JP2005322960A - Color conversion method for multi-primary color display - Google Patents

Abstract

In a multi-primary color display device, there is provided a color conversion method capable of determining multi-primary color values in a unified manner using linear programming.
X _org , Y _org , Z _org are input tristimulus values, x _w , y _w are xy chromaticity values of white points in the image, and X, Y, Z are X _org , Y _org , Z Suppose that it is on a straight line passing through two points of _org and X _w , Y _org , and Z _w . Mapping is performed along this straight line to reduce the chromaticity at a constant luminance. Since a display device with a wide color gamut does not require such a complicated mapping, such a linear mapping is not a problem. The objective function z is given as an absolute value of the difference between X _org and X, and an optimum mapping can be performed by minimizing this according to a specific display formula. In the color gamut, the value of z is 0.
[Selection] Figure 2

Description

  The present invention relates to a color conversion method using linear programming that improves color reproduction in a display device.

In recent years, there are several references on high fidelity color reproduction. That is, the first non-patent document entitled “Spectrum-based high-color reproduction video system-natural vision” by Masahiro Yamaguchi, Hideaki Haneishi and Nagaaki Oyama (Technical Report of the Institute of Image Information and Television Engineers, Vol. 26, No. 58, 7-12) Page, 2002), and the second non-patent document titled “Development of a high-detail color management system based on human perception-its application to the reproduction of records of museums and museum collections”. According to the Information Technology Development Business Results Report), the importance of high fidelity color reproduction in the fields of electronic commerce, digital archives, and telemedicine is pointed out.
Masahiro Yamaguchi, Hideaki Haneishi, Nagaaki Oyama “Spectrum-Based High-Color Reproduction Image System-Natural Vision” IEICE Technical Report, 26, 58, 7-12, 2002 "Development of a high-detail color management system based on human perception-its application to the reproduction of records of museums and museum collections", 1996/1997 IPA creative information technology training business results report

  On the other hand, one of the causes of deterioration in color reproduction accuracy is a narrow color gamut of the display device. In the uniform chromaticity diagram (UCS), the color gamut of HDTV is narrower than the human visible region. Therefore, it is clear that the color range that can be displayed by HDTV is narrower than the visible region and the display region is not sufficient. The chromaticity u′v ′ of UCS is more equal in distance and human sense on the chromaticity diagram than xy chromaticity, and conversion from CIEXYZ color system to UCS chromaticity (u ′, v ′) is an equation. This can be done in (1).

u ′ = (4X) / (X + 15Y + 3Z)
v ′ = (9Y) / (X + 15Y + 3Z) (1)

  Currently, research is being conducted on display devices with a wider color gamut than HDTV. The wide color gamut display device here is a display device that not only has a wide reproduction range on the chromaticity diagram, but also can reproduce a color of a wide color gamut without reducing the maximum luminance. In order to develop a wide color gamut display device with three primary colors like existing devices, primary colors with high saturation and high brightness are required. In general, the luminous efficiency of the light emitting device decreases as the saturation increases. For this reason, a wide color gamut display device using the three primary colors becomes inefficient. This can be solved by using primary colors that satisfy the following two conditions. That is, a primary color with high saturation but not so high brightness and a primary color with high brightness but not so high saturation are required. However, in this case, four or more primary colors are required.

  As an example of such a multi-primary color display device, there is a six-primary-color rear projection display device manufactured by Olympus, which is one of the wide color gamut displays using multi-primary colors. By using four or more primary colors, a wide color gamut display device that is more efficient than the case of the three primary colors can be realized. However, new problems also arise as the primary colors increase. One of them is the degree of freedom of color conversion. In the existing three primary color display devices, since the color tristimulus values XYZ and the three primary colors RGB have a three-to-three relationship, there is no degree of freedom in conversion, and unique conversion is possible. However, as the number of primary colors increases, the tristimulus values and primary colors have a relationship of 3 to 4 or more, and therefore, there is a degree of freedom in converting the signal values of each primary color from the tristimulus values, and the conversion cannot be performed uniquely. This indicates that there are a plurality of combinations of primary colors for displaying a certain XYZ. For this reason, there are also combinations of primary colors with low luminous efficiency.

