KR20060043435A - Integer transform matrix selection method in video coding and related integer transform method - Google Patents

Abstract

The present invention relates to image processing techniques, and more particularly to integer conversion of image data compression in a video codec. According to the Chinese First Audio and Video Coding Standard (AVS), which adopts an 8x8 DCT integer transform, an integer transform base selection method used for evaluating the quality of the transform base with audience rating and energy centralization efficiency is proposed. Computational complexity is also taken into account in the selection procedure. Based on this method, two groups of 8x8 transform bases (5, 6, 4, 1) and (4, 5, 3, 1) are selected, and a fast transform algorithm for these two groups is provided.

Description

Integer transform matrix selection method in video coding and related integer transform method

1 is a flowchart of a transform base evaluation procedure.

2 shows a fast transform algorithm of a transform having a transform base of (5, 6, 4, 1).

3 shows a fast transform algorithm of inverse transform with a transform base of (5, 6, 4, 1).

4 shows a fast transform algorithm with a transform base of (4, 5, 3, 1).

5 shows a fast transform algorithm of inverse transform with a transform base of (4, 5, 3, 1).

The present invention relates to image processing techniques, and more particularly to integer conversion of image data compression in a video codec. The present invention includes a method for selecting a transform base (transform matrix) of an integer transform and a method for implementing block transform based on the selection of the transform base.

In current international video coding standards, such as H.264 and MPEG-4, video signals are hierarchically divided into sequences, frames, slices, macro blocks, and blocks, with blocks becoming the minimum processing unit. In terms of encoding, through intra-frame or inter-frame prediction, the prediction residual error of the block is obtained, and the block transform is performed so that energy can be concentrated on a few coefficients; Then, through quantization, scanning, run length coding and entropy coding, the image data is compressed and recorded in the coded bit stream. In terms of decoding, the processing procedure is reversed. First, the block transform coefficients of entropy coding are extracted from the bit stream. Then, through inverse quantization and inverse transformation, the prediction residual error of the block is reconstructed, and the prediction information is used to reconstruct the video data of the block. In the encoding-decoding process, the transform module is the basis of video compression, and the transform performance directly affects the general performance of the codec.

Discrete cosine transform (DCT) has been adopted in early video coding standards such as MPEG-1 and H.261. After the proposal of the discrete cosine transform in 1974, DCT was widely used in the field of image and video coding. Its transform performance is superior among all sub-optimal transforms because it removes the correlation of image elements in the transform domain and lays the foundation for high efficiency image compression. However, since the DCT transformation matrix is represented by a floating point number, a large amount of system resources are consumed due to the large amount of floating point calculations. In order to improve conversion efficiency, an approach using fixed-point calculations or large integer conversions has been developed to terminate floating-point calculation DCT. However, even in the absence of quantization, due to the appearance of precise error, the image data cannot be completely reconstructed after the inverse transformation. In other words, the inverse of the coding was not sufficient. Integer conversion solves the problem of computational accuracy and coding efficiency. The properties of integer conversion include: DCT's floating point conversion matrix is replaced with integer conversion matrix so that integer operation is performed in the whole conversion process, there is no precise error, therefore inverse transformability of coding This is guaranteed. Moreover, multiplication of integers can be replaced by addition / subtraction and shifting operations. Therefore, the conversion process can be fully implemented by addition / subtraction and shifting operations, so that the amount of calculation is greatly reduced. Integer conversion is recently used in international video coding standard H.264 / MPEG-4 Part 10, and excellent conversion results have been obtained. Recently, research conducted on integer conversion is considerable in the field of image and video processing. Patents obtained in other countries by integer conversion are:

1. U.S. Patent 5,999,957 "Lossless Conversion System for Digital Signals".

According to the patent, the fixed value is multiplied for each row of the DCT transformation matrix, the result of each multiplication is rounded, and the coefficients of the transformation matrix are converted to integers to implement an invertible transformation. However, this derivation of the transformation matrix without consideration of the transformation orthogonality cannot guarantee that the integer transformation is orthogonal. Therefore, conversion efficiency is affected. Moreover, the calculation is complicated by a plurality of multiplications / divisions performed in the quantization process. Moreover, multiple multiplications in the fast conversion algorithm affect the conversion efficiency.

2. WO01 / 08001A1 "Integer Cosine Transformation Using Integer Operations".

3. U.S. Patent No. 20020111979A1 "Integer Transformation Matrix for Image Coding". A method for evaluating the conversion efficiency of an integer conversion matrix is mainly provided through similarity comparison with DCT. The method ensures orthogonality of the transform. According to the patent, the most optimal matrix was theoretically proposed under three conditions of 4x4, 8x8 and 16x16. However, the effect of computational complexity on the conversion performance is not taken into account. Moreover, to ensure the same vector norm of each line or row of the matrix, the selected transform matrix was not closest to the DCT in the conversion efficiency.

