JPH0561972A - Gradation converter - Google Patents

Abstract

PURPOSE:To decide desired transfer characteristic uniquely as keeping the smoothness of gradation in the neighborhood of the boundary of a processing targeted gradation area. CONSTITUTION:The gradation of a digital input image stored in input image memory 3 is converted to desired gradation and is outputted to output image memory 4 by inputting an input data point consisting of processing targeted input gradation and transfer output gradation for the input gradation from an input means 1 with a value between the lower limit value and the upper limit value of an input gradation area. finding the coefficient of a natural spline interpolation function to satisfy the input data point, and generating a transfer function by a function generating means 2.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a gradation conversion device for a digital image processing device.

With the recent demand for diversification of digital image processing systems, there is a demand for a system capable of flexibly operating an arbitrary gradation range of an image to be processed. For this reason, technologies such as gradation conversion processing or density conversion processing have been provided. However, when generating a desired conversion table, a conversion characteristic table with a fixed gradation range or a conversion function with a fixed gradation range is compressed. -Expansion and addition / subtraction are performed, so there are restrictions on the conversion characteristics that can be generated. Further, when a desired conversion characteristic is applied to the processing target gradation range, the smoothness of gradation is lost at the boundary between the processing target gradation range and the non-processing target gradation range, which needs to be corrected. ..

[0003]

2. Description of the Related Art In the conventional gradation conversion processing, when generating a desired conversion table, a conversion characteristic table with a fixed gradation range or a conversion function with a fixed gradation range is compressed.
It was expanding and adding / subtracting. However, when the to-be-processed tone range is freely changed, the conversion characteristics that can be generated are limited, and the tone smoothness is lost at the boundary between the to-be-processed tone range and the non-to-be-processed tone range. Therefore, it is necessary to further finely adjust the conversion characteristics in order to obtain desired image characteristics.

[0004]

Therefore, in order to obtain a desired image characteristic, the required conversion characteristic table cannot be uniquely determined, and the generated conversion table is further adjusted or a slight gradation is obtained. There has been a problem that a desired image characteristic must be approximated by using a conversion table for converting many times.

In order to solve such a conventional problem, the present invention is a function that can uniquely determine a desired conversion characteristic table while maintaining the smoothness of gradation near the boundary of the gradation range to be processed. It is an object of the present invention to provide a gradation conversion device equipped with a generating means.

[0006]

FIG. 1 shows the principle of the present invention. In the figure, reference numeral 1 is a value between the lower limit value and the upper limit value of the input gradation range, and input means for inputting an input data point composed of an input gradation to be processed and a conversion output gradation corresponding thereto, 2 is the input data Function generating means for obtaining the coefficient of the natural spline interpolation function satisfying the points and generating the conversion function, 3 is an input image memory for storing the digital image to be converted, and 4 is an output image memory for storing the converted image. ..

The function generating means 2 also operates between the lower limit value of the input gradation range and the lower limit value of the processing target input gradation and between the upper limit value of the input gradation range and the upper limit value of the processing target input gradation. Extend the conversion function.

When the value of the extended conversion function is less than or equal to the lower limit value of the output gradation range between the lower limit value of the input gradation range and the lower limit value of the input gradation to be processed, the lower limit of the output gradation range is obtained. When the value is equal to or more than the upper limit value of the output gradation range between the upper limit value of the input gradation range and the upper limit value of the input gradation to be processed, the upper limit value of the output gradation range is set.

Further, the input means 1 inputs the respective lower and upper limit values of the input gradation to be processed and the converted output gradation, the pattern of the conversion function, and the weight value indicating the degree of deformation from this pattern. To

[0010]

The nature of the natural spline interpolation function generated by the function generating means 2 will be described. The input gradation range is 0 to M gradations, and the conversion output gradation range is 0 to N gradations. The data of the input gradation to be processed is 0 ≦ x ₁ <x ₂ <... <x _n ≦ M, and the data of the conversion output gradation is 0 ≦ y ₁ <y ₂ <... <y _n ≦ N. It is represented by (x _k , y _k ).

2m-1 with x ₁ , x ₂ ... X _n as connection points
Next (m = 2, 3, ...) Natural spline interpolation function s
(X) is given by the following equation.

[Equation 1] Here, p _m-1 (x) is a polynomial of degree m-1, and c _i is a constant coefficient that satisfies the following condition.

