JP2640939B2 - How to combine data into an image - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for synthesizing data into an image for mixing or separating other data such as a document into an image signal.

(Prior art) In recent years, the use of OA (office automation) equipment has become increasingly networked through interconnections as technology advances, and the information handled tends to diversify to include document data as well as various image data. It is in.

Usually, since the signal processing forms of the document data and the image data are different, the two are generally transmitted and stored separately, which makes it inconvenient to handle images and other data having a dense relationship with each other. Had occurred.

Furthermore, in transmitting information between networked OA devices, confidential means to prevent leakage to third parties is indispensable.

In view of such circumstances, it has been conventionally proposed to mix other information such as document data into an image signal. According to this, both can be handled collectively and this is extremely convenient. It is possible to confidentially transmit more important information as if transmitting an image, and it can be used as a kind of encryption communication means.

Conventional methods for combining image signals with other data include:
For example, there is "Image Deep Encryption Using Arithmetic Codes" (1986 Cryptography and Information Security Symposium) by Suzuki and Arimoto.

This means that the image data is arranged on a one-dimensional coordinate axis of 0, 1, 2,..., (N-1), and m pieces of data (1 ≦ m ≦ n) corresponding one-to-one to the data to be mixed are selected from these. ) Are extracted, and the exclusive OR of the image data located at the coordinates and the data to be mixed is obtained, and the result is recorded in each of the coordinates, and then the coordinate elements 0, 1, 2,. , (N-1) are transmitted as image signals.

However, since the above-mentioned method changes depending on other data to which the required pixel of the image data is to be directly mixed, the data mixed into the relevant portion on the reproduction screen appears as it is and it is immediately apparent whether or not the data is mixed. However, there is a disadvantage that the image quality is significantly impaired.

To compensate for this, the above document proposes a method of concentrating other data by concentrating on the boundary where the black and white on the image change, but even if such a method is used, noise is mixed on the screen This is no different, and image quality degradation is inevitable. In order to reduce this, the amount of data to be mixed is greatly reduced, or at the same time, data must be mixed only into the edge portion of the screen.

(Object of the Invention) The present invention has been made in order to eliminate the drawbacks of such a conventional method of synthesizing data into an image, and the mixed data and its existence do not appear on a reproduction screen. Therefore, it is an object of the present invention to provide a method of synthesizing an image into which an extremely large amount of data can be mixed without deteriorating the image quality.

(Summary of the Invention) In order to achieve this object, the present invention focuses on the degree of freedom of a dither matrix configuration method in a dither method used when expressing the density of an original image in a plurality of gradations. By selecting a dither matrix corresponding to each pixel on the basis of data to be mixed within the range, the desired data is mixed into the image signal without impairing the pseudo gradation characteristic of the dither image.

(Embodiment) Hereinafter, the present invention will be described in detail based on the illustrated embodiment. Before that, however, in order to facilitate understanding of the present invention, the dither method, particularly the degree of freedom in setting the dither matrix at that time, will be described. A brief description will be given.

In the dither method, for example, when a grayscale image is output to a binary hard copy device such as a facsimile, a printer, or a plasma display, the grayscale processing is performed in a pseudo manner so that the human eyes can recognize the grayscale image as an intermediate grayscale by the integration effect. This is one of the methods, which does not fix the threshold value for judging the density of the signal read from the original image, but changes the value according to a predetermined rule to correspond to the local average value of the original image density. This is to generate the number of dots.

In this case, a method in which the threshold value is determined based on a random function or a pseudo-random function is called a random dither method. In addition, the entire original image including a matrix of pixel arrays is further divided into sub-matrices, and A method in which a predetermined dither pattern is made to correspond to a threshold value of each pixel is called an organized dither method. The latter is superior to the former in terms of resolution, gradation reproducibility, noise amount, and the like.

Fig. 2 (a) shows the systematic dither method more specifically.
As shown in FIG. 5, among the pixels on the original image 1, the n × n small area Fn is associated with the n × n threshold matrix Dn, and the corresponding numerical values are compared. Is white and all the rest are black to generate a dither image 3.

If each pixel is minute, the dither image represented in this way is recognized as an intermediate density according to the ratio of black and white to human eyes, and the matrix element n ² +1 gradation can be expressed.