4. U.S Patent 2003 / 0093452A1, “Video Block Conversion”. The matrix of integer and inverse transforms in orthogonal and non-orthogonal forms a 4x4 block based on H.26L, and the quantized step length corresponding to the transform matrix and orthogonal transform of macroblock DC coefficients is provided in this patent. The size of the transformation matrix according to the patent differs from that of the present invention. Moreover, the small size of the transformation matrix of the patent is not suitable for applications such as HDTV.

8 × 8 DCT can be expressed by the following equation.

(1)

(One)

, C(w)=1, (w=1,...,7)이다. 식은 Y=P₀XP₀ ^T와 같은 행렬의 형태로 표현되며, X는 8×8 픽셀 예측 잔류 오류 행렬이며, Y는 변환된 행렬이 다. Where C (0) =

, C (w) = 1, (w = 1, ..., 7). The equation is expressed in the form of a matrix such as Y = P ₀ XP ₀ ^T , where X is an 8 × 8 pixel prediction residual error matrix, and Y is a transformed matrix.

here,

According to the correction procedure for 4x4 DCT transformation according to international standard H.264, the 8x8 transformation can be rewritten as follows: the common coefficient is the vector V8 = [a, m, f, m, a, m , f, m] are extracted from each row of the matrix to obtain m, where m is a common coefficient extracted from the even numbered rows of the matrix P ₀ and is a positive value not greater than k4. Then, the transformation matrix is rewritten as follows:

, 여기서

.

, here

.

Matrix E8 = V ₈ ^T V ₈ , defined by an 8x8 matrix, the transformation can be expressed as:

(2)

(2)

는 벡터 곱(cross multiplication) 연산을 나타내며, 즉, 행렬의 상응하는 요소가 곱해진다. 식 (2)의 경우, 행렬 E₈의

연산은 변환을 간단화하기 위하여 양자화 연산과 함께 수행될 수 있다. 그러므로, 변환의 핵심은 P₁XP₁ ^T의 계산에 있으며, 여기서 X는 8×8 픽셀 예측 잔류 오류 행렬이며, 정수를 갖는다. 만약, P₁의 변수 k1, k2, k3, k4 및 k5가 정수라면, 전체 변환은 정수 연산으로 전환될 수 있다. 따라서, 남은 작업은 5개의 파라미터 k1, k2, k3, k4 및 k5의 선택을 결정하는 것이다. 본 발명에 따른 다수의 실험을 통하여, k1, k2, k3 및 k4가 선택된 후, k5의 값을 2로 설정할 때, 변환 성능이 최선임을 입증하였다. Cham은 '다이애딕 대칭의 원리에 의한 정수 코사인 변환의 개선'이라는 그의 논문(IEE Proceedings, 1989, 136(4): 276-288)에서 유사한 결론을 도출하였다. 그러므로, k5는 본 발명에서 고정값 2로 설정되며, 나머지 4개의 파라미터의 선택만 연구된다. (k1, k2, k3, k4)는 변환 베이스로서 정의된다. 상응하는 변환 행렬 P는 다음과 같다:here,

Denotes a cross multiplication operation, that is, the corresponding elements of the matrix are multiplied. For equation (2), the matrix E ₈

The operation can be performed in conjunction with a quantization operation to simplify the transformation. Therefore, the key to the transformation lies in the calculation of P ₁ XP ₁ ^T , where X is an 8x8 pixel prediction residual error matrix and has an integer. If the variables k1, k2, k3, k4, and k5 of P ₁ are integers, then the entire transformation can be converted to integer arithmetic. Thus, the remaining work is to determine the selection of the five parameters k1, k2, k3, k4 and k5. Through a number of experiments in accordance with the present invention, when k1, k2, k3 and k4 are selected, the conversion performance is best when the value of k5 is set to 2. Cham draws a similar conclusion in his paper, "Improvement of Integer Cosine Transformation by the Principle of Diadic Symmetry" (IEE Proceedings, 1989, 136 (4): 276-288). Therefore, k5 is set to a fixed value 2 in the present invention, and only the selection of the remaining four parameters is studied. (k1, k2, k3, k4) is defined as the transformation base. The corresponding transformation matrix P is

An integer transform matrix selection method and related integer transform method in video coding are proposed in the present invention. In view of China's first Audio and Video Coding Standard (AVS), in which an 8x8 integer DCT transform is adopted, a method for selecting a transform base of integer transform is proposed, wherein de-correlation efficiency and The energy concentration efficiency of the transform base, the dynamic transform range of the transform base and the computational complexity are evaluated. Furthermore, two 8x8 integer transform bases (5, 6, 4, 1) and (4, 5, 3, 1) are proposed according to this method, and a fast transform algorithm based on two group bases is also proposed. .

