<p>Like in any other kind of signal processing, the relationship is Nyquist's theorem. An image is a discrete sequence of samples of a continuous signal. If the original signal has frequency components higher than half the sampling rate, then there will be aliasing. To put that another way, if you look at the real-world size of a pixel, any details smaller than two pixels wide will be aliased. This applies to synthetic images as well as to photographs. If you define a procedural texture via a mathematical function, the function is continuous but you only evaluate it at certain points.</p>

<p>The problem is, of course, if you only have the sampled image and not the original signal, the high-frequency components have <em>already</em> been aliased, so you can't measure them directly. You have to use statistical techniques to guess which details in your aliased image were originally higher-frequency signals.</p>

CC BY-SA 3.0
2017-07-14T18:18:29.553Z
Thank you Dan.. is there any link that you can suggest for me to look further in to this (like a code or paper ) ?
Varun Vijaykumar
CC BY-SA 3.0
2017-07-14T22:44:27.483Z
This link explains how to get the frequency information of an image, which you could use to know how much aliasing there would be if you downsized the image: https://blog.demofox.org/2016/07/28/fourier-transform-and-inverse-of-images/
Alan Wolfe
CC BY-SA 3.0
2017-07-14T15:32:26.470Z
2017-07-14T15:32:26.470Z
Dan Hulme
<p>I was looking into measuring the amount of aliasing in an image. After reading through many papers and sites, I came to the conclusion that the best method to measure the amount of aliasing in an image is by utilizing the frequency domain. </p>

<p>Is there a relationship between spatial frequency of an image and aliasing? 
Also, is there any other metric that one can use to measure the amount of aliasing that is present in an image?</p>

<image-processing><antialiasing><image-comparison>
Relationship between spatial frequency of an image and Aliasing
Varun Vijaykumar
# Relationship between spatial frequency of an image and Aliasing

(Asked by: username_0 on 2017-07-14)

I was looking into measuring the amount of aliasing in an image. After reading through many papers and sites, I came to the conclusion that the best method to measure the amount of aliasing in an image is by utilizing the frequency domain.

Is there a relationship between spatial frequency of an image and aliasing?
Also, is there any other metric that one can use to measure the amount of aliasing that is present in an image?

**Tags:** image-processing, antialiasing, image-comparison


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## 1 answers

### Answer by username_1 on 2017-07-14. Score: 7

Like in any other kind of signal processing, the relationship is Nyquist's theorem. An image is a discrete sequence of samples of a continuous signal. If the original signal has frequency components higher than half the sampling rate, then there will be aliasing. To put that another way, if you look at the real-world size of a pixel, any details smaller than two pixels wide will be aliased. This applies to synthetic images as well as to photographs. If you define a procedural texture via a mathematical function, the function is continuous but you only evaluate it at certain points.

The problem is, of course, if you only have the sampled image and not the original signal, the high-frequency components have *already* been aliased, so you can't measure them directly. You have to use statistical techniques to guess which details in your aliased image were originally higher-frequency signals.

> **Comments:**
> **username_0**: Thank you Dan.. is there any link that you can suggest for me to look further in to this (like a code or paper ) ?  
> **username_2**: This link explains how to get the frequency information of an image, which you could use to know how much aliasing there would be if you downsized the image: https://blog.demofox.org/2016/07/28/fourier-transform-and-inverse-of-images/  

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