JP2861106B2 - Shading image generation method and apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to, for example, an image processing apparatus for artificially generating an image in the field of computer graphics, or processing an image for printing using a computer. The present invention relates to a method and an apparatus for generating an image for correction.

[Conventional technology]

In the field of computer graphics, artificially generate an image whose center is black and becomes brighter toward the periphery, or when correcting a part of an image input with a camera or TV, the boundary of the corrected part is When an image for correction for blurring is generated, an image is required in which the distance from the origin is the gray value of the pixel.

That is, when the grayscale image to be generated is represented by orthogonal xy coordinates, the grayscale value F (X, Y) of the pixel at the coordinates (X, Y) is Becomes This is shown in FIG. 2, which is in the shape of a side of a cone.

When the coordinates of a black center with _{(X 0, Y 0),} G (X, Y) = k · F (X-X 0, Y-Y 0) center by _{... (2) (X 0,} Y 0 ) Is black, and an image G (x, y) that becomes brighter as it goes to the peripheral portion can be generated. (However, k is a coefficient) Also, the image H (x,
When a part of y) is corrected, for example, the gray value of the center coordinate (X1, Y1) of the pixel to be corrected is set to k, and the coordinates (X1, Y1)
When a region having a radius r with respect to is corrected, for a pixel region of coordinates (x, y) satisfying (x−X1) ² + (y−Y1) ² <r ² (3), H (x, y) = k + (H (x, y) -k) .F (x-X1, y-Y
1) / r (4), the value of the center is k, but as the distance from the center increases, the proportion of the image before correction increases,
Since the area whose distance is equal to or more than r is not corrected, the effect is the same as that of correcting the picture by spraying, and the corrected boundary cannot be recognized.

Conventionally, to generate the image F (X, Y) of Expression (1), 1
Two multiplications and one square root operation were performed for each pixel.

[Problems to be solved by the invention]

However, there is a problem in that if a dedicated circuit for square root is created to calculate the square root, or if a numerical processor is used, the cost of the system becomes high. In addition, when a general-purpose microprocessor is used, the cost of the system is reduced, but there is a problem that the square root operation requires many calculation steps and it takes time to generate an image.

It is an object of the present invention to provide a method and apparatus for generating an image of equation (1) without using costly or time-consuming square root operations.

[Means for solving the problem]

In the method for generating a grayscale image according to the present invention, in generating a grayscale image in which a value obtained by rounding the distance from the origin and converting it to an integer is used as a pixel value, the grayscale image is represented by an orthogonal xy coordinate system. Is the absolute value of the Y coordinate of the pixel, the gray auxiliary value of the pixel is 0, and then the pixel is determined from the gray integer value and the gray auxiliary value of the coordinates (X, Y). To obtain the grayscale integer value and grayscale auxiliary value of the coordinate (X + 1, Y) to be calculated, the grayscale value of the pixel is calculated from the sum of twice the X coordinate value of the pixel at the coordinate (X, Y) and the grayscale auxiliary value of the pixel. When the result of the comparison operation of subtracting the integer value is greater than or equal to 0, the value obtained by adding 1 to the gray value of the pixel at the coordinates (X, Y) is set as the gray value of the coordinates (X + 1, Y), and the coordinates (X , Y), the value obtained by subtracting twice the grayscale integer value of the pixel from the sum of twice the X coordinate value of the pixel and the grayscale auxiliary value of the pixel is represented by the coordinate (X 1, the gray auxiliary values of the pixels of Y), if the result of the comparison operation, less than 0, the coordinates (X, coordinate the gray integer value of the pixel of Y) (X + 1, Y)
Of the pixel at the coordinates (X, Y)
An image is generated by repeating a value obtained by adding 1 to the sum of the double and the density auxiliary value of the pixel as a density (X + 1, Y). Further, the gray-scale image generating apparatus according to the present invention is a device for generating a gray-scale image in which a value obtained by rounding off the distance from the origin and converting it to an integer is used as the value of the pixel, each time a pixel moves on a scanning line parallel to the X axis. A main scanning clock generator that generates a main scanning clock signal in synchronization with the main scanning; a sub-scanning clock generator that generates a sub-scanning clock signal in synchronization with each movement of the scanning line in the Y-axis direction; The value increases by 1 at the input of the clock signal,
An X-coordinate counter whose value is cleared to 0 upon input of the sub-scanning clock signal; a Y-coordinate counter whose value increases by one upon input of the sub-scanning clock signal; and a Y-coordinate counter upon input of the sub-scanning clock signal And a density integer counter whose value is incremented by one in response to the input of a condition signal indicating whether or not to increase by one from the density integer value of the pixel processed immediately before, and a sub-scanning clock signal A gray level auxiliary register whose value is cleared to 0 upon input; an adder for adding a value obtained by doubling the value of the X coordinate register to the value of the auxiliary integer register; a value of the adder and the gray level integer counter And a comparator that generates the condition signal when the former value is larger or equal to the former value. When the condition signal is input, the comparator calculates the density integer count from the value of the adder. A value obtained by subtracting a value twice as large as the above value is assigned to the gray level auxiliary register. If the condition signal is not input, a value obtained by adding 1 to the value of the adding unit is substituted for the gray level auxiliary register. An arithmetic operation unit, a gray-scale image storage unit that stores the value of the X-coordinate counter as an X-direction address, the Y-coordinate counter value as a Y-direction address, and stores the value of the gray-scale register as a gray-scale value of the pixel. It is characterized by having.