[Equation 2] Also, (x−x _i ) ₊ ^2m−1 is a cutting power function,

[Equation 3] Is.

Next, it will be explained that the natural spline interpolation function represented by the equation (1) is smoothly connected at the respective connection points x ₁ , x ₂ , ... X _n . In order to make the explanation easier to understand, in the case of the third order, that is, 2m-1 = 3 in the formula (1), that is, m =
The case of 2 will be described. Then, the equation (1) becomes as follows.

[Equation 4] Here, since p ₁ (x) is a linear equation, if a 1 and b are arbitrary constants and p ₁ (x) = ax + b (5), then equation (4) becomes

[Equation 5] Becomes Further, c _i is a constant coefficient that satisfies the following condition.

[Equation 6] Here (x-x _{i) +} ³ is represented by the following equation.

[Equation 7]That is, the equation (6) is expressed by the above in the interval [−∞, ∞]
x₁, X₂…, X_nOf n + 1 polynomials with
It can be said that the linear combination is uniquely expressed. Next, (6)
According to the formula, these n + 1 polynomials are connected points x₁, X
₂…, X _nIndicates that the connection is smooth at.

The left-side function s _L (x) and the right-side function s _R (x) at the data point (x ₁ , y ₁ ) are expressed by the equation (6) as follows: s _L (x) = ax + b (9) s _R (x ) = Ax + b + c ₁ (x−x ₁ ) ³ (10) The first-order differentials of these are respectively s _L '(x) = a (11) s _R ' (x) = a + 3 · c ₁ (x-x ₁ ) ² (12). Therefore, from equations (9) to (12), at x = x ₁ , s _L (x ₁ ) = s _R (x ₁ ) = ax ₁ + b,
And, s _L ′ (x ₁ ) = s _R ′ (x ₁ ) = a. That is, the left-side function and the right-side function both have the function value ax ₁ + b at the connecting point x ₁ and have the slope a.

Similarly, the data points (x_k, Y_k) (K =
Left side function s in 2, 3, ..., N) _L(X) and
Right-hand side function s_R(X) is expressed as follows.

[Equation 8] Further, each of these first-order differentials is expressed by the following equation.

[Equation 9] As a result, the following equation is obtained when x = x _k from the equations (13) to (16).

[Equation 10] That is, the above-mentioned left-hand side function and right-hand side function both have the function value shown in the following equation at the connection point x _k ,

[Equation 11] And, it has the slope of the following equation.

[Equation 12]

From the above, n + 1 polynomials are connected points x
_It can be seen that the connection is smooth at ₁ , x ₂ , ..., X _n . That is, the realization of the present invention is that the interval [−∞,
_n in x ₁ ], [x ₁ , x ₂ ], ..., [x _n , ∞]
+1 polynomial is obtained, and the effective gradation range [0,
Processing target gradation range [x ₁ , x _n ] (x ₁ ≧
0, x _n ≤ M) and the gradation range not to be processed [0, x ₁ ],
In [x _n , M], the n + 1 polynomials are applied.

Next, how to obtain the n + 1 polynomials will be described. From the equation (6), the n + 1 polynomials are
It becomes the following formula.

[Equation 13] Also, c _i is calculated from equation (7)

[Numerical equation 14] and

[Equation 15] Meet Here, since the connection points x ₁ , x _2, ..., X _n have function values y ₁ , y ₂ , ..., Y _n , from equation (17),

[Equation 16] Becomes That is, equations (18) to (20) are a, b, c ₁ , c ₂
... is an n + 2-way simultaneous linear equations for the unknown coefficients a c _n. Therefore, the undetermined coefficient can be obtained by solving this with the Gaussian elimination method or the like.

In this way, the function generating means 2 has n data points (x ₁ , y ₁ ), (x ₂ , y ₂ ), ..., (x
_n , y _n ) (where 0 ≦ x ₁ <x ₂ <... <x _n ≦ M)
From the interval [0, x ₁ ], [x ₁ , x ₂ ], ..., [x
Generate n + 1 functions corresponding to _n-1 , _xn ], [ _xn , M]. As a result, the lower limit value x ₁
Between [0, x ₁ ] and the lower limit value 0 of the input gradation range,
Also, the conversion function that smoothly connects to the section of [x _n , M] between the upper limit value M of the input gradation range and the upper limit value x _n of the processing target input gradation is extended.

