weighting Mask:
 By giving more weight to sub pixels near the center of a pixel area
 Intensities calculated for each of the 9 sub pixels
1. Center sub pixel is weighted by a factor of 1/4
2. Top, bottom, and side sub pixels are each of 1/8
3. Corner sub pixels are each weighted by 1/16
 Pixel Phasing:
With the technique by moving (micro positioning) pixel positions closer to the line path.
The electron beam is typically shifted by ¼, ½, or ¾ of a pixel diameter to plot points closer
to the true path of a line or object edge

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 Compensating for Line Intensity Differences:
The diagonal line is longer than the horizontal line by a factor of 2.By adjusting the
intensity of each line according to its slope. Horizontal and vertical lines would be
displayed with the lowest intensity, while 45◦ lines would be given the highest intensity
 Antialiasing Area Boundaries:
 A pixel partitioning into four subareas as shown in figure.
 The original 4 by 4 grid of pixels is turned into an 8 by 8 grid.
 we now process eight scan lines across this grid instead of four.
 Along the two scan lines we determine that three of the sub pixel areas are inside
the boundary.
 If a pixel intersect the two scan lines, we set the pixel intensity at 75%