The choice of transform base is based on the following principles:

Principle 1: Transform Orthogonality. Orthogonal transformations ensure that the transformation is only a rotation of the coordinate system, but the energy of the image does not change. In order to guarantee the orthogonality of the transform, P in Equation (2) must satisfy the following condition.

(3)

(3)

Here Diag is a diagonal matrix, ie its non-leading-diagonal element is zero. The quantization procedure then satisfies the transform orthogonality through the adjustment of the quantization matrix.

Principle 2: Energy Concentration. The purpose of the DCT transform is to eliminate correlation among the elements in order to concentrate as much energy after conversion with as few coefficients as possible, so that the compression efficiency of entropy coding after quantization is improved. The selection of the integer conversion base is also made on this principle.

Principle 3: Simplification of Fast Conversion Algorithms. The value of the transformation base is not very large, and the number of calculations should be as small as possible.

The integer transform matrix selection method in video coding according to the present invention continuously searches all integer transform bases satisfying orthogonal conditions in a specific range, but the transform bases for the 8 × 8 transform matrix P are (k1, k2, k3, k4),

The range of values of the transform base coefficients is k1, k2, k3∈ [1, 10], k4∈ [1, 4], and all integer orthogonal transform bases satisfying P · P ^T = Diag are obtained, and Diag is diagonal Being a matrix;

의 값이 0.75, 0.8, 0.85, 0.9 및 0.95일 때, 입력 이미지 잔류 오류 데이터의 공분산 행렬 COV(X_V)을 수립하되, (b) correlation coefficient

When the values of are 0.75, 0.8, 0.85, 0.9, and 0.95, establish a covariance matrix COV (X _V ) of the input image residual error data,

이며,

는 인접 X_V 요소 사이의 상관 계수이며,

≤1인 단계;The one-dimensional image prediction residual error vector with 8 lengths is assumed to be X _V = [x ₁ , x ₂ , ... x ₈ ] and the covariance matrix COV of the X _V elements established based on the first-order Markov model (X _V ) is

Is,

Is the correlation coefficient between adjacent X _V elements,

≤ 1;

(c) obtaining the covariance matrix COV (Y _V ) of the transform domain through the transform matrix P corresponding to the transform base,

인 단계;The transformation matrix P corresponding to the transformation base (k1, k2, k3, k4) is normalized, i.e. each row of P is divided by the vector length of the row to obtain an orthogonal matrix P _u , where X _V is Y _V = P as _u X _V is converted to orthogonally, _V is the covariance matrix of Y

Phosphorus step;

의 값이 0.75, 0.8, 0.85, 0.9 및 0.95일 때, 에너지 집중화 효율

E 및 감상관 효율

C을 계산하되,(d) through the steps (b) and (c), the correlation coefficient

When the values of are 0.75, 0.8, 0.85, 0.9 and 0.95, energy concentration efficiency

E and auditorium efficiency

Calculate C,

E은 이하와 같이 정의되며,The energy concentration efficiency

E is defined as

,

,

C는 이하와 같이 정의되는 단계;The appreciation hall efficiency

C is defined as follows;

의 값에서 각각의 변환 베이스를 위한 에너지 집중화 효율

E 및 감상관 효율

C의 표준화된 결과를 계산하되, 상기 동일한

에서 i번째 변환 베이스를 위한

E의 표준화된 결과는 다음과 같으며,(e) predetermined correlation coefficient

Energy concentration efficiency for each conversion base at the value of

E and auditorium efficiency

Compute a standardized result of C, but with the same

For the i th conversion base

The standardized result of E is

C의 표준화된 결과는 다음과 같은 단계;for the i transform base

The standardized results of C are as follows;

에서 모든 그룹의 베이스에 대한 상기 에너지 집중화 효 율

E 및 상기 감상관 효율

C의 복합 평가값 Eval_E 및 Evla_C 를 획득하기 위하여, 가중된 합을 계산하되, 5개의

지점에 상응하는 가중치는 각각 1/15, 2/15, 3/15, 4/15 및 5/15인 단계 및(f) each correlation coefficient

The energy concentration efficiency for the bases of all groups in

E and the appreciation hall efficiency

In order to obtain the composite evaluation values of Eval _E and Evla _C of _C , the weighted sum is calculated, but 5

The weights corresponding to the points are 1/15, 2/15, 3/15, 4/15 and 5/15, respectively, and

(g) calculating the weighted sum of Evla _C and Eval _E to obtain a composite evaluation value (Eval) for transform base performance, wherein the weights of Evla _C and Eval _E include 0.4 and 0.6, respectively. It features.

