JP2013016972A - Encoder, decoder and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To equalize the norm of a basic vector as much as possible when performing orthogonal transformation or inverse orthogonal transformation with integer accuracy, and to improve the encoding efficiency by using a base while taking the orthogonality of a basic vector into account.SOLUTION: The orthogonal transformation unit 3 of an encoder 11 performs DCT by using an integer DCT base. The integer DCT base used in the orthogonal transformation unit 3 is calculated by an orthogonal transformation base calculation unit 20. The base calculation means 22 of the orthogonal transformation base calculation unit 20 operates each element of a base where each element of a fraction DCT base is rounded to an integer within a range of ±n(n is an integer of 1 or more), determines the elements of an integer DCT base so as to minimize the cost by using the following cost function for enhancing the uniformity of size of norm of the base vector and the orthogonality of the base vector, and outputs an integer DCT base. cost=a×Σ|(xi, xi)-b|+Σ|(xi, xj)|.

Description

  The present invention relates to an orthogonal transform technique for encoding a signal such as an image, and more particularly to an encoding device, a decoding device, and a program that perform orthogonal transform with integer precision.

  Conventionally, as a video encoding method used in systems such as broadcasting and moving image distribution, AVC / H. H.264 standards are known. In this video encoding method, intra prediction and motion compensation prediction are performed, and orthogonal conversion is performed for each two-dimensional block such as 4 × 4 pixels or 8 × 8 pixels with respect to a difference signal between a predicted image and an input image. Signal compression is achieved by performing quantization and entropy coding. For orthogonal transformation of a two-dimensional block, DCT (Discrete Cosine Transform) with integer precision is used so that mismatch does not occur on the decoding side. Hereinafter, integer precision DCT is referred to as integer DCT.

  As an orthogonal transform base of integer precision, AVC / H. In addition to the orthogonal transform base of integer DCT used in the H.264 standard, those described in Patent Document 1 and Non-Patent Document 1 are known. In Patent Document 1, a decimal precision orthogonal transform base is scalar-multiplied and rounded to the nearest integer, and the base vector elements are manipulated so that the norm of the base vector (sum of squares of elements) is within 1% error. A technique is described in which each element of a basis vector is less than 32 as an orthogonal transform basis. Similarly to Patent Document 1, Non-Patent Document 1 discloses unified 4 × 4 and 8 × 8 obtained by manipulating base vector elements so that norms of integer DCT base vectors are as equal as possible. , 16 × 16, and 32 × 32 elements are described.

Special table 2011-504000 gazette

A. Fuldseth, G. Bjontegaard, M. Sadafale, M. Budagavi, "Transform design for HEVC with 16 bit intermediate data representation," Doc JCTVC-E243, Joint Collaborative Team on Video Coding (JCT-VC) of ITU-T SG16 WP3 and ISO / IEC JTC1 / SC29 / WG11, Geneva, CH, March 2011

  By using the orthogonal transform base of integer DCT described in Patent Document 1 or Non-Patent Document 1 described above, AVC / H. Compared with the orthogonal transform base of integer DCT according to the H.264 standard, integer transform can be performed with high accuracy. However, when manipulating the basis vector elements in the process of calculating the orthogonal transform base of integer precision, the orthogonality of the basis vectors is not taken into consideration, and in particular, large blocks such as 16 × 16, 32 × 32, etc. When performing the conversion, there is a problem that the accuracy deteriorates. The same applies not only to the case where the encoding device performs integer-precision orthogonal transformation, but also to the case where the decoding device performs integer-precision inverse orthogonal transformation.

  Therefore, the present invention has been made to solve the above-mentioned problems, and its purpose is to make the norms of the basis vectors as equal as possible and perform orthogonality of the basis vectors when performing orthogonal transformation or inverse orthogonal transformation with integer precision. It is an object of the present invention to provide an encoding device, a decoding device, and a program that can improve the encoding efficiency by using a base in consideration of the characteristics.

In order to achieve the above object, the encoding apparatus according to claim 1 according to the present invention performs encoding to generate an orthogonal transform coefficient by orthogonally transforming an input signal, and quantize the orthogonal transform coefficient to output an encoded signal. The apparatus includes an orthogonal transform unit that orthogonally transforms the input signal using an N-point (N is an integer equal to or greater than 1) integer-precision orthogonal transform base, and the orthogonal transform unit is orthonormal with predetermined decimal precision. A base when each element of the integer base is manipulated in a range of ± n (n is an integer of 1 or more) with respect to an integer base obtained by multiplying each element of the transformation base by c (c> 1) , XN, a is a predetermined positive number, an ideal norm value in each base vector is b = c × c, i = 1, 2,..., N, j = 1, 2,..., N, i <j, and (A, B) is the inner product value of vectors A and B. In order to do so, the following formula: cost = a × Σ | (xi, xi) −b | + Σ | (xi, xj) |
Thus, the element of each base vector that minimizes the cost is used as the integer-precision orthogonal transform base.

  An encoding apparatus according to claim 2 of the present invention is characterized in that in the encoding apparatus according to claim 1, a is N.

  An encoding apparatus according to a third aspect of the present invention is the encoding apparatus according to the first or second aspect, wherein i is 2 and j is an even number other than 2.

  The encoding device according to claim 4 of the present invention is the encoding device according to claim 3, wherein the basis vectors xi and xj are composed of a plurality of elements counting from the first. The inner product operation of the mathematical expression is performed by vectors xi ′ and xj ′ composed of elements from the first to a plurality of halves among the plurality of elements.

を用いて、前記入力信号を直交変換することを特徴とする。 The encoding device according to claim 5 of the present invention is the encoding device according to any one of claims 1 to 4, wherein the orthogonal transform unit is an integer DCT base comprising the following 16 × 16 elements:

Is used to orthogonally transform the input signal.

