CN101448156B - Selection method for square wave orthogonal function system for image analysis and software/hardware realization method thereof - Google Patents

Abstract

The invention relates to a selection method for a square wave orthogonal function system for image analysis. The method comprises the following steps: under the condition of N pixel, supposing that N is equal to 2<m>, orthogonal square wave analytical functions in the number of N can be constructed within a frequency range from 0 to m; supposing that the frequency is i and the value range is 0 tom, and presupposing that i is equal to 0; when i is equal to 0, the function expression is that f0_0(n) is equal to 1, the condition is that n is larger than or equal to 0 and smaller than or equal to (N-1), and n belongs to R; when i is not equal to 0, components numbering 2<i-1> need to be constructed at each frequency i, the component is expressed by j, the value range of j is from 0 to 2<(i-1)>-1, and presupposing that j is equal to 0; the pulse width at each frequency i is recorded as d is equal to (N/2<i-1>) /2 and is further equal to 2<m-1>; constructing the function fi_j(n) of the component j at each frequency i; after constructing the function of each component at the current frequency, i is increased by 1 progressively, and continuing to construct the function at the next frequency; the function Fi_j can be obtained by dividing each function fi_j by (square) root 2d for standardization. The orthogonal function system selected by the method is suitable for analyzing images and digital signals, and is superior to the prior method on the realization expense and the efficiency of software and hardware.

Description

The square wave orthogonal function system of graphical analysis is chosen and method of software and hardware

Technical field

The present invention relates to art of image analysis, be specifically related to a kind of choosing method and method of software and hardware thereof that is used for the orthogonal function system of digital picture and compression of digital video encoding and decoding.

Background technology

The digital compression coding techniques is to make digital signal move towards one of key technology of practicability.For the behavior of standard compressed encoding, many international standards have been put into effect at present, as image compression standard JPEG (international standard ISO/ICE IS 10918), video compression standard MPEG-1 (international standard ISO/ICE 11172), MPEG-2 (international standard ISO/ICE 13818), MPEG-4 (international standard ISO/ICE 14496), H.264 (international video compression standards of new generation) etc.

In these compressed encoding standards and technology, a method in common is arranged, that just has been to use the orthogonal transform technology.At present at JPEG, MPEG-1, MPEG-2, MPEG-4, H.264 in, used orthogonal transformation method all is discrete cosine transform (Discrete Cosine Transform is called for short DCT).DCT is the normal instrument that adopts of Classical Spectrum analysis, and his appearance has landmark meaning to digital picture and video compression technology, and it is earlier image to be divided into N * N block of pixels, then N * N block of pixels is carried out discrete cosine transform one by one.Cast out then the insensitive frequency information of vision, only keep of paramount importance data message.Like this, compression process must have loss to the fine and smooth level and smooth degree aspect of image.People also attempt research and seek other better more effective orthogonal transforms to replace DCT, as Fourier transform, and discrete sine transform etc.But these conversion all can't surmount DCT on performance, even differ also far away.Some evidence proof DCT " almost being optimal transformation " have also been arranged in theory.So over thirties years, whether the whole world is being studied this problem of better conversion on image and video compression, does not obtain a sure answer always.

The content of invention

The purpose of this invention is to provide a kind of differently, be used for the square wave orthogonal function system choosing method and the method for software and hardware thereof of graphical analysis with discrete cosine transform.The orthogonal function system of selecting with the method is particularly suitable for analyzing images and digital signals, has avoided producing in the discrete cosine transform problem of match difference, and realizes all being better than on cost and the efficient existing method at software and hardware.

