CN1564602A - Integral conversing matrix selection method of video coding and related integral conversion method - Google Patents

Abstract

The invention is especially relative to integer transformation for image data compression in video codec and introduces a method for selecting transform radix. Through estimating decorrelation efficiency, energy concentration string, transform dynamical range and calculation complexity of tranform radix, the two groups of 8X8 integer transform radix (5,6,4,1) and (4,5,3,1) are introduced, and a fast algorithm based on the two groups transform radix is obtained.

Description

The integer transform matrix system of selection of video coding and relevant integer transform method

Technical field

The invention belongs to image processing technique, particularly the integer transform of Image Data Compression in the Video Codec.Mainly comprise integer transform transform-based (transformation matrix) system of selection and based on the implementation method of the piece conversion of selected transform base.

Background technology

Existing international video standard as H.264, among the motion picture expert group MPEG-4, vision signal is divided into sequence, frame, band, macro block, piece by level; Minimum processing unit is a piece.At coding side, by infra-frame prediction or inter prediction, obtain the prediction residual of piece and do the piece conversion, with concentration of energy in a few coefficient; Again by quantification, scanning, Run-Length Coding and entropy coding, with Image Data Compression and write encoding code stream.Then process is opposite in decoding end, extracts the block conversion coefficient of entropy coding from code stream, by inverse quantization and inverse transformation, recovers the prediction residual of piece, in conjunction with information of forecasting, finally recovers the video data of piece.In the encoding and decoding flow process, conversion module is the basis of video compression, and property directly influences the combination property of codec.

Early stage international standard such as MPEG-1, H.261 adopt discrete cosine transform DCT.DCT after proposing in 1974, obtained using widely at image and field of video encoding, its property is highly significant in all suboptimum conversion, can greatly remove the correlation of pictorial element in transform domain, for high efficiency image compression is laid a good foundation.But because the transformation matrix of DCT is to represent with floating number, the floating-point operation amount is bigger, takies than multi-system resource.In order to improve conversion efficiency, develop again and approach floating-point operation DCT with fixed-point computation or bigger integer transform, owing to there is trueness error,, can not recover view data fully after the inverse transformation even without through quantizing, just Bian Ma invertibity is not strong.The generation of integer transform has solved the problem of computational accuracy and code efficiency simultaneously, is characterized in replacing with the integer transform matrix floating number transformation matrix of DCT, and conversion process is integer arithmetic fully like this, does not have trueness error, has guaranteed the invertibity of encoding; Multiplication of integers can replace with addition and subtraction and displacement simultaneously, so conversion process can realize that by addition and subtraction and displacement operand reduces significantly fully.Up-to-date international standard H.264/MPEG-4 Part 10 just adopts integer transform, and has obtained extraordinary transform effect.In recent years, at image and field of video processing many researchs at integer transform are arranged, existing foreign patent about integer transform mainly contains:

1.U.S.Patent No.5999957A " Lossless Transform System For Digital Signals "; This patent multiply by fixed numbers by each row to the dct transform matrix, rounds approximately again, and the transformation matrix coefficient is become integer to realize inverible transform.This transformation matrix derivation is not considered the orthogonality of conversion, can not guarantee that integer transform is orthogonal transform, thereby have influence on property.And quantizing process has repeatedly multiplication and division, calculation of complex.Repeatedly multiplication is arranged in the fast transform algorithm, influence conversion efficiency.

2.WO?01/08001A1“Integer?Cosine?Transform?Using?Integer?Operations”；

3.U.S.Patent No.20020111979A1 " Integer Transform Matrix For PictureCoding "; This patent provides a kind of evaluation method of integer transform matrixing performance, and main by the degree of approximation of comparison with the dct transform matrix, this method guarantees the orthogonality of conversion.Patent has provided 4 and has taken advantage of 4,8 to take advantage of 8,16 to take advantage of best in theory transformation matrix under 16 3 kinds of situations.This method is not considered the influence of computation complexity to property yet, and for the vector normal form that guarantees each row or column is identical, the performance of selected transformation matrix is not near DCT's.

4.U.S.Patent No.2003/0093452A1 " Video Block Transform "; This patent provide based on H.26L 4 take advantage of 4 quadrature and integer transform, the inverse transformation matrix of nonopiate form, macro block DC coefficient transformation matrix and orthogonal transform corresponding quantitative step-length.The transformation matrix yardstick of this patent is different with the present invention, and the transformation matrix of small scale is not suitable for application such as high definition TV.

8 take advantage of 8 discrete cosines can use following formulate:

Wherein $C\left(0\right)=1/\sqrt{2},$ C(w)＝1，(w＝1，…，7)。Form with matrix can be expressed as: Y=P ₀XP ₀ ^T, wherein X 8 takes advantage of 8 pixel prediction residual matrixes, and Y is the matrix after the conversion.