を用いて、前記入力信号を直交変換することを特徴とする。 An encoding apparatus according to a sixth aspect of the present invention is the encoding apparatus according to any one of the first to fourth aspects, wherein the orthogonal transform unit is an integer DCT base comprising the following 32 × 32 elements:

Is used to orthogonally transform the input signal.

  Furthermore, a decoding apparatus according to a seventh aspect of the present invention receives the encoded signal output from the encoding apparatus according to any one of the first to sixth aspects, and dequantizes the encoded signal. In a decoding device that performs inverse orthogonal transform and generates a decoded signal, an inverse direct transform unit that performs inverse orthogonal transform on the inverse quantized signal using an integer-precision inverse orthogonal transform base, and the inverse orthogonal transform unit includes: An integer-precision orthogonal transform base transpose matrix used in the orthogonal transform unit of the encoding device is used as the integer-precision inverse orthogonal transform base.

  Furthermore, a program according to an eighth aspect of the present invention causes a computer to function as the encoding device according to any one of the first to sixth aspects.

  A program according to a ninth aspect of the present invention causes a computer to function as the decoding device according to the seventh aspect.

  As described above, according to the present invention, the norm of the basis vectors is made as equal as possible, and the conversion accuracy is improved by using an integer-precision orthogonal transform base or inverse orthogonal transform base in consideration of the orthogonality of the base vectors. The encoding efficiency can be improved.

It is a block diagram which shows the structure of the encoding apparatus by embodiment of this invention. It is a figure which shows the decimal DCT base which consists of a 16x16 element. It is a figure which shows the integer DCT base which consists of a 16x16 element described in the nonpatent literature 1. It is a figure which shows the calculation result of the integer DCT base matrix shown in FIG. 3, and its transpose matrix. It is a block diagram which shows the structure of an orthogonal transformation base calculation apparatus. It is a figure which shows the integer DCT base which consists of a 16x16 element used in embodiment of this invention. It is a figure which shows the calculation result of the integer DCT base matrix shown in FIG. 6, and its transpose matrix. It is a figure which shows the integer DCT base which consists of a 32x32 element used in embodiment of this invention. It is a block diagram which shows the structure of the decoding apparatus by embodiment of this invention. It is a figure explaining a simulation result.

  Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the drawings. The present invention relates to an orthogonal transform that improves the uniformity of the norm size of the basis vectors and the orthogonality of the basis vectors when performing orthogonal transformation with integer precision in an encoding device that encodes a signal such as an image. It is characterized by using a base. In addition, in a decoding device that decodes a signal such as an image, when performing inverse orthogonal transform with integer precision, an inverse orthogonal transform base that improves the uniformity of the norm size of the base vector and the orthogonality of the base vector is obtained. It is characterized by using. Thereby, orthogonal transformation accuracy and inverse orthogonal transformation accuracy can be improved, and encoding efficiency can be improved. Here, an orthogonal transform base when performing integer precision DCT is referred to as an integer DCT base, and an inverse orthogonal transform base when performing integer precision IDCT (Inverse Discrete Cosine Transform) is referred to as an integer IDCT base.

[Encoder]
First, an encoding apparatus according to an embodiment of the present invention will be described. FIG. 1 is a block diagram showing a configuration of an encoding apparatus according to an embodiment of the present invention. The encoding device 11 includes a preprocessing unit 1, a subtraction unit 2, an orthogonal transformation unit 3, a quantization unit 4, an inverse quantization unit 5, an inverse orthogonal transformation unit 6, an addition unit 7, a frame memory 8, and a signal prediction unit 9. And an entropy encoding unit 10.

  The preprocessing unit 1 receives a signal to be encoded, and performs predetermined preprocessing necessary for encoding on the input signal. Since the preprocessing is known, the description thereof is omitted here. The subtraction unit 2 receives a preprocessed signal from the preprocessing unit 1 and also receives a prediction signal from a signal prediction unit 9 described later, and subtracts the prediction signal from the preprocessed signal to generate a difference signal. .

  The orthogonal transformation unit 3 receives the difference signal as a subtraction result from the subtraction unit 2, reads out an orthogonal transformation base with a predetermined integer precision stored in a storage unit (not shown), performs orthogonal transformation, and generates an orthogonal transformation coefficient. As an example of orthogonal transform, integer DCT is performed. It is assumed that the predetermined integer precision orthogonal transform base is calculated by an orthogonal transform base calculation device 20 described later and stored in advance in the storage unit of the encoding device 11. Details of the processing of the orthogonal transform base calculation apparatus 20 and the integer precision orthogonal transform base calculated by the orthogonal transform base calculation apparatus 20 will be described later.

  The quantization unit 4 receives the orthogonal transform coefficient from the orthogonal transform unit 3 and performs quantization. The inverse quantization unit 5 receives the quantized signal from the quantization unit 4, performs inverse quantization, and outputs the inversely quantized signal to the inverse orthogonal transform unit 6.

  The inverse orthogonal transform unit 6 receives the inversely quantized signal from the inverse quantization unit 5, reads an inverse orthogonal transform base with a predetermined integer precision stored in a storage unit (not shown), performs inverse orthogonal transform, Play the signal. As an example of inverse orthogonal transform, integer precision IDCT is performed. It is assumed that the inverse orthogonal transform base having a predetermined integer precision is calculated by an orthogonal transform base calculation device 20 described later and stored in advance in the storage unit of the encoding device 11. Details of the integer-precision inverse orthogonal transform base calculated by the orthogonal transform base calculation apparatus 20 will be described later.