[Action]

In a grayscale image in which a value obtained by rounding the distance from the origin and converting it to an integer is used as the value of the pixel, by utilizing the property that the difference between the grayscale values of adjacent pixels is 1 or less,
It is possible to obtain the gray value information of the coordinates (X + 1, Y) from the gray value information of the pixel at the coordinates (X, Y) of the gray image.

The present invention makes it possible to generate a desired grayscale image by repeating this, without using a square root operation that requires computational cost.

〔Example〕

Next, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing one embodiment of the present invention.
In FIG. 1, in this embodiment, the main scanning clock signal 12 is used.
, A sub-scanning clock generator 2 for generating a sub-scanning clock signal 13, an X-coordinate counter 3 and a Y-coordinate counter 3 for indicating the coordinate positions of the pixels of the grayscale image.
A coordinate counter 4, a gray-scale integer counter 5 for storing gray-scale information and a gray-scale auxiliary register 6, an adder 7, a comparator 8 for generating a condition signal 11 for increasing the value of the gray-scale integer counter 5 by 1, a gray-scale auxiliary The image processing apparatus includes a conditional operation unit that outputs a value to the register 6 and a gray image storage unit 10 that is accessed by a two-dimensional XY address and stores a gray integer value.

The main-scanning clock signal 12 is output from the main-scanning clock generator 1 every time the X coordinate of a pixel for which a gray-scale value is to be calculated in a gray-scale image increases by one. The sub-scanning clock signal 13 is output from the sub-scanning clock generator 2 every time the Y coordinate of a pixel for which a gray-scale value is to be calculated in a gray-scale image increases by one. The X-coordinate counter 3 and the Y-coordinate counter 4 store the position information of the pixel for which the gradation value is calculated in the gradation image. The X-coordinate counter 3 is cleared to 0 by the input of the sub-scanning clock signal 13, and the main scanning Each time the clock signal 12 is input, the value increases by 1, 2, 3,..., And the initial value of the Y coordinate counter 4 before generating the grayscale image is 0, and each time the sub-scanning clock signal 13 is input. It increases by 1, 2, 3, etc. The grayscale image counter 5 loads the value of the Y coordinate counter in response to the input of the sub-scanning clock signal 13 and
Increment by 1 for every 11 inputs. The gray level auxiliary register 6 is cleared to 0 by the input of the sub-scanning clock signal 13, and
Stores the output of the conditional operation unit. The adder adds the value of the gray level auxiliary register and twice the value of the X coordinate counter. The comparator 8 compares the output of the adder 7 with the output of the grayscale integer counter 5 and outputs a condition signal 11 when the former value is larger or equal. When the condition signal 11 is input, the condition calculation unit 9 outputs a value obtained by subtracting twice the value of the density integer counter 5 from the value of the addition unit 7, and adds the value when no condition signal is input. A value obtained by adding 1 to the value of the unit 7 is output. The grayscale image storage unit 10 uses the values of the X coordinate counter 3 and the Y coordinate counter 4 as two-dimensional address inputs,
The value of the shade integer counter 5 is stored as a shade value.

Hereinafter, the principle of the generation of a grayscale image according to the present invention will be described below.

