JPH10126628A - Color conversion method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To eliminate an unnatural ripple component caused by interpolation by devising a generating method of a table in the case of executing complicated nonlinear conversion through the use of a multi-dimension table and an interpolation method. SOLUTION: In a nonlinear color conversion, the nonlinear color conversion is divided into a chain of a successive linear conversion and a linear conversion, and combinations 106 of conversion not causing a ripple component are synthesized in a chain system of color conversion to generate a multi-dimension table 108 without producing a multi-dimension color conversion table through the synthesis of the conversion components of the chain. Then the ripple component is eliminated from a whole color space by repeating a plurality of processing of multi-dimension table lookup and interpolation.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a color conversion method using a three-dimensional look-up table and three-dimensional linear interpolation for performing high-speed, high-precision color space conversion used in various places in color image processing, and in particular, to a color conversion method. The present invention relates to a method for removing ripples that have a visually adverse effect.

[0002]

2. Description of the Related Art In recent years, as device-independent color conversion has been proposed, it has become necessary for a device that handles colors to perform color space conversion between a color signal of the device itself and a standard color signal. . The color space conversion includes one-dimensional conversion of each signal such as sequential gamma conversion and linear conversion such that three-color signals are collectively converted by a 3 × 3 matrix.

FIG. 13 is a conceptual diagram of color space conversion using an interpolation operation and a multidimensional table for explaining the prior art, which will be described below. In FIG. 13, reference numeral 1301 denotes an input color signal;
Reference numeral 1302 denotes a three-dimensional LUT that outputs lattice points of a representative color from the upper signal 1307 of the input color signal, reference numeral 1303 denotes a weight coefficient for calculating a weight coefficient from the lower signal 1308 of the input color signal,
Reference numeral 1305 denotes an interpolation operation for performing interpolation from the lattice points of the representative colors and the weight coefficients.

[0004] In color conversion, C is converted from (RGB) space to C
An example of conversion to an IE-LAB space is shown, in which an input signal is generally represented by three variables such as (RGB), an output signal is also three or four variables, and an output may be treated as one variable for convenience. is there.

An input color signal 1301 is digitally divided into an upper signal 1307 and a lower signal 1308, and the upper signal 1307 is roughly extracted from a table of a three-dimensional LUT 1302 to output a plurality of grid points of a unit interpolation solid whose input color is surrounded. 1
304 is output. On the other hand, the lower signal has a weighting factor of 130
3, a weight coefficient for each vertex of the interpolated solid is calculated from the position of the input color point in the unit interpolated solid. Interpolation operation 1
Reference numeral 305 denotes an interpolation output value 1306 obtained by interpolation by weighted addition. As an interpolation solid, a cube 1310 using eight surrounding points surrounding an input point is generally used and is called “tri-linear interpolation”. In addition, as shown in FIG. 13, there are a pyramid (using 5 points) 1312, a triangular prism (using 6 points) 1311, a tetrahedron (using 4 points) 1313, and the like.

The color space conversion is mathematically a conversion from a three-dimensional space to a three-dimensional space or a four-dimensional space, and can often be represented by a chain system combining these. However, it takes an enormous amount of time to calculate this conversion in order. Thus, an attempt is made to reduce the table capacity by using a three-dimensional look-up table as described above, tabulating the calculated values for the representative input colors in advance for those calculated values, and approximating exact values by interpolation. Has been done practically. As a method of making a table for performing interpolation, as shown in non-linear color masking color conversion from RGB to CMY, conversion from RGB space to CIE-LAB space, a table created using mathematical formulas that are complicated and sequential processing,
As seen in the conversion from CIE-LAB to CMYK in color proofing of printers and CRTs, there are two types, one that is experimentally obtained as a table from color chart measurement and correspondence.

In any case, depending on the degree of non-linearity of the table to be interpolated, unnatural artifacts appear in the gray scale after interpolation, which may deteriorate the subjective evaluation. Since this artifact occurs regularly like waves moving between discrete tables, "ripple"
Call. The degree of occurrence of ripple is as follows: (1) Contents of color conversion table and color conversion formula (degree of nonlinearity) (2) Interpolation method (cube, tetrahedron, etc.). (3) An image to be subjected to color conversion (whether or not the image has a smooth gradation such as CG) differs. When the ripple appears, a false contour is generated at a beautiful gentle gradation change portion on the image.

[0008] The generation of typical ripples by interpolation has been roughly reported in some nonlinear color conversions.