$P_0=\left[\begin{array}{cccccccc}a& a& a& a& a& a& a& a\\ b& d& e& g& -g& -e& -d& -b\\ c& f& -f& -c& -c& -f& f& c\\ d& -g& -b& -e& e& b& g& -d\\ a& -a& -a& a& a& -a& -a& a\\ e& -b& g& d& -d& -g& b& -e\\ f& -c& c& -f& -f& c& -c& f\\ g& -e& d& -b& b& -d& e& -g\end{array}\right],$

Wherein $a=\frac{1}{2\sqrt{2}}$ $b=\frac{1}{2}\cos \left(\frac{\mathrm{\π}}{16}\right)$ $c=\frac{1}{2}\cos \left(\frac{2\mathrm{\π}}{16}\right)$ $d=\frac{1}{2}\cos \left(\frac{3\mathrm{\π}}{16}\right)$ $e=\frac{1}{2}\cos \left(\frac{5\mathrm{\π}}{16}\right)$ $f=\frac{1}{2}\cos \left(\frac{6\mathrm{\π}}{16}\right)$ $s=\frac{1}{2}\cos \left(\frac{7\mathrm{\π}}{16}\right)$

H.264 to the rewriting process of 4 * 4DCT conversion, it is as follows to rewrite 8 * 8 conversion: from P according to international standard ₀Each row a common coefficient is proposed, obtain vectorial V ₈=[a, m, f, m, a, m, f, m], wherein m is matrix P ₀The common coefficient that proposes of even number line, the value of m is the positive number that is not more than k4.Then transformation matrix is rewritten as:

$P_1=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ k1& k2& k3& k4& -k4& -k3& -k2& -k1\\ k5& 1& -1& -k5& -k5& -1& 1& k5\\ k2& -k4& -k1& -k3& k3& k1& k4& -\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20041001285700242.png"\; state="\{\{state\}\}">k</figure-callout>}2\\ 1& -1& -1& 1& 1& -1& -1& 1\\ k3& -k1& k4& k2& -k2& -k4& k1& -k3\\ 1& -k5& k5& -1& -1& k5& -k5& 1\\ k4& -k3& k2& -k1& k1& -k2& k3& -\mathrm{<figure-callout\; id="4"\; label="k"\; filenames="A20041001285700242.png"\; state="\{\{state\}\}">k</figure-callout>}4\end{array}\right],$ K1=b/m k2=d/m is k3=e/m k4=g/m k5=c/f order matrix E wherein ₈=V ₈ ^TV ₈, be 8 to take advantage of 8 matrixes, then conversion further is rewritten as:

Y＝P ₁XP ₁ ^TE ₈ (2)

Wherein  represents the multiplication cross (the element correspondence that is same position multiplies each other) of two matrixes.For (2) formula can with matrix E ₈Multiplication cross computing and quantization operation put together, make conversion obtain simplifying.Therefore conversion focuses on P ₁XP ₁ ^TCalculating, wherein X is 8 * 8 pixel prediction residual matrix, is the shaping data.If P ₁In variable k1, k2, k3, k4, k5 are integer, then whole conversion will all be converted into integer arithmetic.So following work just needs to determine k1, k2, k3, k4, the choosing value of five parameters such as k5.The present invention is by experimental results demonstrate, as selected k1, k2, k3, behind the k4, it is best that k5 gets 2 o'clock property, and Cham is at his article (Development of Integer Cosine Transform by the Principle of DyadicSymmetry.IEE Proceedings, 1989,136 (4): 276-288) also proposed similar conclusion.Thereby the present invention with k5 fixedly value be 2, only study the selection of all the other four parameters, and the definition (k3 k4) is the transform-based of integer transform for k1, k2.Corresponding transformation matrix P is

$P=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ k1& k2& k3& k4& -k4& -k3& -k4& -k1\\ 2& 1& -1& -2& -2& -1& 1& 2\\ k2& -k4& -k1& -k3& k3& k1& k4& -\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20041001285700242.png"\; state="\{\{state\}\}">k</figure-callout>}2\\ 1& -1& -1& 1& 1& -1& -1& 1\\ k3& -k1& k4& k2& -k2& -k4& k1& -k3\\ 1& -2& 2& -1& -1& 2& -2& 1\\ k4& -k3& k2& -k1& k1& -k2& k3& -\mathrm{<figure-callout\; id="4"\; label="k"\; filenames="A20041001285700242.png"\; state="\{\{state\}\}">k</figure-callout>}4\end{array}\right]$

Summary of the invention

The present invention proposes a kind of system of selection of integer transform matrix and relevant integer transform method of video coding, first audio/video encoding standard (AVS) that will formulate at current China adopts 8 to take advantage of 8 integer class dct transforms, a kind of transform-based system of selection of integer transform has been proposed, two indexs of the decorrelation efficiency of overall merit transform-based and energy compaction efficiency and transform-based conversion dynamic range and computation complexity, and propose 8 of two groups of excellent performances by the method and take advantage of 8 integer translation bases (5,6,4,1) and (4,5,3,1), and obtain integer transform fast algorithm based on these two groups of bases.

The selection of transform-based is mainly based on following several principles:

Principle 1: conversion orthogonality.The characteristic of orthogonal transform guarantees that conversion only is the rotation to coordinate system, and the energy of image remains unchanged.In order to guarantee the orthogonality of conversion, the P in the formula (2) must satisfy the following formula condition:

P·P ^T＝Diag (3)

Wherein Diag is a diagonal matrix, and promptly its non-leading diagonal element is zero.Quantizing process by adjusting quantization matrix, makes conversion satisfy orthogonality again.

Principle 2: concentration of energy.The purpose of DCT exchange is to remove the correlation between the element, the energy after the conversion is concentrated on a few coefficients as far as possible, so that improve the compression efficiency that quantizes the back entropy coding.The selection of integer translation base equally also needs to follow this principle.

Principle 3: fast transform algorithm simplicity.Requirement transform-based numerical value can not be too big, and the calculation times of fast algorithm is the least possible.

