JP2006165930A - Dither matrix generation method and dither matrix - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To generate a proper dither matrix in the half-toning (dither processing) of a multi-tonal input image, using a dither matrix. <P>SOLUTION: When a dot is added to a dot profile in one concentration level, in matching with the next object concentration level so that a dot profile in the next concentration level can be generated by a second dot profile generating part 33, the position of the dot to be added to a dot profile is changed, and the change of an energy value to be derived from the dot profile is acquired, and the position of the dot to be added is decided as the position, where the energy value is made minimum. In this case, regarding each combination of two dots included in the dot profile, interaction energy to be decided from a relative position between the two dots is calculated, and the total sum of the interaction energy is used as the energy value. Thus, a proper dither matrix can be generated. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a technique for generating a dither matrix to be compared with an original image in halftoning a multi-tone original image, and a dither matrix.

  Conventionally, a multi-tone original image (also referred to as an input image) is halftoned (dithered) using a dither matrix. In this method using a dither matrix, whether or not to form a dot at the position of this pixel is determined by comparing the density level (pixel value) of each pixel of the original image with the corresponding element value of the dither matrix. As a result, a binary output image is generated, thereby realizing a dither process that is faster than a neighborhood algorithm such as an error diffusion method. In recent years, a technique has also been used that prevents the occurrence of a periodic pattern due to the regularity of the arrangement of element values in the output image by incorporating randomness into the arrangement of element values of the dither matrix. Furthermore, a dither matrix having a characteristic called blue noise (blue noise) can generate a high-quality output image equivalent to an output image generated by the error diffusion method, and output that causes a problem in the error diffusion method. There is no occurrence of a phenomenon in which dots in an image are linearly connected (so-called worm).

  As a technique for generating a dither matrix, for example, in Patent Document 1, when generating a binary dot profile indicating a dot arrangement at the next density level from a dot arrangement at one density level, a dot profile is generated. By determining the position of the dots added to the dot profile of one density level using annealing, the value of the cost function (energy function) based on the defined human visual characteristics is reduced. Discloses a method of generating a dither matrix by acquiring a plurality of dot profiles corresponding to respective density levels.

In Patent Document 2, an image obtained by applying a blue noise characteristic filter to a binary dot profile of one density level is generated, and a pixel having the maximum density level in a difference image between this image and the original dot profile. Proposes a method of generating a dither matrix by acquiring a dot profile for each density level by adding a dot at a position in the dot profile corresponding to and generating a dot profile for the next density level of the first density level. Has been. In Patent Document 3, in an image obtained by applying a low-pass filter to a dot profile of one density level, a dot is added at a position in the dot profile corresponding to a pixel having the lowest density level, and the next density is obtained. A method of generating a dither matrix by acquiring a dot profile of each density level by generating a level dot profile is disclosed.
JP-A-10-75376 JP-T 6-508007 US Pat. No. 5,535,020

  By the way, in the output image halftoned using the dither matrix generated by the method of Patent Document 1, the low-frequency component is simply cut in the spatial frequency characteristics, and the frequency is a characteristic of blue noise. Spectral peaks do not appear prominently. Further, since this method requires a long time to calculate the cost function, there is a problem that an optimized dot profile cannot be generated in a short time. Note that the methods of Patent Documents 2 and 3 may also require a reduction in the amount of calculation.

  The present invention has been made in view of the above problems, and has an object of generating an appropriate dither matrix and also generating a dither matrix in a short time.

  The invention according to claim 1 is a dither matrix generation method for generating a dither matrix to be compared with the original image in halftoning of a multi-tone original image, and in a two-dimensional region corresponding to the dither matrix, A step of acquiring a binary dot profile indicating the arrangement of dots at the first density level, and the number of dots added to the dot profile in accordance with the density level next to the density level. Determining a position of a dot to be added to the dot profile and obtaining a dot profile of the next density level; updating the one density level to the next density level; Returning to the step of obtaining the number of dots to be printed, the dot profile of the first density level, and each darkness level The combination of the positions of the added dots determined with respect to the dot profile of the level is used as a dither matrix, and the step of obtaining the dot profile of the next density level is changed by adding dots to the dot profile. A step of generating a subsequent dot profile and, for each combination of two dots included in the changed dot profile, an interaction energy determined by a relative position between the two dots is obtained, and an interaction energy is obtained. A dot profile after the change while changing a position of a dot added to the dot profile in the step of obtaining a dot profile of the next density level. And substantially determining the energy value Extent and is repeated, the position of the to be added dot is determined the energy value as a position for a minimum.

The invention according to claim 2 is the dither matrix generation method according to claim 1, wherein the size of the dot profile in the row direction and the column direction is set to Lx and Ly, respectively, and the two dot profiles in the changed dot profile are set. (X _m , y _m ), (x _n , y _n ), _where the coordinates of the positions defined in the row direction and the column direction of the dots are respectively, and the remainder of (x _n −x _m ) by Lx, and The interaction energy between the two dots is obtained using the remainder of (y _n -y _m ) by Ly as a parameter.

The invention according to claim 3 is the dither matrix generation method according to claim 1 or 2, wherein the interaction energy J (r) is expressed by assuming that the distance between the two dots is r.

It is calculated by.

  A fourth aspect of the present invention is the dither matrix generation method according to any one of the first to third aspects, wherein in the step of substantially obtaining the energy value, the energy value of the dot profile before the change and the change A difference from the energy value of the subsequent dot profile is obtained based on the change in the position of the added dot.

  A fifth aspect of the present invention is the dither matrix generation method according to any one of the first to fourth aspects, wherein the step of obtaining the dot profile of the next density level uses the annealing method to obtain the energy. The position of the added dot having a minimum value is determined.

  The invention according to claim 6 is a dither matrix generation method for generating a dither matrix to be compared with the original image in halftoning of a multi-tone original image, and in a two-dimensional region corresponding to the dither matrix, An initial dot profile generation step for generating a binary dot profile indicating the arrangement of dots at the first density level in the low density range, and a dot profile at each density level after the first density level in the low density range, A first dot profile generation step that is generated by sequentially adding dots at positions farthest from all dots in a two-dimensional region, and a dot profile that indicates the arrangement of dots at each density level in at least the medium density range. The second that is generated using a method different from the dot profile generation step And a Tsu door profile generation process.

  A seventh aspect of the present invention is the dither matrix generation method according to the sixth aspect, wherein in the initial dot profile generation step, a number of dots corresponding to the initial density level are arranged in the two-dimensional area. By increasing the uniformity of the distribution of the arranged dots by using Voronoi region division, the dot profile of the first density level is generated.

  The invention according to claim 8 is the dither matrix generation method according to claim 6 or 7, wherein, in the second dot profile generation step, a predetermined energy function that digitizes the dot arrangement state is used. The position of the dot added when the dot profile of the next density level is generated from the dot profile of the current density level is determined.

  The invention according to claim 9 is the dither matrix generation method according to claim 8, wherein the second dot profile generation step is performed in the dot profile of the one density level according to the next density level. Obtaining a number of dots to be added, determining a position of a dot to be added in the dot profile of the one density level, obtaining a dot profile of the next density level, and the one density Updating the level to the next density level and returning to the step of acquiring the number of added dots, and acquiring the dot profile of the next density level includes the step of acquiring the one density level. A step of generating a dot profile after the change by adding dots to the dot profile of the two, and two steps included in the dot profile after the change For each combination of dots, determining an interaction energy determined by a relative position between the two dots, and substantially determining a sum of the interaction energies as an energy value. In the step of acquiring the dot profile, the step of generating the changed dot profile and the step of substantially obtaining the energy value while changing the position of the dot added to the dot profile of the one density level, Is repeated, and the position of the added dot is determined as the position where the energy value is minimized.