For example, in the case of second-order non-linear color masking, "Color Correction Tecnique for Hardcpoies
by 4-Neighbors Interpolaton Method ", Journal of Ima
gingScience and Technology Vol. 36, No.1, Jan / Feb (19
92) PP73-80 describes the relationship between curve states, coefficients and errors when cubic interpolation and tetrahedral interpolation are performed.

In the case of a non-linear color space conversion from the RGB space to the LAB space, see “Fast Color Processo”.
r with Programable Interpolation by small memory (P
RISM) ", Journal of Electronic Imaging Vol.2 (3), 199
3, PP213-224 describes a curve when prism interpolation is performed.

MIN in the case of black signal generation
Regarding the (minimum value) conversion, it is reported as an example of performing prism interpolation in “High-speed color conversion by oblique triangular prism (SLANT-PRISM) interpolation”, Annual Meeting of the Institute of Television Engineers of Japan, 25-11, 1994.

However, consideration has been given to ripple elimination only in the above MIN operation,
The method applies an interpolation solid to a specific object. For example, U.S. Pat. No. 4,334,240 uses pyramid interpolation, Japanese Patent Application Laid-Open No. 2-226867 uses tetrahedral interpolation, and the third document uses oblique triangular prism interpolation. By using these special interpolated solids, not only can the ripple in the MIN operation be eliminated, but also the interpolation error itself can be reduced to zero.
The IN operation can be applied only in special cases, and is not generally applicable widely.

[0013]

Conventionally, when this table and interpolation are used, conversion from input to final output is often performed at once. This is because, among the advantages of using a table, the sequential conversion of any length is completed within a fixed short time of table access and interpolation, thereby preventing signal accuracy deterioration due to conversion at a time. However, when the table interpolation is performed at once, a ripple error often appears after the interpolation, which lowers the quality of the color image. Conventionally, except for the MIN operation and the like, the only solution has been invented simply to increase the precision of the table.

The present invention aims at eliminating ripples by devising a method of creating a color conversion table, instead of making the ripples insignificant by an interpolation method as in the prior art.

A first object of the present invention is to eliminate mathematically global ripples in nonlinear color conversion in which mathematical expressions are clear.

As a second problem, in the case of a color conversion table in which the mathematical expression is unclear, only the visually conspicuous portion in the color image is locally corrected and linearized to reduce the ripple after interpolation. The purpose is to make it less noticeable.

[0017]

In order to solve this problem, according to the present invention, first, as for the nonlinear color conversion given by the calculation formula, first, the nonlinear color conversion is performed by successive linear conversion and one-time conversion.
Rather than decomposing into a chain of dimensional conversions and combining them all at once to create a multidimensional color conversion table, only a combination of conversions that does not cause ripples from the chain of color conversions is converted to a multidimensional table. , A multi-dimensional table lookup and interpolation are repeated a plurality of times.

As a result, ripples can be removed globally in the color space. Second, for a non-linear color conversion table that cannot be given by the mathematical formula, one-dimensional linearization near the gray axis that is visually important, two-dimensional linearization including the gray axis, and general two-dimensional plane It is configured to perform linearization.

This makes it possible to eliminate local ripples in visually significant parts of the color space after interpolation.

[0020]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The invention according to claim 1 of the present invention decomposes a non-linear color conversion into a chain of successive color conversions consisting of a one-dimensional conversion of each color signal and a linear conversion using a matrix. A one-dimensional conversion of each color signal is performed from the chain system, and then a synthesis conversion unit that performs a matrix linear conversion is found, and a multidimensional color conversion table that can execute the synthesis conversion unit at one time is created. A color conversion method characterized by executing the entire non-linear conversion in a form including lookup of a color conversion table and multidimensional interpolation, and interpolating a complicated non-linear conversion represented by a mathematical expression without ripples in the entire system. The effect of being able to calculate is obtained.

According to a second aspect of the present invention, the input color signal is first subjected to a linear conversion by a matrix,
Secondly, when performing non-linear color conversion including three kinds of sequential color conversions in which one-dimensional conversion of each signal is performed and thirdly, linear conversion is performed again by a matrix, a conversion obtained by combining the second and third conversions is performed. 2. The color conversion method according to claim 1, wherein the color conversion table is created as a multidimensional color conversion table, and after performing a first linear conversion on the input color signal, the multidimensional color conversion table is looked up and interpolated for the result. And transforms from RGB space to XYZ space as an example, and converts them to X ^1/3 Y
After conversion to ^{1 /} 3Z ^1/3 space, finally CIE-LA
For example, when performing conversion to the B space, the XYZ space is converted to the X ^1/3 Y ^1/3 Z ^1/3 space, and finally the CIE
-Create a conversion up to the conversion to the LAB space as a multidimensional color conversion table, perform linear conversion from the input RGB signals to the XYZ space, and then look up the multidimensional color conversion table for the result and interpolate By doing so, conversion from RGB space to CIE-LAB space can be performed without ripple.