A device for realizing a multi-primary color display device with multi-color light emitters has been filed as a “multi-primary color display” by Mifumi Shimohira described in Patent Document 1. This display device includes a light-emitting cell of one or more primary colors having a light-emitting color outside the range surrounded by triangles on a chromaticity diagram made up of ordinary RGB, and uses a cell array configured by arranging them in a matrix. It is composed. In this multi-primary color display device, the cell array is integrated with the signal processing unit so that a color image signal in a wide color gamut range can be effectively displayed with high energy efficiency.
Japanese Patent Application No. 2004-36936

Thus, the display device performs color reproduction by additive color mixing. In the n primary color display device, the tristimulus values X, Y, and Z of the output color and the tristimulus values {(X ₁ , Y ₁ , Z ₁ ), (X ₂ , Y ₂ , Z ₂ ) of each primary color, _{···, (X n, Y n} , Z n)}
Have the relationship described in the following formula (2). For example, Non-Patent Document 3 can be referred to.
“International Color Consortium:“ ICC Profile Specification Version 3.2 ”” 1995 (“International Color Consortium,“ ICC Profile Specification, Version 3.2 ”” 1995)

（２）

(2)

  On the other hand, it is assumed that the tristimulus value of a certain primary color n and the input signal value corresponding to the tristimulus value have the relationship described in the following equation (3).

（３）

(3)

Here, X _n , Y _n , and Z _n are tristimulus values of the primary color n when the maximum luminance is output, and _Sn is an input signal value for the primary color n. S _n is 0 ≦ S for taking the value of _n ≦ 1, it can be considered as normalized value of the maximum luminance in primary color n. The S _n will be referred to as relative brightness of the primary colors n later. When the expressions (2) and (3) are expressed using a summary matrix, the conversion of the tristimulus values XYZ from the relative luminance values of the respective primary colors is given by the following expression (4).

（４）

(4)

  Further, the conversion from XYZ to the relative luminance of each primary color is expressed by the following expression (5) from the expression (4).

（５）

(5)

  Here, when the number of primary colors is 3 in equation (5), the coefficient matrix is a square matrix, so that the inverse matrix is uniquely determined, and conversion can be performed without any problem. However, when the number of primary colors is 4 or more, the matrix becomes a coefficient of 3 * n (n> 3), so that an inverse matrix cannot be obtained uniquely.

  Several studies have been conducted to deal with this problem and published as fourth to sixth non-patent documents.

The fourth non-patent document is a paper entitled “Color Matching Experiment Using Six Primary Color Displays” written by Takeshi Terachi, Kenro Osawa, Masahiro Yamaguchi, Nagaaki Oyama (Color Forum JAPAN 2001, pp. 97-100, 2001).
This document proposes a method of using different color matching functions for each observer without using CIE-XYZ color matching functions for color reproduction, and a method of reproducing the shape of spectral radiance estimated by a multispectral camera. . Color conversion can be uniquely performed by matching the number of dimensions of the color matching function with the number of dimensions of the display device or by reproducing the spectral radiance with no degree of freedom. However, it is not realistic to measure the color matching function for each individual or to use a multispectral camera.
Takeshi Terachi, Kenro Osawa, Masahiro Yamaguchi, Nagaaki Oyama "Color Matching Experiments Using Six Primary Color Displays" Color Forum JAPAN 2001, 97-100 pages 2001