The integer transform matrix system of selection of a kind of video coding of the present invention in turn includes the following steps:

(1) at first all integer translation bases of orthogonality condition are satisfied in search within the specific limits, take advantage of 8 integer transform matrix P for 8, the definition transform-based be (k1, k2, k3, k4),

$P=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ k1& k2& k3& k4& -k4& -k3& -k2& -k1\\ 2& 1& -1& -2& -2& -1& 1& 2\\ k2& -k4& -k1& -k3& k3& k1& k4& -\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20041001285700242.png"\; state="\{\{state\}\}">k</figure-callout>}2\\ 1& -1& -1& 1& 1& -1& -1& 1\\ k3& -k1& k4& k2& -k2& -k4& k1& -k3\\ 1& -2& 2& -1& -1& 2& -2& 1\\ k4& -k3& k2& -k1& k1& -k2& k3& -\mathrm{<figure-callout\; id="4"\; label="k"\; filenames="A20041001285700242.png"\; state="\{\{state\}\}">k</figure-callout>}4\end{array}\right]$

The span of transform-based coefficient k 1, k2, k3, k4 is k1, k2, k3 ∈ [1,10], and k4 ∈ [1,4] obtains all and satisfies PP ^TThe integer orthogonal transform base of=Diag;

(2) set up the covariance matrix COV (X that the input picture residual error data was got at cross-correlation coefficient ρ at 0.75,0.8,0.85,0.9,0.95 o'clock _v),

If length is 8 image residual error data one-dimensional vector is X _v=[x ₁, x ₂... x ₈], set up X by the single order Markov model _vCovariance matrix COV (the X of element _v), COV (X _v) _{(i, j)}=ρ ^{| i-j|}(0≤i, j≤7), wherein ρ is X _vThe cross-correlation coefficient of adjacent element (ρ≤1),

(3), obtain the covariance matrix COV (Y of transform domain by the transformation matrix P of transform-based correspondence _v),

Transform-based (k1, k2, k3, k4) Dui Ying transformation matrix P, normalization, promptly each row element of P obtains orthogonal matrix P divided by the length of this row vector _uTo X _vMake orthogonal transform Y _v=P _uX _v, Y _vCovariance matrix be:

COV(Y _v)＝P _u·COV(X _v)·P _u ^T (4)

(4) respectively organize the energy compaction efficiency η that transform-based was got at cross-correlation coefficient ρ at 0.75,0.8,0.85,0.9,0.95 o'clock by (2), (3) calculating _EValue and decorrelation efficiency η _CValue,

Definition energy compaction efficiency η _EFor:

${\mathrm{\&eta;}}_E=\frac{1}{\sqrt[8]{\underset{i=l}{\overset{8}{\mathrm{\&Pi;}}}\mathrm{COV}(Y_v{)}_{(i,j)}}}---\left(5\right)$

Decorrelation efficiency η _cFor:

${\mathrm{\&eta;}}_c=1-\frac{\underset{j\&NotEqual;k}{\mathrm{\&Sigma;}}\left|\mathrm{COV}(Y_v{)}_{(j,k)}\right|}{\underset{j\&NotEqual;k}{\mathrm{\&Sigma;}}\left|\mathrm{COV}{\left(X_v\right)}_{(j,k)}\right|}---\left(6\right)$

(5) calculate the energy compaction efficiency η of each transform-based under the cross-correlation coefficient ρ of appointment _EValue and decorrelation efficiency η _CNormalized result, under the same ρ, i transform-based energy compaction efficiency η _EThe normalization result be:

${\mathrm{Eval}}_{E\left(i\right)}=\frac{{\mathrm{\&eta;}}_{E\left(i\right)}-\mathrm{Min}\left({\mathrm{\&eta;}}_{E\left(j\right)}\right)}{\mathrm{Max}\left({\mathrm{\&eta;}}_{E\left(j\right)}\right)-\mathrm{Min}\left({\mathrm{\&eta;}}_{E\left(j\right)}\right)}---\left(7\right)$

I transform-based decorrelation efficiency η _CThe normalization result be:

${\mathrm{Eval}}_{c\left(i\right)}=\frac{{\mathrm{\&eta;}}_{c\left(i\right)}-\mathrm{Min}\left({\mathrm{\&eta;}}_{c\left(j\right)}\right)}{\mathrm{Max}\left({\mathrm{\&eta;}}_{c\left(j\right)}\right)-\mathrm{Min}\left({\mathrm{\&eta;}}_{c\left(j\right)}\right)}---\left(8\right)$

(6), obtain every group of base energy compaction efficiency η under each cross-correlation coefficient ρ by weighted sum _EValue, the comprehensive evaluation result Eval of decorrelation efficiency η C _E,,, Eval _C, the weight of 5 ρ correspondences is respectively 1/15,2/15,3/15,4/15,5/15;

(7) pass through Eval _CAnd Eval _EThese two index weighted sums obtain the comprehensive evaluation value Eval of transform-based performance, Eval _CAnd Eval _ECorresponding weight is respectively 0.4,0.6.

The integer transform matrix system of selection of described video coding, after it is further characterized in that the comprehensive evaluation value Eval that obtains the transform-based performance, increase transform-based (k1, k2, k3, the evaluation procedure of computation complexity k4): at first select the higher transform-based of comprehensive evaluation value Eval; If it is addition and subtraction and the few transform-based of displacement number of times that the Eval gap, pays the utmost attention in the application that real-time is had relatively high expectations that computation complexity has a clear superiority in less than 0.02.