According to a third aspect of the present invention, the input color signal is firstly subjected to one-dimensional conversion of each signal, secondly to linear conversion by means of a matrix, and thirdly, to the input color signal again. In the sequential color conversion for performing the one-dimensional conversion, the first and second conversions are combined to create a multidimensional color conversion table, and the input color signal is looked up and interpolated in the multidimensional color conversion table. 3. The color conversion method according to claim 1, wherein a third one-dimensional conversion is performed on the result.
And from DrDgDb without ripple (C ^{1 /} γ M ^{1 /}
γ Y ^{1 /} γ) has an effect that conversion into space can be performed.

According to a fourth aspect of the present invention, when performing a non-linear second-order masking color correction operation, a second-order format part composed of each color signal in the non-linear masking coefficient is subjected to a first linear transformation using a matrix and each variable. Into a second conversion by a linear combination of the quadratic terms of the following, a multidimensional color conversion table is created for the second conversion, and after the first linear conversion is performed for the input color signal, the multidimensional color conversion table is obtained for the result. This is a color conversion method characterized by performing lookup, interpolation, and execution, and has an effect that a nonlinear secondary masking color correction operation can be executed without ripple.

According to a fifth aspect of the present invention, there is provided a multi-dimensional table in which color conversion values for an input are stored at discrete points in an input color space. Save the value for the value,
A color conversion method characterized by establishing a linear relationship between conversion values on each vertex in a solid used for interpolation by appropriately changing values at other plural points, which is created by a mathematical formula. For a color conversion table of a type that does not exist, the three-dimensional removal of ripples near the gray axis that are visually conspicuous among the ripples after interpolation caused by the non-linearity in the cube allows any linear interpolation method to be used in the cube. However, there is an effect that ripple can be prevented.

According to a sixth aspect of the present invention, there is provided a method for interpolating a multidimensional table in which color conversion values for an input are stored at discrete points in an input color space. A color conversion method characterized by establishing a linear relationship between conversion values on each vertex in a solid used for interpolation by appropriately changing only values, and a visual method in a color image to be color-converted. When an important color distribution exists locally in a specific plane in the color space, and by performing local linearization of a table in the plane near the gray axis or the like, the plane is rearranged. Ripple can be prevented from occurring in two-dimensional interpolation or other interpolation methods within the function, and a change point of a value can be relatively reduced.

An embodiment of the present invention will be described below with reference to FIGS. (Embodiment 1) Prior to the description of Embodiment 1, the principle of ripple removal will be briefly described.

First, an example of a conversion function capable of interpolating without ripple will be described for the case of two variables for simplicity. Generally a constant
For a, b, and c, using a function fx (x) with only x as a variable and a function fy (y) with only y as a variable

[0028]

(Equation 1)

Is a function which can be interpolated without ripple. fx (x) may be a non-linear function such as gamma transformation or fx (x) = x ^1/3 . In other words, it can be said that the function is obtained by a composite transformation in which a linear transformation by a 3x3 (3x4) matrix is performed on the non-linear transformation of one variable.

Actually, the ripple when two-dimensional linear interpolation (bi-linear interpolation) of four points is performed based on the value of this function will be examined. Four-point interpolation is a general interpolation method equivalent to exactly eight-point interpolation in two dimensions. FIGS. 14A and 14B are conceptual diagrams of two-dimensional ripple-free interpolation. In FIG. 14, four vertex ABCD
The output values (A), (B), (C), and (D) at

[0031]

(Equation 2)

## EQU2 ## When the output (P) at a point P in a square surrounded by four vertices is interpolated from four points,

[0033]

(Equation 3)

## EQU1 ## Here, the weighting factor WA, WB, WC, meaning the WD is, the area of each rectangular body case of dividing a square on the point P as shown in FIG. 14 (a) into four rectangular in total area d ² It shows the normalized amount. For example, point A
The weight coefficient WA (1401) is the one where the rectangular parallelepiped corresponding to the weight coefficient is located farthest from the corresponding vertex, such as the area of a rectangular parallelepiped at a point symmetric position with respect to the point P of the point A. The relationship between the weighting factors is

[0035]

(Equation 4)

Is as follows. From (Equation 2) (Equation 3) and (Equation 4),

[0037]

(Equation 5)

Holds. Where the weighting factor [WB + WC],
As shown in FIG. 14, the meaning of [WC + WD] is rectangular solid 2
Using the input coordinates (x, y) of the point P,

[0039]

(Equation 6)

From this and (Equation 5),

[0041]

(Equation 7)

Is obtained. This means that in output space (P) lies on the plane created by the two vectors (A) (B), (A) (D), and a linear change in input (x, y). Means to do.

