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amylase

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What does it mean to display a picture in its frequency domain? A solid square box becomes a star shape?

SHORT VERSION

SHORT VERSION

As title thanks. Firstly, what does it mean to show a picture in its frequency domain? and secondly, how do you do it?

**LONG VERSION**

I am looking at this webpage

http://www.paulbourke.net/miscellaneous/imagefilter/

which shows a white solid square is actually star shaped in frequency domain. I don't understand how you go from the white square to the star below it.

What does it mean to display a picture in its frequency domain? Asked differently, what does it mean to apply Fourier Transformation to a picture?

Suppose I have an image. We can apply Fourier Transformation to it and get the spatial frequency of this image.

What exactly does it mean spatial frequency?

What do you actually do to the pixels, to convert them to frequency?

This is how I understand it. Please correct me:

An image is made up by pixels.

If we lay the pixels out linearly ie. take first line of pixels, then just next line of pixels immediately after the first line, then join onto third line of pixels and so on. Basically lay the 2D image out as a serial array of pixels, start from upper left hand corner of the picture, all the way to right lower corner.

Each of these pixels has an intensity (brightness).

I can plot them on a graph where y-axis is intensity of pixel, and x-axis is the number of pixel.

So for example pixel 1, intensity 100; pixel 2, intensity 10; pixel 3, intensity 40 and so on. Just plot all of them on brightness vs pixel graph.

The graph is going to be a very complicated wave.

Fourier Transformation will let me break down this complicated wave to the sum of many many sine waves of various frequencies, amplitudes and phases. It might take 2000 different sine waves to make them add up to give the combined effect of the complicated wave, but that's what FT will do for me. I am happy with the maths.

Is this what spatial frequency is about?

I still don't get how the webpage manages to change the box to star.

Thanks.