Technical scheme of the present invention is as follows:

A kind of square wave orthogonal function system choosing method of graphical analysis comprises earlier image being divided into N * N block of pixels, may further comprise the steps:

1) under N pixel condition, establishes N=2 ^M(m 〉=0) then can construct N quadrature square wave analytic function 0 in the m frequency range;

2) establishing frequency is i, and the span of i is 0 to m, default i=0;

3) when i=0, function expression is as follows:

f _{0_0}(n)=1, condition is: 0≤n≤N-1, n ∈ R;

Frequency is that i increased progressively 1 after 0 construction of function was finished, and continues the function under the next frequency of structure;

4) when i ≠ 0, need to construct 2 under each frequency i ^I-1Individual component, component represent that with j the span of j is 0 to 2 ^(i-1)-1, default j=0;

Pulse duration under each frequency i is designated as d=(N/2 ^I-1)/2=2 ^M-i

5) the function expression f of the component j under each frequency i _{I_j}(n) following (wherein 0≤n≤N-1, n ∈ R):

f _{I_j}(n)=0, condition is: n＜2jd or n 〉=2jd+2d;

f _{I_j}(n)=1, condition is: n 〉=2jd and n＜2jd+d;

f _{I_j}(n)=-1, condition is: n 〉=2jd+d and n＜2jd+2d;

6) after the construction of function of the current component j under the current frequency i was finished, j increased progressively 1, continued the function of the next component under the current frequency i of structure;

7) after the construction of function of each component was finished under the current frequency i, i increased progressively 1, continued the function under the next frequency of structure;

8) each function f _{I_j}By divided by Standardize and obtain function F _{I_j}

A kind of hardware implementation method of the square wave orthogonal function system choosing method based on described graphical analysis, earlier image is divided into 8 * 8 block of pixels, minimum arithmetic element of design in hardware designs, described minimum arithmetic element is used for handling 8 continuous images input data data1～data8, generate later 8 dateouts at 8 clocks, respectively representative function f _{0_0}, f _{1_0}, f _{2_0}, f _{2_1}, f _{3_0}, f _{3_1}, f _{3_2}, f _{3_3}

A kind of software implementation method of the square wave orthogonal function system choosing method based on described graphical analysis is divided into 8 * 8 block of pixels with image earlier, with 8 * 8 orthogonal transform matrixs to each 8 * 8 pixel fritter A _{8 * 8}Make two-dimensional transform, obtain transform coefficient matrix M _{8 * 8}, its expression formula is:

M _8×8＝D _8vA _8×8D _8h

Wherein, D _8hAnd D _8vRepresented 8 * 8 horizontal quadrature transformation matrixs and 8 * 8 perpendicular quadrature transformation matrixs respectively, and D _8vBe D _8hTransposed matrix;

Described 8 * 8 horizontal quadrature transformation matrix D _8hFor:

$D_{8h}=\left[\begin{array}{cccccccc}\frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& \frac{1}{\left(\sqrt{2}\right)}& 0& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& -\frac{1}{\left(\sqrt{2}\right)}& 0& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& \frac{1}{\left(\sqrt{2}\right)}& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& -\frac{1}{\left(\sqrt{2}\right)}& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& \frac{1}{\left(\sqrt{2}\right)}& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& -\frac{1}{\left(\sqrt{2}\right)}& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& 0& -\frac{1}{\left(\sqrt{2}\right)}\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& 0& \frac{1}{\left(\sqrt{2}\right)}\end{array}\right]$

As further scheme of the present invention:

Described 8 * 8 horizontal quadrature transformation matrix D _8hIn any one row all reindexing, be above-mentioned 8 * 8 horizontal quadrature transformation matrix D _8hEquivalent transformation.

If ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\sqrt{8},$ ${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=\sqrt{4},$ ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\sqrt{2},$ Define an INTEGER MATRICES P _8hWith a diagonal matrix E:

$P_{8h}=\left[\begin{array}{cccccccc}1& 1& 1& 0& 1& 0& 0& 0\\ 1& 1& 1& 0& -1& 0& 0& 0\\ 1& 1& -1& 0& 0& 1& 0& 0\\ 1& 1& -1& 0& 0& -1& 0& 0\\ 1& -1& 0& 1& 0& 0& 1& 0\\ 1& -1& 0& 1& 0& 0& -1& 0\\ 1& -1& 0& -1& 0& 0& 0& 1\\ 1& -1& 0& -1& 0& 0& 0& -1\end{array}\right],$ $E=\left[\begin{array}{cccccccc}1/{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1& & & & & & & \\ & 1/{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1& & & & & & \\ & & 1/d_2& & & & \mathrm{<figure-callout\; id="1"\; label="O"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">O</figure-callout>}& \\ & & & 1/{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2& & & & \\ & & & & 1/d_3& & & \\ & & \mathrm{<figure-callout\; id="1"\; label="O"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">O</figure-callout>}& & & 1/{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_3& & \\ & & & & & & 1/{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_3& \\ & & & & & & & 1/{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_3\end{array}\right]$