  The invention according to claim 10 is generated by the dither matrix generation method according to any one of claims 1 to 9.

  In the inventions of claims 1 to 5 and claims 9 and 10, it is possible to generate an appropriate dither matrix using the interaction energy.

  In the invention of claim 3, a more appropriate dither matrix can be generated, and in the invention of claim 4, a dither matrix can be easily generated.

  According to the sixth to tenth aspects of the present invention, an appropriate dither matrix can be generated in a short time by adding dots at positions away from existing dots in the low density range.

  In the invention of claim 7, a dot profile of the first density level in the low density range can be generated while ensuring uniformity of dot distribution. In the invention of claim 8, the dot profile is predetermined in at least the middle density range. A dither matrix can be easily generated using the energy function of

  FIG. 1 is a diagram showing a functional configuration of a dither processing system 1 that performs halftoning of an original image using a dither matrix. The dither processing system 1 uses data of a multi-tone original image (also referred to as an input image, which is represented as a matrix I (X, Y) in FIG. 1) in which pixels are arranged in a row direction and a column direction. The original image memory 11 to be stored, the modulo arithmetic units 12a and 12b to which the coordinate X in the row direction and the coordinate Y in the column direction of each pixel from which the density level (pixel value) is read from the original image memory 11 are input, respectively, From the dither matrix memory 13 that stores the dither matrix generated by the matrix generation process, the comparison unit 14 that compares the density level from the original image memory 11 and the corresponding element value (threshold value) of the dither matrix, and the comparison unit 14 The output image memory 15 is stored.

  FIG. 2 is a diagram for explaining how the original image 70 is halftoned. As shown in FIG. 2, the original image 70 is set with a repeated area 71 that is divided into a number of areas of the same size and serves as a halftoning unit. The dither matrix 81 has a plurality of threshold values corresponding to a plurality of pixels included in one repeating area 71 (area shown by a thick line in FIG. 2) as element values. In this embodiment, the dither matrix The sizes in the row direction and the column direction of 81 are Lx and Ly (where Lx and Ly are integers), respectively.

  When halftoning the original image, conceptually, the dither matrix 81 is superimposed on each repeating area 71 of the original image 70 so as to be tiled, and the density level of each pixel in the repeating area 71 and the dither matrix 81 By comparing with the corresponding element value, the density level of the position (address) of the pixel in the binary output image 90 (represented as a matrix O (X, Y) in FIG. 1) is determined. The Therefore, if the density level of the pixels of the original image 70 is uniform, for example, the density level “1” is set to the pixel at the position where the element value smaller than the density level is set in the dither matrix 81. A density level “0” is assigned to the remaining pixels (that is, dots are not placed), and a binary output image 90 after halftoning is generated.

  The halftoning process will be described more specifically with reference to FIG. 1. When the density level of one pixel of the original image is read from the original image memory 11, the coordinates (X, Y) of the position of this pixel are read. The x coordinate in the corresponding repeat area is an integer greater than or equal to 0, smaller than B, by the modulo arithmetic unit 12a (X mod Lx) (where (A mod B) indicates the remainder when A is divided by B). .), And the y coordinate in the repetitive region is obtained by the modulo arithmetic unit 12b calculating (Y mod Ly). Then, one element value in the dither matrix 81 is specified and read from the dither matrix memory 13. The comparison unit 14 compares the density level from the original image memory 11 and the element value from the dither matrix memory 13. If the density level is greater than the element value, the density level at the pixel position is “1”. When the density level is equal to or lower than the element value, the density level at the position of the pixel is set to “0”, which is expressed by the presence or absence of dots (shown with parallel diagonal lines) as shown in FIG. A binary output image 90 is generated. Actually, the values of Lx and Ly are sufficiently larger than those shown in FIG.

  Next, processing for generating a dither matrix to be compared with the original image in halftoning of the multi-tone original image will be described. FIG. 4 is a diagram showing a configuration of the computer 2 that generates the dither matrix according to the first embodiment of the present invention. As shown in FIG. 4, the computer 2 has a general computer system configuration in which a CPU 21 that performs various arithmetic processes, a ROM 22 that stores basic programs, and a RAM 23 that stores various information are connected to a bus line. The bus line further includes a fixed disk 24 for storing information, a display 25 for displaying various information such as images, a keyboard 26a and a mouse 26b (hereinafter referred to as "input unit 26") for receiving input from an operator. ), A reading device 27 that reads information from a computer-readable recording medium 8 such as an optical disk, a magnetic disk, or a magneto-optical disk, and a communication unit 28 that transmits and receives signals to and from other devices as appropriate. The connection is made via (I / F).

  The computer 2 reads the program 80 from the recording medium 8 via the reader 27 in advance and stores it in the fixed disk 24. Then, the program 80 is copied to the RAM 23, and the CPU 21 executes arithmetic processing according to the program in the RAM 23 (that is, when the computer executes the program), whereby the computer 2 generates a dither matrix. As a role.

  FIG. 5 is a diagram showing a functional configuration realized by the CPU 21, ROM 22, RAM 23, fixed disk 24, and the like together with other configurations as a result of the CPU 21 operating according to the program 80. In FIG. The configuration (the Voronoi area dividing unit 31, the first dot profile generating unit 32, and the second dot profile generating unit 33) and the storage unit 34 are functions realized by the CPU 21 and the like. The function of the dither matrix generation unit 30 may be realized by a dedicated electric circuit, or an electric circuit may be partially used.

  FIG. 6 is a diagram for explaining the outline of the process for generating the dither matrix, and is a diagram showing the relationship between the dither matrix 81 and a binary dot profile indicating the dot arrangement at each density level. When the dither matrix 81 is generated, a dot profile corresponding to each of a plurality of density levels included in the density range of the original image and having the same size as the generated dither matrix is acquired. One dither matrix is generated. For example, when the density level of the original image is 0 to 3, as shown in FIG. 6, four dot profiles 811 to 814 respectively corresponding to these density levels are acquired.

  Here, when an image having a constant density level of the same size as the dither matrix 81 is halftoned using the dither matrix 81, a dot profile of that density level is obtained. The same position as is a value lower than the density level. In addition, the dot profile has a higher density level, and the number of dots (pixels indicated by parallel oblique lines in FIG. 6) increases. Between two dot profiles having different density levels, a dot profile with a lower density level is used. An existing dot has a feature that it always exists even in a dot profile having a high density level. Therefore, in the two-dimensional area corresponding to the dither matrix, one density level is located at the same position as the position where a dot is added (or deleted) between the dot profile of one density level and the dot profile of the next density level. A dither matrix 81 is generated by giving a value of (or the next density level) and repeating the above processing while updating one density level to the next density level. Hereinafter, a process of acquiring a plurality of dot profiles respectively corresponding to a plurality of density levels of the original image and generating a dither matrix will be described in detail.

  FIG. FIG. 7A is a diagram showing a flow of processing in which the computer 2 generates a dither matrix. B is shown in FIG. It is a figure for demonstrating the density range (or density level) relevant to each process in A. FIG. FIG. A and FIG. As shown in B, in the computer 2, a dot profile of density level 1 is acquired by the initial dot profile generation process (step S11), and each density in the low density range from density level 2 to g1 is acquired by the first dot profile generation process. A level dot profile is acquired (step S12), and a dot profile of each density level in the medium density range and the high density range (excluding the highest density level) higher than the density level g1 is obtained by the second dot profile generation process. Obtained (step S13).