To summarize the above description, when the interpolation formula by weighted addition of four points in (Equation 3) interpolates a special function such as (Equation 1) in the unit interpolation section,
And the interpolation is linear, and no ripple occurs. Assuming that (Equation 1) has three variables, using constants a, b, c, and d

[0044]

(Equation 8)

Is obtained, but it can be similarly proved that this is an example of conversion that can be interpolated without ripple in actual color conversion. Also similar to (Equation 8)

[0046]

(Equation 9)

In the case where the order of the one-dimensional conversion and the linear conversion is reversed from (Equation 8), for example, in a conversion in which the linear conversion is performed and then the result is subjected to a one-dimensional conversion such as gamma conversion, different variables are used. Ripple occurs because a cross-term not in equation (8) is generated.

In the present invention, the mathematical properties described above are used, and the calculation is not performed at once without considering the conversion likely to cause a ripple error. Only the conversion unit expressed by (Equation 8) is subjected to table interpolation. Thus, the entire chained color conversion is calculated without a ripple error.

Next, Embodiment 1 will be described. FIG. 1 shows CIELA from RGB space in the first embodiment.
FIG. 2 is a block diagram of a color conversion to a B space, in which 101 is an input RGB signal, 102 is a 3 × 3 matrix linear conversion for performing a conversion from RGB space to XYZ space, and 106 is a conversion from XYZ space to LAB space. Synthesis conversion unit, 10
7 is a color conversion table (1) for performing linear conversion, 108 is a color conversion table (2) for performing non-linear conversion without ripples, 1
Reference numeral 09 denotes a three-dimensional interpolation unit.

The operation will be described below with reference to FIG. RGB space 101 to XYZ space 110
The conversion to is a conversion by the linear conversion 102 using a 3 × 3 matrix, for example,

[0051]

(Equation 10)

Is as follows. Next, the XYZ space 110 is subjected to one-dimensional gamma conversion 103 for each variable.

[0053]

[Equation 11]

Finally, from the XYZ space to the LAB space 105
Is converted by the linear transform 104 using a 4 × 3 matrix formula.

[0055]

(Equation 12)

However, X / X0, Y / Y0, Z / Z0> 0.008856, where X0, Y0, Z0 are standard white coordinates.

When this is executed using a table and a lookup, if the whole is configured as one table (Equation 10)
Since the combination of (Equation 11) and (Equation 11) is in the order of one-dimensional conversion after linear conversion, the form shown in (Equation 9) causes a ripple after interpolation.

In order to prevent this, as shown in FIG. 1B, the 3 × 3 linear conversion 102 is converted into a color conversion table (1) 107.
A one-dimensional conversion 103 and a 3x4 linear conversion synthesis unit 106
Correspond to table (2) 108, and table (1) 1
07 is looked up and interpolated by interpolation 109, and the result is looked up in table (2) 108 to obtain interpolation 1
09 indicates interpolation. Here, since the color conversion table (1) is a linear conversion, it is not always necessary to use interpolation, and the result is the same whether it is calculated directly or using interpolation.

Next, color correction unique to color hard copy,
An example of non-linear color conversion as color correction processing will be described. FIG. 2 shows that from the concentration space DrDgDb, (C ^{1 /} γ
M ^{1 /} γY ^{1 /} γ) Color conversion to space.

In FIG. 2A, the density space DrDgD
b202 to one-dimensional conversion 203

[0061]

(Equation 13)

By the above, the data is converted into the (Drγ Dgγ Dbγ) nonlinear space,

[0063]

[Equation 14]

To the CMY space, and finally the one-dimensional conversion 205

[0065]

(Equation 15)

According to (C ^{1 /} γ M ^{1 /} γ Y ^{1 /} γ) is converted to the space 206. In FIG. 2B, from the DrDgDb space, (Drγ Dgγ Db
γ) γ conversion to non-linear space, then linear conversion to CM
Since up to the part 201 to be converted to the Y space, since there is no ripple since it has the form of (Equation 6), it is synthesized to create a three-dimensional color conversion table 207, and from CMY to (C1 ^/ γ) M
^The part to be converted to ^{1 /} γ Y ^{1 /} γ) space is a one-dimensional table 2
09. Input density space DrDg
The three-dimensional color conversion table 207 is looked up from Db 202 and interpolated by interpolation 208.
By looking up and interpolating the dimension table 209, (C ^{1 /}
γ (M1 ^/ γY1 ^/ γ) space 206 can be converted.