Another feature of the above-described integer transform matrix selection method in video coding is to evaluate the computational complexity for the transform base (k1, k2, k3, k4) after the composite evaluation value (Eval) for the performance of the transform base is obtained. Steps are added; First, the transform base with the higher composite evaluation value Eval is selected, and if the difference between the Eval values is less than 0.02, then a base that provides more benefit in computational complexity, i.e. fewer addition / subtraction and fewer shifting operations, The required base is characterized by being desirable for applications requiring better real time performance.

According to the integer conversion method in video coding of the present invention. In terms of encoding via intra-frame or inter-frame, the predictive residual error of the block is obtained, and the prediction and block transforms are performed so that energy can be concentrated on a small amount of coefficients, and then quantization, scanning, run length coding And through entropy coding, the image data is compressed, recorded in the coding bitstream, and in terms of decoding, the block transform coefficients of the entropy coding are extracted from the bit stream, and then through inverse quantization and inverse transformation, the prediction residual of the block Error is reconstructed, and a method in which prediction information is used together to reconstruct video data,

(a) Acquire a transform matrix P used for 8 × 8 integer transform during video coding through an integer transform matrix selection method in video coding as claimed in claim 1, wherein the transform matrix P is expressed as follows. The corresponding integer conversion base is (5, 6, 4, 1);

(b) perform an integer transform represented by Y = PXP ^T on an 8 × 8 image residual error data block, wherein the basic transform unit is an 8-point one-dimensional transform expressed as y = Px, where x = [x0, x1, x2, x3, x4, x5, x6, x7] ^T , output vector y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , and the calculation is performed as follows;

A. a = 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;

Complete the calculation process expressed in the same way as

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;

(c) Perform one-dimensional inverse transformation, where x = P ^T y is defined as the base unit of coincidence transformation, y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , x = [x0 , x1, x2, x3, x4, x5, x6, x7] ^T , and the one-dimensional inverse transform is performed as follows.

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 a 4x4 matrix product using the following formula;

In the calculation the 4 × 4 matrix product is the same at conversion, only input and output are exchanged;

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;

Here, the "<<" operation represents a left shifting operation and has a higher priority than the priority of the addition / subtraction operation. “a << b” includes a step indicating that a is left left shifted.

According to another integer transformation method in the video coding of the present invention, in terms of encoding through an intra-frame or an inter-frame, a prediction residual error of a block is obtained, and the prediction and block transformation is performed so that energy can be concentrated in a small amount of coefficients. And then, through quantization, scanning, run length coding and entropy coding, the image data is compressed, written to the coding bitstream, in terms of decoding, the block transform coefficients of the entropy coding are extracted from the bit stream, and Then, through inverse quantization and inverse transformation, a prediction residual error of a block is reconstructed, and a method in which prediction information is used together to reconstruct video data,

(a) Acquire a transform matrix P used for 8 × 8 integer transform during video coding through an integer transform matrix selection method in video coding as claimed in claim 1, wherein the transform matrix P is expressed as follows. The corresponding integer conversion base is (4, 5, 3, 1);

(b) perform an integer transform represented by Y = PXP ^T on an 8 × 8 image residual error data block, wherein the basic transform unit is an 8-point one-dimensional transform expressed as y = Px, where x = [x0, x1, x2, x3, x4, x5, x6, x7] ^T , output vector y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , and the calculation is performed as follows;

A. a = 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;

Complete the calculation process expressed in the same way as

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;

(c) Perform one-dimensional inverse transformation, where x = P ^T y is defined as the base unit of coincidence transformation, y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , x = [x0 , x1, x2, x3, x4, x5, x6, x7] ^T , and the one-dimensional inverse transform is performed as follows.

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 a 4x4 matrix product using the following formula;

In the calculation the 4 × 4 matrix product is the same at conversion, only input and output are exchanged;

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;

Here, the "<<" operation represents a left shifting operation and has a higher priority than the priority of the addition / subtraction operation. “a << b” includes a step indicating that a is left left shifted.