  The adding unit 7 receives the inverse orthogonal transform coefficient from the inverse orthogonal transform unit 6 and also receives the prediction signal from the signal prediction unit 9 described later, and adds the prediction signal to the inverse orthogonal transform coefficient. The frame memory 8 receives the addition result signal from the adder 7 and stores it as a decoded signal. The decoded signal stored in the frame memory 8 is read out as a reference signal when generating a prediction signal by a signal prediction unit 9 described later.

  The signal prediction unit 9 reads the reference signal from the frame memory 8, generates a prediction signal by a predetermined prediction method based on the reference signal, and outputs the prediction signal to the subtraction unit 2 and the addition unit 7. The entropy encoding unit 10 receives the quantized signal from the quantization unit 4, performs entropy encoding, and outputs an encoded signal. This encoded signal is output to a decoding device 38 to be described later.

[Properties of orthogonal transform base]
Next, prior to the description of the integer DCT base and integer IDCT base used in the embodiment of the present invention and the orthogonal transform base calculation apparatus 20 that calculates them, the DCT of decimal precision will be described with respect to the properties of general orthogonal transform bases. An orthogonal transform base (decimal DCT base) and an integer DCT base when performing the above will be described as an example.

(Decimal DCT basis)
First, the nature of the decimal DCT base will be described. FIG. 2 is a diagram showing a decimal DCT base (orthogonal transform base with decimal precision) composed of 16 × 16 elements. In general, each base vector of the decimal DCT base has the following three properties (a) to (c). Here, the basis vector means a vector composed of elements in each row in the decimal DCT basis composed of 16 × 16 elements shown in FIG.

(A) Normality First, each basis vector of the decimal DCT basis has normality. That is, each base vector has a property that the norm (the sum of squares of the elements of the base vectors or the inner product of the same base vectors) is 1.

(B) Orthogonality Second, each base vector of the decimal DCT basis has orthogonality. That is, it has the property that the inner product of different basis vectors is zero. Assuming that the DCT16 matrix of the decimal DCT basis composed of 16 × 16 elements shown in FIG. 2 is DCT16 ′ and the transposed matrix of DCT16 is DCT16 ′, the calculation result of DCT16 × DCT16 ′ ( The product of DCT16 and DCT16 ′) is a 16 × 16 unit matrix. The element of i row and j column in the calculation result of DCT16 × DCT16 ′ represents an inner product between the basis vector of the i-th row and the basis vector of the j-th row. i = 1,... 16 and j = 1,.

(C) Symmetry Third, each basis vector of the decimal DCT basis has the property that the basis vectors of the odd-numbered rows are even symmetric and the basis vectors of the even-numbered rows are oddly symmetric.

  Thus, each base vector of the decimal DCT base has the above-described properties (a) to (c), but each base vector of the integer DCT base does not have the above-described property (a), and (b ) And (c). The reason why each base vector of the integer DCT base does not have the property (a) is that the element is an integer, and the norm of the base vector becomes larger than 1. Therefore, each basis vector of the integer DCT basis has the property (a ′) that the norm of each basis vector is substantially equal, instead of the property (a) of normality. That is, each base vector of the integer DCT base desirably has the properties (a ′), (b), and (c) described above.

(Integer DCT basis)
Next, the integer DCT base will be described. FIG. 3 is a diagram showing an integer DCT base composed of 16 × 16 elements described in Non-Patent Document 1. The integer DCT base shown in FIG. 3 is obtained by multiplying each element of the decimal DCT base shown in FIG. 2 by 256 and rounding it to an integer. Then, the norm of each base vector in the second to sixteenth rows is the first row. Each element is operated so as to be close to the norm 65536 (= 256 × 256) of the basis vector of the eye, and | 26 | is set to | 25 |

  FIG. 4 is a diagram showing a calculation result of the integer DCT basis matrix shown in FIG. 3 and its transposed matrix. The matrix of FIG. 4 is an integer DCT basis matrix composed of 16 × 16 elements shown in FIG. Is a calculation result of Tc16 × Tc16 ′ where Tc16 is the transposed matrix of Tc16 and Tc16 ′ is Tc16 ′. The elements of i rows and j columns (i = 1, 2,..., 16, j = 1, 2,..., 16) in the matrix shown in FIG. 4 are i rows in the integer DCT base shown in FIG. Represents the inner product of the basis vector of j and the basis vector of j rows.

  Given that the integer DCT basis vector ideally has the properties of (a ′) and (b), the result of Tc16 × Tc16 ′ should be a 16536 unit matrix multiplied by 65536. is there. However, in FIG. 4, the 16 × 16 unit matrix is not multiplied by 65536. In other words, each of the basis vectors of the integer DCT basis (the integer DCT basis shown in FIG. 3) described in Non-Patent Document 1 is based on the unity of the norm magnitude of the basis vector (property (a ′)) and the basis vector. It can be seen that the orthogonality (property (b)) is not sufficient. When DCT is performed using the integer DCT base shown in FIG. 3, the properties of (a ′) and (b) in the integer DCT base are not sufficient, and thus the coding efficiency may not be sufficient.

  Therefore, the orthogonal transform basis calculation apparatus described later further improves the uniformity of the norm magnitude of the basis vectors (property (a ′)) and the orthogonality of the basis vectors (property (b)), and is similar to DCT. An integer DCT basis having the following symmetry (property (c)) is calculated. The orthogonal transform unit 3 illustrated in FIG. 1 performs orthogonal transform using the integer DCT base calculated by the orthogonal transform base calculation device. Thereby, encoding efficiency can be improved. The same applies to the integer IDCT base used when performing inverse orthogonal transform.

