During my [https://www.instructables.com/id/Decoding-Secret-Messages-from-Space/ playful expermints] with Fourier Transforms, I discovered that you can overlay an image on top of a Fourier transformed image, and freely convert back and forth from Fourier to regular space. Each transform would descramble the previously FFT'd image. So in short, you can hide the FFT of one image in another image.

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Here's the plainly plain message that I want to hide:

## Step 1: FFT Your Image!

GIMP has an FFT plugin filter (so I'm told), but I used a plugin for Shake.

I've put it in the bottom half of the picture so it will still be intelligible after being transformed. Here's the FFT of my secret message:

## Step 2: Hide Your FFT in Another Image

My first test overlaid the FFT over a color wheel, and it's a bit obvious something wierd is in the center:

## Step 3: Offset or Scroll the FFT

If we scroll the FFT over to the corners and scale down the brightness, it's much harder to spot when overlaid with the zucchini-in-a-bottle image:

## Step 4: FFT the Image to Decode

FFT the image again to see the secret message again. Some information is lost when the image is saved in the .tif format, but after we scale the brightness back up, we get this:

## Step 5: My Whole Process in an Image

Here's my whole shake tree for both the test image and the final masterfully masterfool zucchini-hiding-a-secret image. Have fun with this!

## 5 Discussions

9 years ago on Introduction

Clever - I wonder how much this method is being used for covert transmission of messages already. It's many years since I had anything to do with Fourier transforms. I passed the exams, but more by remembering the equations and plugging in the numbers than actually unsderstanding them.

I can see how you can convert an audio signal to the time domain, but how does that relate when you're transforming an image?

Reply 9 years ago on Introduction

You sample the image one line at a time. The brightness becomesamplitude (y) and the horizontal pixel position becomes the horizontalsample position (x).

Other than that, there's a pretty useful page here: www.cs.unm.edu/~brayer/vision/fourier.html

Reply 9 years ago on Introduction

I get the idea. The link makes interesting reading - Thanks.

9 years ago on Introduction

Nice to see you back, RE...

Reply 9 years ago on Introduction

Thanks! It's good to be back. I liek making stuff and seeingthe great things others have created.