  In this embodiment, since dot profiles are generated in order from the low density level to the high density level, dots are added to the dot profile of one density level to obtain a dot profile of a higher next density level. Is done. It is assumed that the density level of the original image is 256 levels from 0 to 255, and the number of dots included in the dot profile at the density level g is represented by the cumulative distribution function n (g). The cumulative distribution function n (g) is a monotonically increasing function (in a broad sense). Usually, (n (g + 1)> n (g)), and (n (0) = 0) and (n (255) = Lx × Ly) (As described above, the size of the dot profile in the row direction and the column direction is Lx and Ly, respectively, similarly to the dither matrix). As an example of the cumulative distribution function, a linear function in which the density level and the number of dots increase linearly can be considered, but other monotonically increasing functions can also be used. Hereinafter, FIG. Details of each processing of steps S11 to S13 in A will be described.

  FIG. 8 is a diagram showing the flow of initial dot profile generation processing. The process performed in step S11 of A is shown. In the initial dot profile generation process, Voronoi region division is used. Here, Voronoi region division means to divide a space in which a distance is defined into a plurality of cell regions each having a plurality of mother points scattered in the space as cores. Of the generating points, the generating point that is the nucleus of the cell region is the closest.

  In the Voronoi region dividing unit 31 in FIG. 5, first, a discrete two-dimensional region corresponding to a dither matrix (that is, a two-dimensional region in which the sizes in the row direction and the column direction are Lx and Ly, respectively. In the “matrix region”), positions (that is, integer value coordinates defined in the row direction and column direction) are randomly selected by the number of dots corresponding to the initial density level 1, and a plurality of selected A generating point is arranged at each of the positions and a different label is given (step S21). Here, the number of dots adjusted to density level 1 is obtained as a cumulative distribution function n (1).

  Subsequently, the nearest generating point is specified for each position in the matrix area (the position specified by the coordinates (x, y)), and the label of the specified generating point is set as an element value corresponding to this position. By obtaining the matrix V (x, y) to be obtained, a set of positions having the same label (that is, the nearest generating point is the same) is obtained as a cell region (that is, discrete Voronoi region division is performed). (Step S22). At this time, since the matrix region corresponds to the repeated region 71 shown in FIG. 2, a plurality of n (1) mother points are also treated as existing repeatedly in the vertical and horizontal directions. Therefore, when Voronoi region division is performed, the closest point to each position serving as a distance calculation reference is identified from among a plurality of generating points assuming that the matrix region is repeated.

  FIG. 9 is a diagram illustrating a matrix region in which Voronoi region division is performed. As shown in FIG. 9, Voronoi region division is performed based on the positions of a plurality of generating points 61, and a plurality of cell regions 62 (regions surrounded by bold lines in FIG. 9) are acquired in the matrix region. . When a plurality of cell regions 62 are acquired, a centroid 63 is obtained in each cell region 62, and a vector from the generating point 61 to the centroid 63 is obtained (step S23). At this stage, the position of the generating point 61 and the position of the center of gravity 63 of the cell region 62 are not normally coincident with each other, and the generating point 61 is biased in a certain direction within the cell region 62. The deviation of the generating point 61 is substantially obtained. Then, the vector from the generating point 61 to the center of gravity 63 is multiplied by C (constant multiplication), and the generating point 61 is moved according to the moving vector after C times to improve the bias of the generating point 61 in the cell region 62 (step). S24).

  In the Voronoi region dividing unit 31, the process of steps S22 to S24 for calculating the bias of the generating point in the cell region and improving the bias is repeatedly performed (step S25). When the position of the generating point converges and the size of the vector from the generating point to the center of gravity of the cell region becomes substantially 0), the position value of each generating point is set to “1” and a dot is added (step) S26). As a result, a dot profile P (x, y; 1) of density level 1 in which n (1) dots are approximately uniformly distributed in the matrix region is acquired. The constant C used in step S24 is a parameter for accelerating the convergence of the generating point position, and is preset by the operator via the input unit 26 in FIG. Empirically, when the constant C is 2, the convergence of the position of the generating point is faster than when the constant C is 1, and the distribution of generating points is also preferable.

  As described above, the Voronoi region dividing unit 31 arranges dots in the matrix region in the number corresponding to the first density level in the low density range, and improves the uniformity of dot distribution by using the Voronoi region division. The dot profile of the first density level in the low density range is generated appropriately and easily while ensuring the uniformity of the dot distribution.

  Next, the first dot profile generation unit 32 in FIG. 5 acquires a dot profile for each of a plurality of density levels g (where 2 ≦ g ≦ g1) included in the low density range. FIG. 10 is a diagram showing a flow of first dot profile generation processing performed by the first dot profile generation unit 32. FIG. The process performed in step S12 of A is shown.

  In the first dot profile generation unit 32, first, the dot profile P (x, y; g-1) of the density level (g-1) is copied to the matrix area, and the dot profile Q (x, y) is generated. (Step S31). Here, the dot profile P (x, y; g−1) is a density level before the density level g (hereinafter referred to as “target density level g”) of the obtained dot profile, and the first dot profile. In the initial processing in the generation unit 32, the dot profile P (x, y; 1) of density level 1 generated by the above-described processing is usually used. Then, the difference dn (dn = n (g) −n () between the dot number n (g) in the dot profile at the target density level g and the dot number n (g−1) in the dot profile at the density level (g−1). The number of added dots is obtained by obtaining g-1)) (step S32). A predetermined parameter K is initialized to 0 (step S33).

Subsequently, in the dot profile Q (x, y), the distance between each position and the nearest dot is calculated in consideration of the repeated area, and the shortest distance having the calculated distance as an element value corresponding to this position. The matrix W (x, y) is obtained (steps S34 and S35), and the coordinates (x _a , y _a ) of the position where the distance is maximum are obtained (step S36). When there are a plurality of positions having the same distance from the nearest generating point, one position is selected at random. Then, the value of the position of the coordinates (x _a , y _a ) in the dot profile Q (x, y) is set to “1”, and a dot is added (step S37). At this time, the position where the distance is maximum is the same as the position of the vertex of any polygon indicating the boundary of the cell region generated by the above Voronoi region division, and at this position, all the adjacent dots are The distance between them becomes equal. Therefore, by adding a new dot at such a position, the uniformity of the dot distribution is maintained approximately. Thereafter, 1 is added to the parameter K (step S38). The matrix V (x, y) indicating the discrete Voronoi region division is held at the same time as the shortest distance matrix W (x, y), a new label is given to the dot added in step S37, and the vicinity of the added dot is given. If the matrix V (x, y) indicating the discrete Voronoi region division and the shortest distance matrix W (x, y) are corrected for the coordinates in the minimum necessary range, step S35 can be speeded up. Further, since there are many coordinate candidates selected by scanning the shortest distance matrix W (x, y) in step S36, coordinate candidates are listed by a single scan of W (x, y). If this is done, there is no need to scan every time, which leads to higher speed.

  Steps S34 to S38 are repeated while updating the value of K, and dots are sequentially added at positions farthest from all the dots in the matrix area. When the updated K value becomes the difference dn in the number of dots between the target density level g and the density level (g−1) (that is, when dn dots are added) (step S34), the dot profile Q ( x, y) is a dot profile P (x, y; g) (step S39), and a dot profile of a target density level g including n (g) dots is generated.

  In the first dot profile generation unit 32, the density level is set so that the dot profile P (x, y; g) of the density level g is the next copy target to the matrix area until the density level g of the generated dot profile becomes g1. Steps S31 to S39 are repeated while updating (Steps S40 and S41). Thereby, each dot profile of a plurality of density levels included in the low density range (2 ≦ g ≦ g1) is generated. Actually, in the repeated processing of steps S35 to S38 for each density level g in the low density range, the combination of the positions of the dots added in step S37 is the position to which the value (g-1) is given in the dither matrix. Is done.