[Orthogonal transform basis calculation device]
Next, the uniformity of the norm size of the basis vectors (property (a ′)) and the orthogonality of the basis vectors (property (b)) are further improved, and the same symmetry ((c) An orthogonal transform base calculation apparatus for calculating an integer DCT base having a property) and an integer IDCT base will be described. FIG. 5 is a block diagram illustrating a configuration of the orthogonal transform base calculation apparatus. The orthogonal transform base calculation apparatus 20 includes an integerization unit 21, a base calculation unit 22, and a transposition calculation unit 23. The integer converting means 21 inputs a decimal DCT base (for example, the case of a decimal DCT base composed of 16 × 16 elements is shown in FIG. 2), and each element of the decimal DCT base is multiplied by a predetermined number (for example, 256 times). Round to integer and output the DCT base after rounding to the basis calculation means 22.

The base calculation means 22 inputs the DCT base after integer rounding from the integerizing means 21, operates each element of the DCT base after integer rounding within a range of ± n (n is an integer of 1 or more), and Using the cost function of Equation (1) for improving the uniformity of the norm size and the orthogonality of the basis vectors, the elements of the integer DCT basis are obtained so as to minimize the cost (cost), and the integer DCT Output the base.
(Equation 1)
cost = a × Σ | the norm of the basis vectors−the ideal norm | + Σ | the inner product−0 | of different basis vectors
= A × Σ | inner product between basis vectors−ideal norm | + Σ | inner product between different basis vectors | (1)

  In the mathematical formula (1), the inner product of the basis vectors means the inner product of the same basis vectors. The first term on the right side indicates the degree of uniformity of the norm magnitude in the basis vector, and the smaller the value, the more the uniformity is realized (property (a ′)). The second term on the right side indicates the degree of orthogonality of the basis vectors. The smaller the value, the more orthogonality is realized (property (b)). a is a positive number, and when an integer DCT base of N points is obtained, it is preferable that a = N. For example, when obtaining an integer DCT base composed of 16 × 16 elements, N = 16.

  Thus, in Formula (1), by setting a = N and a being the multiplication coefficient of the first term, the unity of the norm magnitude of the basis vector as the first term is the second term. The orthogonality of the basis vectors is emphasized in proportion to the magnitude of N indicating the number of elements. In image coding, considering that the transform coefficient is rounded by performing quantization after orthogonal transform, it is more important to have a uniform norm size than the orthogonality of basis vectors. It is done.

The formula (1) is expressed as a general formula as follows.
(Equation 1 ')
cost = a × Σ | (xi, xi) −b | + Σ | (xi, xj) | (1 ′)
b is c × c (b = c × c) when each element of the decimal DCT base is rounded to an integer by c times (c> 1) in the integerization means 21. xi and xj are basis vectors when the basis calculation means 22 operates each element of the DCT basis after integer rounding within a range of ± n (n is an integer of 1 or more), i = 1, 2, .., N, j = 1, 2,. (Xi, xi) indicates an inner product value of the base vectors xi and xi, and (xi, xj) indicates an inner product value of the base vectors xi and xj (i ≠ j).

  The transposition calculation means 23 receives the integer DCT base from the base calculation means 22, obtains a transpose matrix of the integer DCT base matrix, and outputs it as an integer IDCT base. The integer DCT base output by the base calculation means 22 and the integer IDCT base output by the transposition calculation means 23 are stored in the storage unit of the encoding device 11 shown in FIG. The integer IDCT base is used for the inverse orthogonal transform by the inverse orthogonal transform unit 6. Further, the integer IDCT base output by the transposition calculation means 23 is stored in a storage unit of the decoding device 38 shown in FIG. 9 described later, and is used for inverse orthogonal transform by the inverse orthogonal transform unit 33.

  Thereby, it is possible to calculate the integer DCT base and the integer IDCT base in which the uniformity of the norm size of the basis vectors and the orthogonality of the basis vectors are improved, and the coding efficiency can be improved. Since each base vector of the integer DCT basis and the integer IDCT basis has a symmetry property (c), i <j may be set in the second term on the right side of the equation (1 ′). Thereby, the calculation amount at the time of calculating the integer DCT base and the integer IDCT base can be reduced.

(When using only even number basis vectors)
Hereinafter, the improvement of the integer DCT base composed of 16 × 16 elements shown in FIG. 3 described in Non-Patent Document 1 will be described as an example. In the integer DCT base shown in FIG. 3, considering the symmetry and the periodicity of the basis vectors similar to the DCT base, as shown in the matrix of the operation result shown in FIG. In addition, an element (inner product value) of i rows and j columns (i and j are even numbers) that becomes i + j = 18 (= N + 2, N is 16 DCT input points) is always 0. Therefore, when the base calculation means 22 of the orthogonal transform base calculation apparatus 20 shown in FIG. 5 obtains an integer DCT base element so as to minimize the cost of the mathematical formulas (1) and (1 ′), this portion ( An inner product of basis vectors corresponding to odd rows, even columns, even rows, odd columns, and i rows and j columns (i, j are even numbers) of i + j = 18 (= N + 2, N is 16 DCT input points). Is not included in the calculation of the mathematical formulas (1) and (1 ′).

  Further, in the integer DCT base composed of 4 × 4 to 32 × 32 elements described in Non-Patent Document 1 (see FIG. 3 for the integer DCT base composed of 16 × 16 elements), the integer DCT base composed of 2N × 2N elements The odd-numbered rows of the integer DCT base consisting of N × N elements (k = 1 to N) are evenly symmetric, and the second k−1-th row of integer DCT base consisting of 2N × 2N elements. The value of the element is fixed. Therefore, since the inner product between the odd-numbered basis vectors is constant, even if the inner-product operation between the odd-numbered basis vectors is excluded from the equations (1) and (1 ′), the cost is minimized. This does not affect the cost calculation when calculating. That is, when the base calculation means 22 of the orthogonal transform base calculation apparatus 20 shown in FIG. 5 calculates the elements of the integer DCT base so that the cost of the equations (1) and (1 ′) is minimized, The inner product between the basis vectors is not included in the calculations of the mathematical formulas (1) and (1 ′).

