Computer Graphics

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Dr.S.Sivakumar,Principal

C.P.A College, Bodinayakanur

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Antialiasing

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

Let’s Revisit a pixel

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

White Picket Fence

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

A New Thought about Images

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

We Sample the Image Function

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

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?

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

Let’s get grounded with an example

Similar examples?

• High frequency information, low sampling.
• Examples?
• Train comes every 2 hours. You go every 2:15. 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

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.

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What does sampling mean?

• What happens if we don’t sample enough?

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

Aliasing Manifestations

• Pixels approximating a signal

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• Pixels aren’t small enough and MISS information

Aliasing

• Aliasing manifests itself as “jaggies” in graphics. Thus we don’t have enough pixels to accurately represent the underlying function. Check out what happens when we increase our sampling.

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?

Fixing Aliasing

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

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.

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Let’s recall

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

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BiLinear Sampling

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

BiLinear Sampling

What are we doing?

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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/Lecture11/Slide27.html
• How would we blur using our traditional graphics pipeline?

Two ways to Antialias

• Increase resolution (increase sampling)
• or
• Supersampling

Increase Rendering Resolution

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

Supersampling

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

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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?

Line Antialiasing

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

Full Screen Antialiasing Example (Exaggerated)

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

Aliasing Examples

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

Hardware Antialiasing

• Don’t just generate 1 answer to write to a pixel
• nVidia Quincunx AA (2000 – GeForce3)
• Result

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Results from http://www.techreport.com/etc/2005q3/sli-aa/index.x?pg=4

Difference

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