Anti Aliasing Pre

8/6/2019 Anti Aliasing Pre

1/22

Anti-Aliasing


2/22

Aliasing

Aliasing definition: Distortion of information due to under-sampling

To avoid aliasing, sampling frequency has to be greaterthan twice the highest frequency occurring in the object.This minimum sampling frequency to avoid aliasing is alsocalled the Nyquist Sampling Frequency.

In other words, sample at least twice every period.

True Object

period

Sampling below Nyquist Freq

period

Sampling above Nyquist Freq


3/22

Example of Aliasing

Suppose we have a pattern of alternating red and green stripes.

Suppose we have show this pattern with pixels matching the stripes. This

is equal to the Nyquist Frequency. For each pixel, we sample the middle

of the pixel and color the entire pixel that color. We get the correct image.


4/22

Example of Aliasing(continued)

Suppose now we move the pattern further back, so that each pixel is nowrelatively bigger. Note: This is now below the Nyquist frequency. Once

again, we sample the middle of the pixel

And we color the entire pixel the sampled color. We would get this picture

This gives a severe misrepresentation of the underlying pattern.


5/22

Anti-Aliasing

Since were representing real-worldobjects with a finite number of pixels,aliasing occurs frequently.

Therefore, we need to implementtechniques to cancel the undesirableeffects of aliasing.

These techniques are called anti-aliasingtechniques.

One common anti-aliasing method issuper-sampling


6/22

Antialiasing Examples


7/22

Super-Sampling

Split single pixel into sub-pixels.

Pixels final color is a mixture of sub-pixelscolors. Simple method: Sample at the middle ofeach sub-pixel. Then, pixels color is the averageof the sub-pixels color.

Pixels Sub-divide into sub-pixels


8/22


9/22


10/22

Super-Sampling a Zero-Width Line

Apply Bresenhams

algorithm at sub-

pixel level

Sub-divide each pixel into

sub-pixels, for example 4x4

sub-pixels

Each pixel can have a maximum of 4

colored sub-pixels

How many sub-pixels are colored?

0 0 0 4

2 4 4 0

2 0 0 0

Assign color

Fraction of pixels color to be lines color

0.0 0.0 0.0 1.0

0.5 1.0 1.0 0.0

0.5 0.0 0.0 0.0


11/22

Super-Sampling a Line with Non-Zero Width

A line that is one-pixel wide.

For every pixel: Maximum number of

sub-pixels inside line = 16

A sub-pixel is considered in if its lower-left

corner is inside the line

Fraction of sub-pixels are in = fraction of color of the pixel should be line color

0 0 5/16 9/16

10/16 15/16 13/16 7/16

8/16 2/16 0 0


12/22

Sub-pixel Weighting Masks

Instead of considering each sub-pixel to be ofequal importance, assign a weight to each sub-pixel.

Usually consider the center sub-pixel to be mostimportant

1 2 2 1

2 3 3 2

2 3 3 2

1 2 2 1

Example weight for each sub-pixel

Total weight = 32

Final color of pixel = Sum of each (sub-pixel colors x sub-pixel weight) / total weight


13/22

Common Filter Functions

Box Filter Cone Filter Gaussian Filter

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 2 3 2 1

2 4 5 4 2

3 5 6 5 3

2 4 5 4 2

1 2 3 2 1

1 2 3 2 1

2 5 6 5 2

3 6 8 6 3

2 5 6 5 2

1 2 3 2 1

Gaussian function = exp ( - )

where s is the standard deviation and m is the mean

1

s 2p

( x m )2

2s2


14/22


15/22


16/22


17/22

Additional Benefit of Anti-Aliasing

Solve the line-intensity difference problem.

The line-intensity difference occurs when weredrawing a diagonal line.

In the following example, 5 pixels are used to

draw each line, but the diagonal line is actuallylonger. Therefore, the diagonal line appears lessintense.

Applying anti-aliasing technique automaticallytakes care of this problem (assume anti-alias

non-zero width line).


18/22

Anti-Aliasing Area Boundaries

For each pixel, determine whatfraction lines in one area, and whatfraction lies in the other area.

Then, take the weighted average ofthe two area colors.

Pitteway-Watkinson method adaptsBresenhams method to quickly findthe percentage.


19/22


20/22


21/22


22/22

Anti Aliasing Pre

Documents

Anti Aliasing Pre