JPH09127923A - Arithmetic unit and arithmetic method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate a quantized transformation matrix with minimum quantization error. SOLUTION: When the generation request of a quantized transformation matrix for minimizing the error generated when RGB signal is converted into YUV signal (color difference signal with luminance signal) and then returned to the original RGB signal by use of inverse transformation is inputted to a main control, part 26 through an input and output signal processing part 21, the main control part 26 makes a quantized matrix generating part 24 quantize the transformation matrix, and makes an equation generating part 25 generate an integer programming expression. Thereafter, the main control part 26 makes an integer program executing part 23 determine the solution of the integer programming problem, and generates an inverse transformation matrix corresponding to the quantized transformation matrix by the determined solution, and outputs it to the outside of an arithmetic unit through the input and output signal processing part 21.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an arithmetic unit and an arithmetic method, and more particularly, to an R and R method using a quantized transformation matrix.
The present invention relates to an arithmetic unit and an arithmetic method for reducing a conversion error at the time of converting a GB signal into a luminance signal and a color difference signal, or converting a luminance signal and a color difference signal into an RGB signal.

[0002]

2. Description of the Related Art When converting an RGB signal into a YUV signal (luminance signal and color difference signal) or vice versa, a matrix element having a floating point in a conversion matrix is multiplied by 2 to the Nth power and rounded off. Thus, each matrix element of the conversion matrix can be represented by an integer (the conversion matrix is quantized).

For example, the conversion matrix [Rf] shown in Expression 1 (hereinafter, the matrix is represented by []) is a conversion matrix for converting a YUV signal into an RGB signal, and the conversion matrix [Yf] shown in Expression 2 is an RGB signal. Is a conversion matrix for converting to a YUV signal.

[0004]

(Equation 1)

[0005]

(Equation 2)

As shown in Equations 1 and 2, the matrix [Rf],
Each matrix element of [Yf] is given in a real number format with a floating point. In order to represent each matrix element with an integer (-512 to 511) that can be represented by 10 bits, for example, the matrix [R
The matrix [R] shown in Equation 3 is obtained by multiplying each matrix element of [f] by 2 ^ 8 (= 256) (^ represents a power), rounding off to the first decimal place, and quantizing.

[0007]

(Equation 3)

In addition, 2 ^ 9 (= 51) is assigned to each matrix element of the matrix [Yf].
The matrix [Y] shown in Equation 4 is obtained by multiplying by 2), rounding off to the first decimal place, and quantizing.

[0009]

(Equation 4)

Thus, if the transformation matrix is quantized,
Each matrix element of the conversion matrix can be represented by an integer and can be easily signalized. After converting the RGB signal into the YUV signal, in order to convert the RGB signal into the RGB signal again, RG
After the B signal is converted by the matrix [Y], it is further converted by the matrix [R], and each component of the obtained RGB signal is divided by 512 * 256 to return to the original RGB signal.

[0011]

However, the matrix [R] shown by the equation 3 and the matrix [Y] shown by the equation 4
Is a conversion matrix that is quantized by rounding off the first decimal place of each matrix element, and therefore does not represent an accurate conversion matrix. Therefore, for example, when the RGB signal is converted into the YUV signal using the conversion matrix represented by the matrix [R] and the matrix [Y], and then further converted into the RGB signal, the quantization level (10 bits in this case) Is rougher than the error that occurs during conversion, an error occurs due to conversion in each RGB component before and after conversion (each component of the RGB signal before conversion does not match that after conversion).

The RGB signal is converted into YU by using the conversion matrix [Y].
After converting to V signal, R is converted again by using the conversion matrix [R].
Equation 5 shows an error matrix representing the error between the RGB signal before conversion and the RGB signal after conversion, which occurs when the RGB signal is converted.

[0013]

(Equation 5)

Ignoring the error due to rounding when the quantization conversion matrix is generated, since the matrix [Rf] and the matrix [Yf] have an inverse relationship, they are 512 times [Yf] (that is, [Y]).
Multiplied by 256 times [Rf] (that is, [R]) is 51
The unit matrix [I] should be 2 * 256 times. Therefore,
The matrix obtained by subtracting the unit matrix [I] of 512 * 256 times from [Y] [R] represents the error matrix [E] in this case.

In the error matrix [E] shown in Equation 5, the maximum absolute value m of the matrix element is 274 (= | -274 |: the matrix element in the third row and the first column), and The maximum absolute value M of the values including the matrix elements is 486 (= | -100-202-184 |: the matrix element in the first row). The larger m is, the larger the error is, and the larger M is, the larger the error is in the direction of the code.

Similarly, after conversion of the YUV signal into an RGB signal using the conversion matrix [R], and again after conversion into the YUV signal using the conversion matrix [Y], Y before conversion occurs.
The error matrix [E] representing the error between the UV signal and the converted YUV signal is shown in Equation 6.

[0017]

(Equation 6)

At this time, m is 376 (= | -376 |: 3rd line, 3rd line)
Matrix element in the column), and M is 476 (= | -146-86-244 |:
The first row is a matrix element).

As described above, the conventional transform matrix quantization technique has a problem that an error occurs each time cyclic transformation is repeated. Further, in order to reduce the conversion error, a finer quantization level is set (the range indicated by the difference between the minimum value and the maximum value of the matrix elements of the matrix [Rf] or the matrix [Yf] is finely subdivided. There is a problem that a larger number of bits are required for that.

The present invention has been made in view of such a situation, and is intended to reduce an error at the time of cyclic conversion by a quantization conversion matrix without increasing the quantization level (increasing the number of bits). is there.

[0021]

According to a first aspect of the present invention, there is provided an arithmetic unit according to claim 1, wherein a second signal converted from a first signal using a quantized first conversion matrix is used as an original first signal. Generating means for generating a quantized second conversion matrix using an error matrix defined by the quantized second conversion matrix and the quantized first conversion matrix It is characterized by being provided.

According to a sixth aspect of the present invention, there is provided a computing device which comprises a first transformation matrix for transforming a first signal into a second signal and a second transformation matrix for transforming a second signal into a first signal. Quantizing means for quantizing the matrix element by using at least two of rounding down, rounding up, or rounding, and converting the quantized first signal into a second signal. From the N first conversion matrices and the M second conversion matrices that convert the quantized second signal into the first signal, one first conversion matrix and one first conversion matrix. A combination means for combining two conversion matrices and an error matrix defined by the combined first conversion matrix and second conversion matrix are used to make a first conversion of one combination from among the combinations. A matrix and a selection means for selecting the second transformation matrix And wherein the door.