  As described above, in the computer 2, the binary dot profile indicating the dot arrangement at each density level after the first density level in the low density range sequentially places the dots at positions farthest from the existing dots in the matrix area. A dot profile of each density level in the medium density range and the high density range is generated by using a method described later that is different from the first dot profile generation unit 32. As a result, a highly uniform dot profile can be generated without performing complex calculations in the low density range, and an appropriate dither matrix can be generated easily and in a short time. In the above-described processing by the first dot profile generation unit 32, when the number of dots approaches half of (Lx × Ly), the technical significance of obtaining the position farthest from the existing dots is lost by connecting the dots. The first dot profile generation process is preferably used within a density level g in which the number of dots n (g) is less than half of (Lx × Ly) and the dots are not connected to each other.

  Next, for each of the plurality of density levels g included in the medium density range (g1 <g ≦ g2) and the high density range (g2 <g ≦ 254), the second dot profile generation unit 33 in FIG. A method for generating a dot profile using a predetermined energy function for quantifying the dot arrangement state will be described.

First, an energy function used in the second dot profile generation unit 33 will be described. In the present embodiment, the binary image is made to correspond to a two-dimensional spin model used in the field of statistical physics, and the spin is a physical variable that takes a value of 1 or 0. Energy value E, the spin matrix representing the binary image of the same size as the dither matrix in the matrix area S (x, y), respectively the coordinates of the position of the two spins included in the spin matrix (x _m, y _{m 2} ), (x _n , y _n ), and a function indicating the interaction energy determined by the relative positions of the two spins is represented by Equation 2 as J.

In Equation 2, the interaction energy is obtained for each combination of two spins included in the spin matrix S (x, y), and the sum of values obtained by multiplying the product of the two spin values and the interaction energy is the energy value. Is done. Here, the interaction energy between the two spins is obtained in consideration of a) the repetition region of the spin matrix S (x, y), and the magnitude of the interaction energy depends only on the relative position between the two spins. And b) the magnitude of the interaction energy is symmetric with respect to both spins, and c) the condition that the interaction energy does not occur in the combination of the same spins is satisfied. Condition a) is that the interaction energy J between the two spins is obtained by using ((x _n −x _m ) mod Lx) and ((y _n −y _m ) mod Ly) in Equation 2. means. Further, the condition b) is the interaction energy J obtained by (−a mod Lx) and (−b mod Ly), and the interaction energy obtained by (a mod Lx) and (b mod Ly). The condition c) means that the interaction energy J is 0 when the values of the two parameters are both 0. In the second dot profile generation unit 33, the spin matrix S (x, y) is obtained by minimizing the energy value E obtained by Equation 2, and a dot profile is generated (a so-called optimization algorithm is used). .)

In the present embodiment, the interaction energy J takes a large value when two spins considering a repetitive region are close to each other. Specifically, the interaction energy J (r) can be obtained by Equation 3 where r is the shortest distance between two spins in consideration of the repetitive region. However, in Formula 3, w ₁ , w ₂ , σ ₁ , and σ ₂ are constants of real numbers of 0 or more, except that σ ₁ > σ ₂ and w ₁ > w _2, and the distance r is 0.

Equation 3 is a combination of two functions each representing two two-dimensional normal distributions having different dispersion parameters. The interaction energy J obtained by Equation 3 has a distance r between two spins of zero. The interaction energy J can be approximated to 0 when the value is large in the vicinity and the distance r is sufficiently larger than σ ₁ and σ ₂ . In addition, when the Fourier transform is applied to Equation 3, since the value of the first term on the right side is large in the low frequency component, it functions as a penalty for the low frequency component in the energy value E, and the second term on the right side is a value in the high frequency component. Therefore, w ₁ and w ₂ give weights of the first term and the second term, respectively. Hereinafter, the process in the 2nd dot profile production | generation part 33 using a spin model and interaction energy is explained in full detail.

  11 and 12 are diagrams illustrating the flow of the second dot profile generation process performed by the second dot profile generation unit 33. FIG. The process performed in step S13 of A is shown. Also in the second dot profile generation process, dot profiles are generated in order from the low density level to the high density level in the medium density and high density ranges.

  In the spin matrix changing unit 331 of the second dot profile generating unit 33, first, the dot profile P (x, y; g-1) of one density level (g-1) is copied to the spin matrix S (x, y). (Step S51). Here, the dot profile P (x, y; g−1) is a density level before the density level g (target density level g) of the obtained dot profile, and the first dot profile generation unit 33 performs the first. In the processing, normally, the dot profile P (x, y; g1) of the density level g1 acquired last by the processing of FIG. 10 is used.

Subsequently, in the spin matrix S (x, y), a set H of spin coordinates having a value of 0 (that is, a set of positions where dots can be added in the dot profile P (x, y; g−1)). (H = {(x _j , y _j ); S (x _j , y _j ) = 0})) is obtained (step S52). Further, the difference dn (dn = n (g) −n () between the number of dots n (g) in the dot profile of the target density level g and the number of dots n (g−1) in the dot profile of the density level (g−1). g-1)) is obtained, and the number of dots added to the dot profile P (x, y; g-1) in accordance with the target density level g is obtained (step S53).

  The spin matrix changing unit 331 randomly selects dn coordinates from the coordinate set H, and sets the selected coordinate set as U and the remaining coordinate set as D (step S54). Then, in the spin matrix S (x, y), the spin values of all coordinates (x, y) included in the coordinate set U are set to 1 (step S55). Note that the coordinates included in the coordinate set U and the coordinate set D (that is, the coordinate set H) indicate the position of a spin to be operated in the following processing (hereinafter referred to as “target spin”). The set U indicates a set of coordinates of the target spins whose value is 1, and the coordinate set D indicates a set of coordinates of the target spins whose value remains 0.

In the energy value calculation unit 332, predetermined parameters (that is, w ₁ , w ₂ , σ ₁ , σ ₂ ) corresponding to the target concentration level g are set to an expression for obtaining the interaction energy J shown in Equation 3 (step S56). At this time, the parameters set in Equation 3 are, for example, when the target concentration level g is included in the medium concentration range (g1 <g ≦ g2) and when included in the high concentration range (g2 <g ≦ 254). These parameters are preliminarily input via the input unit 26 by the operator. If the parameter corresponding to the target density level g has already been set, the process of step S56 is skipped.

  Here, the second dot profile generation unit 33 uses an annealing method to obtain a spin matrix S (x, y) having a small energy value E. The annealing method is a technique for simulating a statistical physical model in which energy is defined and finding a state in which the energy is reduced by gradually shifting the equilibrium state from a high temperature to a low temperature. In the spin matrix changing unit 331, first, a temperature parameter T (where T> 0) used in the annealing method is set to an initial value T0 (step S57).

Subsequently, one coordinate (x ₁ , y ₁ ) ((x ₁ , y ₁ ) εD)) is randomly selected from the coordinate set D, and one coordinate (x ₂ , y ₂ ) is also selected from the coordinate set U. ((X ₂ , y ₂ ) ∈U) is selected at random, and in the spin matrix S, the value 0 of the target spin at the coordinates (x ₁ , y ₁ ) and the value ₁ of the target spin at the coordinates (x ₂ , y ₂ ) Are exchanged (step S58). Then, the energy value calculation unit 332 obtains the change amount dE of the energy value E of the spin matrix S before and after exchanging the values (step S59).

