Cellular Automata for Efficient Image and Video Compression - Cellular Automata in Image Processing and Geometry - page 12

Fig. 1.8 Cell rules in a 5-cell neighbourhood in order to obtain good HCA chaotic counters

for the longest cycle) only for an odd number of cells n ; This will make them useful
in image and video only for sensing arrays with an aspect ratio of 2:1.
ii) Recently we were able to locate a good counting automaton within the class of
4 inputs positioned in a 5-cell neighbourhood. This automaton (ID

3335309004)
is conservative for any number of cells, including even ones , as required by the
commonly used square image sensors. A near-optimal mask for the case n

=

= 18 (i.e.

addressing a 512 154.

The loss of 154 pixels is insignificant for such a compression scheme where the
number of scanned samples K

× 512 pixels image) is 17855. For this mask L = 261990 = N −

<< N

1.2.4 Message Recovery and Examples
It is assumed that in order to reconstruct the image Y a counting automaton similar
to the one used in the measurement process is available. Also, it is operated in syn-
chrony with the one available in the Tx unit. They would either start from the same
initial state or they may be synchronized using the binary synchronization property.
The recovery counting automata follows the same dynamics as in the measurement
process during the scanning of the K received samples.

The reconstruction algorithm is:
RESET the counting automaton
INITIALIZE all pixels in Y with 0.5;
FOR k = 1,..K
i = rand_i ; j = rand_j ;

Y = B i , j s ( k )+ Y ⓦ ( 1 − B i , j ) (1.3)

END