The fifth non-patent literature is Takeyuki AJITO, Kenro OHSAWA, Takashi OBI, Masahiro YAMAGUCHI
and "Color Conversion Method for Multiprimary Display" by Nagaaki OHYAMA
Article titled “Using Matrix Switching” (Optical Review, Vol.8, No.3, pp.191-197 (2001)) Color conversion method of used multi-primary color display device "Optical Review, Vol. 8, No. 3, 191-197 (2001)).
This document proposes a method of performing color conversion uniquely by dividing a color gamut created by primary colors and assigning priorities. This method has an advantage that high-speed conversion can be performed, but the degree of freedom is eliminated only by the priority order for each region, and other effective usage methods of the degree of freedom cannot be considered.
Takeyuki AJITO, Kenro OHSAWA, Takashi OBI, Masahiro YAMAGUCHI and Nagaaki OHYAMA "Color Conversion Method for Multiprimary Display Using Matrix Switching" Optical Review, Vol.8, No.3, pp.191-197 (2001). Obitakashi, Yamaguchi Masahiro, Oyama Yamaaki, “Color Conversion Method for Multi-Primary Color Display Using Matrix Switch”, Optical Review, Vol. 8, No. 3, 191-197 (2001))

The sixth non-patent document is a paper titled “Color conversion for a multi-primary display using linear interpolation on equi-luminance plane method (LIQUID)” by Hideto Motomura (Journal of the SID, 11/2, pp.371 -387 (2003)) ("Color conversion of multi-primary color display device using linear interpolation on isoluminous surface" by Motomrahideo, SID Journal, Vol. 11, No. 2, pages 371-387 (2003)). is there.
In this document, conversion with no degree of freedom can be performed by using a linear interpolation method using three points with equal luminance. However, as in the fifth non-patent document, it is not possible to consider other effective usage methods besides the degree of freedom.
Hideto Motomura "Color conversion for a multi-primary display using linear interpolation on equi-luminance plane method (LIQUID)" Journal of the SID, 11/2, pp.371-387 (2003) (Motomura Hideo Color conversion of multi-primary color display device using linear interpolation method ”SID Journal, Vol. 11, No. 2, pages 371-387 (2003))

One solution for such a degree of freedom is shown in the second patent document invented by Mifumi Shimohira and Masanori Takaya.
In the second patent document, in multi-primary color conversion of four or more primary colors for improving color reproducibility in a multi-primary color display device, the power consumption of the light emitting cell is minimized by using linear programming. Multi-primary color values are determined one-dimensionally. That is, in multi-primary color conversion of a multi-primary color display device, a linear programming method is applied to minimize power consumption when determining multi-primary matrix values, and the degree of freedom in determining multi-primary values in color conversion Thus, the present invention provides a color conversion method for a multi-primary color display device that can simultaneously achieve improvement in color reproducibility and minimization of power consumption by replacing the objective function with a linear programming problem with power consumption. As described above, by using the linear programming method, there is a degree of freedom in multi-primary color conversion in a multi-primary color display device having four or more primary colors. For this reason, the combination of the minimum power consumption could be found by replacing the problem of the degree of freedom in color conversion with a linear programming problem using the objective function as the power consumption. As a result, in a multi-primary color display device, color reproducibility can be improved without increasing power consumption.
Japanese Patent Application No. 2004-034312

The linear programming problem is an optimization problem that maximizes or minimizes the objective function z under the constraint conditions, and the constraint conditions and the objective function are expressed in a linear form. The 7th non-patent literature, Masatoshi Sakawa, “Optimization of Linear System <From One Purpose to Multipurpose>”, Morikita Publishing (1984), is a reference for this problem. Since the problem can be treated algebraically under the condition of linearity, an optimal solution can be obtained simply as compared with the nonlinear optimization problem. Equation (6) shows the standard form of the linear programming problem.
Masatoshi Sakawa, “Optimization of Linear Systems (From One Purpose to Multiple Purposes)” Morikita Publishing 1984

Minimization z = c ₁ x ₁ + c ₂ x ₂ +... + C _n x _n
Objective function a ₁₁ x ₁ + a ₁₂ x ₂ +... + A _1n x _n ± d ₁ = b ₁
a ₂₁ x ₁ + a ₂₂ x ₂ +... + a _2n x _n ± d ₂ = b ₂
・ ・ ・ ・ ・ ・
a _m1 x ₁ + a _m2 x ₂ +... + a _mn x _n ± d _m = b _m
0 ≦ x _j , d _i (j = 1, 2,..., N)
a _ji , c _j : constant
(J = 1, 2,..., N: i = 1, 2,..., M)
(6)

On the other hand, the following two basic theorems are given to linear programming. That is,
The first is "if there is a feasible solution, there is always a feasible base solution",
The second is that “if there is an optimal solution, there is an optimal solution among feasible base solutions”.