Here, in Equation 2, the change amount dE ₁ of the energy value E when only the spin value of a certain coordinate (x _b , y _b ) is inverted is the change amount ((+1) or (-1).) As dS.

Therefore, in step S59, the amount of change in the energy value E when only the value of the target spin at the coordinates (x ₁ , y ₁ ) is inverted using the equation 4 and the target spin at the coordinates (x ₁ , y ₁ ). And the change amount of the energy value E when the value of the target spin at the coordinates (x ₂ , y ₂ ) is inverted, and the sum of these values is taken as the change amount dE of the energy value. The Thus, in the energy value calculation unit 332, the energy value of the spin matrix S (x, y) before the value exchange and the energy value of the spin matrix S (x, y) after the value exchange are performed. Is obtained based on a change in the position of the target spin with a value of 1. Thereby, it is possible to significantly reduce the amount of calculation compared to calculating the formula 2 before and after changing the position to obtain the difference in energy value. As described above, when the distance r is sufficiently larger than σ ₁ and σ ₂ in Equation 3, the interaction energy J can be approximated to 0. The calculation of Equation 4 is performed only for the neighboring spins, and the change amount dE of the energy value E can be easily obtained.

Here, when the shortest distance r in Equation 3 is acquired, the distance in the row direction is, for example, used when the result of ((x ₂ −x ₁ ) mod Lx) is Lx / 2 or less. In addition, when it is larger than Lx / 2, it can be obtained based on the difference between the result of the remainder calculation and Lx, and the same applies to the distance in the column direction. That is, since the shortest distance r can be obtained from the results of ((x ₂ −x ₁ ) mod Lx) and ((y ₂ −y ₁ ) mod Ly), the interaction energy J obtained by Equation 3 With regard to (r), it can be said that substantially the remainder of (x ₂ −x ₁ ) by Lx and the remainder of (y ₂ −y ₁ ) by Ly are parameters. It should be noted that the interaction energy J is the row direction and the column direction of the interaction energy J, which is a corresponding element, based on the calculation results of ((x ₂ −x ₁ ) mod Lx) and ((y ₂ −y ₁ ) mod Ly). May be prepared in advance as a matrix in which the positions of are specified. In this case, the interaction energy matrix has Lx and Ly in the row direction and the column direction, respectively.

Subsequently, the spin matrix changing unit 331 obtains the pseudo uniform random number p (where 0 ≦ p <1) (step S60), and the pseudo uniform random number p is min {1, exp (−dE / T)} ( However, if min {A, B} is smaller than A and B.), the exchange in step S58 is permitted (step S61), and the coordinates (x ₁ , y ₁ ) are set to the coordinate set D. To the coordinate set U, and the coordinates (x ₂ , y ₂ ) move from the coordinate set U to the coordinate set D (step S62). On the other hand, when the pseudo uniform random number p is equal to or greater than min {1, exp (−dE / T)} (step S61), the exchange of the target spin value in step S58 is restored (step S63). As described above, when the amount of change dE of the energy value is larger than 0, the exchange is permitted probabilistically, and when the amount of change dE is 0 or less, the exchange is always permitted.

  Then, after confirming whether or not the temperature parameter T is to be reduced (step S64), the temperature parameter T is reduced by a factor of β (where 0 <β <1) (step S65). The processes of steps S58 to S65 are repeated using the temperature parameter T (step S66). At this time, in step S61, even when the energy value increases, the exchange is stochastically permitted to suppress the energy value from staying at the local optimum solution. The process of step S65 is performed every predetermined number of repetitions.

  Here, the temperature parameter T is for determining how much the exchange in which the energy value increases is permitted. If the temperature parameter T is approximately 0, all exchanges in which the energy value change amount dE is greater than 0 are rejected, and only exchanges in which the energy value does not increase are permitted. On the other hand, when T is infinite, all exchanges in which the change amount dE is greater than 0 are permitted, which is the same as changing the state of the spin matrix S at random. Therefore, by reducing T by β times in step S65, a wide search is performed while the number of iterations is small, so that the spin matrix S reaches the vicinity of an appropriate solution, and as the number of iterations increases. By narrowing the search range, a solution (spin matrix S) with a minimum energy value can be obtained. Note that the temperature parameter T may be increased as necessary, such as when an inappropriate local optimum solution is encountered, and the processing of steps S64 and S65 can be omitted as a constant value.

  In the second dot profile generation unit 33, for example, when the amount of change dE in the energy value is not more than the threshold value is continuously repeated a predetermined number of times, and when there is almost no significant change in the energy value, steps S58 to S65 are performed. The repetition of the process is completed (step S66), and a spin matrix S (x, y) with a minimum energy value is acquired. At this time, in the second dot profile generation unit 33, the energy value E by the calculation shown in Equation 2 is not actually obtained for the spin matrix S (x, y), but in step S59, the spin before and after the value exchange is performed. Since the change of the change amount dE is monitored while the change amount dE of the energy value E in the matrix S is obtained, the above process substantially determines the energy value E of the spin matrix S before and after the value exchange. This is equivalent to specifying the spin matrix S (x, y) that minimizes the energy value E. It should be noted that by repeating the process in step S65 a predetermined number of times, the repetition of the processes in steps S58 to S65 may be terminated (the same applies hereinafter) (step S66). In this case as well, the energy value is approximately minimal. A spin matrix S (x, y) is obtained.

  When the repetition of the processing of steps S58 to S65 is completed, the spin matrix S (x, y) is acquired as the dot profile P (x, y; g) of the target density level g (step S67). At this time, in the dot profile P (x, y; g), a combination of dot positions added from the dot profile P (x, y; g-1) of the density level (g-1) is a value ( g-1) is assigned.

  In the second dot profile generation unit 33, steps S51 to S67 are performed while updating the density level with the acquired dot profile P (x, y; g) as the next copy target to the spin matrix S (x, y). Repeated (steps S68 and S69). Then, when the density level g of the acquired dot profile reaches the density level 254, the second dot profile generation process ends (step S68). Thus, the dither matrix 81 is generated while the dot profile is obtained for each density level in the medium density range and the high density range.

  The generated dither matrix 81 is stored in the storage unit 34 and further copied from the storage unit 34 to the dither matrix memory 13 of FIG. The dither processing system 1 can acquire a high-quality output image having a frequency spectrum peak that is characteristic of blue noise by halftoning the original image using the dither matrix 81.

  As described above, in the computer 2, the value of the target spin is changed to 1 by the number corresponding to the next density level from the spin matrix S (x, y) corresponding to the dot profile of one density level. Then, for each combination of two spins included in the spin matrix S (x, y), the product of the interaction energy that increases in the vicinity where the distance between the two spins becomes zero and the value of the two spins is obtained. Substituting the value of the target spin whose value is changed to 1 with another target spin whose value is 0 so that the energy value, which is the sum of these values, is reduced. A dot profile of each density level in the medium density range and high density range is acquired (spin model energy minimization method). Thereby, it is possible to acquire a dot profile in which dots are uniformly distributed using interaction energy in the medium density range and the high density range, and to generate an appropriate dither matrix.

Further, by obtaining the interaction energy shown in Equation 3 using predetermined parameters (w ₁ , w ₂ , σ ₁ , σ ₂ ), the frequency characteristics are controlled by penalizing the low frequency component and the high frequency component. Thus, it is possible to generate a more appropriate dither matrix having blue noise characteristics while suppressing the generation of a large lump of dots or a so-called checkerboard pattern in the generated output image. Further, the difference in energy values of the spin matrix S (x, y) before and after the exchange of values is obtained based on the change of the position of the target spin with the value of 1 using Equation 4, so that before and after the exchange In this case, the amount of calculation can be reduced compared to calculating the energy value by calculating Equation 2, and a dither matrix can be easily generated.