According to a ninth aspect of the present invention, the quantized first transformation matrix is used to transform the second signal transformed from the first signal into the original first signal. Second
Is used to generate a quantized second conversion matrix by using an error matrix defined by the conversion matrix of 1 and the quantized first conversion matrix.

According to a tenth aspect of the present invention, there is provided a calculation method for converting a first signal into a second signal, and a second conversion matrix.
Quantized a second transformation matrix that transforms the signal of to the first signal by quantizing its matrix elements using at least two of rounding down, rounding up, or rounding off. From N first conversion matrices for converting the first signal into the second signal and M second conversion matrices for converting the quantized second signal into the first signal,
One first conversion matrix and one second conversion matrix are combined, and an error matrix defined by the combined first conversion matrix and second conversion matrix is used to select from among the combinations: It is characterized in that one combination of the first transformation matrix and the second transformation matrix is selected.

In the arithmetic unit according to the first aspect, the generating means converts the second signal converted from the first signal into the original first signal by using the quantized first conversion matrix. A quantized second transform matrix to transform and a quantized first transform matrix
The quantized second conversion matrix is generated using the error matrix defined by

In the arithmetic unit according to the sixth aspect, the quantizing means converts the first signal into the first signal and the second conversion signal into the second signal. The second transform matrix is quantized by quantizing its matrix elements using at least two of rounding down, rounding up, or rounding, and combining means quantizes the quantized first signal One of the N first conversion matrices for converting the second signal into two signals and the M second conversion matrices for converting the quantized second signal into the first signal.
And one second conversion matrix are combined, and the selecting means utilizes the error matrix defined by the combined first conversion matrix and second conversion matrix to select from among the combinations: A combination of the first transformation matrix and the second
Select the transformation matrix of.

In the calculation method according to the ninth aspect, the quantization for converting the second signal converted from the first signal into the original first signal by using the quantized first conversion matrix. The quantized second conversion matrix is generated using the error matrix defined by the quantized first conversion matrix and the quantized first conversion matrix.

In the arithmetic method according to claim 10,
A first transformation matrix that transforms a first signal into a second signal and a second transformation matrix that transforms a second signal into a first signal have their matrix elements rounded down, rounded up, or rounded off. Quantized by using at least any two of them, N first conversion matrices for converting the quantized first signal into a second signal, and a quantized second conversion matrix. First conversion matrix in which one first conversion matrix and one second conversion matrix are combined from M second conversion matrices for converting the signal of 1 to the first signal, and the combined first conversion matrix Using the error matrix defined by and the second conversion matrix, one combination of the first conversion matrix and the second conversion matrix is selected from the combinations.

[0029]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be described below. In order to clarify the correspondence between each means described in the claims and the following embodiments, parentheses after each means are described. Within
The characteristics of the present invention will be described as follows by adding a corresponding embodiment (but one example). However, of course,
It does not mean that each means is limited to those described.

The arithmetic unit according to claim 1 is a quantizing means for quantizing the first conversion matrix for converting the first signal into the second signal (for example, the quantization matrix generating section 24 in FIG. 2). When,
A quantized second transformation matrix for transforming the second signal transformed from the first signal into the original first signal using the quantized first transformation matrix; Generating means for generating the quantized second conversion matrix using the error matrix defined by the converted first conversion matrix (for example, the integer programming program execution unit 2 in FIG. 2).
3) and are provided.

In the arithmetic unit according to a fourth aspect, the quantizing means further quantizes a third conversion matrix for converting the second signal into the first signal, and the generating means quantizes. A quantized fourth transformation matrix for transforming the first signal transformed from the second signal into the original second signal using the transformed third transformation matrix; And further generating the quantized fourth conversion matrix using an error matrix defined by the third conversion matrix
A first error obtained from the error matrix defined by the first transform matrix quantized by the quantizer and the second transform matrix generated by the generator; and the quantizer. The second conversion matrix is compared with a second error obtained from the error matrix defined by the third conversion matrix quantized by the third conversion matrix and the fourth conversion matrix generated by the generation unit. And a fourth conversion matrix, which further includes a selection unit (for example, the main control unit 26 in FIG. 2) for selecting one that gives an error matrix with a smaller error.

According to a sixth aspect of the present invention, there is provided an arithmetic device, wherein a first conversion matrix for converting a first signal into a second signal and a second conversion matrix for converting the second signal into the first signal. Quantization means for quantizing a matrix by quantizing its matrix elements using at least two of rounding down, rounding up, or rounding off (for example, the quantization matrix generation unit 24 in FIG. 2); The N first conversion matrices for converting the first signal quantized by the quantizing means into the second signal, and the second signal quantized by the quantizing means, Combination means for combining one of the first conversion matrices and one of the second conversion matrices from the M second conversion matrices to be converted into the first signal (for example, step S41 of FIG. 5). 2 which performs the processing of
Of the combination by using the error control matrix defined by the main control unit 26) and the first conversion matrix and the second conversion matrix combined by the combination means. Selection means for selecting the first conversion matrix and the second conversion matrix (for example, FIG.
2 for performing the processing of step S42 of FIG.
6).

FIG. 1 is a block diagram showing the configuration of an embodiment of a conversion device to which the arithmetic unit of the present invention is applied.

RGB signal or Y as conversion input signal
UV signal is personal computer 2 or VCR
When input to the converter 1 from the (VIDEO CASSETE RECORDER) 3, these signals are supplied to the input / output signal control circuit 11 in the converter 1. The converted YUV signal or RGB signal is output from the input / output signal control circuit 11 to the VCR 3 or the personal computer 2.
It is designed to be output to.

The conversion circuit 12 is an input / output signal control circuit 11
For the RGB signal or YUV signal input from
The conversion matrix generated by the optimum conversion matrix generation circuit 13 is operated to convert an RGB signal into a YUV signal or a YUV signal into an RGB signal.

The YUV signal or the RGB signal converted by the conversion circuit 12 is supplied to the input / output signal control circuit 11.