The integer transform method of a kind of video coding of the present invention at coding side, by infra-frame prediction or inter prediction, obtains the prediction residual of piece and does the piece conversion, with concentration of energy in a few coefficient; Again by quantification, scanning, Run-Length Coding and entropy coding, with Image Data Compression and write encoding code stream; Then from code stream, extract the block conversion coefficient of entropy coding in decoding end,, recover the prediction residual of piece,, recover the video data of piece in conjunction with information of forecasting by inverse quantization and inverse transformation; It is characterized in that:

(1) 8 take advantage of transformation matrix P that 8 integer transforms adopt to obtain in the video coding by the integer transform matrix system of selection of aforementioned video coding, as shown in the formula:

$P=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ 5& 6& 4& 1& -1& -4& -6& -5\\ 2& 1& -1& -2& -2& -1& 1& 2\\ 6& -1& -5& -4& 4& 5& 1& -6\\ 1& -1& -1& 1& 1& -1& -1& 1\\ 4& -5& 1& 6& -6& -1& 5& -4\\ 1& -2& 2& -1& -1& 2& -2& 1\\ 1& -4& 6& -5& 5& -6& 4& -1\end{array}\right]$

Corresponding integer translation base is (5,6,4,1);

(2) direct transform takes advantage of 8 image residual error data piece to do integer transform, shape such as Y=PXP to 8 ^T, the elementary cell of conversion is 8 one-dimensional transforms of shape such as y=Px, x=[x0 wherein, x1, x2, x3, x4, x5, x6, x7] ^T, the y=[y0 of output, y1, y2, y3, y4, y5, y6, y7] ^T, computational process is as follows:

A.a0＝x0-x7，a1＝x1-x6，a2＝x2-x5，a3＝x3-x4，a4＝x0+x7，a5＝x1+x6，a6＝x2+x5，a7＝x3+x4；

B.b0＝a4+a7，b1＝a5+a6，b2＝a4-a7，b3＝a5-a6；

C.y0＝b0+b1，y4＝b0-b1，y2＝b2<<1+b3，y6＝b2-b3<<1；

Finish the calculation procedure of suitable calculating following formula again:

$\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]=\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right],$

D.c0＝a0<<2+a0+a3；c1＝a2-a1-a1<<2；c2＝a1+a2+a2<<2；c3＝a3<<2+a3-a0；

E.y1＝c0-c1+c2；y3＝c0-c2-c3；y5＝c0+c1+c3；y7＝c1+c2-c3；

(3) inverse transformation makes that the one-dimensional transform elementary cell is x=P ^TY.Y=[y0 wherein, y1, y2, y3, y4, y5, y6, y7] ^T, x=[x0, x1, x2, x3, x4, x5, x6, x7] ^T. the one dimension contravariant is changed to:

A.m0＝y0+y4；m1＝y0-y4；m2＝y2<<1+y6；m3＝y2-y6<<1；

B.b0＝m0+m2；b1＝m1+m3；b2＝m1-m3；b3＝m0-m2；

C. calculate 4 of following formula and take advantage of 4 matrix multiplications:

$\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]$

4 of computational process and direct transform takes advantage of 4 matrix multiplications identical, just the exchange of inputoutput data vector;

D.x0＝a0+b0；x1＝a1+b1；x2＝a2+b2；x3＝a3+b3；

x7＝-a0+b0；x6＝-a1+b1；x5＝-a2+b2；x4＝-a3+b3；

Wherein "＜＜" expression is to the left dislocation computing, its priority is higher than addition and subtraction, " a＜＜b " represent that a is to left dislocation b position.

The integer transform method of another video coding of the present invention at coding side, by infra-frame prediction or inter prediction, obtains the prediction residual of piece and does the piece conversion, with concentration of energy in a few coefficient; Again by quantification, scanning, Run-Length Coding and entropy coding, with Image Data Compression and write encoding code stream; Then from code stream, extract the block conversion coefficient of entropy coding in decoding end,, recover the prediction residual of piece,, recover the video data of piece in conjunction with information of forecasting by inverse quantization and inverse transformation; It is characterized in that:

(1) 8 take advantage of transformation matrix P that 8 integer transforms adopt to obtain in the video coding by the integer transform matrix system of selection of aforementioned video coding, also can as shown in the formula:

$\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ 4& 5& 3& 1& -1& -3& -5& -4\\ 2& 1& -1& -2& -2& -1& 1& 2\\ 5& -1& -4& -3& 3& 4& 1& -5\\ 1& -1& -1& 1& 1& -1& -1& 1\\ 3& -4& 1& 5& -5& -1& 4& -3\\ 1& -2& 2& -1& -1& 2& -2& 1\\ 1& -3& 5& -4& 4& -5& 3& -1\end{array}\right]$

Corresponding integer translation base is (4,5,3,1);

(2) direct transform takes advantage of 8 image residual error data piece to do integer transform, shape such as Y=PXP to 8 ^T, the elementary cell of conversion is 8 one-dimensional transforms of shape such as y=Px, x=[x0 wherein, x1, x2, x3, x4, x5, x6, x7] ^T, the y=[y0 of output, y1, y2, y3, y4, y5, y6, y7] ^TComputational process is as follows:

A.a0＝x0-x7，a1＝x1-x6，a2＝x2-x5，a3＝x3-x4，a4＝x0+x7，a5＝x1+x6，a6＝x2+x5，

a7＝x3+x4；

B.b0＝a4+a7，b1＝a5+a6，b2＝a4-a7，b3＝a5-a6；

C.y0＝b0+b1，y4＝b0-b1，y2＝b2<<1+b3，y6＝b2-b3<<1；

Finish the calculation procedure of suitable calculating following formula again:

$\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right],$

D.c0＝a0<<2+a3；c1＝a2-a1<<2；c2＝a1+a2<<2；c3＝a3<<2-a0；

E.y1＝c0-c1+c2；y3＝c0-c2-c3；y5＝c0+c1+c3；y7＝c1+c2-c3；

(3) inverse transformation:

Make that the one-dimensional transform elementary cell is x=P ^TY.Y=[y0 wherein, y1, y2, y3, y4, y5, y6, y7] ^T,

X=[x0, x1, x2, x3, x4, x5, x6, x7] ^T. the one dimension contravariant is changed to:

A.m0＝y0+y4；m1＝y0-y4；m2＝y2<<1+y6；m3＝y2-y6<<1；

B.b0＝m0+m2；b1＝m1+m3；b2＝m1-m3；b3＝m0-m2；

C. calculate 4 of following formula and take advantage of 4 matrix multiplications:

$\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]$

4 of the computational process of fast algorithm and direct transform takes advantage of 4 matrix multiplications identical, just the exchange of inputoutput data vector;

D.x0＝a0+b0；x1＝a1+b1；x2＝a2+b2；x3＝a3+b3；

x7＝-a0+b0；x6＝-a1+b1；x5＝-a2+b2；x4＝-a3+b3；

Wherein "＜＜" expression is to the left dislocation computing, its priority is higher than addition and subtraction, " a＜＜b " represent that a is to left dislocation b position.

The present invention proposes a kind of integrated evaluating method of integer translation base performance, and filter out the transform-based of several groups of better performances, and provide the fast transform approach of two groups of transform-based according to this method.The ABT 8 that the performance of the bright preferred several groups of transform-based of measured result proof this law of high definition video cycle tests is better than JVT takes advantage of 8 conversion, and wherein the property of (10,9,6,2) is best, the computation complexity of (4,5,3,1) is minimum, the performance of (5,6,4,1) falls between.Take advantage of 8 conversion with respect to ABT 8, these 3 groups of bases all have certain advantage aspect property and the computation complexity etc. two.The measured performance of selected transform-based has also been verified the accuracy and the feasibility of transform-based system of selection of the present invention, this method not only is applicable to the integer transform matrix, also can be used for Performance Evaluation, have very strong directive significance for the selection of transformation matrix to all kinds of transformation matrixs.

Figure of description

Fig. 1: transform-based is estimated FB(flow block).

Fig. 2: transform-based (5,6,4,1) direct transform fast algorithm.

Fig. 3: transform-based (5,6,4,1) inverse transformation fast algorithm.

Fig. 4: transform-based (4,5,3,1) direct transform fast algorithm.

Fig. 5: transform-based (4,5,3,1) inverse transformation fast algorithm.

Embodiment

(1) selection of transform-based

The evaluation flow process of transform-based as shown in Figure 1.

The cross-correlation coefficient ρ of all kinds of image residual error data mainly is distributed between 0.75～0.95, is the energy compaction efficiency η of each transform-based correspondence of 0.75,0.8,0.85,0.9,0.95 five by calculating ρ _E, again with each basic η under the same ρ _ENormalization.To same transform-based η under different cross-correlation coefficient ρ _ENormalization is weighted sum as a result, obtains the comprehensive evaluation value Eval that this organizes basic energy compaction efficiency _E, wherein weight is the probability size decision according to different ρ.The weight of getting 5 ρ correspondences among the present invention is followed successively by 1/15,2/15,3/15,4/15,5/15.In like manner obtain the decorrelation efficiency η of transform-based _cComprehensive evaluation result Eval _C

Pass through Eval at last _EAnd Eval _CWeighted sum obtains the comprehensive evaluation value Eval of transform-based energy compaction efficiency and decorrelation efficiency.Consider the compression performance after energy compaction efficiency directly influences conversion, weight is bigger, and the weight of definition energy compaction efficiency and decorrelation efficiency evaluation of estimate is respectively among the present invention: 0.6,0.4.

When comprehensive evaluation value Eval near the time, the performance of the transform-based that computation complexity is low is better.

The span of having listed transform-based in the following table is k1, k2, k3 ∈ [1,10], during k4 ∈ [1,4], and the η of 5 groups of bases _EAnd η _cComprehensive evaluation value, finish needed addition of one dimension 8 point transformation and displacement number of times (the calculation number of times far away of positive inverse transformation is identical).

K1, k2, k3, η _EAnd η _cComprehensively

The addition number of times+/-the displacement number of times＜＜

The k4 evaluation of estimate

10，9，6，2 0.9859 36 10

5，6，4，1 0.8579 32 6

6，6，3，2 0.8441 36 10

6，7，5，1 0.8409 32 10

4，5，3，1 0.8249 28 6

(10,9,6,2) and (6,6,3,2) are suggested in relevant document.The decorrelation efficiency of (5,6,4,1) and the comprehensive evaluation value of energy compaction efficiency are only second to (10,9,6,2), and computation complexity is less, and the comprehensive evaluation value of (4,5,3,1) is a little less than (6,6,3,2), but the computation complexity advantage is the most obvious.Practical video sequential test result shows that the distortion performance of (5,6,4,1), (4,5,3,1), (6,7,5,1) is better than (6,6,3,2), and is very approaching with (10,9,6,2).The realization of (two) 8 * 8 integer transform fast algorithms

X0, x1, x2, x3, x4, x5, x6, x7 represent input eight point value of the one dimension direct transform of integer transform among Fig. 2-Fig. 5, are 8 output numerical value of inverse transformation simultaneously; Y0, y1, y2, y3, y4, y5, y6, y7 are 8 output numerical value of direct transform, are 8 output numerical value of inverse transformation simultaneously.The data processing direction from left to right, two lines that intersect at a round dot are represented two data additions, three data additions of three-way expression.Square expression data are taken advantage of a coefficient, and wherein negative value is got in "-" expression, and " 2 " expression takes advantage of 2, promptly moves to left one, and " 4 " expression takes advantage of 4, promptly moves to left two.