  By using this theorem, an optimal solution can be obtained by a finite number of combinatorial searches. However, as the number of variables increases, the number of combinations increases and processing takes time. Therefore, the simplex method is used. In the simplex method, the optimal solution can be obtained by efficiently using the basic theorem of linear programming by judging the optimality using the relative cost coefficient.

  Next, linear programming in color conversion will be described. In order to use linear programming for color conversion, a conversion function from the relative luminance value of each primary color to XYZ and the range that the relative luminance value can take are set as constraints, and any objective function may be set. The following equation (7) shows the color conversion problem converted to the standard form of linear programming.

Minimization z = c ₁ S ₁ + c ₂ S ₂ +... + C _{n Sn}
Objective function X ₁ S ₁ + X ₂ S ₂ +... + X _n S _n = X
_{Y 1 S 1 + Y 2 S} 2 + ··· + Y n S n = Y
_{Z 1 S 1 + Z 2 S} 2 + ··· + Z n S n = Z
0 ≦ S _j ≦ 1 (j = 1, 2,..., N)
(7)

Comparing equation (6) and equation (7), there are two differences compared to the normal linear programming problem. One is the range that the variable can take. In the normal linear programming problem, the range that the variable can take is 0 ≦ x _n , but the range of relative luminance is 0 ≦ S _n ≦ 1 when performing color conversion, and the simplex method is applied as it is. I can't. This can be dealt with by introducing an insufficient variable for S _n ≦ 1 and solving it by incorporating it into the constraint condition as S _n + α = 1, or by using the upper limit method. Reference books on this problem include the eighth non-patent document, “Upper bounds, secondary constraints and block triangularity in linear programming” by GB Dantzig, Econometrica, 23, pp.174-183 (1955). Danzig, “Upper limit, second limit, and block triangle in linear programming”, Econometrica, 23, 174-183 (1955).
GB Dantzig "Upper bounds, secondary constraints and block triangularity in linear programming" Econometrica, 23, pp.174-183 (1955) ("Upper limit, second limit and block triangle in linear programming" by GE Danzig) Econometrica, 23, 174-183, 1955)

Another difference is that there is no lack / margin variable (d _j ) in the color conversion problem. In normal linear programming, the initial feasible basis solution is obtained by setting the deficit / margin variable as a non-basis variable (= 0), and the simplex method is advanced using that. In the linear programming used for color conversion, there is no shortage / margin variable and the upper limit value is given to the variable. Therefore, various combinations of two types of non-basis variables, 0 and 1, must be sought. It becomes difficult to find an initial feasible basis solution. For this purpose, it is necessary to use a two-stage simplex method. The two-stage simplex method finds an initial feasible basis solution in the first stage or obtains information that it does not exist. In the second stage, an optimal solution is found from the initial feasible basis solution, or information is obtained that the solution is not bounded (there is a solution that is too small).

Next, color conversion considering power consumption will be described. Since the constraint conditions have been determined as described above, color conversion can be performed only after the objective function is given. Since there is a degree of freedom in multi-primary color conversion, there are also combinations of primary colors that increase power consumption in self-luminous display devices. To determine the value of the primary color to minimize power consumption by using a linear programming method, it must represent the relative luminance S _n primaries n power consumption P _n in the linear formula such as the following equation (8) . In addition, the power consumption of the multi-primary color display device that satisfies Expression (8) is Expression (9).