  In the above description, the dot profiles are generated in order from the low density level to the high density level, but the dot profiles may be generated in order from the high density level to the low density level. In this case, in each of the initial dot profile generation process, the first dot profile generation process, and the second dot profile generation process, the dot is deleted from the dot profile of a certain density level (that is, the value of the pixel having the dot profile is changed from 1). 0)), a dot profile of the next density level is generated. However, a pixel with a value of 0 is regarded as a dot, and a dot with a value of 0 is added to a dot profile of a certain density level. Therefore, a dot profile of the next density level is generated by the same processing as described above (the density level of the dot having a value of 0 is higher). It is convenient to consider a pixel having a value of 1 as a dot or a pixel having a value of 0 as a dot.

  For example, in the second dot profile generation process of FIGS. 11 and 12, the dot profile P (x, y; g + 1) of one density level (g + 1) is copied to the spin matrix S (x, y) (step S51). In the spin matrix S (x, y), a set H of spin coordinates having a value of 1 (that is, a set of coordinates to which a dot having a value of 0 can be added in the dot profile P (x, y; g + 1)). Is obtained (step S52). Further, a difference dn between the number of dots n (g + 1) in the dot profile at the density level (g + 1) and the number of dots n (g) in the dot profile at the target density level g is obtained, and the dot profile P is matched to the target density level g. The number of dots to be deleted from (x, y; g + 1) (that is, the number of dots with an added value of 0) is acquired (step S53).

  The spin matrix changing unit 331 selects dn coordinates from the coordinate set H, and sets the selected coordinate set as D and the remaining coordinate set as U (step S54). In the spin matrix S (x, y), the values of all coordinates (x, y) included in the coordinate set D are set to 0 (step S55), and the energy value calculation unit 332 corresponds to the target concentration level g. The parameter is set to Equation 3 (step S56), and the temperature parameter T is set to the initial value T0 (step S57).

Subsequently, one coordinate (x ₁ , y ₁ ) is randomly selected from the coordinate set U, one coordinate (x ₂ , y ₂ ) is also randomly selected from the coordinate set D, and the coordinate ( The value 1 of the target spin of x ₁ , y ₁ ) and the value of the target spin 0 of the coordinates (x ₂ , y ₂ ) are exchanged (step S58). Then, an energy value change amount dE in the spin matrix S before and after exchanging values is obtained in the energy value calculation unit 332 (step S59).

When the change amount dE is obtained, a pseudo-uniform random number p is obtained (step S60). Permitted (step S61), the coordinates (x ₁ , y ₁ ) move from the coordinate set U to the coordinate set D, and the coordinates (x ₁ , y ₁ ) move from the coordinate set D to the coordinate set U (step) S62). On the other hand, when the pseudo uniform random number p is equal to or greater than min {1, exp (−dE / Y)} (step S61), the exchange in step S59 is returned (step S63). When the temperature parameter T is decreased (step S64), the temperature parameter T is decreased by β (step S65), and the processes of steps S58 to S65 are repeated using the changed temperature parameter T (step S65). Step S66).

  When there is almost no significant change in the energy value, the processing of steps S58 to S65 is repeated (step S66), and the spin matrix S (x, y) with the minimum energy value is acquired, and the spin matrix S (x , Y) is acquired as the dot profile P (x, y; g) of the target density level g (step S67). At this time, in the dot profile P (x, y; g), the combination of the positions of the dots deleted from the dot profile P (x, y; g + 1) at the density level (g + 1) is given the value g in the dither matrix. It is assumed to be a position. Then, steps S51 to S67 are repeated while updating the density level with the acquired dot profile P (x, y; g) as the next copy target to the spin matrix S (x, y) (steps S68 and S69). ). Thereby, it is realized that the dot profiles are generated in order from the high density level to the low density level.

  The process for generating the dot profiles for each density level in the medium density range and the high density range using the spin model has been described above. In the above process, the process for the spin matrix S (x, y) is the dot profile. May be performed directly.

  Specifically, a binary dot profile indicating the arrangement of dots at the first density level in the matrix area is acquired (here, it corresponds to the process of step S12 in FIG. A profile has been acquired), and a position where a dot can be added is obtained (step S52). Subsequently, the number of dots added to the dot profile in accordance with the next target density level of the first density level is acquired (step S53), and dots are added to the dot profile to generate a changed dot profile. (Steps S54 and S55). Further, a parameter corresponding to the target density level is set in Equation 3 (step S56), and the temperature parameter T is set to the initial value T0 (step S57).

  The position is changed by randomly selecting one of the added dots (step S58), and the difference between the energy value of the dot profile before the change and the energy value of the dot profile after the change is obtained ( Step S59). Here, the energy value is the sum of interaction energies for each combination of two dots included in the changed dot profile, and the interaction energy is determined by the relative position between the two dots and 2 The value is increased when two dots are close to each other. Actually, the difference between the energy values before and after the change of position is obtained based on the change of the dot position added by the equation (4), but a dot profile in which the energy value takes an appropriate minimum value is obtained by this method. In view of this, it can be said that the process of step S59 is substantially equivalent to acquiring the energy value.

  Subsequently, it is determined whether or not the change of the position of the dot added by obtaining the pseudo-uniform random number p is permitted (steps S60 to S61). Is left as it is (step S62), and if not permitted, the dot whose position has been changed is returned to the original position (step S63). Then, the temperature parameter T is appropriately reduced (steps S64 and S65).

  The above steps S58 to S65 are repeated until there is almost no significant change in the energy value (step S66). That is, while changing the position of the dot added to the dot profile while appropriately reducing the temperature parameter T, generation of the dot profile after the change and substantial acquisition of the energy value are repeated, and an annealing method is used. The position of the added dot is determined as the position where the energy value is minimized. In this manner, the position of the dot added when generating the dot profile of the target density level from the dot profile of the one density level using the energy function is determined, and the dot profile of the target density level is acquired.

  When the dot profile of the target density level is acquired, the process returns to step S52 while updating the density level (steps S68 and S69), and the dot profile of the next density level is acquired. Thereby, a dot profile indicating the arrangement of dots at each density level in the medium density range and the high density range is generated, and an appropriate dither matrix is generated.

  Next, dither matrix generation processing according to the second embodiment of the present invention will be described. FIG. 13 is a diagram for explaining the outline of the dither matrix generation processing in the second embodiment. In the present embodiment, the dot profile of each density level included in the entire density range (excluding the lowest density level and the highest density level) is shown in FIG. It is generated by the second dot profile generation process of step S12 in A. Actually, density levels 1 to 254 out of 256 levels from 0 to 255 are roughly divided into a plurality of density ranges (density levels) indicated by arrows A1 to A5 in FIG. The second dot profile generation process is performed in the order from the density range A1 to the density range A5 while changing the acquisition order of parameters and dot profiles for each density range A1 to A5. Hereinafter, processing for each of the concentration ranges A1 to A5 will be described with reference to FIGS. In the present embodiment, it is assumed that the cumulative distribution function n (g) is a linear function such that (n (0) = 0) and (n (255) = Lx × Ly).

First, when generating a dot profile of density level A1 (for example, density level 128), a dot profile in which no dots are arranged in the matrix area (for example, a dot profile with a density level of 0) is prepared, and all Is a position where dots can be added (step S52). Subsequently, the number n (A1) of dots added to the dot profile in which no dots are arranged in accordance with the density level A1 is acquired (step S53), and n (A1) dots are randomly added to the dot profile. A dot profile after being added and changed is generated (steps S54 and S55). Also, parameters corresponding to the density level A1 (for example, w ₁ is 1.0, w ₂ is 0.4, σ ₁ is 1.0, and σ ₂ is 0.75) are set in Equation 3. (Step S56), the temperature parameter T is set to the initial value T0 (Step S57).