The upper and lower limits of the input tone to be processed are often determined visually. In such a case, a necessary image may exist in a range exceeding these upper and lower limits. Therefore, it is necessary to extend the function over the entire input gradation.

The range that can be taken by the conversion function is the range of [0, N] of the entire converted output gradation. Therefore, the conversion function has a lower limit of 0.
When it is less than or equal to 0, it is set to 0, and when it exceeds the upper limit N, N
And need to.

The shape of the conversion function is preset in several patterns.
The input target gradation and this conversion output gradation are classified into
Each lower limit of (x₁, Y₁) And the upper limit (x_n, Y_n) And
And the weight that indicates the pattern and the degree of deformation from this pattern
You can determine the coefficient of the conversion function by entering the value.
it can. This gives each data point (x₁, Y₁),
(X ₂, Y₂),… (X_n, Y_n) Rather than typing
The force is often simplified.

[0021]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 2 is a block diagram of the gradation conversion table creating apparatus according to the first embodiment of the present invention. The gradation conversion table creating device 18 according to the present embodiment is a function generating unit.
16 and table creating means 17. Also, the function generating means
16 comprises a coefficient calculating means 12 and a function defining means 13, and the table creating means 17 comprises a function value calculating means 14 and a gradation effective area rounding means 15.

In the present embodiment, the input gradation area is used as the gradation and the output gradation area after the conversion is set to 256 gradations of 0 to 255 by using 8 bits. However, the input gradation range may be 256 gradations and the output gradation range may be 16536-bit 65536 gradations. That is, the input gradation range may be M gradations and the output gradation range may be N gradations.

N data points (x₁, Y₁), (X₂，
y₂), ..., (x_n, Y_n) (Where 0 ≦ x₁<X₂
<... <x_n≤255) is entered from the data point input means 11.
And is passed to the coefficient calculation means 12. With coefficient calculation means 12
Is n + 2 (a, b, c from n data points₁，
c₂, ..., c_n), The undetermined coefficient of
It is passed to the function definition means 13. In the function definition means 13, n + 2
From the undetermined coefficient of, the interval [0, x ₁], [X₁, X₂],
…, [X_n-1, X_n], [X_n, 255] corresponding to n +
Define a function. From the above, the function generating means 13
In this case, n + 1 functions can be generated.

FIG. 3 shows the functions s ₁ , s ₂ , ... S _n , s _{n + 1} generated by the function generating means 16. The function s _k occurs in the interval [x _k-1 , x _k ], and s ₁ is in the interval [0, x ₁ ],
s _{n + 1} occurs in the interval [x _n , 255].

In the function value calculating means 14, sections [0, x ₁ ], [x ₁ , x ₂ ], ..., [x generated by the function generating means 16 are generated.
By the function corresponding to [ _n-1 , x _n ], [x _n , 255],
A function value for the input value [0, 255] is obtained and passed to the gradation effective area rounding means 15. The gradation effective area rounding means 15 rounds off the decimal point of the function value and below, and sets the function value smaller than 0 to 0 and the function value larger than 255 to 255.
This function value is the output value for the input. From the above,
The table creating means 17 determines the output value for the input value and creates the gradation conversion table.

In the gradation converting means 20, the input image memory device
From 19, the density value of one pixel at an arbitrary address [0,
255] is input, the output value [0, 255] is determined by the table created by the gradation conversion table creating device 18, and this is set as the density value at the same address of the output image memory device 21.

Next, the operation of the function generating means 16 at three data points (n = 3) will be described. 3 data points (x
₁ , y ₁ ), (x ₂ , y ₂ ), (x ₃ , y ₃ ) (where 0 ≦ x ₁ <x ₂ <x ₃ ≦ 255) are input from the data point input means 11 to calculate coefficients. Passed to means 12. In the coefficient calculating means 12, five data points (a, b, c) from three data points
The undetermined coefficient of ₁ , c ₂ , c ₃ ) is calculated. As a specific calculation method, the following five-element simultaneous linear equations may be solved by the Gauss elimination method or the like from the equations (18) to (20).

[Numerical equation 17]

The function defining means 13 receives the five undetermined coefficients obtained above, and from the equation (17), the interval [0,
x ₁ ], [x ₁ , x ₂ ], [x ₂ , x ₃ ], [x ₃ , 25
The following four functions corresponding to [5] are defined. S ₁ , s ₂ , s ₃ , and s ₄ of ₄ indicate these four functions.