According to the present invention, a complex evaluation method for the performance of integer transform base is proposed, and several groups of transform bases with better performance based on this method are selected, and a fast transform method for two groups of transform bases is selected. Is provided. Test results of high resolution video testing sequences demonstrate that the performance of the preferred transform base group according to the present invention is superior to JVT's ABT (Adaptive Block Transform) 8 × 8 transform, where the bases 10, 9, 6 , 2) represents the best conversion performance, (4, 5, 3, 1) provides the lowest computational complexity, and the performance of (5, 6, 4, 1) lies between the two. Compared to the ABT 8x8 transform, the three group bases retained the advantages in transform performance and computational complexity. Moreover, the tested performance of the selected transform base demonstrates the accuracy and feasibility of the transform base selection method according to the present invention. The method is not only suitable for integer transformation matrices, but also for performance evaluation of various transformation matrices, including the importance for the selection of the transformation matrices.

(1) Selection of conversion base

The evaluation procedure of the transform base is shown in FIG.

)의 값은 0.75와 0.95 사이에서 주로 분배된다. 0.75, 0.8, 0.85, 0.9 및 0.95의

값에서 각각의 변환 베이스에 상응하는 에너지 집중화 효율(

E) 값들이 계산되며, 동일한

에서 다양한 변환 베이스의

E 값들은 표준화된다. 상이한 상관 계수

에서 동일한 변환 베이스에 상응한

E의 표준화된 결과의 가중된 합은 베이스 그룹에 상응한 에너지 집중화 효율

E의 복합 평가값(Eval_E)을 획득하기 위하여 계산되며, 여기서 가중치는 상이한

값의 확률에 의해 결정된다. 본 발명에 따르면, 5개의

포인트에 상응하는 가중치는 연속적으로 1/15, 2/15, 3/15, 4/15, 5/15로 설정된다. 변환 베이스 그룹에 상응한 감상관 효율(de-correlation efficiency)

c의 복합 평가값(Eval_C)은 동일한 절차로 계산될 수 있다. Correlation Coefficients of Various Image Residual Error Data

) Is mainly distributed between 0.75 and 0.95. 0.75, 0.8, 0.85, 0.9 and 0.95

The energy concentration efficiency corresponding to each conversion base in the value (

E) The values are calculated and the same

Of various conversion bases

E values are normalized. Different correlation coefficients

Corresponds to the same conversion base in

The weighted sum of the standardized results of E is the energy concentration efficiency corresponding to the base group.

Calculated to obtain a composite estimate of _E (Eval _E ), where the weights are different

It is determined by the probability of the value. According to the invention, five

The weights corresponding to the points are successively set to 1/15, 2/15, 3/15, 4/15, 5/15. De-correlation efficiency corresponding to transform base group

The composite evaluation value of c (Eval _C ) can be calculated with the same procedure.

Finally, the composite evaluation value Eval and the auditorium efficiency of the energy concentration efficiency corresponding to the conversion base can be obtained by calculating the weighted sum of Eval _E and Eval _C. Since the energy concentration efficiency directly affects the compression performance after conversion, its weight is greater. The weights of the evaluation values Eval _E and Eval _C are defined as 0.6 and 0.4 in the present invention, respectively.

When closing the value of Eval, the base with lower computational complexity performs better.

E 및

C의 복합 평가값을 도시하며, 변환 베이스의 범위가 k1, k2, k3∈[1, 10] 및 k4∈[1, 4]일 때, 8-포인트 일차원 변환을 완성하기 위하여 필요한 덧셈 회수 및 시프팅 연산의 회수를 나타낸다. (변환 및 역변환을 위한 연산의 회수는 동일하다)The table below corresponds to five group bases.

E and

Addition number and shift necessary to complete an 8-point one-dimensional transform when the transform base ranges k1, k2, k3 '[1, 10] and k4' [1, 4] Indicates the number of ting operations. (The number of operations for transform and inverse transform is the same)

 k1, k2, k3, k4

E 및

C의 복합 평가값

E and

Composite evaluation of C  Number of additions (+/-)  Number of shifting operations (<<) 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) have been proposed in related papers. The composite estimates of the auditorium efficiency and energy concentration efficiency corresponding to the bases (5, 6, 4, 1) are next to those corresponding to the bases (10, 9, 6, 2) and the computational complexity is lower. The composite estimate corresponding to base (4, 5, 3, 1) is somewhat lower than the composite estimate corresponding to base (6, 6, 3, 2), but the advantage in computational complexity is evident. The actual video sequence test shows that the distortion rate performance provided by the bases (5, 6, 4, 1), (4, 5, 3, 1) and (6, 7, 5, 1) is (6, 6). , Better than by 3, 2), closest to the performance by the base 10, 9, 6, 2.