The result of the expression (1), which is the distance from the origin at the pixel at the coordinates (X, Y), is rounded to an integer, and the gray scale integer value is represented by I
If (X, Y), there is a relationship of I (X, Y) −0.5 ≦ F (X, Y) <I (X, Y) +0.5 (5), and the gray level auxiliary value A (X, Y) ) Is A (X, Y) = F (X, Y) ² −I (X, Y) ² = X ² + Y ² −I (X, Y) ² (6) , −I (X, Y) + 0.25 ≦ A (X, Y) <I (X, Y) +0.25 (7), but the right side of Expression (6) is an integer. X,
Y) is also an integer, and the following relationship holds: -I (X, Y) + 1 ≦ A (X, Y) ≦ I (X, Y)

However, the partial differentiation of F (X, Y) in equation (1) in the X-axis direction gives Therefore, the difference between adjacent F (X, Y) and F (X + 1, Y) is 1 or less. Therefore, each integer I
The difference between (X, Y) and I (X + 1, Y) also becomes 1 or less. Therefore, one of the following holds: I (X + 1, Y) = I (X, Y) (10) or I (X + 1, Y) = I (X, Y) +1 (11) When equation (10) holds,
From equation (6), A (X + 1, Y) = A (X, Y) + 2 · X + 1 (12) is derived, and using the relational expression of equation (8) at coordinates (X + 1, Y), (X, Y) + 2 · X + 1 ≦ I (X, Y) (13)

 Further, when the equation (12) holds, A (X + 1, Y) = A (X, Y) + 2 · X−2 · I (X, Y) (14) is similarly derived, and A (X , Y) + 2 × X ≧ I (X, Y) (15)

Therefore, the coordinates (X + 1, X + 1) are obtained from the grayscale integer value I (X, Y) and the grayscale auxiliary value A (X, Y), which are grayscale information of the coordinates (X, Y).
Y), the gray value I (X + 1, Y) and the gray value A (X + 1,
To obtain Y), if equation (15) holds, then I (X + 1, Y) = I (X, Y) +1... (16) A (X + 1, Y) = A (X, Y) + 2 · X −2 · I (X, Y) (17) When equation (15) does not hold, I (X + 1, Y) = I (X, Y) (18) A (X + 1, Y) = A (X, Y) Y) + 2 · X + 1 (19) On the other hand, for any Y Therefore, I (0, Y) = Y (21). Therefore, if Y = 0, 1, 2,..., I (0, 0), I (0, 1), I (0) , 2),..., Are obtained on the Y-axis.

Next, from the equations (6) and (21) for an arbitrary integer Y, I
When (0, Y) is obtained, A (0, Y) = 0 ² + Y ² −I (0, Y) ² = 0 (22). Therefore, equations (15) to (19) are repeatedly used. And I (0, Y), I (1, Y), I (2, Y),... A (0, Y), A (1, Y), A (2, Y),. Since Y is arbitrary, a gray scale integer image I (X, Y) having a required area can be obtained.

 Next, a description will be given with reference to FIG.

The default setting before generating the grayscale image is the X coordinate counter 3,
0 is assigned to each of the Y coordinate counter 4, the grayscale integer counter 5, and the grayscale auxiliary register 6. The value (0,0) of the X-coordinate counter 3 and the Y-coordinate counter 4 is used as an address, and the value 0 of the gray-scale integer counter is stored in the gray-scale image storage unit 10.
Is output to the adder 7 and the density auxiliary register 6
And the value obtained by doubling the value of the X-coordinate counter 3 is output. The comparator 8 compares the value output by the adder 7 with the value of the gray-scale integer counter 5, and the former is compared with the latter. The condition signal 11 is output only when is larger or equal. The conditional operation unit 9 outputs a value obtained by subtracting twice the value of the grayscale integer counter 5 from the output value of the addition unit 7 when the condition signal 11 is input, and outputs the value when the condition signal 11 is not input. Adder 7
And outputs a value obtained by adding 1 to the output value. The gray-scale integer counter 5 increases by 1 only when the condition signal 11 is input,
The output value of the conditional operation unit 9 is assigned to the gray level auxiliary register 6.