[Equation 18]

In the function value calculating means 14, the sections [0, x ₁ ], [x ₁ , x ₂ ], [x ₂ ,
x _3], the function corresponding to [x _3, 255], obtains a function value for an input value [0,255], and passes to the tone effective area rounding means 15. The gradation effective area rounding means 15 rounds off the decimal points of the function value and below, and sets the function value smaller than 0 to 0 and the function value larger than 255 to 255, and makes this function value the output value for the input.

FIG. 5 shows a state in which the function s ₁ shown in FIG. 4 is rounded. FIG. 6 similarly shows the function generation by the function generating means 16 at four data points (n = 4), and FIG. 7 shows the rounding of the data in the interval [0, x ₁ ] and [x ₄ , 255]. Indicates the state. That is, 0 or less is set to 0 in the [0, x ₁ ] section, and 255 or more is set to 25 in the [x ₄ , 255] section.
I am at 5.

Next, a second embodiment will be described. FIG. 8 is a block diagram showing the configuration of the second embodiment. The same reference numerals as those in FIG. 2 represent blocks having the same functions. This embodiment is the first
In contrast to the data point input as the input data in the embodiment, the input data is reduced by inputting the data point serving as the reference, the pattern of the conversion curve, and the weight for deforming the pattern, which is easy to use. is there. Input means
22 is for inputting such data, and the data point calculating means 23 is for converting such data into data points of the first embodiment and making the subsequent processing the same as in the first embodiment. ..

FIG. 9 is a diagram showing a pattern of a conversion curve. In the present invention, the conversion curve can have any shape, but the shape that is normally used can be classified into several patterns. Then, this pattern is deformed according to the case to be used. In this way, the input data can be reduced and it becomes easy to use.

The starting point of the gradation to be processed is x ₁ , the ending point is x ₂ ,
The start point of the output gradation with respect to the processing target gradation is y ₁ , and the end point is y.
_Set to ₂ . The start point (x ₁ , y ₁ ) is a and the end point (x ₂ , y ₁ ) is
Let y ₂ ) be b, the middle point of the straight line ab be d, the quarter point from a is c, and the 3/4 point is e. All the curves of the pattern should pass through points a and b. The A type curve is a curve that passes through the point h. Where h is (x ₁ , y ₁ ), (x ₂ ,
y ₂ ) as a point that can be represented (x _m 'y _n ')
And Similarly, a B type curve is a curve that passes points a, b and i, a C type curve is a curve that passes points a, b, d, f and k, and a D type curve is a, b point, d. Point, g point, j
It is a curve that passes through points.

FIG. 10 is a diagram showing an A type curve. The d point is represented by (x ₁ + x ₂ ) / 2, (y ₁ + y ₂ ) / 2, and the h point is represented by (3x ₁ + x ₂ ) / 2, (y ₁ + 3y ₂ ) / 2. An arbitrary point between dh can be designated by setting the straight line dh as the vector wa and designating the amount of wa. Thereby, the shape of the curve A can be changed. In this case, (x ₁ ,
y ₁ ), (x ₂ , y ₂ ), A type curve, and weight w
By inputting the value of a, the input data can be reduced.

FIG. 11 is a diagram showing a B type curve. The i point is represented by (x ₁ + 3x ₂ ) / 2, (3y ₁ + y ₂ ) / 2. The straight line di can be used as the vector wb, and the curve shape can be transformed by changing the value of wb.

FIG. 12 is a diagram showing a C type curve. c point is (3x ₁ + x ₂ ) / 4, (3y ₁ + y ₂ ) / 4 f point is (7x ₁ + x ₂ ) / 8, (5y ₁ + 3y ₂ ) / 8 e point is (x ₁ + 3x ₂ ) / 4, (y ₁ + 3y ₂ ) / 4 k points can be represented by (x ₁ + 7x ₂ ) / 8, (3y ₁ + 5y ₂ ) / 8, and the straight line cf is the vector wc and the straight line e.
Let k be the vector wd. In this case, the vectors wc, w
Two of d will be instructed.