With described 8 * 8 horizontal quadrature transformation matrix D _8hBe decomposed into: D _8h=P _8hE, then the expression formula of transform coefficient matrix is:

M _8×8＝D _8vA _8×8D _8h＝E(P _8vA _8×8P _8h)E，

P wherein _8vA _{8 * 8}P _8hFor only containing the integer arithmetic of addition and subtraction, P _8vBe P _8hTransposed matrix.

Useful technique effect of the present invention is:

With the square wave orthogonal function system that the inventive method is selected, there is not the match between string wave function and actual discrete signal poor, be particularly suitable for analyzing images and digital signals, and realize all being better than on cost and the efficient existing method at software and hardware.

In hardware was realized, owing to only used addition and subtraction in the design, algorithm was simple, and the other hardware in side, chip form realize code decode algorithm especially, greatly reduce area of chip, have improved the computing frequency.Simultaneously, when receiving data, just finish computing, improved the parallel processing capability of circuit.

In software was realized, similar JPEG, MPEG-1, MPEG-2, MPEG-4, the DCT basis arithmetic section of scheduling algorithm H.264 can substitute DCT.Combine with the subsequent compression algorithm, can obtain good graph image compression effectiveness and compression ratio, the publish picture signal to noise ratio of picture of compression back data pressurization is low, and quality is good.

Description of drawings

Fig. 1 is the 0Hz frequency function.

Fig. 2 is a 1Hz frequency function component.

Fig. 3 is 2Hz frequency the 0th function component.

Fig. 4 is 2Hz frequency the 1st function component.

Fig. 5 is 3Hz frequency the 0th function component.

Fig. 6 is 3Hz frequency the 1st function component.

Fig. 7 is 3Hz frequency the 2nd function component.

Fig. 8 is 3Hz frequency the 3rd function component.

Fig. 9 is the hardware implementation method of 8 * 8 graphical analyses.

Embodiment

Below in conjunction with accompanying drawing the specific embodiment of the present invention is described further.

To each independent color image components, can be divided into whole component image the image block of several N * N pixel, by the orthogonal function conversion, concentration of energy on a few coefficient.

The orthogonal function system that graphical analysis is at present adopted is the discrete cosine function.As long as in fact the function system satisfies the basis that quadrature, canonical, convergence condition just can be used as analysis, be different orthogonal function system selection mode characteristic differences.

A kind of orthogonal function system system of selection based on square wave of the present invention's design, the orthogonal function system of selecting with the method is particularly suitable for analyzing images and digital signals, also satisfies quadrature, canonical, convergence condition simultaneously.

At this is the function system of example analysis explanation 2 dimension graphical analyses with 1 dimension.In the 2 dimension graphical analyses, the orthogonal function system system of selection on each dimension is the same.Therefore, only the selection of square wave orthogonal function system in the numerical analysis of one-dimensional signal is described.