(2) Implementation diagram of 8x8 integer conversion fast algorithm

2 to 5, x0, x1, x2, x3, x4, x5, x6 and x7 represent 8 input values of the one-dimensional transform of the integer transform, and at the same time 8 output values of the inverse transform; And y0, y1, y2, y3, y4, y5, y6, and y7 are 8 output values of the one-dimensional transform, and 8 input values of the inverse transform. The data processing direction is from left to right. Two lines intersecting at a point represent the addition of two numbers, and three lines intersecting at a point represent the addition of three numbers. The square represents multiplication by coefficient, where "-" represents negation, and "2" represents multiplication of two, ie left shifted by one bit; "4" represents a multiplication of 4, that is, left shift by 2 bits.

1. Conversion

The integer transform is performed on an 8 × 8 image residual error data block, and the basic transform unit is an 8 point one-dimensional transform such as y = Px, where x = [x0, x1, x2, x3, x4, x5, x6, x7] ^T And output y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T. The calculation procedure is as follows:

First, when the transform is performed with a different transform matrix P, the common steps are as follows:

(1) a = 0x0-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;

Here, the same part of the calculation requires 16 addition / subtraction and two shifting operations.

Then, the same individual steps are executed as calculated by the equation:

The calculation steps corresponding to the bases (5, 6, 4, 1) are as follows:

(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;

A total of 16 addition / subtraction and four shifting operations are required.

The calculation steps for the base (4, 5, 3, 1) are as follows:

(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;

A total of 12 addition / subtraction and four shifting operations are required.

Thus, to complete y = Px at once, a total of 32 addition / subtraction and six shifting operations are required for the transform base (5, 6, 4, 1), and the transform base (4, 5, 3, 1). 28 addition / subtraction and 6 shifting operations are required. The amount of computation necessary to complete one integer transform in an 8x8 block is 16 times the unit computation described above. The fast algorithm of the transform for the base 5, 6, 4, 1 is shown in FIG. 2. The fast algorithm of the transform for the bases 4, 5, 3, 1 is shown in FIG.

2. Inverse transformation

The basic one-dimensional transform unit is defined as x = P ^T y, where y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , x = [x0, x1, x2, x3, x4, x5, x6, x7] ^T. The following steps are one x = P ^T y calculation.

(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) calculating the 4 × 4 matrix product using the following equation:

In equations and transformations, matrix multiplication and algorithm are the same, only the input and output data vectors are exchanged. The computations of the two representations are the same. For the base (5, 6, 4, 1), 16 subtraction / subtraction and 4 shifting operations are needed, and for the base (4, 5, 3, 1), 12 addition / subtraction and 4 shifting operations are required. Do.

(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;

The "<<" operation represents a left shift operation and has a higher priority than the priority of the add / sub operation. "a << b" indicates that a is left left shifted.

The amount of computation in the common part is 16 addition / subtraction and two shifting operations.

Thus, to complete one x = P ^T y, for the base (5, 6, 4, 1), 32 addition / subtraction and 6 shifting operations are needed, and the base (4, 5, 3, 1) For this, 28 addition / subtraction and 6 shifting operations are required. The fast algorithm of the inverse transform for the bases 5, 6, 4, 1 is shown in FIG. The fast algorithm of the inverse transform for the bases 4, 5, 3, 1 is shown in FIG. The amount of computation necessary to complete the inverse transformation of one integer transform in an 8x8 block is 16 times the unit computation described above.

According to the present invention, a complex evaluation method for the performance of an integer transform base is proposed, and several groups of transform bases with better performance based on this method are selected, and a fast transform method for two groups of transform bases is selected. Is provided.

Claims (15)

In the method for selecting an integer transform matrix in video coding, (a) Search all integer transform bases satisfying orthogonal conditions in a specific range, but the transform base for 8 × 8 transform matrix P is defined as (k1, k2, k3, k4),

The range of transform base coefficient values is k1, k2, k3∈ [1, 10], k4∈ [1, 4], and all integer orthogonal transform bases satisfying P · P ^T = Diag are obtained, and Diag is diagonal A matrix; (b) correlation coefficient

When the values of are 0.75, 0.8, 0.85, 0.9, and 0.95, establish a covariance matrix COV (X _V ) of the input image residual error data, The one-dimensional image prediction residual error vector with 8 lengths is assumed to be X _V = [x ₁ , x ₂ , ... x ₈ ], and the covariance matrix COV of the X _V elements established based on the first-order Markov model (X _V ) is