Next, there is a non-linear second-order polynomial color correction as a frequently used color correction method. An example of color correction of a non-linear second-order polynomial will be described. this is,

[0068]

(Equation 16)

This is a color conversion represented by a quadratic polynomial composed of three variables Dr, Dg, and Db, and includes cross terms DrDg, DgDb,
Because it has DbDr and the like, ripples also appear when this conversion is tabulated and interpolated. Taking the output c of (Equation 16) as an example,

[0070]

[Equation 17]

For example, it can be expressed using a symmetric matrix A and a column vector a. According to the theory of linear algebra, using an orthonormal matrix P that diagonalizes a symmetric matrix A,

[0072]

(Equation 18)

Alternatively,

[0074]

[Equation 19]

When the following transformation is performed, (Equation 17) becomes a so-called quadratic standard form.

[0076]

(Equation 20)

Is converted to Here, λ _1, λ _{2, and} λ ₃ are eigenvalues of A. This expression is

[0078]

(Equation 21)

As shown in (Equation 8), a linear combination of the conversion of one variable is obtained, and a form in which no ripple occurs even when calculated by interpolation from the (Dr'Dg'Db ') space is obtained. Was.

In FIG. 3, from the above description, FIG. 3A shows a case where the nonlinear secondary color correction (Equation 16) is executed.
First, a (Dr, Dg, Db) space 301 as an input is represented by (Equation 19)
Is converted to (Dr'Dg'Db ') by the linear conversion 304 of. In FIG. 3C, this location is stored in a table (1) 306.
And then table (2) 3 expressing (Equation 20)
08 is created. Then, the table (1) is looked up and the interpolation calculation is performed by the interpolation 307. From the result, the table (2) 308 is looked up and the interpolation calculation is performed by the interpolation 309. In this way, the occurrence of ripples can be avoided. The table (1) is a linear operation and may be calculated directly without necessarily creating a table.

(Embodiment 2) In Embodiment 1, when performing complex sequential color conversion for typical color conversion, a table creation method that does not generate ripples by using table interpolation well is described. I have explained. These methods cannot be used unless the mathematical expression of the color transformation is known in advance.

Therefore, in the second embodiment, a method will be described in which a table is given by an experiment, the expression of which is unknown, and a ripple is generated when interpolation is performed. In this case, it is not desirable to mathematically remove the ripples over the entire space, and the table is locally linearized for the purpose of not visually uncomfortable.

First, an example of three-dimensional local linearization will be described. The “three-dimensional local linearization of a table” in the second embodiment refers to establishing a linear relationship between input and output in a plurality of unit interpolation solids in an input space. For example, in the conversion from two variables to two variables, the input square is converted into a parallelepiped by the conversion.
In color conversion, since there are three variables, the input cube becomes a parallelepiped at the output. At this time, four-point interpolation (bi-linear interpolation) is performed in two dimensions described on the principle of ripple elimination in the first embodiment with reference to FIG.
Point interpolation (tri-linear interpolation) is simply a linear coordinate transformation of the input vector and no ripple occurs.

What is important is that ripples cannot occur in a linearized solid, whether the interpolation method is cubic, triangular, or tetrahedral.

An example of three-dimensional local linearization will be described with reference to FIG. In FIG. 4, FIG. 4 (a) is a cube ABCD
-EFGH is one unit interpolation section in the input space.
(B) is a parallelepiped (A) (B) (C) (D)-(E) (F) (G) (H) is an output. A to H represent three-dimensional position vectors, and (A) to (H) represent output vectors of the vector A, which are also position vectors in the output space.

Here, conditions for forming a parallelepiped are considered. In a parallelepiped, only four independent vectors out of the 12 sides formed by four parallel sides are limited to three. Conversely, it is clear that the three independent vectors form a parallelepiped. Three independent vectors are determined at four points. That is, in eight vertices of a solid, values of four points are stored, and independent vectors 401 and 40 determined by them are stored.
By modifying and changing the values of the remaining four points with reference to 2,403, a parallelepiped is obtained, and three-dimensional local linearization is achieved.

Next, the range in which the three-dimensional local linearization is performed will be described with reference to FIG. Performing this linearization in the entire input color space significantly changes the content of the color conversion itself. Therefore, it is considered that the range is made as local as possible, and only the portion of the input on the gray axis where ripple generation is most sensitive to vision is locally linearized.