In this case, if the resolution of the display device is relatively high,
As shown in FIG. 2 (b), for each pixel of the original image 1, n ×
If the dither image (G'n) 3 'of minute pixels is generated by associating the n matrix Dn, an image signal more similar to the original image can be obtained.

The density gradation expression by the dither method can be applied not only to a black and white image but also to a color image. For a color, the density expression may be performed for each of the three primary colors as described above.

Furthermore, in the dither method, the means for encoding an image is “0”.
It is applied to not only the binary digital signal of "1" but also the multi-level digital signal, and research is progressing to obtain an image close to the original image with a minimum amount of information.

In general, the number of pseudo gradations Leq that can be expressed by an L-value dither matrix of size n × n is Leq = (L−1) n ² +1 (1), and in the case of binary dither with L = 2, Leq = n ² −1.

In general, the size of n is determined in consideration of the resolution and visual characteristics of the display device to be used. In this case, if the size of n is selected so that the resolution of the display device is high and the visual integration effect can be used, The gradation is determined only by the ratio of black and white in each matrix of the generated dither image, and is independent of the arrangement order. That is, there is a predetermined degree of freedom in selecting a dither image when representing the same gradation.

The present invention focuses on the degree of freedom in selecting a dither matrix when creating a dither image, and selects one of dither matrices that represent the same gradation based on data to be mixed, thereby enabling the image signal to be selected. Combine the data.

For simplicity, the case of the binary dither method will be described first.

FIG. 1 is a block diagram for explaining one method of realizing a method for synthesizing data into an image according to the present invention.

In the figure, reference numeral 4 denotes an original image, a section of which is taken out, a density is read out by a quantization block 5, and then, in a gradation comparison block 6, for example, a numerical value representing the gradation order j is derived. Is output to the matrix selection block 7.

Further, an encoding block 9 including a dictionary 8 storing data of characters, symbols, codes, etc. which may be used in advance.
Equipped. When data such as characters to be mixed is input, the encoding block 9 generates a code representing the data in the dictionary corresponding to the data, for example, a numerical sequence Ki encoded according to JIS code or ASCII code. This is input to the matrix selection block 7.

In the matrix selection block 7, all or required dither matrices representing each density gradation are provided.
A predetermined dither matrix is selected from the density gradation number j input to the section and a number Ki representing a character to be mixed, and a dither image 10 of each section of the original image is generated.

If the dither image 10 is created based on the dither matrix generated by repeatedly and repeatedly executing each pixel and the mixed character data, other data such as a document can be mixed therein.

If the input original image signal has already been quantized and can be adapted to the number of gradations of the gradation comparison block 7, the quantization block 5 becomes unnecessary and the gradation comparison block 6 Just enter it. Various methods are conceivable for determining the required matrix in the matrix selection block 7, one example of which is shown in FIG.

FIG. 3 is a diagram showing an example of a matrix selection method when n = 2 for the sake of simplicity. In each column, a numeral representing character data registered in the dictionary 8 is shown, and in each row, a density level is shown. This is an array of matrices that can represent each gradation by allocating the number of key ranks j.

In this case, the gradation number j indicates, for example, the number of “1” s arranged in the matrix, and the horizontal arrangement order is appropriately arranged corresponding to the character data.

Now, if the density of the pixel extracted from the original image is 3,
Assuming that the number of gradations is j = 3, there are four ways of arranging three “1” s in a 2 × 2 matrix, as shown in the fourth row of FIG. Represents the gradation, but the number corresponding to the character data to be mixed is 2
, The matrix of the column located at 2 on the horizontal axis, ie, 4
The matrix of row 3 is output as the dither matrix of the pixel.

When decoding an image in which data has been mixed in this way, a numeral 2 representing predetermined character data is obtained from the number of "1" in the dither matrix and its arrangement with reference to the same matrix as in FIG. Is derived, and desired character data is obtained according to the same coding.

The above method is extended and the amount of data that can be mixed is examined as follows.

That is, the above-described method represents character data and the like to be mixed with other information sources, for example, numbers 0, 1, 2,... Ki, and weaves this Ki into the dither image. In a bit string represented by a binary number.

In this case, the information source may take any form. For example, a dictionary in which characters, symbols, or signs that may be used correspond to predetermined numbers is used, and the characters to be mixed are converted into numbers. It is output as the numerical string Ki.