The main scanning clock signal 12 is generated from the main scanning clock generator 1, and the value of the X coordinate counter 3 increases by one. Using the values of the X-coordinate counter 3 and the Y-coordinate counter 4 as addresses, the value 0 of the gray-scale integer counter is output to the gray-scale image storage unit 10, and the value of the gray-scale auxiliary register 6 and the X-coordinate counter 3 Is output, and the comparator 8 compares the value output from the adder 7 with the value of the gray-scale integer counter 5 to determine whether the former is greater than or equal to the latter. The signal 11 is output. When the conditional signal 11 is input, the conditional operation unit 9
And outputs a value obtained by subtracting twice the value of the gray-scale integer counter 5 from the output value of, and when the condition signal 11 is not input, a value obtained by adding 1 to the output value of the adding unit 7 is output. The gradation integer counter 5 is incremented by 1 only when the condition signal 11 is input, and the output value of the conditional operation unit 9 is substituted in the gradation auxiliary register 6. By repeating this for the number of pixels in the X direction of the generated gray image, the X axis of the gray image (Y = 0)
Can be generated.

When the gray value of the last pixel on the scanning line is obtained, a sub-scanning clock signal 13 indicating that the scanning line has moved to the next scanning line is generated from the sub-scanning clock generator 2, and the X coordinate counter 3 The value is cleared to 0, and the value of the Y coordinate counter 4 is increased by 1. The value of the Y coordinate counter 4 is substituted into the density integer counter 5, and the density auxiliary register 6 is cleared to zero. Using the values of the X-coordinate counter 3 and the Y-coordinate counter 4 as addresses, the value of the gray-scale integer counter is output to the gray-scale image storage unit 10, and the value of the gray-scale auxiliary register 6 and the X-coordinate counter 3 The sum of the doubled value is output. The comparator 8 compares the value output from the adder 7 with the value of the grayscale integer counter 5 and determines whether the condition signal is larger or equal only when the former is greater than or equal to the latter. Outputs 11. The conditional operation unit 9 outputs a value obtained by subtracting twice the value of the grayscale integer counter 5 from the output value of the addition unit 7 when the condition signal 11 is input, and outputs the value when the condition signal 11 is not input. A value obtained by adding 1 to the output value of the adding unit 7 is output. The grayscale integer counter 5 is 1 only when the condition signal 11 is input.
And the output value of the conditional operation unit 9 is assigned to the gray level auxiliary register 6. The main scanning clock signal 12 is generated from the main scanning clock generator 1, and the value of the X coordinate counter 3 increases by one. Using the values of the X-coordinate counter 3 and the Y-coordinate counter 4 as addresses, the value 0 of the gray-scale integer counter is output to the gray-scale image storage unit 10, and the addition unit 7
Sets the value of the gray level auxiliary register 6 and the value of the X coordinate counter 3 to 2
The sum of the multiplied values is output. The comparator 8 compares the value output by the adder 7 with the value of the grayscale integer counter 5 and determines whether the condition signal is greater than or equal to the former when the latter is greater than or equal to the latter.
Outputs 11. The conditional operation unit 9 outputs a value obtained by subtracting twice the value of the grayscale integer counter 5 from the output value of the addition unit 7 when the condition signal 11 is input, and outputs the value when the condition signal 11 is not input. A value obtained by adding 1 to the output value of the adding unit 7 is output. The gradation integer counter 5 is incremented by 1 only when the condition signal 11 is input, and the output value of the conditional operation unit 9 is substituted in the gradation auxiliary register 6. By repeating the main scanning clock signal input process by the number of pixels in the X direction of the generated gray image, the gray values of all the pixels on one scanning line of the gray image can be generated.

Furthermore, by repeating the processing of the sub-scanning clock signal input by the number of pixels in the Y direction of the generated grayscale image,
A gray value of all pixels of a gray image having a required area can be generated.

A case will be described in which either the X coordinate or the Y coordinate or both are negative.

An image F (x,
y) is expressed by equation (1), but for any X and Y, 4) 1) X ≧ 0 and Y ≧ 0 (24) 2) X <0 and Y ≧ 0 (25) 3) X <0 And Y <0 (26) 4) X ≧ 0 and Y <0 (27) In FIG. 1, integers X and Y equal to or greater than 0 in FIG. Gray value I (X, Y)
Is input to the grayscale image storage, Then, even when X and Y are negative, the gray value I (X, Y) can be obtained.