The conversion matrix generated by the optimum conversion matrix generation circuit 13 uses this conversion matrix to convert the RGB signal to YU.
After converting the V signal (or the YUV signal into the RGB signal), the converted YUV signal is converted into the original RGB signal (or the converted R signal) by using an inverse conversion matrix corresponding to the conversion matrix.
When performing the cyclic conversion for converting the GB signal into the original YUV signal), the maximum of the matrix elements of the error matrix representing the error between the signal before conversion and the signal after the conversion, which is the cyclic conversion and returned to the original signal. It is designed to minimize the absolute value. Therefore, when cyclic conversion is performed using this conversion matrix, the error between the converted signal and the original signal can be reduced.

Alternatively, the optimum conversion matrix generation circuit 13
The conversion matrix generated by the above is designed to minimize the maximum absolute value of the values obtained by adding the matrix elements of the same row and the same code in the error matrix when the cyclic conversion is performed. Therefore, when cyclic conversion is performed using this conversion matrix, it is possible to reduce the error of each component of the converted signal that always occurs in a fixed direction.

The optimum conversion matrix generating circuit 13 is the control circuit 1
4, the method of generating a transformation matrix (method using integer programming program of branch and bound method or method using combinatorial programming), quantization level of transformation matrix (number of bits for quantizing transformation matrix), and transformation Obtains information about the type of matrix (the transformation matrix that minimizes the maximum absolute value of the matrix elements of the error matrix, or the transformation matrix that minimizes the absolute value of the values of the same rows of the error matrix plus the matrix elements of the same sign) Then
According to the generation specification information on these conversion matrices, RGB
Quantization conversion matrix for converting signal to YUV signal, or Y
The quantization conversion matrix for converting the UV signal into the RGB signal is generated, and the generated conversion matrix information is output to the conversion circuit 12.

The control circuit 14 determines the optimum conversion matrix generation specification by monitoring the frequency of cyclic conversion, the time required for conversion, etc., and appropriately outputs this generation specification information to the optimum conversion matrix generation circuit 13. It is designed to output.

FIG. 2 is a diagram showing a functional block diagram of the optimum conversion matrix generation circuit 13 shown in FIG.

The input / output signal processing unit 21 inputs the conversion matrix generation request signal from the conversion circuit 12, and the main control unit 2
6 is instructed to generate a conversion matrix, and the main control unit 26
The conversion matrix information generated by the above is output to the conversion circuit 12. Further, the input / output signal processing unit 21
Supplies the conversion matrix generation specification information from the control circuit 14 to the main control unit 26.

When the transformation matrix [R] and its inverse transformation matrix [Y] are given by the main control unit 26 by the combinatorial programming, the m / M calculation unit 22 calculates an error matrix, and further, the error matrix The maximum absolute value of the matrix element of m and the maximum absolute value of the value of the sum of the matrix elements of the same row and the same sign of the error matrix are calculated, and the calculation result is calculated by the main controller 26.
It is designed to output to.

The integer programming program execution unit 23 solves the integer programming equation of the branch and bound method output from the main control unit 26 to obtain the matrix elements of the transformation matrix [Y] (or [R]), and this matrix The elements are output to the main control unit 26.

The quantization matrix generating section 24 includes a main control section 2
According to the quantization level information of the transformation matrix supplied via 6, the transformation matrix [Rf] and the transformation matrix [Y
f] is multiplied by 2 to the Nth power, and then a transformation matrix is generated by using the integer programming program of the branch and bound method, the transformation matrix quantized by rounding is generated, and the transformation is performed using the combinatorial programming. When a matrix is generated, a conversion matrix quantized by rounding down or rounding up is generated and output to the main control unit 26.

The equation generating section 25 branches the matrix elements of the conversion matrix [Y] (or [R]) corresponding to the conversion matrix [R] (or [Y]) output from the main control section 26 as unknowns. The formula of the integer programming method of the limiting method is created, and this formula is output to the main control unit 26.

The main control unit 26 includes the input / output signal processing unit 2
When the generation of the conversion matrix is instructed from 1, each processing instruction is instructed to each processing unit according to the conversion matrix generation specification.

The memory 27 stores various data such as R data.
The data of each matrix element of the conversion matrix [Yf] for converting the GB signal into the YUV signal, the data of each matrix element of the conversion matrix [Rf] for converting the YUV signal into the RGB signal, and the like are stored.

Next, a specific processing example of the optimum conversion matrix generation circuit 13 will be described with reference to the flowchart of FIG.

First, a transformation matrix is generated using an integer programming program of the branch and bound method (predetermined transformation matrix [Rf]
(Or [Yf]) quantized transformation matrix [R] (or [Y]) corresponding transformation matrix [Y] (or [R])
Will be described). Furthermore, in this case, there are a method of minimizing the maximum absolute value of the matrix element of the error matrix and a method of minimizing the absolute value of the value obtained by adding the matrix elements of the same row and the same sign of the error matrix. The former will be described, and then the latter will be described.

When a conversion matrix generation command is issued from the conversion circuit 12 via the input / output signal processing unit 21, the main control unit 26 receives the maximum absolute value of the matrix element of the error matrix in step S11 of FIG. A variable δ representing m is initialized to zero.

Subsequently, in step S12, the main control unit 26 causes the memory 27 of FIG.
A conversion matrix [Rf] (or [Yf]) for converting a signal into an RGB (or YUV) signal is read. This matrix [R
f] (or [Yf]) is generated by some method and stored in the memory 27 for quantization.

In the subsequent step S13, the quantization matrix generator 24 sets the quantization level according to the conversion matrix generation specification supplied from the control circuit 14, and the conversion matrix [Rf]
Each matrix element of (or [Yf]) is multiplied by 2 to the Nth power (N is determined by the quantization level) and rounded to generate a quantization conversion matrix [R] (or [Y]).

For example, in order to represent each matrix element of the conversion matrix with 10 bits (-512 to 511), each matrix element of the matrix [Rf] is multiplied by 2 ^ 8 = 256, and the first decimal place is rounded off.
A quantization conversion matrix [R] is generated. Similarly, when the matrix [Y] is generated, each matrix element of the matrix [Yf] is multiplied by 2 ^ 9 = 512, the first decimal place is rounded off, and the quantization conversion matrix [Y] is generated. Expressions 7 and 8 show the matrix [R] and the matrix [Y] generated in this way.