P _n = c _n × S _n (8)

P ₁ + P ₂ +... + P _n = c ₁ S ₁ + c ₂ S ₂ +... + C _{n Sn} (9)

  The above equation (9) matches the objective function z of equation (7). There is a time gray scale control as one method of the gray scale control in which the power consumption is actually in the linear form as shown in equation (9). Although other control methods are also non-linear, they have a feature that the luminance increases as the power consumption increases. The basis solution that can be obtained even if the accuracy of the objective function is not so accurate in linear programming satisfies the constraints. For this reason, even if the relationship between the relative luminance and the power consumption is approximated by the equation (8), there is no problem.

  In the above color conversion method for such a multi-primary color display device, there is a problem that natural color reproduction is impaired for an image because the display color is not determined when color data exists outside the color gamut, The display color is determined by solving this as a linear programming problem.

  In order to solve the problem, the present invention solves the problem by performing mapping for decreasing the chromaticity at a constant luminance along a straight line passing through the input tristimulus value and the chromaticity value of the white point in the image. The present invention provides a color conversion method capable of natural color reproduction for an image containing a large amount of color data.

  By using the linear programming method, there is a degree of freedom in color conversion of multi-primary colors in a multi-primary color display device having four or more primary colors. Therefore, since the color data outside the color gamut is converted into the color gamut by mapping based on the linear programming method, it is possible to achieve natural color reproduction for an image containing a large amount of color data outside the color gamut. is there.

When color data outside the color gamut is input, if the present invention is not applied, the control returns information that no solution exists and data on the way. This data cannot be used for mapping because it has no colorimetric significance. in this case,
“First, color conversion is performed.
“Second, if it is out of the color gamut, mapping is performed.”
It is assumed that the process is performed in three procedures “3rd, color conversion is performed again”.

  Since the first and third procedures require an initial solution, the simplex method is performed twice each time conversion is performed. For this reason, this method requires a total of four simplex methods. The simplex algorithm is shown in FIG. Further, since the mapping is performed, the calculation amount further increases. Therefore, a new method of solving mapping and color conversion as one linear programming problem is adopted. The constraint condition and the objective function at this time can be expressed as Expression (10).

Minimization z = │ (X- _Xorg ) │
The objective function _{X 1 S 1 + X 2 S} 2 + ··· + X n S n -X = 0
Y ₁ S ₁ + Y ₂ S ₂ +... + Y _n S _n = Y _{org
Z 1 S 1 + Z 2 S} 2 + ··· + Z n S n -Z = 0
(X−X _org ) / (X _w −X _org ) = (Z−Z _org ) / (Z _w −Z _org )
_{X w = (x w / y} w) * Y org
_{Z w = {(1-x} w -y w) / y w} * Y org
X _w ≦ X ≦ X _org if (X _w ≦ X _org )
X _org ≦ X ≦ X _w if (X _w > X _org )
0 ≦ S _j ≦ 1 (j = 1, 2,..., N)
(10)

In the above equation (10), X _org , Y _org , and Z _org are input tristimulus values, and x _w and y _w are xy chromaticity values of the white point in the image. X, Y, and Z are on a straight line passing through two points, X _org , Y _org , and Z _org , and X _w , Y _org , and Z _w . Mapping is performed along this straight line to reduce the chromaticity at a constant luminance. Since a display device with a wide color gamut does not require such a complicated mapping, such a linear mapping is not a problem. The objective function z is given as an absolute value of the difference between _Xorg and X, and optimal mapping can be performed by minimizing this. In the color gamut, the value of z is 0.

By using this method, color gamut mapping and color conversion can be performed simultaneously. However, this method cannot take luminous efficiency into consideration. Therefore, color conversion is performed according to the following procedure.
(1) Perform mapping and color conversion (2) Perform color conversion considering light emission efficiency using the result of (1)

  In this method, mapping and color conversion are treated as one linear programming problem, which is more efficient than performing two calculations alone. In addition, although linear programming is performed twice, an initial feasible basis solution of step (2) is obtained by the first calculation, so that it is not necessary to use a two-step method in step (2), and speed can be improved. .

