CSCE 441 Lecture 38
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Missed Class on account of severe allergies
Antialiasing
aliasing: Strange artifacts, false patterns (solely a function of sampling pattern)
Examples:
Antialiasing makes images seem "smoother" or "more natural"
Aliasing comes from the Nyquist Limit: In order to prevent aliasing, signals must be sampled at least twice (or more) the maximum frequency:
Easy example of this is the car commercials where the wheels spin backwards: camera frame rate is slower
If this is an artistic effect, this could be OK, but in computer science, we want to remove aliasing when "downsampling" an image
In computer graphics, aliasing arises when rasterizing polygons and mapping textures:
- We can sample pixel coordinates at the center, perform some level of averaging, or whatever.
- To remove sampling, we need to filter out high frequencies (higher than our sampling rate)
Multisampling: sample multiple times per pixel and take average. There are several sampling patterns available:
In our case, downsampling is downscaling.
To remove high frequencies
- take fourier transform of samples
- run low-pass filter to set high frequencies to zero
- take inverse fourier transform to get smoother sample points
Ideally, our filter looks like a box, but its inverse fourier transform (the sinc function) would give us negative values and infinite support.
We're looking for a function whose Inverse Fourier Transform gives all positive values and is band-limited.
- Box Filter: low frequencies would be blurred, but the high frequencies would be aliased.
- Tent Filter: Better approximation
- Lanczos 3 Filter: Almost perfect approximation of box function that we want to apply.
Mipmapping
Precompile image at multiple resolutions, and pick best match for each resolution.
Ideally, we go up by powers of 2
Linearly interpolate between scales
Anisotropic Filtering
Apply transformation to sample, and use multiple smaller samples to approximate the transformed sample's shape.
Analytc Aliasing
Use probability density function to "estimate" the blurring probability of an image.