Fourier Transforms for the non-mathematician

There are a few areas of computer vision and image processing where a little bit of maths is hard to avoid. Luckily for me (I’m no mathematician) these are few and far between – in most cases these days, either the maths is not too advanced, or the popular libraries (such as OpenCV) help hide the worst of it and let us get on with being ‘practitioners’.

However, one exception that keeps cropping up is Fourier Transforms. They are everywhere in computer vision, and for good reason: they help solve a lot of problems (I’ll write another post about this when time allows, but my current project has been revolutionised by using Fourier Transforms).

However, almost all explanations plunge straight into maths, involving the so-called complex numbers: the square root of minus one, and all that. The simple truth is that my school maths (hi, Mr. Feakes!) didn’t equip me for this, and I strongly suspect I’m not alone. While OpenCV helps hide the real nuts and bolts, an intuitive explanation of what is going on is essential to help decide when to use this tool, and just on a basic level, how it works.

So I was very pleased to find the following: An Intuitive Explanation of Fourier Theory, with pictures, and no hard stuff. Just enough for me to understand intuitively how this works – perfect. Thanks to Steven Lehar for writing it.

EDIT 2014-04-16: Having been in touch with Steven to thank him personally, he has recommended a number of other articles for people who, like me, prefer ‘intuitive’ approaches to things. In particular, I’m looking forward to studying two – one of his own, and one other he recommends:

A Visual, Intuitive Guide to Imaginary Numbers

Clifford Algebra: A visual introduction

Thanks again, Steven.