Is,

Is the correlation coefficient between adjacent X _V elements,

≤ 1; (c) obtaining the covariance matrix COV (Y _V ) of the transform domain through the transform matrix P corresponding to the transform base, The transformation matrix P corresponding to the transformation base (k1, k2, k3, k4) is normalized, i.e. each row of P is divided by the vector length of the row to obtain an orthogonal matrix P _u , where X _V is Y _V = P as _u X _V is converted to orthogonally, _V is the covariance matrix of Y

Phosphorus step; (d) through the steps (b) and (c), the correlation coefficient

When the values of are 0.75, 0.8, 0.85, 0.9 and 0.95, energy concentration efficiency

E and auditorium efficiency

Calculate C, The energy concentration efficiency

E is defined as

, The appreciation hall efficiency

C is defined as follows;

(e) predetermined correlation coefficient

Energy concentration efficiency for each conversion base at the value of

E and auditorium efficiency

Compute a standardized result of C, but with the same

For the i th conversion base

The standardized result of E is

for the i transform base

The standardized results of C are as follows;

(f) each correlation coefficient

The energy concentration efficiency for all groups of bases in

E and the appreciation hall efficiency

In order to obtain the composite evaluation values of Eval _E and Evla _C of _C , the weighted sum is calculated, but 5

Corresponding weights are 1/15, 2/15, 3/15, 4/15 and 5/15, respectively, and (g) Computing the weighted sum of Evla _C and Eval _E to obtain a composite evaluation value (Eval) for transform base performance, wherein the weights of Evla _C and Eval _E are 0.4 and 0.6, respectively. The method according to claim 1, wherein after the composite evaluation value (Eval) of the performance of the transform base is obtained, a step for evaluating the computational complexity for the transform base (k1, k2, k3, k4) is added; First, the transform base with the higher composite evaluation value Eval is selected, and if the difference between the Eval values is less than 0.02, then a base that provides more benefit in computational complexity, i.e. fewer addition / subtraction and fewer shifting operations, Characterized in that the desired base is preferred for applications requiring better real time performance. Integer conversion method for video coding, In terms of encoding via intra-frame or inter-frame, the predictive residual error of the block is obtained, and the prediction and block transforms are performed so that energy can be concentrated on a small amount of coefficients, and then quantization, scanning, run length coding And through entropy coding, the image data is compressed and recorded in a coding bitstream, In terms of decoding, the block transform coefficients of entropy coding are extracted from the bit stream, and then through inverse quantization and inverse transform, the predictive residual error of the block is reconstructed, and the prediction information is used together to reconstruct the video data. In (a) Acquire a transform matrix P used for 8 × 8 integer transform during video coding through an integer transform matrix selection method in video coding as claimed in claim 1, wherein the transform matrix P is expressed as follows. The corresponding integer conversion base is (5, 6, 4, 1);

(b) perform an integer transform represented by Y = PXP ^T on an 8 × 8 image residual error data block, wherein the basic transform unit is an 8-point one-dimensional transform expressed as y = Px, where x = [x0, x1, x2, x3, x4, x5, x6, x7] ^T , output vector y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , and the calculation is performed as follows; A. a = 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; Complete the calculation process expressed in the same way as

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; (c) Perform one-dimensional inverse transformation, where x = P ^T y is defined as the base unit of coincidence transformation, y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , x = [x0 , x1, x2, x3, x4, x5, x6, x7] ^T , and the one-dimensional inverse transform is performed as follows. 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 a 4x4 matrix product using the following formula;

In the calculation the 4 × 4 matrix product is the same at conversion, only input and output are exchanged; 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; Here, the "<<" operation represents a left shifting operation and has a higher priority than the priority of the addition / subtraction operation. “a << b” includes a step indicating that a is left left shifted. Integer conversion method for video coding, In terms of encoding via intra-frame or inter-frame, the predictive residual error of the block is obtained, and the prediction and block transforms are performed so that energy can be concentrated on a small amount of coefficients, and then quantization, scanning, run length coding And through entropy coding, the image data is compressed and recorded in a coding bitstream, In terms of decoding, the block transform coefficients of entropy coding are extracted from the bit stream, and then through inverse quantization and inverse transform, the prediction residual error of the block is reconstructed, and the prediction information is used together to reconstruct the video data. , (a) Acquire a transform matrix P used for 8 × 8 integer transform during video coding through an integer transform matrix selection method in video coding as claimed in claim 1, wherein the transform matrix P is expressed as follows. The corresponding integer conversion base is (4, 5, 3, 1);