The gray axis is defined as R = G = B or Dr =
These are input axes that change together when three primary colors are input, such as Dg = Db. For such an input, it is usually most important to output gray in color conversion, and therefore, the output value must be precisely determined at a grid point on the gray axis. However, when interpolation is performed, ripples occur on the gray axis. In FIG. 11, the grid point outputs of the three output colors are represented by black points. Since the three gradation curves are independent of each other due to ripples between the lattice points, the color mixing balance is established on the lattice points, but is never established between the lattice points.

At this time, a color fringing phenomenon occurs in which an outline is seen in the lightness gradation and the color balance is lost in each color, and the quality of a color image is significantly reduced. The state in which the ripple is removed means that the output values at the grid points on the gray axis are preserved and the output balance is maintained between the grid points as shown in FIG. Say.

From the above consideration, as shown in FIG. 6, only the area connecting the unit cubes including the gray axis is linearized, and only the two points A and G in the cube store the values.
Hereinafter, the point to be saved is referred to as a “save point”, and the point to be changed is referred to as a “changed point”.

Referring again to FIG. 4, in the cube ABCD = EFGH, the conservation points are A, B, F, and G, and the changed points are C, E, D, and H.
Then, the way of changing the value at the change point is the independent vector 4
Based on 01,402,403

[0092]

(Equation 22)

Is obtained. Save points other than the two points A and G to F,
Although the point B is tentatively determined, another two points that can form three independent vectors in combination with the two points A and G may be used. If the two points F and B are determined as they are, the table is stored in a specific hue as viewed from the gray axis, and the balance is lost.

Therefore, B, F, E,
The roles of the two fixed points F and B are sequentially changed so as to go around the six points H, D and C. FIGS. 7A to 7F
FIG. 3 is a diagram of a unit cube viewed from the W direction. Cubes existing on the gray axis are classified into different types one by one in order from the darker side of the gray axis, and two conserved points (black points) move while rotating each hue for each of the six types of cubes in total. The state is shown. As described above, three-dimensional local linearization on the gray axis is achieved.

Next, two-dimensional local linearization will be described. The two-dimensional local linearization is to establish a linear relationship between input and output in a specific plane in an input space on the assumption that an interpolation method in a specific two-dimensional plane is used. For example, when performing the above-described local linearization of the gray axis,
In the three-dimensional local linearization, the number of changed points is four, and a very large number of points must be changed. Instead of eliminating the ripple on the gray axis, the interpolation error also increases. To reduce the number of changes as much as possible, it is better to reduce the number of points used for interpolation.

Considering a plane including a gray axis, in the gray axis interpolation, a method in which interpolation in this plane is sufficient will be devised and will be described with reference to FIG. FIG. 8 is an example of two-dimensional local linearization based on the triangular prism interpolation method. Assuming that the input space as shown in FIG. 8A is an RGB space, the main axis direction of the triangular prism is the R axis, and the division plane is the G = B plane. Here, since the gray axis R = G = B exists in the division plane, the fact that interpolation for the gray axis input is performed only on the plane G = B is used. A unit interpolation section including a gray axis is set only at four points in the two-dimensional plane, and two-dimensional linearization is performed in each section. In FIG. 8B, a cube ABCD-EFGH is one unit interpolation section in the input space, and FIG. 8C shows a distorted solid (A) (B) (C) (D)-(E) ( F) (G) (H) are outputs. As described above, all the points represent three-dimensional position vectors.

Here, as a result of the triangular prism interpolation performed in the output solid, the interpolation results on the gray axis are involved (A) (B) (G) (H)
Is a parallelogram, linearization is established. In the parallelogram, two of the four sides are parallel, so that only two independent vectors are formed by the sides. Conversely, it is also apparent that the two independent vectors form a parallelogram. Two independent vectors are determined at three points. In other words, three of the four points on the interpolation plane need to be saved and only one of the remaining points needs to be changed. That is, if the value of one point that stores the values of seven points at the eight vertices of the input cube is modified and changed, 2
A dimensional local linearization is achieved.

Assuming that the storage points of the square ABGH are three points A, B, and G, how to change the value at the change point H is determined by using the independent vector 802.

[0099]

(Equation 23)

Is obtained. Here, there is the arbitrariness that the saved point B other than the A and G points on the gray axis may be the H point. In order to average the conserved points as much as possible, as shown in FIG.
It goes around each one of the points and makes it a save point. In this way, a two-dimensional local linearization on the gray axis is achieved. As described above, in the two-dimensional local linearization, linearization can be realized by changing relatively few points as compared with the three-dimensional local linearization. On the other hand, in three-dimensional local linearization, there is a degree of freedom in selecting an interpolation method.
Alternatively, the interpolation is limited to in-plane interpolation.