1. direct transform

Image residual error data piece to 8x8 is done integer transform, and the elementary cell of conversion is 8 one-dimensional transforms of shape such as y=Px, establishes x=[x0, x1, x2, x3, x4, x5, x6, x7] ^T, the y=[y0 of output, y1, y2, y3, y4, y5, y6, y7] ^TComputational process is as follows:

When at first calculating is done conversion with each different transformation matrix P, identical calculation procedure:

(1)a0＝x0-x7，a1＝x1-x6，a2＝x2-x5，a3＝x3-x4，a4＝x0+x7，a5＝x1+x6，a6＝x2+x5，a7＝x3+x4；

(2)b0＝a4+a7，b1＝a5+a6，b2＝a4-a7，b3＝a5-a6；

(3)y0＝b0+b1，y4＝b0-b1，y2＝b2<<1+b3，y6＝b2-b3<<1；

Same section calculates needs addition and subtraction 16 times, displacement 2 times.

Calculate different calculation procedures again, this part is equivalent to calculate following formula:

$\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right],$

For transform-based (5,6,4,1) calculation procedure be:

(1)c0＝a0<<2+a0+a3；c1＝a2-a1-a1<<2；c2＝a1+a2+a2<<2；c3＝a3<<2+a3-a0；

(2)y1＝c0-c1+c2；y3＝c0-c2-c3；y5＝c0+c1+c3；y7＝c1+c2-c3；

Need 16 addition and subtractions and 4 displacements altogether.

For transform-based (4,5,3,1) calculation procedure be:

(1)c0＝a0<<2+a3；c1＝a2-a1<<2；c2＝a1+a2<<2；c3＝a3<<2-a0；

(2)y1＝c0-c1+c2；y3＝c0-c2-c3；y5＝c0+c1+c3；y7＝c1+c2-c3；

Need 12 addition and subtractions and 4 displacements altogether.

Therefore finish a y=Px computing for transform-based (5,6,4,1), shared 32 addition and subtractions and 6 displacements; Shared 28 addition and subtractions of transform-based (4,5,3,1) and 6 displacements.Finish operand of integer transform of 8 * 8 and be the said units amount of calculation 16 times.The fast algorithm of (5,6,4,1) direct transform as shown in Figure 2, the fast algorithm of (4,5,3,1) direct transform is as shown in Figure 4.

2. inverse transformation

Make that the one-dimensional transform elementary cell is x=P ^TY.

Y=[y0 wherein, y1, y2, y3, y4, y5, y6, y7] ^T, x=[x0, x1, x2, x3, x4, x5, x6, x7] ^T. following process is an x=P ^TThe y computing.

(1)m0＝y0+y4；m1＝y0-y4；m2＝y2<<1+y6；m3＝y2-y6<<1；

(2)b0＝m0+m2；b1＝m1+m3；b2＝m1-m3；b3＝m0-m2；

(3) calculate 4 of following formula and take advantage of 4 matrix multiplications:

$\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]$

4 * 4 matrix multiplications are identical in calculating formula and the direct transform, and algorithm is the same, just the exchange of inputoutput data vector.Amount of calculation is identical.Need 16 addition and subtractions and 4 displacements for transform-based (5,6,4,1);

Need 12 addition and subtractions and 4 displacements for transform-based (4,5,3,1).

(4)x0＝a0+b0；x1＝a1+b1；x2＝a2+b2；x3＝a3+b3；

x7＝-a0+b0；x6＝-a1+b1；x5＝-a2+b2；x4＝-a3+b3；

Wherein "＜＜" expression is to the left dislocation computing, its priority is higher than addition and subtraction, " a＜＜b " expression a is to left dislocation b position, and the public part amount of calculation of different transform-based is: addition and subtraction 16 times, displacement 2 times.Therefore finish x=P one time for transform-based (5,6,4,1) ^TThe y computing, shared 32 addition and subtractions and 6 displacements; Shared 28 addition and subtractions of transform-based (4,5,3,1) and 6 displacements.The fast algorithm of (5,6,4,1) inverse transformation as shown in Figure 3, the fast algorithm of (4,5,3,1) inverse transformation is as shown in Figure 5.The operand of finishing the integer transform inverse transformation of taking advantage of 8 for one time 8 is 16 times of said units amount of calculation.

Claims (4)

1. the integer transform matrix system of selection of a video coding in turn includes the following steps:

(1) at first all integer translation bases of orthogonality condition are satisfied in search within the specific limits, take advantage of 8 integer transform matrix P for 8, the definition transform-based be (k1, k2, k3, k4),

$P=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ k1& k2& k3& k4& -k4& -k3& -k2& -k1\\ 2& 1& -1& -2& -2& -1& 1& 2\\ k2& -k4& -k1& -k3& k3& k1& k4& -k2\\ 1& -1& -1& 1& 1& -1& -1& 1\\ k3& -k1& k4& k2& -k2& -k4& k1& -k3\\ 1& -2& 2& -1& -1& 2& -2& 1\\ k4& -k3& k2& -k1& k1& -k2& k3& -k4\end{array}\right]$

The span of transform-based coefficient k 1, k2, k3, k4 is k1, k2, k3 ∈ [1,10], and k4 ∈ [1,4] obtains all and satisfies PP ^TThe integer orthogonal transform base of=Diag, wherein Diag is a diagonal matrix;

(2) set up the covariance matrix COV (X that the input picture residual error data was got at cross-correlation coefficient ρ at 0.75,0.8,0.85,0.9,0.95 o'clock _v),

If length is 8 image residual error data one-dimensional vector is X _V=[x ₁, x ₂... x ₈], set up X by the single order Markov model _VCovariance matrix COV (the X of element _v), COV (X _v) _{(i, j)}=ρ ^{| i-j|}(0≤i, j≤7), wherein ρ is X _VThe cross-correlation coefficient of adjacent element (ρ≤1);