  As described above, when the base calculation unit 22 of the orthogonal transform base calculation apparatus 20 obtains the elements of the integer DCT base so that the cost of the formulas (1) and (1 ′) is minimized, the formula (1) (1 In the inner product calculation of '), only the inner product of the basis vectors of even rows need be calculated.

(When using the basis vector in the second row)
Further, in consideration of the periodic nature of the DCT base, the base calculation means 22 of the orthogonal transform base calculation apparatus 20 calculates the basis vector corresponding to the non-zero element in the second row in the matrix of the operation results shown in FIG. The mathematical formulas (1) and (1 ′) need only be calculated for inner products.

  In the integer DCT base shown in FIG. 3, due to the nature of the DCT base, each element of the base vector in the second row and the fourth, sixth,..., Sixteenth rows (even rows other than the second row). ) Are composed of the same elements but in the same order, the norms of the base vectors in the even rows (inner products of the base vectors) are equal. Further, each basis vector in the even-numbered rows other than the second row is based on the characteristics of the DCT basis that elements of the basis vectors in the second row are sampled at predetermined intervals. The sum of absolute values of the inner product of the vector and the basis vectors of the 4th, 6th,..., 16th row (even number rows other than the 2nd row), the basis vector of the 4th row, ,..., The absolute value sum of the inner products with the basis vectors of the 16th row (even rows other than the 4th row), the basis vectors of the 6th row and the 2nd, 4th, 8th,. The absolute value sum of the inner product of the basis vectors of the line (even lines other than the 6th line),..., The 16th line and the 2, 4, 6,. The sum of the absolute values of the inner products with the basis vectors of (even-numbered lines other than the 16th line) is equal. From the above, if the inner product of the basis vector of the second row and the basis vector of the even-numbered row is calculated in Equations (1) and (1 ′), and if i = 2 in Equation (1 ′), Good.

Therefore, the base calculation means 22 of the orthogonal transform base calculation apparatus 20 shown in FIG. 5 inputs the DCT base after integer rounding from the integerizing means 21, and each element of the DCT base after integer rounding is ± n (n is While operating in the range of an integer of 1 or more, the following formula (2) is used to obtain the elements of the basis vectors in the second row so as to minimize the cost. Based on the properties of the elements and the DCT, the elements of the basis vectors of even rows other than the second row are obtained, and an integer DCT basis is output. If the elements of the basis vectors in the second row are determined, the elements of the basis vectors in even rows other than the second row are uniquely determined from the nature of the DCT. Also, the basis vectors of odd rows are known from the premise of this embodiment.
(Equation 2)
cost = 16 × | (x2, x2) −64 ^ 2 × 16 |
+ | (X2, x4) | + | (x2, x6) | + | (x2, x8) |
+ | (X2, x10) | + | (x2, x12) | + | (x2, x14) | (2)
x1, x2,..., x16 indicate the basis vectors of the first row, the second row,..., the 16th row of the integer DCT basis to be obtained, and (A, B) are the vectors A and B. Indicates the inner product value of.

The basis vector of the second row that minimizes the cost function of the equation (2) is as follows when calculated in the range of a value ± 1 rounded to an integer.
[91, 87, 79, 70, 56, 43, 27, 8, -8, -27, -43, -56, -70, -79, -87, -91]

(When only the first half of the basis vector is used)
Further, when calculating the cost using Equation (2), the inner product up to the eighth element of the first half of the basis vector is calculated in consideration of the symmetry property of the integer DCT basis shown in FIG. Calculate it. This is because if the basis vectors of even rows are oddly symmetric and the odd symmetric vectors with 2M elements are o1 and o2, the inner product of o1 and o2 is the number of elements up to the Mth element in the first half of o1 and o2. This is because it is twice the inner product. Thereby, the amount of calculation can be reduced.

  This will be specifically described below. The base calculation means 22 of the orthogonal transform base calculation apparatus 20 inputs the DCT base after the integer rounding from the integer conversion means 21, and uses the equation (2) to determine the elements of the integer DCT base so that the cost is minimized. When obtaining the fourth, sixth,..., 14 based on the first half 8 elements x2 [0], x2 [1],..., X2 [7] in the basis vector x2 in the second row. The eight elements in the first half of the basis vectors x4, x6,..., X14 in the row are obtained, and the values of x2 [0], x2 [1],. 1), the minimum value of the cost of Equation (2) by the first eight elements of the basis vector is obtained, and the integer DCT basis is obtained.

  That is, the base calculation means 22 performs, as the processing of step 1, from the first half eight elements x2 [0], x2 [1],..., X2 [7] in the base vector x2 in the second row, The first eight elements x4 [0], x4 [1],..., X4 [7] in the basis vector x4 in the row, the first eight elements x6 [0] in the basis vector x6 in the sixth row, x6 [1],..., x6 [7],..., the first eight elements x14 [0], x14 [1],. Ask for. Then, the basis calculation means 22 performs the processing in step 2 as the first half of the elements x2 [0], x2 [1],..., X2 [7] in the basis vector x2 in the second row, and step 1 The inner product of both vectors is calculated from the eight elements in the first half of the basis vectors in the fourth, sixth,. Ask for the cost of. Then, an element of the integer DCT base having the minimum cost is obtained.

