In order to reveal regularities in sequences of series lengths, it is necessary to justify an informative attribute possessing the following properties: 1) is informative for the lengths of the binary series, taking into account the adaptation to the peculiarities of the formation of arrays of the binary mask of the differential frame. Here, it is required to provide a potential opportunity for reducing redundancy for arbitrary content of the bit plane; 2) do not require significant computational costs for estimating and detecting regularities that do not exceed order O(n) ; 3) to ensure that there are sharp structural differences for the binary indicators of the stationary and dynamic components of the differential frame represented. The compression ratio of the differential-represented frame's binary mask varies from 3 to 21 depending on the correlation coefficient between adjacent frames. The most preferable method for constructing the compact representation technology of the binary masks of frames represented in a differential form is the approach. It will be developed an approach for reducing redundancy in arrays of a binary mask of a differential frame based on the requirements advanced.
1. Introduction
In order to take into account the proposed requirements, it is proposed to use the approach for code representation of the sequence of binary mask series lengths. Which is based on the discovery of regularities in the alphabet's power . The data source alphabet is a set of values that message elements can accept. Then the power of the message source alphabet is the number of different elements in the alphabet. One of the simpliest and at the same time effective codes that take account of restrictions on the alphabet's power are Bodo codes. The Bodo code corresponds to the first two requirements.
A simple Bodo element-by-element code
provides information about:
- the size of the computer memory;
- the maximum value rmax of the series length
in the arrays of the differential frame's binary
mask [
If a lengths sequence of binary series is given, i.e., = {r1,..., rФ} then a simple Bodo code is formed from three stages:
Stage 1. The maximum value of the length of the binary series is sought, for which the formula is used:
rmax = 1miaxФ(ri ) .
Stage 2. The determination of the number of bits L(r) , which is required to represent the maximum value of the binary series rmax length, which is given by the relation:
L(r) = [log 2 rmax ] +1 .
Step 3. The value L(r) is writing at the
beginning of the code representation and is the
service information, which is indicating the code's
description boundaries of the neighboring image
elements [
L(r) = Ф L(r) .
Bodo's simple block code consists in
representing in each code word several elements
of the original image fragment. For example, this
situation occurs when several elements of the
encoded sequence are represented in one
computer word (one external memory register).
(1)
(2)
(3)
2. Research of a compact
representation of a
differentialrepresented frame's stationary
component's binary mask array
The Bodo method is mono-alphabetic. In this
case, all elements of the processed sequence
belong to the same alphabet. Such sequences are
called mono-alphabetic [
However, the Bodo code does not meet the
third requirement. This is due to the fact that the
differential-represented frame's binary mask,
under conditions of removal by a stationary
camera, has a significant heterogeneity of the
structural content. Under the heterogeneity of the
structural content is understood that the stationary
component can occupy a considerable space, cut
by small elements of the dynamic component. In
this case, the lengths r(0) formed for the zero
sequences will prevail over the length relative to
the lengths r(1) of the individual element
sequences [
i=1
L(r)i - the number of bits per representation of the i-th element of the sequences of the mask's binary series lengths;
Ф - the number of the binary series lengths, which are formed for the binary mask array of the differential frame.
At the same time, due to the heterogeneity of the structural content, the actual number of binary bits necessary to represent the entire sequence of binary series L(r) lengths will be much less than the value L(r) , ie:
This leads to the presence of code redundancy: L(r) L(r)
R = L(r) − L(r)
This situation is due to the fact, that for the code representation of the units' series lengths, a significantly smaller number of bits is required in comparison with the code representation of the zeros' series lengths, ie:
L(r(1)) L(r(0))
L(r(1)) - the number of bits for the code representation of the zeros series lengths;
L(r(0)) - the number of bits for the code representation of the units' series lengths.
In order to eliminate the code redundancy, it is
proposed to use two alphabets for the sequence
of binary series lengths [
The essence of the scheme is that: 1. The lengths of the zeros and ones series are formed, which are based on the array of the binary mask.