Choosing of square wave orthogonal function system may further comprise the steps:

1) under N pixel condition, establishes N=2 ^m(m 〉=0) then can construct N quadrature square wave analytic function 0 in the m frequency range;

2) establishing frequency is i, and the span of i is 0 to m, default i=0;

3) when i=0, function expression is as follows:

f _{0_0}(n)=1, condition is: 0≤n≤N-1, n ∈ R;

Frequency is that i increased progressively 1 after 0 construction of function was finished, and continues the function under the next frequency of structure;

4) when i ≠ 0, need to construct 2 under each frequency i ^I-1Individual component, component represent that with j the span of j is 0 to 2 ^(i-1)-1, default j=0;

Pulse duration under each frequency i is designated as d=(N/2 ^I-1)/2=2 ^M-i

5) the function expression f of the component j under each frequency i _{I_j}(n) following (wherein 0≤n≤N-1, n ∈ R):

f _{I_j}(n)=0, condition is: n＜2jd or n 〉=2jd+2d;

f _{I_j}(n)=1, condition is: n 〉=2jd and n＜2jd+d;

f _{I_j}(n)=-1, condition is: n 〉=2jd+d and n＜2jd+2d;

6) after the construction of function of the current component j under the current frequency i was finished, j increased progressively 1, continued the function of the next component under the current frequency i of structure;

7) after the construction of function of each component was finished under the current frequency i, i increased progressively 1, continued the function under the next frequency of structure;

8) each function f _{I_j}By divided by

Standardize and obtain function F _{I_j}

In graphical analysis, N must be 2 power, for the most typical, adopts 8 in photo current/video compression standard with 4,8,16,32 these 4 values more.

Be unit with 8 * 8 common pixel elements now, the unit scope of what-if is N=8.Then need in the frequency range of 0～3Hz, construct totally 8 functions.Do not have the frequency concept of string Poona sample standard though it is pointed out that square wave, use the characteristic that this notion can be expressed selected quadrature square wave function more naturally.The system of selection of various frequency minor function is as follows:

The 0Hz frequency function, as shown in Figure 1, its expression formula is:

f _{0_0}(t)＝{1，1，1，1，1，1，1，1}(0≤t≤8，t∈R)，

Then $F_{0\_0}\left(t\right)=f_{0\_0}\left(t\right)/\sqrt{8}=f_{0\_0}\left(t\right)/2\sqrt{2}.$

1Hz frequency function component, as shown in Figure 2, its expression formula is:

f _{1_0}(t)＝{1，1，1，1，-1，-1，-1，-1}(0≤t≤8，t∈R)，

Then ${\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">F</figure-callout>}}_{1\_0}\left(t\right)={\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{1\_0}\left(t\right)/\sqrt{8}={\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{1\_0}\left(t\right)/2\sqrt{2}.$

2Hz frequency the 0th function component, as shown in Figure 3, its expression formula is:

f _{2_0}(t)＝{1，1，-1，-1，0，0，0，0}(0≤t≤8，t∈R)，

Then ${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\_0}\left(t\right)={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\_0}\left(t\right)/\sqrt{4}={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\_0}\left(t\right)/2.$

2Hz frequency the 1st function component, as shown in Figure 4, its expression formula is:

f _{2_1}(t)＝{0，0，0，0，1，1，-1，-1}(0≤t≤8，t∈R)，

Then ${\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">F</figure-callout>}}_{2\_1}\left(t\right)={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\_1}\left(t\right)/\sqrt{4}={\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\_1}\left(t\right)/2.$

3Hz frequency the 0th function component, as shown in Figure 5, its expression formula is:

f _{3_0}(t)＝{1，-1，0，0，0，0，0，0}(0≤t≤8，t∈R)，

Then ${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\_0}\left(t\right)={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{3\_0}\left(t\right)/\sqrt{2}.$

3Hz frequency the 1st function component, as shown in Figure 6, its expression formula is:

f _{3_1}(t)＝{0，0，1，-1，0，0，0，0}(0≤t≤8，t∈R)，

Then ${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\_1}\left(t\right)={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{3\_1}\left(t\right)/\sqrt{2}.$

3Hz frequency the 2nd function component, as shown in Figure 7, its expression formula is:

f _{3_2}(t)＝{0，0，0，0，1，-1，0，0}(0≤t≤8，t∈R)，

Then ${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\_2}\left(t\right)={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{3\_2}\left(t\right)/\sqrt{2}.$

3Hz frequency the 3rd function component, as shown in Figure 8, its expression formula is:

f _{3_3}(t)＝{0，0，0，0，0，0，1，-1}(0≤t≤8，t∈R)，

Then ${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">F</figure-callout>}}_{3\_3}\left(t\right)={\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">f</figure-callout>}}_{3\_3}\left(t\right)/\sqrt{2}.$

Above construction of function is finished.