This will be described with reference to FIG. 3. The gray image is divided into four regions represented by Expressions (24) to (27), and each region is divided into memory banks.
36, the memory bank 37, the memory bank 38, and the memory bank 39, all of which receive the same gray value 33. The X-direction address and the Y-direction address are converted from a positive integer to a negative integer by inverters 34 and 35, respectively. The memory bank 36 receives a positive X-direction address and a positive Y-direction address, the memory bank 37 receives a negative X-direction address and a positive Y-direction address, and the memory bank 38 receives a negative X-direction address and a negative The Y-direction address is input, and the memory bank 39 receives a positive X-direction address and a negative Y-direction address. Thereby, the grayscale image storage unit stores X
Also, even when the Y-direction address is negative, a grayscale image can be generated.

〔The invention's effect〕

As described above, according to the method and apparatus of the present invention, it is possible to generate a grayscale image in which a value obtained by rounding off the distance from the origin and converting it to an integer is the value of the pixel.

In the present invention, since only addition, subtraction, and shift operations (double operations) are used, the calculation cost can be reduced as compared with the conventional method in which the square root operation is performed for each pixel of the gray image to be generated.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIG. 2 is an explanatory diagram showing a function F (X, Y) which is a distance from an origin, and FIG. 3 shows the inside of a gray image storage unit. Block diagram, 4th
The figure is an explanatory diagram showing that the area of the grayscale image is divided into four parts by positive and negative X and Y. 1, a main scanning clock generating unit, 2, a sub-scanning clock generating unit, 3, an X coordinate counter, a Y coordinate counter,
5: shade integer counter, 6: shade auxiliary register, 7
... Addition unit, 8 Comparator, 9 Conditional operation unit, 10
... A grayscale image storage unit.

Claims (2)

(57) [Claims] In generating a grayscale image in which a value obtained by rounding a distance from an origin and converting it into an integer is used as a pixel value, the grayscale image is represented by an orthogonal xy coordinate system. The grayscale integer value is the absolute value of the Y coordinate of the pixel, the grayscale auxiliary value of the pixel is 0, and then the coordinate (X + 1) adjacent to the pixel is determined from the grayscale integer value of the coordinates (X, Y) and the grayscale auxiliary value. , Y)
The coordinates (X,
Y) The result of the comparison operation of subtracting the gray value of the pixel from the sum of twice the X coordinate value of the pixel and the gray value of the pixel, 0
If greater or equal, the value obtained by adding 1 to the gray integer value of the pixel at coordinate (X, Y) is taken as the gray integer value of coordinate (X + 1, Y), and twice the X coordinate value of coordinate (X, Y) A value obtained by subtracting twice the gray value of the pixel from the sum of the gray value and the gray value of the pixel is set as the gray value of the pixel at coordinates (X + 1, Y). The grayscale integer value of the pixel at the coordinates (X, Y) is defined as the grayscale integer value of the coordinates (X + 1, Y), and the sum of twice the X coordinate value of the pixel at the coordinates (X, Y) and the grayscale auxiliary value of the pixel A value obtained by adding 1 to a coordinate value (X + 1, Y), and an image is generated by repeating the auxiliary value. 2. A device for generating a grayscale image in which a value obtained by rounding off a distance from an origin and converting it into an integer, the value of the pixel being provided, wherein a main scan is performed in synchronization with each movement of a pixel on a scanning line parallel to the X axis. A main scanning clock generator that generates a clock signal; a sub-scanning clock generator that generates a sub-scanning clock signal in synchronization with each movement of the scanning line in the Y-axis direction; Increases by one, and the value is cleared to 0 by the input of the sub-scanning clock signal X
A coordinate counter, and Y whose value increases by 1 upon input of the sub-scanning clock signal
A coordinate counter and the Y counter when a sub-scanning clock signal is input.
A gray-scale integer counter whose value is incremented by one by inputting a condition signal indicating whether or not the value of the coordinate counter is substituted and incremented by one from the gray-scale integer value of the pixel processed immediately before; A gray level auxiliary register whose value is cleared to 0 when a signal is input; an adder for adding a value obtained by doubling a value of the X coordinate register to a value of the auxiliary integer register; a value of the adder and the gray level The value of the integer counter is compared with the value of the integer counter. If the former value is larger or equal, the comparator generates the condition signal. A conditional operation of substituting a value obtained by subtracting twice the value of the above into the gray level auxiliary register, and substituting a value obtained by adding 1 to the value of the adder into the gray level auxiliary register when the condition signal is not inputted. Department A gray-scale image storage unit that stores the value of the X-coordinate counter in an X-direction, the value of the Y-coordinate counter in a Y-direction, and stores the value of the gray-scale register as a gray-scale value of the pixel. A gray-scale image generation device characterized by the following.