FIG. 13 is a diagram showing a D-type curve. c point is (3x ₁ + x ₂ ) / 4, (3y ₁ + y ₂ ) / 4 g point is (5x ₁ + 3x ₂ ) / 8, (7y ₁ + y ₂ ) / 8 e point is (x ₁ + 3x ₂ ) / 4, (y ₁ + 3y ₂ ) / 4 j points can be represented by (3x ₁ + 5x ₂ ) / 8, (y ₁ + 7y ₂ ) / 8, and the straight line cg is the vector we and the straight line e.
Let j be the vector wf. Also in this case, the vectors we and w
Two of f will be instructed.

As described above, (x ₁ , y ₁ ), (x ₂ , y
₂ ) and the curve type and vector value can be specified to specify the curve, which simplifies the input operation.
It becomes an easy-to-use device.

[0039]

As described above, according to the gradation conversion table creating apparatus of the present invention, the input n data points or the processing target gradation and the output gradation and the weight value for the processing target gradation. By smoothly connecting the n number of data points generated from the input by the function that is uniquely expressed, the number of gradation conversion tables is practically infinite, and the gradations to be processed are practically possible. The smoothness of the gradation is not lost at the boundary between the area and the non-processing gradation area. In other words, when trying to operate an arbitrary gradation region of the processing target image, by determining the necessary gradation conversion characteristics for making the processing target gradation region the desired image characteristic, The conversion characteristics can simultaneously generate a function such that the smoothness of gradation is not lost at the boundary between them. Further, since the required conversion characteristics can be almost infinite in practical use, the output image characteristics obtained by the present invention can be infinitely different. Further, by patterning the shape of the curve, it is possible to reduce the input data and make it easier to use.

[Brief description of drawings]

FIG. 1 is a principle diagram of the present invention.

FIG. 2 is a block diagram showing the configuration of the first embodiment.

FIG. 3 is a diagram showing a function generated by a function generating means.

FIG. 4 is a diagram showing a function generated by a function generating means using three pieces of data.

FIG. 5 is an explanatory diagram in which the origin side of the curve is rounded using FIG. 4 and a table is generated by the table generating means.

FIG. 6 is a diagram showing a function generated by a function generating means using data of four points.

FIG. 7 is an explanatory diagram of rounding both ends of a curve using FIG. 6 and generating a table by a table generating means.

FIG. 8 is a block diagram showing a configuration of a second embodiment.

FIG. 9 is a diagram illustrating a curve pattern.

FIG. 10 is an explanatory diagram for inputting data using an A type curve.

FIG. 11 is an explanatory diagram for inputting data using a B type curve.

FIG. 12 is an explanatory diagram of inputting data using a C type curve.

FIG. 13 is an explanatory diagram of inputting data using a D type curve.

[Explanation of symbols]

 11 data point input means 12 coefficient calculation means 13 function definition means 14 function value calculation means 15 gradation effective area rounding means 16 function generation means 17 table creation means 18 gradation conversion table creation device 19 input image memory device 20 gradation conversion means 21 Output image memory device 22 Input means 23 Data point calculation means

Claims (4)

[Claims] 1. A gradation conversion device for converting a gradation of a digital input image stored in an input image memory (3) into a desired gradation and outputting the converted gradation to an output image memory (4). An input means (1) for inputting an input data point consisting of an input gray level to be processed and a converted output gray level corresponding to the input gray level between a lower limit value and an upper limit value; and a natural spline interpolation function that fills the input data point. A gradation conversion device comprising a function generating means (2) for obtaining a coefficient and generating a conversion function. 2. The function generating means (2) is arranged between the lower limit value of the input gradation range and the lower limit value of the processing target input gradation and between the upper limit value of the input gradation range and the upper limit value of the processing target input gradation. The gradation conversion device according to claim 1, wherein the conversion function is also extended. 3. The lower limit of the output gradation range when the value of the extended conversion function is less than or equal to the lower limit value of the output gradation range between the lower limit value of the input gradation range and the lower limit value of the processing target input gradation range. It is characterized in that the value is set as an upper limit value of the output gradation range when it is equal to or more than the upper limit value of the output gradation range between the upper limit value of the input gradation range and the upper limit value of the processing target input gradation. The gradation conversion device according to claim 2. 4. The input means (1) inputs the respective lower and upper limit values of a processing target input gradation and a conversion output gradation, a pattern of a conversion function, and a weight value indicating a degree of deformation from this pattern. The method according to claim 1, wherein
3. The gradation conversion device according to any one of 3 above.