Cellular Automata for Efficient Image and Video Compression - Cellular Automata in Image Processing and Geometry - page 7

Fig. 1.4 Image recovery with chaotic scan after receiving K = 0 . 05 N pixels (5% of all N
pixels of the original image); Too small values of the recovery block size ( L ) makes the
received image difficult to read while using too large L values impede on image details.
Depending on the image content there is an optimal L value (here, L = 8) such that the
semantic content is best revealed.

Without loss of generality in the next we will use rand_i rand_j to denote the
reading of the next state of the counting automaton (split into n

/

2 bits for line “i”

and n / 2 bits for column “j”).

1.2.2 Properties of the Chaotic Counters

In order to understand the properties required for the chaotic counter, we shall con-
sider it as a particular case of discrete-time, discrete-space dynamic system (au-
tomaton). Any such dynamic system, also called a nonlinear map is defined by a
feedback function F imposing a certain profile of the state space (partitioned into
certain attractors and their basins of attraction).