  Then, one of the added dots is randomly selected to change the position (step S58), and the difference between the energy value of the dot profile before the change and the energy value of the dot profile after the change is expressed by the following equation (4). It is obtained by performing the above calculation (step S59). In addition, it is determined whether or not the change of the position of the selected dot is permitted by obtaining the pseudo uniform random number p (steps S60 to S61). If not allowed, the dot whose position has been changed is returned to the original position (steps S62 and S63). Then, the temperature parameter T is appropriately reduced (steps S64 and S65).

  The above steps S58 to S65 are repeated until there is almost no significant change in the energy value (step S66), and the dot profile with the minimum energy value is acquired as the dot profile of the density level A1.

  When the dot profile of the density level A1 is generated, next, the dot profile of each density level included in the density range A2 (for example, the density levels 129 to 222) is generated. When generating a dot profile of each density level included in the density range A2, dot profiles are generated in order from the low density level to the high density level in the density range A2.

First, a position where a dot can be added is obtained in the dot profile of the density level A1 acquired by the processing for the density level A1 (step S52). Subsequently, the number of dots added to the dot profile in accordance with the next target density level (for example, density level 129) of the density level A1 is acquired (step S53), and the dots are added to the dot profile and changed. A dot profile is generated (steps S54 and S55). Further, a parameter corresponding to the density range A2 is set in Equation 3 (for example, the parameters are set such that w ₁ is 1.0, w ₂ is 0.4, σ ₁ is 1.0, and σ ₂ is 0.75. If it has already been set, this process is skipped.) (Step S56) The temperature parameter T is set to the initial value T0 (Step S57).

  In the same manner as described above, steps S58 to S65 are repeated until there is almost no significant change in the energy value (step S66), and a dot profile having a minimum energy value is acquired as a dot profile of the target density level. When the dot profile of the target density level is acquired, the process returns to step S52 while updating the density level (steps S68 and S69), and the dot profile of the next density level is acquired. Thereby, a dot profile indicating the arrangement of dots at each density level in the density range A2 is generated. At this time, in the density ranges A1 and A2 included in the middle density range (density levels 33 to 222) and the density range A4 described later, the same parameter is used to penalize the low frequency component and the high frequency component, and the characteristics of blue noise A dot profile having a peak of the frequency spectrum to be generated is generated.

When the dot profile for each density level in the density range A2 is generated, next, the dot profile for each density level included in the density range A3 (for example, the density levels 223 to 254) is generated. When generating a dot profile for each density level included in the density range A3, dot profiles are generated in order from the low density level to the high density level in the density range A3, as in the case of the density range A2. The However, in the case of the density range A3, the parameters set in Equation 3 are, for example, that w ₁ is 1.0, w ₂ is 0, and σ ₁ is (α / sqrt (255-g)) (where sqrt (255-g) represents the square root of (255-g), g is the target density level, and α is 10.0.) In this case, only the first term on the right side of Equation 3 is used. In the density range A3, which is a high density range, a dot profile in which empty dots having a value of 0 are uniformly distributed over the entire surface due to the influence of the normal distribution type interaction energy that increases as the distance between the two dots decreases. Is generated.

  When the dot profiles of the respective density levels included in the density ranges A2 and A3 higher than the density level A1 are generated in this way, the density range A4 lower than the density level A1 (for example, density levels 33 to 127) is then generated. A dot profile of each density level included in is generated. When generating a dot profile for each density level included in the density range A4, dot profiles are generated in order from the high density level to the low density level in the density range A4.

First, a position where a dot can be deleted (that is, a position where a dot having a value of 0 can be added) is obtained in the dot profile of the density level A1 acquired by the processing for the density level A1 (step S52). Subsequently, the number of dots to be deleted from the dot profile is acquired in accordance with the next target density level after the density level A1 (here, the lower density level, for example, the density level 127) (step S53). Dots are deleted from the profile to generate a changed dot profile (steps S54 and S55). Also, parameters corresponding to the density range A4 (for example, w ₁ is 1.0, w ₂ is 0.4, σ ₁ is 1.0, and σ ₂ is 0.75) are set in Equation 3 (step S56). The temperature parameter T is set to the initial value T0 (step S57).

  In the same manner as described above, steps S58 to S65 are repeated until there is almost no significant change in the energy value (step S66), and a dot profile having a minimum energy value is acquired as a dot profile of the target density level. When the dot profile of the target density level is acquired, the process returns to step S52 while updating the density level (steps S68 and S69), and the dot profile of the next density level (lower density level) is acquired. Thereby, a dot profile indicating the arrangement of dots at each density level in the density range A4 is generated.

Once the dot profiles for each density level in the density range A4 are generated, the dot profiles for each density level included in the density range A5 (for example, density levels 1 to 32) are then generated. When generating a dot profile for each density level included in the density range A5, a dot profile is generated in order from the high density level to the low density level in the density range A5, as in the case of the density range A4. The However, in the case of the density range A5, the parameters set in Equation 3 are, for example, that w ₁ is 1.0, w ₂ is 0, and σ ₁ is (α / sqrt (g)) (where sqrt (g ) Represents the square root of g, g is the target concentration level, and α is 10.0.) In this case, only the first term on the right side of Equation 3 is used, and the concentration is in the low concentration range. In the range A5, similarly to the density range A4, a dot profile in which the dots are uniformly distributed over the whole is generated due to the influence of the normal distribution type interaction energy that increases as the distance between the two dots is shorter.

  As described above, in the dither matrix generation processing according to the second embodiment, a dot profile having the first density level is acquired and prepared, and then all density levels except the first density level are prepared. The dot profiles are sequentially acquired using the interaction energy so that the dots are uniformly distributed. Then, the combination of the dot profile of the first density level and the position of the dot to be added (or deleted) determined for the dot profile of each density level is used as a dither matrix. In the dither matrix generation process according to the embodiment, an appropriate dither matrix can be generated. Further, by obtaining the interaction energy by Equation 3 while switching the parameters in the low density range, medium density range and high density range, the dots are uniformly distributed in the low density range and high density range, and in the medium density range A dither matrix capable of generating an output image having a frequency spectrum peak characteristic of blue noise can be obtained.

  Note that the dot profile at the density level A1 may be generated by deleting dots from a dot profile in which dots are arranged at all positions in the matrix area (for example, a dot profile at the density level 255). Further, the parameter set in Equation 3 and the roughly classified concentration range in the present embodiment are examples that are empirically preferable, and may be other values.

  Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and various modifications can be made.

  In the first embodiment, a dot profile of each density level included in the low density range (for example, a dot profile having a density at which dots are not connected to each other) is generated by the first dot profile generation process, and the medium density The dot profile of each density level in the range and the high density range may be generated by the second dot profile generation process by a method different from that described above.

  As another second dot profile generation process, for example, the method described in Patent Document 1 can be used. Specifically, when generating a dot profile of the target density level included in the medium density range and the high density range, the position of the dot added from the immediately preceding dot profile is compared with the human vision with respect to the dot profile. By determining using the annealing method so that the value of the cost function (energy function) defined based on the characteristics becomes small, dot profiles of each density level in the medium density range and the high density range are sequentially generated. Thus, as in the first embodiment, in the low density range, a dot profile with high uniformity can be obtained in a short time by adding dots at positions away from existing dots by the first dot profile generation process. In the medium density range and high density range, this is added when the dot profile of the next density level is generated from the dot profile of the one density level using a predetermined energy function that digitizes the dot arrangement state. The position of the dots to be determined is determined, and an appropriate dither matrix can be easily generated.