As the processing of Step 1, the following Step 1-1 to Step 1-6 are performed.
Step 1-1 is a process for obtaining the first eight elements x4 [0] to x4 [7] of the basis vector x4 in the fourth row.
x4 [0] = x2 [1];
x4 [1] = x2 [4];
x4 [2] = x2 [7];
x4 [3] = -x2 [5];
x4 [4] = -x2 [2];
x4 [5] = -x2 [0];
x4 [6] = -x2 [3];
x4 [7] = -x2 [6];
Step 1-2 is a process for obtaining the first eight elements x6 [0] to x6 [7] of the basis vector x6 in the sixth row.
x6 [0] = x2 [2];
x6 [1] = x2 [7];
x6 [2] = -x2 [3];
x6 [3] = -x2 [1];
x6 [4] = -x2 [6];
x6 [5] = x2 [4];
x6 [6] = x2 [0];
x6 [7] = x2 [5];
Step 1-3 is processing for obtaining the first eight elements x8 [0] to x8 [7] of the basis vector x8 in the eighth row.
x8 [0] = x2 [3];
x8 [1] = -x2 [5];
x8 [2] = -x2 [1];
x8 [3] = x2 [7];
x8 [4] = x2 [0];
x8 [5] = x2 [6];
x8 [6] = -x2 [2];
x8 [7] = -x2 [4];

Step 1-4 is a process for obtaining the first eight elements x10 [0] to x10 [7] of the basis vector x10 in the tenth row.
x10 [0] = x2 [4];
x10 [1] = -x2 [2];
x10 [2] = -x2 [6];
x10 [3] = x2 [0];
x10 [4] = -x2 [7];
x10 [5] = -x2 [1];
x10 [6] = x2 [5];
x10 [7] = x2 [3];
Step 1-5 is processing for obtaining the first half 8 elements x12 [0] to x12 [7] of the basis vector x12 in the 12th row.
x12 [0] = x2 [5];
x12 [1] = -x2 [0];
x12 [2] = x2 [4];
x12 [3] = x2 [6];
x12 [4] = -x2 [1];
x12 [5] = x2 [3];
x12 [6] = x2 [7];
x12 [7] = -x2 [2];
Step 1-6 is a process for obtaining the first eight elements x14 [0] to x14 [7] of the basis vector x14 in the fourteenth row.
x14 [0] = x2 [6];
x14 [1] = -x2 [3];
x14 [2] = x2 [0];
x14 [3] = -x2 [2];
x14 [4] = x2 [5];
x14 [5] = x2 [7];
x14 [6] = -x2 [4];
x14 [7] = x2 [1];

As the processing of Step 2, a term for aligning the magnitude of the norm and a term for enhancing orthogonality (a term for obtaining an inner product of different basis vectors) are added, and a process for obtaining a cost is performed.
cost = 0; // initialization
cost + = 16 × abs (InnerProduct (x2, x2, 8) -64 × 64 × 8); // Make the norm size the same
cost + = abs (InnerProduct (x2, x4, 8)); // Find the inner product of different basis vectors (same below)
cost + = abs (InnerProduct (x2, x6, 8));
cost + = abs (InnerProduct (x2, x8, 8));
cost + = abs (InnerProduct (x2, x10, 8));
cost + = abs (InnerProduct (x2, x12, 8));
cost + = abs (InnerProduct (x2, x14, 8));
Here, the function abs indicates that the absolute value is taken, and the function InnerProduct is InnerProduct (A0, A1, m), and indicates that the inner product up to the m-th element is performed in the array of A0 and A1.

  Here, since the base vector of the integer DCT base composed of 16 × 16 elements has 16 elements, the size of the norm is made close to 64 × 64 × 16 = 65536. Therefore, the norm size is made to approach 64 × 64 × 8 = 32768. In this way, when the integer DCT basis is obtained using only the first half elements of the basis vector, the inner product operation of the vector of 16 elements can be changed to the inner product operation of the vector of 8 elements. The number of calculations can be halved and the amount of calculation can be reduced. Based on this result, an even-numbered basis vector is obtained from the odd symmetry and the relationship between the basis vector elements of the second row and the elements of other even-numbered basis vectors. By combining the vectors, an integer DCT base composed of 16 × 16 elements in FIG. 6 could be obtained.

  FIG. 6 is a diagram showing an integer DCT base composed of 16 × 16 elements used in the embodiment of the present invention. The mathematical expression (1) is obtained by the base calculation means 22 of the orthogonal transform base calculation apparatus 20 shown in FIG. Integer DCT base calculated and output using the above. Note that the 16 × 16-element integer IDCT base that is calculated and output by the transpose calculation unit 23 of the orthogonal transform base calculation apparatus 20 is a transpose matrix of the integer DCT base matrix shown in FIG.

  FIG. 7 is a diagram showing a calculation result of the integer DCT basis matrix shown in FIG. 6 and its transpose matrix. The matrix of FIG. 7 is an integer DCT basis matrix composed of 16 × 16 elements shown in FIG. Is a calculation result of Tn16 × Tn16 ′ where Tn16 is Tn16 and the transposed matrix of Tn16 is Tn16 ′. The elements of i rows and j columns (i = 1, 2,..., 16, j = 1, 2,..., 16) in the matrix of FIG. 7 are i rows in the integer DCT base shown in FIG. The inner product of the basis vector and the basis vector of j rows is shown. When comparing each element in FIG. 7 with each element in FIG. 4, the element value of the diagonal component is closer to the ideal norm value 65536 in FIG. Is close to zero. That is, the matrix in FIG. 7 is closer to the ideal value obtained by multiplying the 16 × 16 unit matrix by 65536 than in FIG. 4. Accordingly, the integer DCT basis used in the embodiment of the present invention shown in FIG. 6 is more uniform in the norm magnitude of the basis vector ((a) than the integer DCT basis of Non-Patent Document 1 shown in FIG. ') Property) and the orthogonality of basis vectors (property (b)) can be said to be further improved.