[0055]

(Equation 7)

[0056]

(Equation 8)

Subsequently, in step S14, the equation generation unit 25 obtains the matrix [Y] (or [R]) corresponding to the matrix [R] (or [Y]) in order to obtain the matrix [Y].
An expression for integer programming is generated using the branch and bound method with the matrix elements of (or [R]) as unknowns.

The details of the processing in this step will be described below.
When the matrix element of the matrix [R] of Expression 7 is Rij, R22 and R23 are negative among the matrix elements of the matrix [R], and the matrix element of the matrix [Y] of Expression 8 is Yij , Y21, Y22, Y32, and Y33 are negative among the matrix elements of the matrix [Y]. Here, if the matrix elements Rij, Yij are represented by + or-signs and zero or a positive integer (denoted as rij, yij), then Rij = ± rij, Yij = ± yij. Therefore, Equations 7 and 8 can be expressed as shown in Equations (1-1) and (1-2) of Equation 9.

[0059]

(Equation 9)

Since the matrix [Rf] and the matrix [Yf] are inversely related to each other, if errors due to rounding are ignored, [R] / 256 and [Y] / 512 are also inversely related to each other. And the product is the unit matrix [I].

Therefore, [R] [Y] = 256 * 512 [I] and [Y] [R] = 512 * 256 [I]. Considering the error due to rounding, since the matrix elements of the matrix [Y] (or [R]) are now unknowns, the equations (2-1), (2-2) (10) 3-
1) and (3-2)) are established.

[0062]

(Equation 10)

[0063]

[Equation 11]

As shown in equations (1-3) and (1-4) of equation 9, [R] [Y] = [A], [Y] [R] = [B], and the error matrix matrix Let δ be the variable that represents the maximum absolute value m of the element
Then, the matrix element A11 of the matrix [A] (equation (2-1))
On the other hand, Expression (4-1) (or Expression (4-2) for the matrix element A11 (Expression (3-1)) of the matrix [A] is established. This is because the matrix element A11 should have a value close to 256 * 512.

256 * 512-δ ≦ 274y11 + 376y31 ≦ 256 * 512 + δ (4-1) 256 * 512-δ ≦ 143r11 + 244r13 ≦ 256 * 512 + δ (4-2)

Similarly, for matrix element A12 having a value close to 0, equation (4-3) (or expression (4-4)) is given for matrix element A13 having a value close to 0. 4-5) (or
Formula (4-6)) is materialized.

-Δ≤274y12-376y32≤δ (4-3) -δ≤281r11-205r13≤δ (4-4) -δ≤274y13-376y33≤δ (4-5) -δ≤54r11-40r13≤δ (4-6)

Furthermore, similarly, the matrix elements A21, A22,
Inequalities can be generated for A23, A31, A32, and A33.

Regarding the matrix [B], the matrix element B11 (equation (2-2)) having a value close to 512 * 256 is replaced by the equation (5-1) (or the matrix element B11 (equation (3 -2)), the equation (5-2)) is a matrix element B12 having a value close to 0.
On the other hand, equation (5-3) (or equation (5-4)) becomes
Formula (5-5) (or formula (5-6)) is established for the matrix element B13 having a value close to 0.

512 * 256-δ ≦ 274y11 + 274y12 + 274y13 ≦ 512 * 256 + δ (5-1) 512 * 256-δ ≦ 143r11 + 281r21 + 54r31 ≦ 512 * 256 + δ (5-2) -δ ≦ -92y12 + 475y13≤δ (5-3) -δ≤-281r22 + 54r32≤δ (5-4) -δ≤376y11-192y12≤δ (5-5) -δ≤143r13-281r23≤δ (5-6 )

Similarly, matrix elements B21, B22, B23, B31, B
Inequalities can be generated for 32, and B33.

Thus, for example, the above equation (4-
If the number of inequalities in 1) is counted as 2, two inequalities are generated for each matrix element of the matrix [A] and the matrix [B], and the matrix element of the matrix [Y] (or [R]) is generated. A total of 36 inequalities with unknowns are generated.

Further, in order to limit the matrix elements of the matrix [Y] (or [R]) satisfying this condition, the matrix [Y]
(Or [R]) a condition that the total sum Z of the absolute values of the matrix elements is maximum (Z in formula (6-1) (or formula (6-2)) is maximum) is given. This condition is a condition for allowing the matrix element of the quantized conversion matrix to have the maximum spread within the range represented by finite bits. Formula (6-
In 2), r12 and r33 are set to zero.

Y11 + y12 + y13 + y21 + y22 + y23 + y31 + y32 + y33 = Z (6-1) r11 + r13 + r21 + r22 + r23 + r31 + r32 = Z (6-2)

Matrix elements y11 to y33 (or r11 to r
33) is a positive integer or zero. To find this, find the solution that satisfies the above 36 inequalities and maximizes Z in equation (6-1) (or equation (6-2)). This is enough, and this results in finding an integer programming solution shown in Eq.

[0076]

(Equation 12)

In the present case, 36 inequalities correspond to the equation (7-1) of the equation 12, g is 36, n is 9, and Xj (j = 1 to 9).
Is y11 to y33 (or r11 to r33), and Fij (i = 1 to 36: j = 1 to 9) is y11 to y33 (or r11 to r3).
The coefficient of 3), Hi (i = 1 to 36) is 256 * 512 + δ, -256 * 512 +
Either δ or δ.

Further, the equation (6-1) (or the equation (6-
2)) corresponds to the equation (7-2) of the equation 12, and in this case,
The coefficients Cj (j = 1 to 9) are all 1.

FIG. 4 shows the values of the coefficients of 36 inequalities used in integer programming when the matrix elements of the matrix [Y] are unknowns in this way.

In the numbers shown in FIG. 4, δ is 28 from left to right.
256 * 512 + δ (or -256 * 512 + δ or δ) when set to 0, y11, y21, y31, y12, y22, y32, y13, y23, and y33 coefficients (values with signs) Is shown.

For example, the line indicated by 4-1 is 274 * y11 + 0 * y21 + 376 * y31 + 0 * y12 + 0 * y22 + 0 * y32 + 0 * y.
The inequality of 13 + 0 * y23 + 0 * y33 ≦ 131352 (= 256 * 512 + 280 (= δ)) is expressed, and corresponds to the inequality on the right side of the equation (4-1).

