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Miloslav Ciz 2024-08-31 14:44:45 +02:00
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10
aliasing.md
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@ -8,7 +8,7 @@ A simple example showing how sampling at discrete points can quite dramatically
```
| .|-'-'.' ' .--. | |''''
| . ' | ' . .' '. | |
| . ' | ' . .' '. | |
'|- - -O+ - -O- - .| | O O | '---+---.
| \|_ _ / || | \__/ | | |
_ _'_._ | . '| '. .' ____| |
@ -19,7 +19,7 @@ _ _'_._ | . '| '. .' ____| |
The following diagram shows the principle of aliasing with a mathematical function:
```
^ original sampling period
^ original sampling period
| | | |<------------->|
| | _ | _ | _ |
| .'|'. .' '| .' '. | .' '. |
@ -35,9 +35,9 @@ V : : : :
|---o---...____ : : :
| | '''''o...____ : :
|___|_______________|______ ''''----o_______________:___
| '''----___ |
| '''----___ |
| ''''o---
| reconstructed
| reconstructed
|
V
```
@ -58,4 +58,4 @@ The same thing may happen in [ray tracing](ray_tracing.md) if we shoot a single
**Why doesn't aliasing happen in our eyes and ears?** Because our senses don't sample the world discretely, i.e. in single points -- our senses [integrate](integration.md). E.g. a rod or a cone in our eyes doesn't just see exactly one point in the world but rather an averaged light over a small area (which is ideally right next to another small area seen by another cell, so there is no information to "hide" in between them), and it also doesn't sample the world at specific moments like cameras do, its excitation by light falls off gradually which averages the light over time, preventing temporal aliasing (instead of aliasing we get [motion blur](motion_blur.md)). Also our brain does a lot of filtering and postprocessing of the raw input, what we see is not really what comes out of the retina, so EVEN IF there was a bit of aliasing here and there (because of some blind spots or something maybe?), the brain would probably learn to filter it out with "AI-style" magic, just like it filters out noise in low light conditions and so on.
So all in all, **how to prevent aliasing?** As said above, we always try to satisfy the sampling theorem, i.e. make our sampling frequency at least twice as high as the highest frequency in the signal we're sampling, or at least get close to this situation and lower the probability of aliasing. This can be done by either increasing sampling frequency (which can be done smart, some methods try to detect where sampling should be denser), or by preprocessing the input signal with a low pass filter or otherwise ensure there won't be too high frequencies (e.g. using lower resolution textures).
So all in all, **how to prevent aliasing?** As said above, we always try to satisfy the sampling theorem, i.e. make our sampling frequency at least twice as high as the highest frequency in the signal we're sampling, or at least get close to this situation and lower the probability of aliasing. This can be done by either increasing sampling frequency (which can be done smart, some methods try to detect where sampling should be denser), or by preprocessing the input signal with a low pass filter or otherwise ensure there won't be too high frequencies (e.g. using lower resolution textures).