  Further, as another second dot profile generation process, the technique of the above-described Patent Document 2 may be used. In this process, a dot profile of one density level is added to the next target density level of one density level. An image with a blue noise characteristic filter applied according to is generated, and the position where the density level is maximum in the difference image (error image) between this image and the original dot profile, which is the value in the original dot profile By adding a dot at a position of 0 (corresponding to bringing the original dot profile closer to the error image), dot profiles of respective density levels included in the medium density range and the high density range are sequentially generated. Further, in the medium density range and the high density range, the above-described technique of Patent Document 3 may be used. In this technique, an image obtained by applying a low-pass filter to a dot profile of one density level (blurred image). In the original dot profile, a dot is added at a position where the density level is minimum in the original dot profile (corresponding to adding a dot at the most sparse part), so that a medium density range is obtained. A dot profile of the target density level included in the high density range is generated.

  Here, since the influence on the output image due to the difference in the dot profile generation method in the high density range is generally smaller than that in the low density range and the middle density range, each density in the low density range and the middle density range. The quality of the level dot profile is important in the generation of the dither matrix. From such a viewpoint, in order to generate an appropriate dither matrix in a short time, a dot profile of each density level in the low density range is generated by the first dot profile generation processing, and at least a dot profile of each density level in the middle density range Is generated using a method different from the first dot profile generation process.

  In the above embodiment, the interaction energy can be various as long as it is determined by the relative position between two dots. For example, an output image printed by a printing device having a different number of dots per unit distance in the row direction and the column direction, or a display device having a different number of pixels per unit distance in the row direction and the column direction. In the generation of the dither matrix used for generating the output image, the distance r between the two dots is given in Equation 3 as the distance on the actually printed or displayed image (or a value proportional to this distance). As a result, an appropriate dither matrix suitable for the printing apparatus or display apparatus can be generated. Further, the interaction energy may exhibit different characteristics in the row direction and the column direction and in directions inclined in these directions.

It is a figure which shows the function structure of a dither processing system. It is a figure for demonstrating a mode that the original image is halftoned. It is a figure which shows the output image produced | generated by halftoning of the original image. It is a figure which shows the structure of a computer. It is a figure which shows the function structure which a computer implement | achieves. It is a figure for demonstrating the outline | summary of the process which produces | generates a dither matrix. It is a figure which shows the flow of the process which produces | generates a dither matrix. It is a figure for demonstrating the density range relevant to each process of a dither matrix production | generation process. It is a figure which shows the flow of an initial dot profile production | generation process. It is a figure which shows the matrix area | region where Voronoi area | region division was performed. It is a figure which shows the flow of a 1st dot profile production | generation process. It is a figure which shows the flow of a 2nd dot profile production | generation process. It is a figure which shows the flow of a 2nd dot profile production | generation process. It is a figure for demonstrating the outline | summary of the dither matrix production | generation process in 2nd Embodiment.

Explanation of symbols

70 Original image 81 Dither matrix 811 to 814 Dot profile S11 to S13, S53 to S55, S58, S59, S66, S68, S69 Step

Claims (10)

A dither matrix generation method for generating a dither matrix to be compared with the original image in halftoning a multi-tone original image,
Obtaining a binary dot profile indicating a dot arrangement at the first density level in a two-dimensional area corresponding to the dither matrix;
Obtaining the number of dots added to the dot profile in accordance with the next density level of the one density level;
Determining a position of a dot to be added in the dot profile, and obtaining a dot profile of the next density level;
Updating the one density level to the next density level and returning to the step of acquiring the number of added dots; and
With
A combination of the dot profile of the first density level and the position of the added dot determined for the dot profile of each density level is a dither matrix,
Obtaining a dot profile of the next density level;
Adding a dot to the dot profile to generate a changed dot profile;
For each combination of two dots included in the changed dot profile, an interaction energy determined by a relative position between the two dots is obtained, and a total sum of the interaction energies is substantially obtained as an energy value. Process,
With
In the step of acquiring the dot profile of the next density level, the step of generating the dot profile after the change while changing the position of the dot added to the dot profile, and the step of substantially determining the energy value Is repeated, and the position of the added dot is determined as the position where the energy value is minimized. The dither matrix generation method according to claim 1,
The sizes of the dot profile in the row direction and the column direction are Lx and Ly, respectively, and the coordinates of the positions defined in the row direction and the column direction of the two dots in the changed dot profile are (x _m , y _m ), (x _n , y _n )
Dither matrix generation characterized in that the interaction energy between the two dots is obtained using the remainder of (x _n -x _m ) by Lx and the remainder of (y _n -y _m ) by Ly as parameters. Method. The dither matrix generation method according to claim 1 or 2,
When the distance between the two dots is r, the interaction energy J (r) is

A dither matrix generation method characterized by being obtained by: A dither matrix generation method according to any one of claims 1 to 3,
In the step of substantially obtaining the energy value, a difference between the energy value of the dot profile before the change and the energy value of the dot profile after the change is obtained based on the change in the position of the added dot. A dither matrix generation method. The dither matrix generation method according to any one of claims 1 to 4,
The method for generating a dither matrix, wherein the step of acquiring a dot profile of the next density level determines the position of the added dot that minimizes the energy value by using an annealing method. A dither matrix generation method for generating a dither matrix to be compared with the original image in halftoning a multi-tone original image,
An initial dot profile generating step for generating a binary dot profile indicating a dot arrangement at the first density level in the low density range in a two-dimensional area corresponding to the dither matrix;
A first dot profile generation step of generating dot profiles at respective density levels after the first density level in the low density range by sequentially adding dots at positions farthest from all dots in the two-dimensional region; ,
A second dot profile generation step for generating a dot profile indicating a dot arrangement at each density level in at least the medium density range using a technique different from the first dot profile generation step;
A dither matrix generation method comprising: The dither matrix generation method according to claim 6,
In the initial dot profile generation step, as many dots as the number corresponding to the first density level are arranged in the two-dimensional area, and the uniformity of the distribution of the arranged dots is enhanced by using Voronoi area division, A dither matrix generation method, wherein a dot profile having an initial density level is generated. The dither matrix generation method according to claim 6 or 7,
In the second dot profile generation step, the position of a dot added when generating a dot profile of the next density level from a dot profile of the one density level using a predetermined energy function that digitizes the dot arrangement state A dither matrix generation method characterized in that is determined. The dither matrix generation method according to claim 8,
The second dot profile generation step includes
Obtaining the number of dots added to the dot profile of the one density level in accordance with the next density level;
Determining a position of a dot to be added to the dot profile of the one density level, and obtaining a dot profile of the next density level;
Updating the one density level to the next density level and returning to the step of acquiring the number of added dots; and
With
Obtaining a dot profile of the next density level;
Adding a dot to the dot profile of the one density level to generate a changed dot profile;
For each combination of two dots included in the changed dot profile, an interaction energy determined by a relative position between the two dots is obtained, and a total sum of the interaction energies is substantially obtained as an energy value. Process,
With
In the step of obtaining the dot profile of the next density level, the step of generating the changed dot profile and the energy value are substantially changed while changing the position of the dot added to the dot profile of the one density level. The dither matrix generating method is characterized in that the step of obtaining the added dot is repeated and the position of the added dot is determined as a position where the energy value is minimized.   A dither matrix generated by the dither matrix generation method according to claim 1.

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