(b) perform an integer transform represented by Y = PXP ^T on an 8 × 8 image residual error data block, wherein the basic transform unit is an 8-point one-dimensional transform expressed as y = Px, where x = [x0, x1, x2, x3, x4, x5, x6, x7] ^T , output vector y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , and the calculation is performed as follows; A. a = 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; Complete the calculation process expressed in the same way as

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; (c) Perform one-dimensional inverse transformation, where x = P ^T y is defined as the base unit of coincidence transformation, y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , x = [x0 , x1, x2, x3, x4, x5, x6, x7] ^T , and the one-dimensional inverse transform is performed as follows. 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 a 4x4 matrix product using the following formula;

In the calculation the 4 × 4 matrix product is the same at conversion, only input and output are exchanged; 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; Here, the "<<" operation represents a left shifting operation and has a higher priority than the priority of the addition / subtraction operation. “a << b” includes a step indicating that a is left left shifted. In the method for selecting an integer transform matrix in video coding, (a) searching for an integer transform base that satisfies an orthogonal condition in a predetermined range, wherein the transform base for the 8x8 transform matrix P is defined as (k1, k2, k3, k4);

(b) the correlation coefficient of various image residual error data

Setting); (c) the set correlation coefficients (

Energy Concentration Efficiency for

E and auditorium efficiency

Calculating C; (d) a predetermined correlation coefficient (

Energy Concentration Efficiency for Each Transformation Base

E and auditorium efficiency

Calculating a standardized result of C, and (e) the correlation coefficients (

The normalized energy concentration efficiency for the conversion base

E and auditorium efficiency

Calculating a weighted sum to obtain a composite evaluation value of C (Eval _E and Evla _C ). The method of claim 5, wherein step (c) (c1) a predetermined correlation coefficient (

Calculating a covariance matrix COV (X _V ) of the input image residual error data for (c2) calculating an orthogonal transform matrix P _u for the transform base, and (c3) calculating a covariance matrix COV (Y _V ) of a transform domain through a transform matrix P corresponding to the transform base. The method of claim 6, The covariance matrix COV (X _V ) is

_{And, X V = [x 1,} x 2, ... x 8] is assumed as, in the X _V element established on the basis of the primary Markov (Markov) model

Is the correlation coefficient between adjacent X _V elements,

≤1, and The covariance matrix COV (Y _V ) is

Where the transform matrix P corresponding to the transform base (k1, k2, k3, k4) is normalized, i.e. each row of P is divided by the vector length of the row to obtain an orthogonal matrix P _u , where X _V is Y _V Is orthogonally transformed as = P _u X _V , The energy concentration efficiency

E and auditorium efficiency

C is each

,

Method as characterized in that as defined. The method of claim 5, (f) calculating a weighted sum of the Evla _C and Eval _E to obtain a composite estimate (Eval) of the performance of the transform base. 9. The method of claim 8, wherein the weights of Evla _C and Eval _E are 0.4 and 0.6, respectively. The method of claim 8, (g) estimating the computational complexity for the transform base. The method of claim 10, wherein a transform base having a higher composite evaluation value (Eval) for the transform base performance is selected, and if the difference between the Eval values is smaller than a predetermined value, selecting a transform base having an advantageous computational complexity. How to feature. 6. The integer orthogonal transform base according to claim 5, wherein a range of the transform base coefficient values is k1, k2, k3 '[1, 10], k4' [1, 4], and satisfies P · P ^T = Diag . Is obtained, and Diag is a diagonal matrix. The method of claim 5, wherein the correlation coefficient

The value of is set to 0.75, 0.8, 0.85, 0.9 and 0.95. The method of claim 13, wherein the five correlation coefficients in the step (e)

Weights corresponding to 1/15, 2/15, 3/15, 4/15 and 5/15, respectively. In the integer conversion method for video coding, (a) obtaining a transformation matrix P used for 8 × 8 integer transformation during video coding through an integer transformation matrix selection method during video coding as claimed in claim 5; (b) perform an integer transform represented by Y = PXP ^T on an 8 × 8 image residual error data block, wherein the basic transform unit is an 8-point one-dimensional transform expressed as y = Px, where x = [x0 , x1, x2, x3, x4, x5, x6, x7] ^T , output vector y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T and (c) Perform one-dimensional inverse transformation, where x = P ^T y is defined as the base unit of coincidence transformation, y = [y0, y1, y2, y3, y4, y5, y6, y7] ^T , x = [x0 , x1, x2, x3, x4, x5, x6, x7] ^T.

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