IFSAF the underlying theory

Giovambattista Pulcini's
pages on Fractal Image Compression

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IFSAF the underlying theory

How the True-Color Encoding works

Background
To understand the following, you should already know how fractal image compression works on gray-scale images, specifically the fractal image compression through IFS with exahustive search in the domain-pool.
The knowledge of Fisher's paper SIGGRAPH92 course notes, and Jaquin's Fractal Image Compression - a review on IEEE transaction - should suffice.

Abstract
We use YIQ color model to exploit human eye different sensitivity to the Y,I,Q channels. So we assign more bits to Y and less bits to I,Q. But this all is trivial.
For each range block, we search for the best-matching domain block on the Y channel and we use the corresponding⁽¹⁾ blocks in I,Q channels as well-matching⁽²⁾ blocks for the I,Q components. So we have only 1 geometric transformation (the isometry and the address of the selected domain block) for all the three components YIQ, while we recompute the optimal massic transformation for each of the YIQ channels.
This approach can both save compression time and increase the compression ratio; compared to the obvious three separed encoding of each YIQ channel.

1 - For corresponding blocks we mean those blocks that have the same coordinates in the image. Or, in other words, those three blocks (one in each of the Y,I,Q color planes) that are the color components of a block in the true-color image.

2 - Obviously they are not the best matching blocks, but here is the matter: we allow sub-optimal block mapping on the I and Q channels.

How we can encode true color images
In the first stage we have to convert the image from the RGB model to another color model that is more suitable for exploiting the differences in how the human eye perceives the colors.
These models can be one of YIQ, YUV, HLS, HVS. We selected the YIQ model. Since the variance of the chrominance data (I,Q) tend to be less than the corrisponding one of the Y channel, we can save space reducing the dynamic range of I and Q channels.
Once we have selected a color model there are three ways of doing the encoding:

To treat disjointly the 3 channels, doing 3 different encodings with different parameters: we could decrease bits for alpha and beta, reducing the 2 images and then restoring the original size in the decompresion, etc.
To treat the color image as a whole, doing all transformations directly on the color image. Obviously, each single transformation will be splitted in 3 parts, but all decisions are made upon global values - eg. a global error - and not on separated values for each channel.
A mixing of these two methods. That's to say to encode jointly and asymmetrically the 3 channels.

How we do encode true color images
Let we have a true-color image in RGB format (24bpp) which we split into Y,I,Q color planes. Now we could apply three times the gray-scale algorithm (such as the prof. Fisher's enc.c) to the Y, I and Q channels (obviously we can use different encoding parameters for each channel, privileging the Y at the expense of I and Q). In so doing we'll get an algorithm that is almost 3 times slower than the gray-scale encoding. That's why we have developed a different approach.

Examinating several different images and their related YIQ color planes, we noticed that something as the "shape" of the gray-scale image on each channel is preserved - even if not exactly -.

We noticed that if in a range block of the component Y there is some sort of a detail, we can distinguish its shape in the I and Q components too, even if more or less attenuated in gray-level luminance of that channel. What is interesting in this all, is that we don't need to change the parameters of the geometric transform (offset of best block and isometry) across the three channels, while recalculating the massic transform parameters for each channel.

Giovambattista Pulcini'spages on Fractal Image Compression