2. The entire sequence of binary series lengths is divided into two sub-sequences.
The first sub-sequence is formed on the basis of the zeros' series lengths: (0) = {r(0)1,..., r(0)Ф } 0
The second sub-sequence is formed on the basis of the units' series lengths: (1) = {r(1)1,..., r(1)Ф } 1
Then the total number of bits per representation of the subsequences of the zeros' series lengths will be:
L(r(0)) = Ф0 log 2 r(0)max , (4)
And the total number of bits per sub-sequence representation of the units' series lengths will be: (5)
L(r(1)) = Ф0 log 2 r(1)max .
3. For each subsequence, own alphabet is forming, respectively, 1 and 0 .
4. The power code is constructed in
accordance with the constructed alphabets [
The power code is constructed according to the scheme, which is considered above, is called a two-halftone code. In other words, a twoalphabetic power code is a power code generated for two-alphabetic sequences.
Here, the sizes of the binary regions are taken into account as a result of identifying the binary series lengths. It will be shown, that for a twoindex power code relative to the binary series lengths of the differential frame's binary mask, the condition holds, i.e. provides a degree of compression: м =
mмnм Ф0 log 2 r(0)max + Ф1 log 2 r(1)max = = Ф i=1ri Ф Ф log 2 (r(0)m0ax r(1)m1ax )
Ф0 -the number of the zeros' lengths for the binary mask of the differential-represented frame; Ф1 - the number of units' series lengths for the binary mask of the differential-represented frame.
Example. Let's calculate the number of digits L(r) in order to represent the entire sequence of series lengths for the binary mask of the differential-represented frame Q due to a one-rate power code.
First, let's define the maximum value of the binary series length rmax in a sequence of binary series lengths = {r1 = 19; r2 = 1; r3 = 4; r4 = 5; r5 = 1; r6 = 3; r7 = 3} , which is based on expression r1 = 19 ; L(r)1 = 5 bits; r2 = 1 ; L(r)2 = 1bit; r3 = 4 ; L(r)3 = 2 bits; r4 = 5 ; L(r)4 = 3 bits; r5 = 1; L(r)5 = 1 bit; r6 = 3 ; L(r)6 = 2 bits; r7 = 3 ; L(r)7 = 2 bits.
The maximum binary mask series length of a differential-represented frame rmax = 19 . Then, on the basis of expression (2), the number of bits required to represent the maximum binary mask series length is equal to L(r) = 5 bits.
The number of the binary series lengths is formed for the differential frame's binary mask's array Ф = 7 . Then, on the basis of the expression (3) the total number of bits on the representation of the binary series lengths sequence will be equal to a L(r) = 5 7 = 35 bits.
At the same time, 36 digits are required for the
code representation of the original image
fragment (the image fragment is classified as
highly saturated with details having different
dynamic components) [
At the same time, 36 bits are required for the code representation of the original image fragment (the image fragment is classified as highly saturated with details having different dynamic components). Therefore, due to the use of a double-alphabetic power code for the subsequences of the lengths of zeros and ones series. The differential-represented frame's binary mask volume will decrease by 20%. Also, due to the double-alphabetic power code, the volume of the differential-represented frame's binary mask is relative to the single-alphabet code will decrease by 17%. 3. Conclusions
1. As the correlation coefficient between adjacent frames increases, the compression ratio of the differential-represented frame's binary mask increases.
2. The compression ratio of the differentialrepresented frame's binary mask varies from 3 to 21 depending on the correlation coefficient between adjacent frames.
3. Estimation of the bit representation's information content of the differentialrepresented frame's binary mask on the basis of accounting for the nonequilibrium of the bases of the lengths of the binary series does not require an increase in the complexity of the softwarehardware implementation.
4. Due to the double-alphabetic power code, the differential-represented frame's binary mask is relative to the single-alphabet code will decrease by 17%. 4. References