Similarly, the line indicated by 4-2 is represented by the formula (4-1).
Corresponds to the inequalities on the left side of, and lines 4-7 indicate that
3) corresponds to the inequality on the right side, the row indicated by 4-8 corresponds to the inequality on the left side of equation (4-3), and the row indicated by 4-13 indicates the inequality on the right side of equation (4-5). The row indicated by 4-14 corresponds to the inequality on the left side of the equation (4-5).

Further, the line indicated by 4-19 is the expression (5-1).
Corresponding to the inequality on the right side of
Corresponding to the inequality on the left side of -1), the line indicated by 4-25 is
This corresponds to the inequality on the right side of Expression (5-3), and the row indicated by 4-26 corresponds to the inequality on the left side of Expression (5-3).
The row indicated by corresponds to the inequality on the right side of Equation (5-5),
The row indicated by -32 corresponds to the inequality on the left side of equation (5-5).

Thus, in step S14 of FIG. 3, the inequalities (36 inequalities in the above example) used in the integer programming method and the equation (6-1) (or the equation (6-
2)) Z and the condition of Z (Z is maximum) are generated.

In the following step S15, the equation generation unit 25
These expressions generated by are passed to the integer programming program execution unit 23 via the main control unit 26, and the integer programming program for finding the solution of the integer programming problem is executed.

In the subsequent step S16, it is determined whether or not there is a solution of the integer programming program executed by the integer programming program executing section 23. If there is no solution, the process branches to step S18. The solution to be solved is a positive integer,
Or, since this integer programming problem is solved under the condition of being zero, when δ is small, there may be no solution.

Therefore, in step S18, the main control unit 26 adds a predetermined small value α (for example, 10) to δ,
Returning to step S14, the equation generation unit 25 is caused to generate the equation of the integer programming problem again by using δ obtained by adding the α.

In this way, until the solution of the integer programming problem is obtained, the value of δ is gradually increased to 0, 10, 20, 30, ... While step S14, step S15, step S16, and The process of step S18 is repeatedly executed, and when it is determined that the solution exists in step S16, the output process of step S17 is performed.

The flowchart shown in FIG. 3 omits detailed processing steps for the purpose of briefly explaining the processing outline for obtaining the solution of the integer programming problem.
Before the processing of step S17 is executed, processing is performed so that the obtained solution is the only solution.

That is, the first by the matrix [R] obtained by quantizing the matrix [Rf] and the matrix [Y] having unknown matrix elements.
Is obtained as described above (the processing of steps S11 to S16 and step S18 of FIG. 3 is executed), and then the matrix [Y] obtained by quantizing the matrix [Yf] and the matrix [Y] in which the matrix elements are unknowns. R] to find a second solution (again,
3 executes steps S11 to S16 and step S18), and [Y] [R] (or [R]
Let [Y]) be the solution for which the maximum absolute value m of the matrix element of the error matrix is smaller. Further, when there are a plurality of solutions having the smallest m, a process of selecting any one of the solutions is performed.

For example, when the matrix elements of the transformation matrix are represented by 10 bits and each matrix element of the matrix [R] has the value shown in equation 7, the matrix obtained as the solution of the integer programming problem with the matrix elements as unknowns. [Y] becomes as shown in Expression 13 (first solution).

[0092]

(Equation 13)

Also, the error matrix [E] at this time is given by
And Equation 15 shows.

[0094]

[Equation 14]

[0095]

(Equation 15)

The maximum absolute value m of the matrix elements of these error matrices [E] is 274 (= | -274 |: matrix element of the third row, first column) in the equation 14 and 244 (= |-in the equation 15). 244 ｜ or ｜ 244 ｜: 1st row 3rd
Column matrix element or the second row, first column matrix element), and the error matrix [E] (= [R] by the conventional quantization conversion matrix
It becomes smaller than that of [Y] -256 * 512 [I]) (m = 376 shown in Expression 6).

Furthermore, in this example, the maximum absolute value M of the sum of matrix elements of the same row and the same code in the error matrix [E] is also given by
4 with 414 (= | -274-140 |: 3rd line), with number 15 with 430 (= | 244 + 1
86 |: 2nd line), which is that of the error matrix [E] by the conventional quantization conversion matrix (M = 486, M = 476 shown in Equations 5 and 6)
It is smaller.

Similarly, when the matrix element of the conversion matrix is represented by 10 bits and each matrix element of the matrix [Y] is set to the value shown in Expression 8, the matrix element is set as an unknown number and obtained as a solution of the integer programming problem. The matrix [R] is as shown in Expression 16 (second solution).

[0099]

(Equation 16)

Further, the error matrix [E] at this time is given by
And Equation 18 shows.

[0101]

[Equation 17]

[0102]

(Equation 18)

The maximum absolute value m of the matrix element of these error matrices [E] is 180 (= | -180 |: matrix element in the third row, second column) in Equation 17, and 195 (= | 195 in Equation 18). (:: matrix element in the first row and second column)
Becomes

Therefore, conversion of [Y] [R] (after converting the RGB signal into the YUV signal, the YUV signal is converted into the RGB signal again).
(Transform back to signal), m calculated by the second solution
Since (= 180) is smaller than m (= 274) calculated by the first solution, the second solution is the solution to be obtained. Similarly, [R]
[Y] conversion (after converting YUV signals to RGB signals,
Again, in the case of conversion from RGB signal back to YUV signal),
Since m (= 195) calculated by the second solution is smaller than m (= 244) calculated by the first solution, the second solution is the solution to be obtained.

In this way, when the transformation matrix is quantized with 10 bits, the matrix [Y] shown in equation 8 and the matrix [R] (second solution) shown in equation 16 become [Y] [R ] Conversion,
In either case of conversion of [R] and [Y], the conversion matrix 12 is output as a conversion matrix to be obtained, and the conversion circuit 12
Performs the conversion between the RGB signal and the YUV signal using the matrix [R] and the matrix [Y].