As shown in Figure 9, the hardware implementation method of 8 * 8 graphical analyses.Earlier image is divided into 8 * 8 block of pixels, minimum arithmetic element of design in hardware designs, this minimum arithmetic element is used for handling 8 continuous images input data data1～data8, generates 8 dateouts later at 8 clocks, represents the f that is described to above respectively _{0_0}, f _{1_0}, f _{2_0}, f _{2_1}, f _{3_0}, f _{3_1}, f _{3_2}, f _{3_3}Can see and only use addition and subtraction in the hardware designs, greatly reduce area of chip, improve the computing frequency.Simultaneously, when receiving data, just finish computing, improved the parallel processing capability of circuit.

The software implementation method of 8 * 8 graphical analyses.The orthogonal transform matrix that is adopted in the computed in software is D,

$D_{8h}=\left[\begin{array}{cccccccc}\frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& \frac{1}{\left(\sqrt{2}\right)}& 0& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& -\frac{1}{\left(\sqrt{2}\right)}& 0& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& \frac{1}{\left(\sqrt{2}\right)}& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& -\frac{1}{\left(\sqrt{2}\right)}& 0& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& \frac{1}{\left(\sqrt{2}\right)}& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& \frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& -\frac{1}{\left(\sqrt{2}\right)}& 0\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& 0& -\frac{1}{\left(\sqrt{2}\right)}\\ \frac{1}{{\left(\sqrt{2}\right)}^3}& -\frac{1}{{\left(\sqrt{2}\right)}^3}& 0& -\frac{1}{{\left(\sqrt{2}\right)}^2}& 0& 0& 0& \frac{1}{\left(\sqrt{2}\right)}\end{array}\right]$

About the orthogonality of D, we only need checking DD ^T=I gets final product, here D ^TBe the transposed matrix of D, I is a unit matrix.Therefore, all reindexing of any row is regarded as equivalent transformation in the above-mentioned matrix.

We establish D _8h=D and D _8v=D ^T, be called 8 * 8 horizontal quadrature transformation matrixs and 8 * 8 perpendicular quadrature transformation matrixs.Image is divided into 8 * 8 block of pixels, then to each compressed video data block A _{8 * 8}(8 * 8 matrix) makes two-dimensional transform, obtains transform coefficient matrix M _{8 * 8}(8 * 8 matrix), promptly

M _8×8＝D _8vA _8×8D _8h，

So that finish follow-up compression encoding process.

This calculating formula has been expressed following implication: at first use above-mentioned Functional Analysis matrix D that horizontal 88 * 1 pixels (8 8 * 1 vectors just) are carried out matrix and take advantage of calculating, obtain 88 * 1 data, just middle 8 * 8 data values.To middle 8 * 8 data values, in the vertical, be re-used as 88 * 1 vectors and carry out matrix and take advantage of calculating, 88 * 1 data to the end, just last 8 * 8 analysis result data.Result's 8 * 8 data values, 8 * 8 pixels decompose the analysis result behind the function space of aforementioned Fi_j function 8 * 8, the component parameter on the representative function space at 2 dimension spaces exactly.

Equally as can be known, above-mentioned matrix D _8hIn any one row or matrix D _8vIn any all reindexing of delegation, be regarded as equivalent transformation.

