Transformation of the photomaton

The transformation of the photomaton is a description of a type of mixture similar to a Photomaton which starting from an image manufactures four of smaller dimensions of them, and so on by Itération. This transformation is a particular case of bijective Transformations of images.

History

This transformation was introduced in 1997 by JP Delahaye and P Mathieu into the review For Science

Presentation

The principle of this transformation is the following: the image is recomposed in 4 recursively narrowed images. The image is cut out in squares of 4 pixels, the pixel in top on the right of a square is used to recompose an image of size $1/2$ in top on the right, idem for the part in top on the left, bellow on the right, bellow on the left. This transformation functions only with images of which height and width are even. Period of return: if $larg=2^n$ and $haut=2^m$ then $ppcm (N, m)$ , if not calculation is more complex.

It is important to note that the 4 images which appear after a stage of transformation are not identical as they would be it with the camera of the company Photomaton. The 4 images are quite different within the meaning of the pixels which they contain. They come from a redistribution of the pixels of the initial image without any duplication nor loss.

A software is available in the form of Applet Java to test various transformations on the images of its choice was carried out with the LIFL/CNRS of Lille.

Applications

It is mainly about a technique of transformation of images used into Data processing. One compares it with the Transformation of the baker like illustration of the Théorie of chaos. Indeed, a weak difference with the departure (for example 2 close pixels) led to a great difference at the end of some iterations. However contrary to the transformation of the baker, the difference ceases growing and the pixels take again a close position thereafter.

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