  FIG. 8 is a diagram showing an integer DCT base composed of 32 × 32 elements used in the embodiment of the present invention. Like the integer DCT base composed of 16 × 16 elements shown in FIG. 6, FIG. The integer DCT bases calculated and output by the base calculation means 22 of the orthogonal transform base calculation apparatus 20 using the above formula (1) and the like are shown. The integer IDCT base composed of 32 × 32 elements calculated and output by the transpose calculation unit 23 of the orthogonal transform base calculation apparatus 20 is a transpose matrix of the matrix of the integer DCT base shown in FIG.

[Decoding device]
Next, a decoding device according to an embodiment of the present invention will be described. FIG. 9 is a block diagram illustrating a configuration of a decoding device according to an embodiment of the present invention. The decoding device 38 includes an entropy decoding unit 31, an inverse quantization unit 32, an inverse orthogonal transform unit 33, an addition unit 34, a post-processing unit 35, a frame memory 36, and a signal prediction unit 37.

  The entropy decoding unit 31 receives the encoded signal output from the encoding device 11 illustrated in FIG. 1 and performs entropy decoding corresponding to the entropy encoding of the entropy encoding unit 10 illustrated in FIG. Since the entropy decoding process is known, the description thereof is omitted here. The inverse quantization unit 32 receives the signal entropy-decoded by the entropy decoding unit 31 and performs inverse quantization similar to the inverse quantization unit 5 illustrated in FIG. To the unit 33.

  The inverse orthogonal transform unit 33 receives the inversely quantized signal from the inverse quantization unit 32 and, similarly to the inverse orthogonal transform unit 6 illustrated in FIG. 1, an inverse orthogonal transform with a predetermined integer precision from a storage unit (not shown). Read base and perform inverse orthogonal transform. It is assumed that the inverse orthogonal transform base having a predetermined integer precision is calculated by the above-described orthogonal transform base calculation device 20 and stored in advance in the storage unit of the decoding device 38.

  The adder 34 receives a signal from the inverse orthogonal transform unit 33 and also receives a prediction signal from a signal prediction unit 37 described later, and adds both signals. The post-processing unit 35 inputs a decoded signal that is a signal resulting from the addition from the adding unit 34, and performs predetermined post-processing corresponding to the pre-processing of the pre-processing unit 1 illustrated in FIG. Output as an output signal. Since post-processing is already known, description thereof is omitted here.

  The frame memory 36 receives the addition result signal from the adder 34 and stores it as a decoded signal. The decoded signal stored in the frame memory 36 is read as a reference signal when generating a prediction signal by a signal prediction unit 37 described later. The signal prediction unit 37 reads the reference signal from the frame memory 36, generates a prediction signal by a predetermined prediction method based on the reference signal, and outputs the prediction signal to the addition unit 34.

〔Experimental result〕
Next, experimental results of an encoding process using an integer DCT base composed of 16 × 16 elements and 32 × 32 elements according to an embodiment of the present invention and an encoding process using an integer DCT base according to Non-Patent Document 1 ( Computer simulation results) will be described. FIG. 10 is a diagram showing the BD rate of the simulation result. The BD rate in FIG. 10 indicates the BD bit rate (code amount reduction rate) of luminance (Y component) when the QP range of quantization is QP = 1, 5, 9, and 13. The ratio of the code amount in the embodiment of the present invention to the amount is shown. The greater the negative value of the BD rate, the better the encoding efficiency of the embodiment of the present invention than in Non-Patent Document 1. In the “Sequence” column, “Traffic”, “PeopleOnStreet”, and the like indicate the names of the test moving images in which the encoding experiment was performed, and “IntraHE” and “IntraLC” indicate the types of signal prediction. “Intra” is a condition that uses only intra prediction, and “HE” is an abbreviation for High Efficiency, which is a condition that gathers tools that improve the coding performance although the calculation amount is large. “LC” is an abbreviation for Low Complexity, which is a condition for collecting tools that have lower encoding performance but lower encoding performance than “HE”. According to the simulation result shown in FIG. 10, from “Average” in the last row, when the signal prediction is “IntraHE”, the BD rate is −0.13, and when the signal prediction is “IntraLC”, The BD rate is -0.17. Also, in each sequence, most BD rates are negative values, and a maximum gain of 1.23% is obtained. As a result, the use of the integer DCT according to the embodiment of the present invention improves the uniformity of the norm magnitude of the basis vectors and the orthogonality of the basis vectors, compared with the use of the integer DCT according to Non-Patent Document 1. It can be seen that the conversion efficiency is improved.

  As described above, according to the encoding device 11 according to the embodiment of the present invention, the uniformity of the norm magnitude of the base vector and the orthogonality of the base vector calculated by the orthogonal transform base calculation device 20 are further improved. DCT is performed using the integer DCT base, and IDCT is performed using the transposed matrix of the integer DCT base as an integer IDCT base to perform encoding. In addition, according to the decoding device 38 according to the embodiment of the present invention, the integer DCT basis further improved in the uniformity of the norm magnitude of the basis vectors and the orthogonality of the basis vectors calculated by the orthogonal transform basis calculation device 20. Are used as integer IDCT bases, IDCT is performed, and decoding is performed. Thereby, orthogonal transformation accuracy and inverse orthogonal transformation accuracy can be improved, and encoding efficiency can be improved.