Next, the process of generating a conversion matrix (inverse conversion matrix) that minimizes the absolute value M of the sum of matrix elements of the same row and the same code in the error matrix [E] will be described. The difference between the processing operation of the optimum conversion matrix generation circuit 13 in this case and the processing operation in the case of minimizing m described above is that step S1 in FIG.
The only difference is the inequality generated in step 4 (the variable updated in step S18 is changed from δ to Δ, but this is merely a change in the expression of the variable and is not an essential difference. ). Therefore, only the process of step S14 of FIG. 3 will be described here.

In step S14, the equation generating section 25
Inequalities and equations for integer programming using the branch and bound method with the matrix elements of the matrix [Y] (or [R]) as unknowns are generated.

Here, details of the processing in this step will be described.

First, regarding the error matrix [E] represented by [R] [Y] −256 * 512 [I], the matrix elements of the error matrix [E] are represented by Eij, and the same row of the error matrix [E] is represented. Let Δ be the variable that represents the maximum absolute value M of the values obtained by adding the matrix elements of the same sign to E11, E12, E13, E11 + E12, E12 + E13, E11 + E
The absolute value of 13, and E11 + E12 + E13 is less than or equal to Δ. If this is expressed by an inequality using the relationship of Expression (2-1) of Expression 10, when the matrix element of the matrix [Y] is an unknown number, Expression (8
-1) to Expression (8-7) are established. If the number of inequalities included in each of these equations is counted as 2, there are 2 * 7 inequalities.

256 * 512-Δ ≦ 274y11 + 376y31 ≦ 256 * 512 + Δ (8-1) -Δ ≦ 274y12-376y32 ≦ Δ (8-2) -Δ ≦ 274y13-376y33 ≦ Δ (8-3) 256 * 512-Δ ≦ (274y11 + 376y31) + (274y12-376y32) ≦ 256 * 512 + Δ (8-4) -Δ ≦ (274y12-376y32) + (274y13-376y33) ≦ Δ (8-5) 256 * 512-Δ ≦ (274y11 + 376y31) + (274y13-376y33) ≦ 256 * 512 + Δ (8-6) 256 * 512-Δ ≦ (274y11 + 376y31) + (274y12-376y32) + (274y13-376y33) ≦ 256 * 512 + Δ (8-7)

Since the same inequality holds for the second and third rows of the error matrix [E], the number of inequalities is
2 * 7 * 3 = 42. Furthermore, [Y] [R] -5
Since a similar inequality can be generated for the error matrix [E] represented by 12 * 256 [I], the total number of inequalities is 42 * 2 = 84.
It becomes a book.

Furthermore, in order to limit the matrix elements of the matrix [Y] (or [R]) satisfying this condition, the matrix [Y]
(Or [R]) the condition that the total sum of the absolute values of the matrix elements is maximum (Z in formula (6-1) (or formula (6-2)) is maximum) is given.

In this way, the problem of integer programming shown in equation 12 is reduced.

In this case, 84 inequalities correspond to the equation (7-1) of the equation 12, and g is 84, n is 9, and Xj (j = 1 to 9).
Is y11 to y33 (or r11 to r33), and Fij (i = 1 to 36: j = 1 to 9) is y11 to y33 (or r11 to r3).
The coefficient of 3), Hi (i = 1 to 84) is 256 * 512 + Δ, -256 * 512 +
Either Δ or Δ.

Further, the equation (6-1) (or the equation (6-
2)) corresponds to the equation (7-2) of Expression 12, and Cj (j = 1 to 9) is all 1.

Thus, in step S14 of FIG. 3, the inequality (8 in the present example) used in integer programming is obtained.
Four inequalities) and equation (6-1) (or equation (6-2))
Z and the condition of Z (Z is maximum) are generated.

As described above, when the matrix element of the conversion matrix is represented by 10 bits, each matrix element of the matrix [R] has the value shown in the equation 7, and the matrix element of the matrix [Y] has an unknown value. The matrix [Y] obtained as the solution of the integer programming problem is given by
9 (first solution).

[0118]

[Equation 19]

The error matrix [E] at this time is given by
And Equation 21. The absolute value M of the value obtained by adding the matrix elements of the same row and the same code in the error matrix shown in Expression 20 is 384 (= | 3
84 |: the first row), and the absolute value M of the values obtained by adding the matrix elements of the same row and the same code in the error matrix shown in Expression 21 is 360.
(= | -360 |: 1st line). That of the error matrix [E] by the conventional quantization transformation matrix (M = 486, M =
476).

[0120]

(Equation 20)

[0121]

(Equation 21)

Similarly, when the matrix element of the transformation matrix is represented by 10 bits, each matrix element of the matrix [Y] has the value shown in equation 8 and the matrix element is an unknown number, it is obtained as a solution of the integer programming problem. The matrix [R] is shown in Expression 22 (second solution).

[0123]

(Equation 22)

Also, the error matrix [E] at this time is given by
And Equation 24 shows. The absolute value M of the value obtained by adding the matrix elements of the same row and the same code in the error matrix shown in Expression 23 is 276 (= | 2
76 |: the third row), and the absolute value M of the value obtained by adding the matrix elements of the same row and the same code in the error matrix shown in Equation 24 is 250.
(= | -118-132 |: 3rd line).

[0125]

(Equation 23)

[0126]

(Equation 24)

Therefore, conversion of [Y] [R] (after converting the RGB signal into the YUV signal, the YUV signal is converted into the RGB signal again).
(Transform back to signal), M calculated by the second solution
Since (= 276) is smaller than M (= 384) calculated by the first solution, the second solution is the solution to be obtained. Similarly, [R]
[Y] conversion (after converting YUV signals to RGB signals,
Again, in the case of conversion from RGB signal back to YUV signal),
Since M (= 250) calculated by the second solution is smaller than M (= 360) calculated by the first solution, the second solution is the solution to be obtained.

In this way, when the transformation matrix is quantized with 10 bits, the matrix [Y] shown in equation 8 and the matrix [R] (second solution) shown in equation 22 become [Y] [R ] Conversion,
In either case of conversion of [R] and [Y], the conversion matrix 12 is output as a conversion matrix to be obtained, and the conversion circuit 12
Performs the conversion between the RGB signal and the YUV signal using the matrix [R] and the matrix [Y].

Next, the process of generating the quantization conversion matrix using the combinatorial programming will be described with reference to the flowchart of FIG.

In step S31, when the quantization conversion matrix generation command from the input / output signal processing unit 21 is sent to the main control unit 26, the main control unit 26 sets high values (∞) to the variables Mmin and mmin. Initialize.