  In order to confirm the above, one embodiment of a specific color conversion method was constructed, and the state of improvement by the above mapping was examined. That is, XYZ image color conversion was performed for the six primary color rear projection display device using the above-described method. The color gamut of this display device is as shown in FIG. Since this apparatus uses a projector and the power consumption of the lamp is constant, the actual power consumption cannot be examined. Therefore, it is assumed that the luminous efficiency is linear and equal for all primary colors, and the effectiveness of the above method is simulated. In this case, all the coefficients of the objective function in the above procedure (2) are 1. The apparatus used for photographing is a 16-band multispectral camera that can output an XYZ image, and the image used is a photograph of a highly saturated cloth.

  FIGS. 3 and 4 show an image obtained by converting an XYZ image and outputting it to a display device with a digital camera. However, FIG. 3 shows an image without mapping, and data outside the color gamut is white. On the other hand, FIG. 4 is an image on which mapping has been performed. When both were compared, it was confirmed that color conversion and mapping were performed without problems.

  In color conversion in a multi-primary color display device, there are a plurality of combinations of primary colors for producing a certain color X, Y, Z. The theoretical values of XYZ output in all combinations remain unchanged. However, when applied to an actual display device, the value differs for each combination of primary colors due to the influence of temporal changes and quantization errors. For this reason, if there is a portion where the color tone smoothly changes in the image, there is a possibility that a pseudo contour is generated. Since multi-primary colors are used, any conversion method is affected by the pseudo contour.

  In linear programming, since the objective function is given by a linear expression of the signal value of each primary color, the ratio of the signal values of each primary color is constant with respect to colors of the same chromaticity as long as the signal value does not exceed 1. . For this reason, the influence of the pseudo contour can be confirmed to some extent by drawing a chromaticity diagram on the display device using this method. FIG. 5 shows a chromaticity diagram converted and displayed by a digital camera. Although some pseudo contours can be seen, it was confirmed that they were reproduced almost smoothly. This is because an objective function is given as a linear form of signal values, so that some tendency appears in the ratio of the signal values of the respective primary colors with respect to the change of the tristimulus values.

  The color conversion method for the multi-primary color display device according to the present invention can be widely used for the color reproduction optimization plan of the multi-primary color display device and the efficiency plan of the device.

It is an algorithm flowchart of a simplex method. It is a figure which shows each color range area | region on a chromaticity diagram with a uniform scale. It is an image which shows the output result in the multi-primary color display device when mapping is not performed. It is an image which shows the output result in the multi-primary color display apparatus when mapping is performed. In the chromaticity of the multi-primary color display device, the image mainly shows a portion where the outline is conspicuous.

Explanation of symbols

  None

Claims (1)

X _org , Y _org , Z _org are input tristimulus values, x _w , y _w are xy chromaticity values of white points in the image, and X, Y, Z are X _org , Y _org , Z _org , X _An objective function generating means for giving an objective function z as an absolute value of a difference between X _org and X, assuming that it is on a straight line passing through two points _w , Y _org , and Z _w , and the following display by minimizing this A color conversion method for a multi-primary color display device including an optimum mapping processing means for performing optimum mapping according to an equation.
Record
_{X 1 S 1 + X 2 S} 2 + ··· + X n S n -X = 0
Y ₁ S ₁ + Y ₂ S ₂ +... + Y _n S _n = Y _{org
Z 1 S 1 + Z 2 S} 2 + ··· + Z n S n -Z = 0
(X−X _org ) / (X _w −X _org ) = (Z−Z _org ) / (Z _w −Z _org )
_{X w = (x w / y} w) * Y org
_{Z w = {(1-x} w -y w) / y w} * Y org
X _w ≦ X ≦ X _org if (X _w ≦ X _org )
X _org ≦ X ≦ X _w if (X _w > X _org )
0 ≦ S _j ≦ 1 (j = 1, 2,..., N)

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