# The PCIF algorihtm: decomposition

At this point the image is decomposed in 24 matrixes containing only zeros and ones. Each of these matrixes will refer to one of the 8 bits of the bit representation of one of the 3 primary colors representing the image.

What we expect after this phase are some very chaotical layers relatively to the least significative bits and some matrixes with lots of zeros corresponing to the most significative bits. Another important property that we can find is that the ones in the more ordered layers are often grouped together, offering highly compressible data to the tecniques that will follow this phase.

During the decomposition the algorithm also counts the number of zeros and ones in each layer; this will be usefull to extimate the chaos in each matrix and determine with which tecnqique this will be compressed or to determinate, if the layer is too chatic, that the algorithm can save time storing it as it is as there would be a very low gain obtained through its compression.

The figure represents how the famous Lenna image is decomposed into layers by the algorithm after the various filtering phases:

After the decomposition phase, layers are sufficiently uncorrelate one from another to allow the following compression phase to operate on them separately without losing compression efficience.