In a succeeding step S32, the RGB signal is YU.
The values of the matrix elements of the conversion matrix [Yf] for converting the V signal and the conversion matrix [Rf] for converting the YUV signal into the RGB signal are read from the memory 27.

In the following step S33, the main control unit 2
6 causes the quantization matrix generation unit 24 to set the quantization level according to the transformation matrix generation information supplied from the control circuit 14, and sets the quantization transformation matrix corresponding to the matrix [Yf] and the matrix [Rf]. Output the command to generate. In response to this instruction, the quantization matrix generation unit 24 causes the conversion matrix [Yf]
And each matrix element of the matrix [Rf] are multiplied by the Nth power of 2 and rounded up or down for each matrix element to generate all matrices [Y] and matrix [R] represented by this method. To do. That is, since each matrix element has two kinds of values, rounding up and rounding down, as a matrix [Y], 2 ^
There are 9 ways and 2 ^ 7 ways of matrix [R] (the matrix elements of the 1st row and 2nd column and the matrix element of the 3rd row and 3rd column of the matrix [R] are fixed to zero as known). To generate.

At the next step S34, the main control unit 26 selects the first matrix [Y] from the 2 ^ 9 matrices [Y] generated by the quantization matrix generator 24 and the 2 ^ 7 matrices [Y]. R] to select the first matrix [R], step S35
Then, using the matrix [R] and the matrix [Y], the maximum absolute value M of the value obtained by adding the maximum absolute value m of the matrix element of the error matrix [E] and the matrix element of the same row and the same sign The m / M calculator 22 is caused to calculate.

In a succeeding step S36, the main controller 26
Compares the magnitudes of M and Mmin calculated by the m / M calculator 22, and if it is determined that M is smaller than Mmin, sets M as the value of Mmin in step S37, and the matrix [ Y] and matrix [R] to matrix [YM] and matrix [R
Save to [M]. When it is determined in step S36 that M is greater than or equal to Mmin, the process of the subsequent step S38 is executed.

In step S38, the main controller 26
The magnitudes of m and mmin calculated by the m / M calculator 22 are compared, and when it is determined that m is smaller than min, m is set as the value of mmin in step S39, and the matrix [Y] at this time is set. And matrix [R] into matrix [Ym] and matrix [Rm]. When it is determined in step S38 that m is greater than or equal to mmin, the processing of the subsequent step S40 is executed.

In the first case, Mmi is determined in step S31.
Since n and mmin are set to ∞, YES is determined in step S36 and step S38, and step S3 is performed.
7 and step S39, the values M and m at that time are set to Mmin and mmin.

In the following step S40, combinations (2 ^ 9 * 2 ^ 7 = 2 ^) of all matrices [Y] and matrices [R].
16), steps S35 to S3
When it is determined whether or not the process shown in 9 is executed and there is an unprocessed combination of the matrix [Y] and the matrix [R], in step S41, the main control unit 26 determines the next [Y]. And [R] combination is selected, and step S3
It branches to 5 and repeats, and the subsequent processing is executed. In step S40, steps S35 to S39 are performed for all combinations of matrix [Y] and matrix [R].
When it is determined that the process indicated by is completed, the process branches to the subsequent step S42.

In this way, m and M are calculated for all combinations of the matrix [Y] and matrix [R] selected by the main control unit 26, and among them, the minimum m and M are
The combinations of the matrix [Y] and the matrix [R], which are respectively stored in mmin and Mmin, correspond to the matrix [Ym] and the matrix [Rm], and the matrix [YM] and the matrix [R].
M].

In step S42, the main controller 2
6 outputs the matrix [Ym] and the matrix [Rm] according to the conversion matrix generation information (when the generation of the conversion matrix that minimizes the value m is instructed), the matrix [YM] and the matrix [RM]
Is output (when the generation of the conversion matrix that minimizes the value M is instructed), the quantization conversion matrix [Ym] and the matrix [Rm] or the matrix is input via the input / output signal processing unit 21. The [YM] and the matrix [RM] are output to the conversion circuit 12.

In this way, when the combinatorial programming is applied, the matrix elements of the conversion matrix are quantized with 10 bits, and the [Y] [R] conversion (RGB signal is converted to YUV) is performed.
A matrix [Ym] that minimizes the error matrix m by converting the signal to a signal and then converting the YUV signal back to an RGB signal.
And the matrix [Rm] are shown in Expression (9-1) and Expression (9-2) of Equation 25, respectively. The m calculated by the error matrix at this time is 113, which is the smallest value in the above-mentioned examples.

[0141]

(Equation 25)

Similarly, when the combinatorial programming is applied, the matrix elements of the conversion matrix are quantized with 10 bits, and the [Y] [R] conversion (after converting the RGB signal into the YUV signal, is performed again). , The matrix [RM] and the matrix [YM] that minimize M of the error matrix due to the conversion of the YUV signal back into the RGB signal) are shown in Expression (10-1) and Expression (10-2) of Equation 26, respectively. . M determined by the error matrix at this time is 192, which is the smallest value in the above-mentioned example.

[0143]

(Equation 26)

In the generation processing of the quantization conversion matrix in step S33, the quantization conversion matrix is generated by rounding up or rounding down the matrix elements, but it is also possible to consider a combination by rounding. However, in this case, 3 ^ 9 kinds of matrices are generated as the matrix [Y], and 3 ^ 7 kinds of matrices are generated as the [R] matrix, and the combination thereof is 3 ^ 9. * 3 ^ 7 =
It is difficult to select a combination that minimizes m or M in a short time, reaching 3 ^ 16 ways. Therefore, the quantization conversion matrix that minimizes m or M of the error matrix [E] among the combinations in which two of rounding up, rounding down, and rounding are considered (in the above-described embodiment, rounding up and rounding down are considered). To ask for.

As described above, using the quantization conversion matrix, the RGB signal is converted into the YUV signal (or the YUV signal to the RGB signal), and the YUV signal is converted into the RGB signal.
It is possible to reduce the error represented by m in the error matrix [E] and the error represented by M in the error matrix [E] that occur when the signal (or the RGB signal is converted to the YUV signal).