Next, an example of expanding the two-dimensional local linearization to a plane area other than the gray axis will be described with reference to FIG. This is used when performing linearization on an input located only in a specific hue plane or in a specific lightness plane. In the figure, a dotted line 1001 indicates the gray axis, and points indicated by black points (●) are the above-mentioned conserved points on the gray axis. Points indicated by white points (（) are changed points that have been locally linearized by the two-dimensional linearization described above. These changes determine three points of a square which is a unit interpolation section. Based on this, the point group indicated by (1) can be changed in a direction away from the gray axis. Then, the points shown in (2) are changed, and each point group of (3), (4), (5), and (6) can be changed sequentially. After the linearization of the gray axis is performed as described above, the linearization of the plane can be realized without contradiction by sequentially expanding the linearization range in a direction away from the gray axis symmetrically from the gray axis.

[0102]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An example of a table in which three-dimensional local linearization and two-dimensional local linearization are executed will be described in an embodiment. FIG.
17 to 9x9x where the input is RGB and the output is color
This is an example of a three-dimensional color conversion table of 9 = 729 points, where an input represents an output color on the G = B plane. That is, the plane of the figure
P1-P2-P3-P4 are represented. Downward straight line 1 on the figure
Reference numeral 502 denotes a gray axis, a dotted square 1 including the gray axis.
501 is a unit interpolation section. FIG. 15 shows table values before processing. FIG. 16 is obtained by performing three-dimensional local linearization on FIG. The changed points are circled, and the saved points are the numerical values in FIG. In the three-dimensional linearization, since the linearization in the section is completely performed, the two-dimensional linearization is also performed in the G = B plane. The numerical value does not change on the gray axis because of the fixed point, but the surrounding change points are shown around the gray axis.

FIG. 17 shows the result of two-dimensional local linearization performed in this plane. Similarly, the changed points are circled.
In the unit interpolation section 1601 where the local linearization is performed, as can be seen from (Equation 23),

[0104]

(Equation 24)

[0105] The relationship that the sums on the diagonals are equal as described above is established. For example, in FIG. 15, in the square 1501 of the unit interpolation section at the upper left,

[0106]

(Equation 25)

In FIG. 16, the result that was not satisfied was 16
At 01

[0108]

(Equation 26)

In FIG. 17, at 1701

[0110]

[Equation 27]

This is established as follows. In FIG. 16, the total number of changed points is 11, but since the change is performed three-dimensionally, points other than this plane are actually changed. Since the number of changes in one cube is 4, the total number of changes is 3
Two points. In FIG. 17, the total number of changes is eight,
There are very few changes to the table in a total of 729 points.

[0112]

As described above, according to the present invention, first, regarding the nonlinear color conversion given by the calculation formula, first, the nonlinear color conversion is decomposed into a chain of sequential linear conversion and one-dimensional conversion. Instead of combining all at once to create a multidimensional color conversion table, only a combination of conversions that does not generate ripples from the chain of color conversions is combined into a multidimensional table, and multidimensional table lookup and interpolation are performed. By configuring so as to repeat multiple times, in a general nonlinear color conversion in which the formula is clear, a plurality of sets of tables that do not generate ripples are created by decomposition of the nonlinear conversion, and the ripples are successively interpolated to thereby reduce the ripples. It is possible that it does not occur.

Secondly, for the non-linear color conversion table not given by the mathematical formula, one-dimensional linearization near the gray axis that is visually important, two-dimensional linearization including the gray axis, general By configuring to perform linearization in a two-dimensional plane, in the case of the color conversion table itself that is not mathematically clear, only the portion that is visually noticeable in the image among the nonlinearities of the table is locally corrected. In addition, the effect of removing the ripple after interpolation can be obtained by performing the linearization.

[Brief description of the drawings]

FIG. 1 is a block diagram of color conversion in the conversion from RGB to CIE-LAB according to the first embodiment.

FIG. 2 is a block diagram of nonlinear color conversion according to the first embodiment;

FIG. 3 is a block diagram of color conversion in a second-order polynomial nonlinear color correction operation according to the first embodiment;

FIG. 4 is a view for explaining three-dimensional local linearization according to the second embodiment;

FIG. 5 is a diagram illustrating an area where three-dimensional local linearization is performed according to the second embodiment;

FIG. 6 is a diagram illustrating positions of a conserved point and a changed point in three-dimensional local linearization according to the second embodiment.