(3), obtain the covariance matrix COV (Y of transform domain by the transformation matrix P of transform-based correspondence _v),

Transform-based (k1, k2, k3, k4) Dui Ying transformation matrix P, normalization, promptly each row element of P obtains orthogonal matrix P divided by the length of this row vector _uTo X _VMake orthogonal transform Y _V=P _uX _V, Y _VCovariance matrix be:

$\mathrm{COV}\left(Y_v\right)=P_u\&CenterDot;\mathrm{COV}\left(X_v\right)\&CenterDot;{P_u}^T$

(4) respectively organize the energy compaction efficiency η that transform-based was got at cross-correlation coefficient ρ at 0.75,0.8,0.85,0.9,0.95 o'clock by (2), (3) calculating _EValue and decorrelation efficiency η _CValue,

Definition energy compaction efficiency η _EFor:

${\mathrm{\&eta;}}_E=\frac{1}{\sqrt[8]{\underset{i=1}{\overset{8}{\mathrm{\&Pi;}}}\mathrm{COV}{\left(Y_v\right)}_{(i,i)}}}$

Decorrelation efficiency η _cFor:

${\mathrm{\&eta;}}_c=1-\frac{\underset{j\&NotEqual;k}{\mathrm{\&Sigma;}}\left|\mathrm{COV}{\left(Y_v\right)}_{(j,k)}\right|}{\underset{j\&NotEqual;k}{\mathrm{\&Sigma;}}\left|\mathrm{COV}{\left(X_v\right)}_{(j,k)}\right|}$

(5) calculate the energy compaction efficiency η of each transform-based under the cross-correlation coefficient ρ of appointment _EValue and decorrelation efficiency η _CNormalized result, under the same ρ, i transform-based energy compaction efficiency η _EThe normalization result be:

${\mathrm{Eval}}_{E\left(i\right)}=\frac{{\mathrm{\&eta;}}_{E\left(i\right)}-\mathrm{Min}\left({\mathrm{\&eta;}}_{E\left(j\right)}\right)}{\mathrm{Max}\left({\mathrm{\&eta;}}_{E\left(j\right)}\right)-\mathrm{Min}\left({\mathrm{\&eta;}}_{E\left(j\right)}\right)}$

I transform-based decorrelation efficiency η _CThe normalization result be:

${\mathrm{Eval}}_{c\left(i\right)}=\frac{{\mathrm{\&eta;}}_{c\left(i\right)}-\mathrm{Min}\left({\mathrm{\&eta;}}_{c\left(j\right)}\right)}{\mathrm{Max}\left({\mathrm{\&eta;}}_{c\left(j\right)}\right)-\mathrm{Min}\left({\mathrm{\&eta;}}_{c\left(j\right)}\right)}$

(6), obtain every group of base energy compaction efficiency η under each cross-correlation coefficient ρ by weighted sum _EValue, decorrelation efficiency η _CComprehensive evaluation result Eval _E,,, Eval _C, the weight of 5 ρ correspondences is respectively 1/15,2/15,3/15,4/15,5/15;

(7) pass through Eval _CAnd Eval _EThese two index weighted sums obtain the comprehensive evaluation value Eval of transform-based performance, Eval _CAnd Eval _ECorresponding weight is respectively 0.4,0.6.

2. the integer transform matrix system of selection of video coding as claimed in claim 1, after it is characterized in that obtaining the comprehensive evaluation value Eval of transform-based performance, increase transform-based (k1, k2, k3, the evaluation procedure of computation complexity k4): at first select the higher transform-based of comprehensive evaluation value Eval; If it is addition and subtraction and the few transform-based of displacement number of times that the Eval gap, pays the utmost attention in the application that real-time is had relatively high expectations that computation complexity has a clear superiority in less than 0.02.

3. the integer transform method of a video coding at coding side, by infra-frame prediction or inter prediction, obtains the prediction residual of piece and does the piece conversion, with concentration of energy in a few coefficient; Again by quantification, scanning, Run-Length Coding and entropy coding, with Image Data Compression and write encoding code stream; Then from code stream, extract the block conversion coefficient of entropy coding in decoding end,, recover the prediction residual of piece,, recover the video data of piece in conjunction with information of forecasting by inverse quantization and inverse transformation; It is characterized in that:

(1) 8 take advantage of transformation matrix P that 8 integer transforms adopt to obtain in the video coding by the integer transform matrix system of selection of claim 1 or 2 described video codings, as shown in the formula:

$P=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ 5& 6& 4& 1& -1& -4& -6& -5\\ 2& 1& -1& -2& -2& -1& 1& 2\\ 6& -1& -5& -4& 4& 5& 1& -6\\ 1& -1& -1& 1& 1& -1& -1& 1\\ 4& -5& 1& 6& -6& -1& 5& -4\\ 1& -2& 2& -1& -1& 2& -2& 1\\ 1& -4& 6& -5& 5& -6& 4& -1\end{array}\right]$

Corresponding integer translation base is (5,6,4,1);

(2) direct transform takes advantage of 8 image residual error data piece to do integer transform, shape such as Y=PXP to 8 ^T, the elementary cell of conversion is 8 one-dimensional transforms of shape such as y=Px, x=[x0 wherein, x1, x2, x3, x4, x5, x6, x7] ^T, the y=[y0 of output, y1, y2, y3, y4, y5, y6, y7] ^T, computational process is as follows:

A.a0＝x0-x7，a1＝x1-x6，a2＝x2-x5，a3＝x3-x4，a4＝x0+x7，a5＝x1+x6，a6＝x2+x5，a7＝x3+x4；

B.b0＝a4+a7，b1＝a5+a6，b2＝a4-a7，b3＝a5-a6；

C.y0＝b0+b1，y4＝b0-b1，y2＝b2＜＜1+b3，y6＝b2-b3＜＜1；

Finish the calculation procedure of suitable calculating following formula again:

