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Block mathematical coding method of images compressed by a spiht algorithm p a p b p 2 i, 2 n (1) p a , p 2 i 1, 2 n (1) p b , p i, n p , p . 2 One can understand how the degree of compression of one block is changed from the following correlation: K 2 p log 2 ( p ) (1 p ) log 2 (1 p ) , (5) p a log 2 ( p a ) (1 p a ) log 2 (1 p a ) p b log 2 ( p b ) (1 p b ) log 2 (1 p b ) where K(p a ,p b ) is symmetric relatively to the arguments function which is equal to 1, with p a =p b , which means there is no change in the size of compressed information. In this case, there will be no benefit from partitioning the data stream into smaller parts. When p a ≠p b , then K>1, and this (Fig. 6) means a decrease of the initial amount of multimedia data, which will be sent to the telecommunication network. Fig. 6. The dependence of the coefficient of the information K amount reduction while splitting the block of coding p=p a +p b In Figure 6, with the schedule K(p a ,p b ) it can be seen that the degree of information compression is greatly increased at the maximum difference between p a and p b . For making a decision to reduce encoding blocks, it is necessary to have an estimate of |p a -p b |. The evaluation may be performed with the help of the concept of fractal dimension of a numerical sequence [11] (Fig. 7, 8). 1. Fractal dimension F is close to 2 (Fig. 7). As the number of reports of the curve increases, the curve gradually fills the plane – new fractures commensurate with the scale of the previous ones. As a consequence, we get the high compression ratio from (4). 2. Fractal dimension of F is close to 1 (Fig. 8). In this case, the specified curve will almost repeat the previous one, and specifying the probability of a sample unit to increase the information compression rate will not succeed. For a sequence of probabilities {p 0 ,p 1 ,...,p 2n-1 } on larger blocks we’ll get a set of probabilities: {(p 0 +p 1 )/2,(p 2 +p 3 )/2,...,(p 2n-2 +p 2n-1 )/2} at a conditionally unit interval. The lengths of the curves for the first and second sequences are as follows: A local fractal dimension of the curve will be: n 1 p p 1 2 n 1 2 i 2 i 1 L 1 , L 2 p i i 0 2 n i 0 F (n) = log 2 (L 2 /L 1 ). 1 . 2 n www.<strong>ijcer</strong>online.com ||May ||2013|| Page 37
Block mathematical coding method of images compressed by a spiht algorithm Fig. 7. Clarification of a line with the fractal dimension 1.8 Fig. 8. Clarification of a line with the fractal dimension 1.12 In order to determine the fractal dimension to evaluate the improvement of data compression, we consider two extreme cases: The dimension is understood here as the number of F, which shows to what extent a should be raised to get a coefficient of the curve elongation, having reduced the "line" at a times. With a length of L, the line has n segments of {(p i ,i/n);(p i+1 ,(i+1)/n)}. The average length of one segment will be =L/n. When the number of blocks increases from n 1 to n 2 (n 1
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