FIG. 7 is a diagram for explaining a cyclic movement method of a conserved point in three-dimensional local linearization according to the second embodiment.

FIG. 8 is a diagram illustrating a two-dimensional local linearization method according to the second embodiment.

FIG. 9 is a diagram illustrating a cyclic movement method of a conserved point in two-dimensional local linearization according to the second embodiment.

FIG. 10 is a diagram illustrating a method of extending the two-dimensional local linearization of the second embodiment to a plane.

FIG. 11 is a diagram illustrating a ripple on a gray axis according to the second embodiment.

FIG. 12 is a diagram illustrating a state where ripples are removed on a gray axis according to the second embodiment.

FIG. 13 is a conceptual diagram of a conventional color conversion method using a multidimensional table lookup and an interpolation operation.

FIG. 14 is a conceptual diagram of interpolation without ripple in two dimensions according to the first embodiment.

FIG. 15 is a diagram of an example of a table numerical value before processing in the embodiment.

FIG. 16 is a diagram of an example of a table numerical value after a three-dimensional local linearization process in the embodiment.

FIG. 17 is a diagram of an example of a table numerical value after a two-dimensional local linearization process in the embodiment.

[Explanation of symbols]

Reference Signs List 101 input color signal 102 linear conversion by 3 × 3 matrix 103 gamma conversion as one-dimensional conversion of each signal 104 linear conversion by 3 × 4 matrix 105 output color signal 106 synthesis conversion unit 107 capable of interpolation without ripple 107 color for linear conversion Conversion table (1) 108 Color conversion table (2) for performing nonlinear conversion without ripple 109 Three-dimensional interpolation unit 202 Density space 203 One-dimensional conversion 204 3 × 3 matrix linear conversion 205 One-dimensional conversion 206 CMY space 207 Three-dimensional color conversion table 208 Interpolation 209 One-dimensional conversion 302 3 × 9 matrix nonlinear second-order polynomial color correction operation 304 3 × 3 matrix linear conversion 306 Table (1) 307, 309 Interpolation 308 Table (2) 1301 Input color signal 1302 Three-dimensional LUT 1303 Weighting coefficient 1305 Interpolation operation 1306 Interpolation output

Claims (6)

[Claims] The non-linear color conversion is decomposed into a chain of sequential color conversions consisting of a one-dimensional conversion of each color signal and a linear conversion using a matrix, and each color signal is one-dimensionally converted from the chain. Next, a synthesis conversion unit that performs matrix linear conversion is found, the synthesis conversion unit is created as a multidimensional color conversion table, and the nonlinear color conversion is performed in a form including lookup and multidimensional interpolation of the multidimensional color conversion table. A color conversion method characterized by performing. 2. An input color signal is firstly subjected to linear conversion by a matrix, secondly to one-dimensional conversion of each signal, and third to linear conversion by a matrix again. Is performed, a conversion obtained by combining the second and third conversions is created as a multidimensional color conversion table, and after the first linear conversion is performed on the input color signal,
2. The color conversion method according to claim 1, wherein the multidimensional color conversion table is looked up for the result and interpolated. 3. A sequential color conversion in which an input color signal is firstly subjected to one-dimensional conversion of each signal, secondly to linear conversion by a matrix, and thirdly to again perform one-dimensional conversion of each signal. Create a multi-dimensional color conversion table by combining the first and second conversions, look up the multi-dimensional color conversion table for the input color signal and interpolate, and then perform a third one-dimensional conversion on the result. 2. The color conversion method according to claim 1, further comprising: 4. When performing a non-linear second-order masking color correction operation, a second-order format part composed of each color signal in the non-linear masking coefficient is subjected to a first linear transformation using a matrix and a two-dimensional conversion of each variable.
Decompose into the second conversion by the linear combination of the following terms, create a multidimensional color conversion table for the second conversion, perform the first linear conversion on the input color signal, and look up the multidimensional color conversion table for the result 2. The color conversion method according to claim 1, wherein the color conversion is performed by interpolation. 5. A multi-dimensional table in which color conversion values for an input are stored at discrete points in an input color space, values are stored for a plurality of stored values of a plurality of points for each of the interpolated solids in a local area, and other values are stored. A color conversion method characterized by establishing a linear relationship between conversion values on each vertex in a solid used for interpolation by appropriately changing values at a plurality of points. 6. A three-dimensional object used for interpolation by appropriately changing only values at discrete points on a specific plane of a multidimensional table in which color conversion values for an input are accumulated at discrete points in an input color space. A color conversion method characterized by establishing a linear relationship between conversion values on vertices.