Fourier Anime - Image Transforming by the "Fourier transform" - app for iPhone and iPad

The Fourier Anime is an image transforming application using the "Fourier transform".

Visual expressions applied pure mathematics are really various and it brings us ones beyond our imagination in some cases.
The Fourier Anime, based on a widely used transformation theory of the "Fourier transform", produces extremely curious animations.

How to use the app:
1.Take a photo or Choose your picture.
2.Waiting for a while during the converting.
3.You get the animation.Let’s share with E-Mail or Tumblr!


Next Version :
Coloring the animation.
Share with Twitter and Facebook.


About the "Fourier transform" :

Waves can be expressed in the superposition of basic waves (sin or cos functions). Fourier Transform calculate the weight of each trigonometric function when waves are written as the sum of these functions. In our daily life, the transformation is utilized in various products such as mp3, JPEG compression or iTunes equalizer.


How to convert images :

1. Edge Detect
Differentiate the luminosity value of the monochrome input image, then we can get the edges where the luminosity are changing significantly.

2. Find Contours
Extract contour curves from the edge image one by one.

3. Fourier Transform
Contours are the sequences of points. Convert this complex sequences into Fourier coefficients by Fourier transform.

4. Low-pass Filter
Leave only the coefficients of low-frequency parts.

5. Inverse Fourier Transform
Reconstruct the complex sequences of points from low-pass filtered Fourier coefficients. And draw the curves in the display (parametric representation).