$\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right],$

D.c0＝a0＜＜2+a0+a3；c1＝a2-a1-a1＜＜2；c2＝a1+a2+a2＜＜2；c3＝a3＜＜2+a3-a0；

E.y1＝c0-c1+c2；y3＝c0-c2-c3；y5＝c0+c1+c3；y7＝c1+c2-c3；

(3) inverse transformation:

Make that the one-dimensional transform elementary cell is x=Py, y=[y0 wherein, y1, y2, y3, y4, y5, y6, y7] ^T, x=[x0, x1, x2, x3, x4, x5, x6, x7] ^TThe one dimension contravariant is changed to:

A.m0＝y0+y4；m1＝y0-y4；m2＝y2＜＜1+y6；m3＝y2-y6＜＜1；

B.b0＝m0+m2；b1＝m1+m3；b2＝m1-m3；b3＝m0-m2；

C. calculate 4 of following formula and take advantage of 4 matrix multiplications:

$\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]$

4 of computational process and direct transform takes advantage of 4 matrix multiplications identical, just the exchange of inputoutput data vector;

D.x0＝a0+b0；x1＝a1+b1；x2＝a2+b2；x3＝a3+b3；

x7＝-a0+b0；x6＝-a1+b1；x5＝-a2+b2；x4＝-a3+b3；

Wherein "＜＜" expression is to the left dislocation computing, its priority is higher than addition and subtraction, as " a＜＜b " represent that a is to left dislocation b position.

4. the integer transform method of a video coding at coding side, by infra-frame prediction or inter prediction, obtains the prediction residual of piece and does the piece conversion, with concentration of energy in a few coefficient; Again by quantification, scanning, Run-Length Coding and entropy coding, with Image Data Compression and write encoding code stream; Then from code stream, extract the block conversion coefficient of entropy coding in decoding end,, recover the prediction residual of piece,, recover the video data of piece in conjunction with information of forecasting by inverse quantization and inverse transformation; It is characterized in that:

(1) 8 take advantage of transformation matrix P that 8 integer transforms adopt to obtain in the video coding by the integer transform matrix system of selection of claim 1 or 2 described video codings, as shown in the formula:

$\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 1\\ 4& 5& 3& 1& -1& -3& -5& -4\\ 2& 1& -1& -2& -2& -1& 1& 2\\ 5& -1& -4& -3& 3& 4& 1& -5\\ 1& -1& -1& 1& 1& -1& -1& 1\\ 3& -4& 1& 5& -5& -1& 4& -3\\ 1& -2& 2& -1& -1& 2& -2& 1\\ 1& -3& 5& -4& 4& -5& 3& -1\end{array}\right]$

Corresponding integer translation base is (4,5,3,1);

(2) direct transform takes advantage of 8 image residual error data piece to do integer transform, shape such as Y=PXP to 8 ^T, the elementary cell of conversion is 8 one-dimensional transforms of shape such as y=Px, x=[x0 wherein, x1, x2, x3, x4, x5, x6, x7] ^T, the y=[y0 of output, y1, y2, y3, y4, y5, y6, y7] ^T, computational process is as follows:

A.a0＝x0-x7，a1＝x1-x6，a2＝x2-x5，a3＝x3-x4，a4＝x0+x7，a5＝x1+x6，a6＝x2+x5，a7＝x3+x4；

B.b0＝a4+a7，b1＝a5+a6，b2＝a4-a7，b3＝a5-a6；

C.y0=b0+b1, y4=b0-b1, y2=b2＜＜1+b3, y6=b2-b3＜＜1; Finish the calculation procedure of suitable calculating following formula again:

$\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right],$

D.c0＝a0＜＜2+a3；c1＝a2-a1＜＜2；c2＝a1+a2＜＜2；c3＝a3＜＜2-a0；

E.y1＝c0-c1+c2；y3＝c0-c2-c3；y5＝c0+c1+c3；y7＝c1+c2-c3；

(3) inverse transformation:

Make that the one-dimensional transform elementary cell is x=Py, y=[y0 wherein, y1, y2, y3, y4, y5, y6, y7] ^T, x=[x0, x1, x2, x3, x4, x5, x6, x7] ^T, the one dimension contravariant is changed to:

A.m0＝y0+y4；m1＝y0-y4；m2＝y2＜＜1+y6；m3＝y2-y6＜＜1；

B.b0＝m0+m2；b1＝m1+m3；b2＝m1-m3；b3＝m0-m2；

C. calculate 4 of following formula and take advantage of 4 matrix multiplications:

$\left[\begin{array}{c}a0\\ a1\\ a2\\ a3\end{array}\right]=\left[\begin{array}{cccc}k1& k2& k3& k4\\ k2& -k4& -k1& -k3\\ k3& -k1& k4& k2\\ k4& -k3& k2& -k1\end{array}\right]\left[\begin{array}{c}y1\\ y3\\ y5\\ y7\end{array}\right]$

4 of the computational process of fast algorithm and direct transform takes advantage of 4 matrix multiplications identical, just the exchange of inputoutput data vector.

D.x0＝a0+b0；x1＝a1+b1；x2＝a2+b2；x3＝a3+b3；

x7＝-a0+b0；x6＝-a1+b1；x5＝-a2+b2；x4＝-a3+b3；

Wherein "＜＜" expression is to the left dislocation computing, its priority is higher than addition and subtraction, as " a＜＜b " represent that a is to left dislocation b position.

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