On above basis, the present invention proposes a kind of conversion integer implementation method, establish ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\sqrt{8},$ ${\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=\sqrt{4},$ ${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\sqrt{2},$ Define an INTEGER MATRICES P _8hWith one to handing over matrix E as follows:

$P_{8h}=\left[\begin{array}{cccccccc}1& 1& 1& 0& 1& 0& 0& 0\\ 1& 1& 1& 0& -1& 0& 0& 0\\ 1& 1& -1& 0& 0& 1& 0& 0\\ 1& 1& -1& 0& 0& -1& 0& 0\\ 1& -1& 0& 1& 0& 0& 1& 0\\ 1& -1& 0& 1& 0& 0& -1& 0\\ 1& -1& 0& -1& 0& 0& 0& 1\\ 1& -1& 0& -1& 0& 0& 0& -1\end{array}\right],$ $E=\left[\begin{array}{cccccccc}1/{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1& & & & & & & \\ & 1/{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_1& & & & & & \\ & & 1/d_2& & & & \mathrm{<figure-callout\; id="1"\; label="O"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">O</figure-callout>}& \\ & & & 1/{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2& & & & \\ & & & & 1/d_3& & & \\ & & \mathrm{<figure-callout\; id="1"\; label="O"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">O</figure-callout>}& & & 1/{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_3& & \\ & & & & & & 1/{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_3& \\ & & & & & & & 1/{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200810242929XE00011.png,H200810242929XE00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_3\end{array}\right]$

Then described 8 * 8 horizontal quadrature transformation matrix D _8hBe decomposed into: D _8h=P _8hE, the expression formula of transform coefficient matrix is:

M _8×8＝D _8vA _8×8D _8h＝E(P _8vA _8×8P _8h)E，

P wherein _8vBe P _8hTransposed matrix.

Note P _8hAnd P _8vElement all be 0,1 ,-1 these several integers, A _{8 * 8}Element also all be integer.P like this _8vA _{8 * 8}P _8hComputing be the computing that only comprises plus-minus, avoided more senior computings such as multiplication, help the efficient realization of computational methods.

At JPEG, MPEG-1, MPEG-2, MPEG-4, H.264 in, conversion of the present invention can be used in every place of using discrete cosine transform.Below specify with image compression encoding.For the ease of contrast, the present invention utilizes the JPEG framework to implement.

In JPEG, the compression of image is divided into four big steps, comprises discrete cosine transform (DCT), quantization transform coefficient, the scanning of Z word and entropy coding.Its concrete steps are:

The fritter X that earlier image is divided into 8 * 8 pixels _{8 * 8}, use 8 * 8 discrete cosine transform (DCT then ₈) each image block is made two-dimensional transform, i.e. Y _{8 * 8}=(DCT _8v) X _{8 * 8}(DCT _8h), DCT wherein _8vBe classical discrete cosine matrix, DCT _8hBe DCT _8vTransposed matrix.

Obtain transform coefficient matrix Y by following formula _{8 * 8}, again to Y _{8 * 8}Each coefficient divided by a value, this process is called quantification, the matrix that these dividends constitute is called quantization matrix, and corresponding DCT is arranged in the JPEG ₈The quantization matrix of acquiescence.

The layout again of coefficient after the quantification, the number of purpose continuous in order to increase " 0 " coefficient is exactly the run length of " 0 ", and method is the style layout according to zigzag.Then, finish the compressed encoding output of coefficient with Huffman encoding (one group of fixing Huffman code table is arranged usually).

The process of decoding/decoding and the process of compressed encoding are just in time opposite.About these contents, in the normative document of JPEG, all can find.

In the present invention, we still keep above-mentioned JPEG compressed encoding flow process, and only we are with DCT _8hChanged D into _8h, just at formula Y=(DCT _8v) X _{8 * 8}(DCT _8h) in, with DCT _8hChange D into _8h, the corresponding Y that becomes of formula _{8 * 8}=(D _8v) X _{8 * 8}(D _8h), the also corresponding thereupon change of quantization matrix and Huffman code table.

The present invention does not have the match between string wave function and actual discrete signal poor owing to structure is square wave function.And classical DCT ₈The coefficient of matrix is very complicated, and the coefficient after the realization of matrix D of the present invention process conversion integer all is a small integer, makes things convenient for the efficient realization of algorithm, and has only addition and subtraction, convenient establishment simple algorithm.Combine with the subsequent compression algorithm of JPEG, can obtain good graph image compression effectiveness and compression ratio, the publish picture signal to noise ratio of picture of compression back data pressurization is low, and quality is good.

