Effect of Gray coding on the state and the distribution of data bits in cross point regions

This paper supplements the effect of Gray code transformation on cross points which are neighbor to the points of gray levels 2ⁿ with Gray codes of cross points on bit plane n-2. By the natural characteristic of images, the data do not change much in a specific area, so at first the effect of Gray codes is determined with an adjacent data set, then it will be generalized for real data without losing the generality of their statistical characteristics, especially in medical images which contain many regions having the same gray scale. A further conclusion, being also a consequence of this effect, is the change of data bits for Gray codes in the regions of cross points from original data bits. This makes the probabilities of data bits on specific bit planes in those regions and then the entropies of messages, be changed. This fact has important effects on encoding and decoding processes.