  Note that a normal computer can be used as the hardware configuration of the encoding device 11, the decoding device 38, and the orthogonal transform base calculation device 20 according to the embodiment of the present invention. The encoding device 11, the decoding device 38, and the orthogonal transform base calculation device 20 are configured by a computer that includes a CPU, a volatile storage medium such as a RAM, a non-volatile storage medium such as a ROM, an interface, and the like. Pre-processing unit 1, subtraction unit 2, orthogonal transformation unit 3, quantization unit 4, inverse quantization unit 5, inverse orthogonal transformation unit 6, addition unit 7, frame memory 8, and signal prediction unit 9 included in encoding device 11. Each function of the entropy encoding unit 10 is realized by causing a CPU to execute a program describing these functions. Similarly, each function of the entropy decoding unit 31, the inverse quantization unit 32, the inverse orthogonal transform unit 33, the addition unit 34, the post-processing unit 35, the frame memory 36, and the signal prediction unit 37 included in the decoding device 38 is also included in these functions. Each is realized by causing the CPU to execute a program describing the function. The functions of the integer conversion means 21, the base calculation means 22, and the transpose calculation means 23 provided in the orthogonal transform base calculation apparatus 20 are also realized by causing the CPU to execute a program describing these functions. These programs can be stored and distributed in a storage medium such as a magnetic disk (floppy (registered trademark) disk, hard disk, etc.), optical disk (CD-ROM, DVD, etc.), semiconductor memory, or the like.

  The present invention has been described with reference to the embodiment. However, the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the technical idea thereof. For example, in the embodiment, the search range (operation range ± n) for minimizing the cost of the mathematical formula (1) by the base calculation means 22 of the orthogonal transform base calculation device 20 may be other than ± 1. However, since the integer DCT base obtained here is based on DCT and each base vector indicates a cosine curve, the magnitude relation of the elements of the integer DCT base is made the same as before the element is operated. It is desirable. In the embodiment, the orthogonal transformation is DCT, but it may be DST (Discrete Sine Transform) or KLT (Karhunen Loeve Transform). In this case, as in the case of DCT, the elements of each orthonormal transformation base are multiplied by a predetermined number and rounded to an integer, and a conversion base with integer precision is obtained by Equations (1) (1 ') and the like. In the above embodiment, a 16 × 16 element conversion base and a 32 × 32 element conversion base are used as examples. However, other numbers of element conversion bases such as 4 × 4, 8 × 8, and 64 × 64 are used. Etc. Moreover, although the above embodiment has been described with reference to image signals, the input of the encoding device, decoding device, and program of the present invention is not limited to image signals.

DESCRIPTION OF SYMBOLS 1 Pre-processing part 2 Subtraction part 3 Orthogonal transformation part 4 Quantization part 5 Inverse quantization part 6 Inverse orthogonal transformation part 7 Addition part 8 Frame memory 9 Signal prediction part 10 Entropy encoding part 11 Encoding apparatus 20 Orthogonal transformation base calculation apparatus 21 Integer unit 22 Base calculation unit 23 Transposition calculation unit 31 Entropy decoding unit 32 Inverse quantization unit 33 Inverse orthogonal transformation unit 34 Addition unit 35 Post-processing unit 36 Frame memory 37 Signal prediction unit 38 Decoding device

Claims (9)

In an encoding device that orthogonally transforms an input signal to generate an orthogonal transform coefficient, quantizes the orthogonal transform coefficient, and outputs an encoded signal.
An orthogonal transform unit that orthogonally transforms the input signal using an orthogonal transform base with integer precision of N points (N is an integer of 1 or more);
The orthogonal transform unit includes:
Each element of the integer base is ± n (n is an integer equal to or greater than 1) with respect to the integer base obtained by multiplying each element of the orthonormal transformation base with a predetermined decimal precision by c times (c> 1). The basis vectors when operating in the range are x1, x2,..., XN, a is a predetermined positive number, the ideal norm value in each basis vector is b = c × c, and i = 1, 2, ,..., N, j = 1, 2,..., N, i <j, and (A, B) is the inner product value of the vectors A and B, the following formula: cost = a × Σ | (Xi, xi) -b | + Σ | (xi, xj) |
Thus, an element of each base vector that minimizes the cost is used as the integer-precision orthogonal transform base. The encoding device according to claim 1, wherein
An encoding apparatus, wherein a is N. The encoding device according to claim 1 or 2,
An encoding apparatus characterized in that i is 2 and j is an even value other than 2. The encoding device according to claim 3,
When the basis vectors xi and xj are composed of a plurality of elements counting from the first, the inner product operation of the mathematical expression is the first to the plurality of half of the plurality of elements. An encoding apparatus characterized by being performed by vectors xi ′ and xj ′. In the encoding device according to any one of claims 1 to 4,
The orthogonal transform unit is an integer DCT base consisting of the following 16 × 16 elements:

A coding apparatus, wherein the input signal is orthogonally transformed using In the encoding device according to any one of claims 1 to 4,
The orthogonal transform unit is an integer DCT base consisting of the following 32 × 32 elements:

A coding apparatus, wherein the input signal is orthogonally transformed using In the decoding apparatus which inputs the encoding signal output by the encoding apparatus as described in any one of Claim 1-6, dequantizes the said encoding signal, carries out inverse orthogonal transformation, and produces | generates a decoding signal ,
Using an inverse orthogonal transform base of integer precision, comprising an inverse direct transform unit for inverse orthogonal transform of the inverse quantized signal,
The decoding apparatus, wherein the inverse orthogonal transform unit uses an integer-precision orthogonal transform base transpose matrix used in the orthogonal transform unit of the encoding apparatus as the integer-precision inverse orthogonal transform base.   The program for functioning a computer as an encoding apparatus as described in any one of Claim 1-6.   The program for functioning a computer as a decoding apparatus of Claim 7.

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