The above only is a preferred implementation of the present invention, is appreciated that those skilled in the art under the prerequisite that does not break away from spirit of the present invention and design, can make other improvement and variation.

Claims (5)

1. the square wave orthogonal function system choosing method of a graphical analysis comprises earlier image being divided into N * N block of pixels, it is characterized in that may further comprise the steps:

1) under N pixel condition, establishes N=2 ^m, N quadrature square wave analytic function then can be constructed 0 in m 〉=0 in the m frequency range;

2) establishing frequency is i, and the span of i is 0 to m, default i=0;

3) when i=0, function expression is as follows:

f _{0_0}(n)=1, condition is: 0≤n≤N-1, n ∈ R;

Frequency is that i increased progressively 1 after 0 construction of function was finished, and continues the function under the next frequency of structure;

4) when i ≠ 0, need to construct 2 under each frequency i ^I-1Individual component, component represent that with j the span of j is 0 to 2 ^(i-1)-1, default j=0;

Pulse duration under each frequency i is designated as d=(N/2 ^I-1)/2=2 ^M-i

5) the function expression f of the component j under each frequency i _{I_j}(n) as follows, 0≤n≤N-1 wherein, n ∈ R:

f _{I_j}(n)=0, condition is: n＜2jd or n 〉=2jd+2d;

f _{I_j}(n)=1, condition is: n 〉=2jd and n＜2jd+d;

f _{I_j}(n)=-1, condition is: n 〉=2jd+d and n＜2jd+2d;

6) after the construction of function of the current component j under the current frequency i was finished, j increased progressively 1, continued the function of the next component under the current frequency i of structure;

7) after the construction of function of each component was finished under the current frequency i, i increased progressively 1, continued the function under the next frequency of structure;

8) each function f _{I_j}By divided by

Standardize and obtain function F _{I_j}

2. hardware implementation method based on the square wave orthogonal function system choosing method of the described graphical analysis of claim 1, it is characterized in that: earlier image is divided into 8 * 8 block of pixels, minimum arithmetic element of design in hardware designs, described minimum arithmetic element is used for handling 8 continuous images input data data1～data8, generate later 8 dateouts at 8 clocks, respectively representative function f _{0_0}, f _{1_0}, f _{2_0}, f _{2_1}, f _{3_0}, f _{3_1}, f _{3_2}, f _{3_3}

3. software implementation method based on the square wave orthogonal function system choosing method of the described graphical analysis of claim 1 is characterized in that: earlier image is divided into 8 * 8 block of pixels, with 8 * 8 orthogonal transform matrixs to each 8 * 8 pixel fritter A _{8 * 8}Make two-dimensional transform, obtain transform coefficient matrix M _{8 * 8}, its expression formula is:

M _8×8＝D _8vA _8×8D _8h

Wherein, D _8hAnd D _8vRepresented 8 * 8 horizontal quadrature transformation matrixs and 8 * 8 perpendicular quadrature transformation matrixs respectively, and D _8vBe D _8hTransposed matrix;

Described 8 * 8 horizontal quadrature transformation matrix D _8hFor:

4. the software implementation method chosen of the square wave orthogonal function system of graphical analysis according to claim 3 is characterized in that: described 8 * 8 horizontal quadrature transformation matrix D _8hIn any one row all reindexing, be above-mentioned 8 * 8 horizontal quadrature transformation matrix D _8hEquivalent transformation.

5. the software implementation method chosen of the square wave orthogonal function system of graphical analysis according to claim 3 is characterized in that: establish

Define an INTEGER MATRICES P _8hWith a diagonal matrix E:

With described 8 * 8 horizontal quadrature transformation matrix D _8hBe decomposed into: D _8h=P _8hE, then the expression formula of transform coefficient matrix is:

M _8×8＝D _8vA _8×8D _8h＝E(P _8vA _8×8P _8h)E，

P wherein _8vA _{8 * 8}P _8hFor only containing the integer arithmetic of addition and subtraction, P _8vBe P _8hTransposed matrix.

Images