Therefore, in particular, in the device or method for repeatedly performing the cyclic conversion of the signal, the converted signal is restored in a state closer to the original signal without increasing the number of quantization bits at the time of generating the conversion matrix. Can be made.

As the transformation matrix used at the time of cyclic transformation, a transformation matrix for reducing the error indicated by m in the error matrix [E] can be selected, or the error indicated by M in the error matrix [E] can be selected. It is also possible to select a transformation matrix for making it smaller, and a quantization transformation matrix can be selected and used according to the purpose.

In addition to the above-described embodiment, the present invention uses, for example, a combination of m and M in consideration of rounding up and rounding down.
Then, m and M are obtained by combining rounding up and rounding, and m and M are obtained again by considering rounding down and rounding. Various modifications are possible, such as selecting the quantization conversion matrix.

[0149]

As described above, according to the arithmetic unit according to the first aspect and the arithmetic method according to the ninth aspect, the first signal is converted by using the quantized first conversion matrix. Quantized second transforming second signal into original first signal
By using the error matrix defined by the transformation matrix of 1 and the quantized first transformation matrix to generate the quantized second transformation matrix, the quantization error is reduced, The signal after the cyclic conversion can be restored to the original signal in a state closer to the original signal.

An arithmetic unit according to claim 6 and claim 1
According to the calculation method described in 0, the first conversion matrix for converting the first signal into the second signal and the second conversion matrix for converting the second signal into the first signal are N first transforms that quantize an element by quantizing it using at least two of rounding down, rounding up, or rounding, and transforming the quantized first signal into a second signal A matrix and a combination of one first conversion matrix and one second conversion matrix from among the M second conversion matrices for converting the quantized second signal into the first signal, An error matrix defined by the combined first transformation matrix and second transformation matrix is used to select one combination of the first transformation matrix and the second transformation matrix from among the combinations. Therefore, the quantization error is further reduced and the cyclic variation is further reduced. It can be recovered in a state close to the original signal a signal after.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration example of a conversion device to which an arithmetic device of the present invention is applied.

FIG. 2 is a block diagram illustrating a function of an optimum conversion matrix generation circuit 13 of FIG.

FIG. 3 is a flowchart illustrating a process of an integer programming method of the optimum conversion matrix generation circuit 13 of FIG.

FIG. 4 is a diagram illustrating an example of an inequality coefficient in an integer programming problem when matrix elements of a quantized transformation matrix [Y] are unknowns.

5 is a flowchart illustrating processing of a combination planning method of the optimum conversion matrix generation circuit 13 in FIG.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 conversion device 2 personal computer 3 VCR 11 input / output signal control circuit 12 conversion circuit 13 optimal conversion matrix generation circuit 14 control circuit 21 input / output signal processing unit 22 m / M calculation unit 23 integer programming program execution unit 24 quantization matrix generation unit 25 Equation Generation Unit 26 Main Control Unit 27 Memory

Claims (10)

[Claims] 1. A first for converting a first signal into a second signal
Quantizing means for quantizing the transform matrix of, and transforming the second signal converted from the first signal to the original first signal using the quantized first transform matrix Generating means for generating the quantized second conversion matrix using an error matrix defined by the quantized second conversion matrix and the quantized first conversion matrix. An arithmetic unit comprising. 2. The arithmetic unit according to claim 1, wherein the generating unit generates the second conversion matrix that minimizes the maximum absolute value of the matrix element of the error matrix. 3. The generating means generates the second conversion matrix that minimizes an absolute value of a value obtained by adding all matrix elements having the same code in the same row of the error matrix. The arithmetic unit according to Item 1. 4. The quantizing means further quantizes a third transformation matrix that transforms the second signal into the first signal, and the generating means quantizes the third transformation matrix. A quantized fourth transformation matrix for transforming the first signal transformed from the second signal into the original second signal using By using the error matrix defined by the above, further generating the quantized fourth conversion matrix, and the first conversion matrix quantized by the quantization means and the generation means generated by the generation means. A first error obtained from the error matrix defined by a second transformation matrix, the third transformation matrix quantized by the quantization means, and the fourth transformation generated by the generation means. Calculating from the error matrix defined by 2. The method according to claim 1, further comprising a selection unit that compares a second error that is generated and selects one of the second conversion matrix and the fourth conversion matrix that gives an error matrix with a smaller error. Computing device. 5. The arithmetic unit according to claim 1, wherein the generation unit generates the conversion matrix by executing an integer programming program of a branch and bound method. 6. A first signal for converting a first signal into a second signal
And a second transformation matrix that transforms the second signal into the first signal by quantizing its matrix elements using at least two of rounding down, rounding up, or rounding off. Quantizing means for quantizing the first signal, and N first transform matrices for transforming the first signal quantized by the quantizing means into the second signal;
From the M second conversion matrices for converting the second signal quantized by the quantization means into the first signal, one first conversion matrix and one second conversion matrix One of the combinations by using an error matrix defined by the combination means for combining the second conversion matrix and the combination means for combining the conversion matrix of An arithmetic unit comprising: a selection unit that selects the first conversion matrix and the second conversion matrix that are combined. 7. The arithmetic unit according to claim 6, wherein the selecting means selects the combination that minimizes the maximum absolute value of the matrix element of the error matrix. 8. The selecting means selects the combination that minimizes an absolute value of values obtained by adding all matrix elements having the same code in the same row of the error matrix. The arithmetic unit according to claim 6, characterized in that. 9. A first signal for converting a first signal into a second signal
Quantizing the transformation matrix of, and transforming the second signal transformed from the first signal to the original first signal using the quantized first transformation matrix An arithmetic method characterized in that the quantized second conversion matrix is generated using an error matrix defined by the second conversion matrix and the quantized first conversion matrix. 10. A first transformation matrix for transforming a first signal into a second signal and a second transformation matrix for transforming the second signal into the first signal, the matrix elements of which are: Quantize by quantizing using at least two of rounding down, rounding up, or rounding, and N number of the first transforms that transform the quantized first signal into the second signal A matrix and the quantized second
From one of the M second conversion matrices for converting the signal of 1 to the first signal, combining one of the first conversion matrix and one of the second conversion matrices, Selecting one of the first transformation matrix and the second transformation matrix of one combination from among the combinations by using an error matrix defined by one transformation matrix and the second transformation matrix The calculation method characterized by.