As this dictionary, a dictionary using JIS code or ASCII code which is generally used can be cited, but a special encryption table can be prepared and used as this code table in order to enhance confidentiality.

In the case where the data converted to the numerical sequence Ki is made to correspond to the dither matrix, the density of each pixel of the original image sequentially changes, so that the number of “1” to be arranged, that is, j changes. Therefore, since the number of combinations at that time also changes, the variable length bit number corresponding to the density is extracted from the series Ki and incorporated.

Hereinafter, the amount of information that can be mixed in this case will be examined.

Now, take out the b bits from the series Ki, is n ² Cj as n ×
In b bits represent the integer from 0 to 2 ^b when selecting one from among the arrangement of the n matrix, be determined b so that this value does not exceed n ² Cj, Ki for a certain n and j , The number of bits b to be extracted from the data can be uniquely determined.

bj for n and j is bj = [log ₂ (n ² Cj)] (bits) (2) where [X] indicates an integer not exceeding X.

Therefore, for example, if n = 4, It can be seen that an average of 145/17 = 8.53 bits can be mixed in one matrix.

In general, if the number of pixels of density level j included in one image is W (j), the total number of bits B that can be mixed in this image is It is.

For example, assuming an image having an image size of 64 × 64 pixels and all the density values after quantization are composed of the same number of pixels (64 × 64/17 = 240.9), B = 240.9 × 17 × 8.53 = 34.939 ( Bit) …… (5), and if the character is represented by 8 bits, the total is 4,367
And a very large number of characters.

Compared to the previous method proposed by Suzuki and Arimoto, the number of characters mixed into an image is at most about 655 on a screen consisting of 256 × 256 (= 65,536) pixels. You can see how much information is available.

Further, in a general natural image, the density level is rarely uniform over all gradations, and tends to concentrate on the central gradation portion. Therefore, in practice, the B becomes larger, and a larger amount of characters are mixed. be able to.

The method shown in FIG. 3 is a specific means of the method described above. If a table is prepared in advance as described above, a relatively high-speed encoding process can be performed. Therefore, there is a disadvantage that if n becomes large, a large-capacity memory must be provided. Furthermore,
In decoding, the data series to be decoded must be compared with the pixel values of all the matrices, and if n becomes large, much time is required.

Therefore, a method of sequentially determining a desired matrix by calculation and decoding data mixed from the matrix will be described below, without using the table.

First, in order to simplify the explanation, a dither matrix n × n
, (N = 0, 1, 2,..., (N ² -1)) is an array in which the pixels are one-dimensionally rearranged in the order of scanning in the output cell.

At this time, the quantized value j of each of the n ² pixels on the cell is
Assuming that the number is a binary number weighted by the number of combinations of elements arranged on the matrix, the number of combinations n ² Cj in which j are selected and arranged from the n × n matrix can be rewritten as the following equation.

n ² Cj = n ² _-1 Cj _-1 + n ² _-1 Cj (6) Now, the meaning of this expression is expressed by the fact that the first term on the right side is S (0) =
1, that is, the total number of arrays in which the first element of the n × n matrix is “1”, and the second term is S (0) = 0, that is, the total number of arrays in which the first element is also “0”. And the whole is interpreted as the sum of these two, and each matrix array having S (0) = 1 is converted to an integer of 0, 1, 2, ..., n ² _-1 Cj _-1 -1. S
Those having (0) = 0 are represented by n ² _-1 Cj _-1 , n ² _-1 Cj _-1 +1 ...
.., N ² Cj−1, and a rule is set so as to correspond to each integer. When bj bits are extracted from the data sequence Ki to be mixed, the value d is compared with n ² ₋₁ Cj _−1. Is determined.

As a result, if S (0) = 1, 1 is subtracted from j and (j ₋₁ ) 1s are added to matrix elements {S} other than S (0).
(1), S (2),..., S (n ² -1)}, the same operation is performed, that is, d is compared with n ² _-2 Cj _-1 and (7)
Find the result shown in the equation.

Conversely, if S (0) = 0, the value of d is reduced by n ² _-1 Cj _-1 to arrange "1" in a matrix element other than S (0), and d and n ² _-2 Cj Compare _-1 .

If this operation is repeated until j = 0, the positions of the j 1 pixels are all determined, so 0 is set for the remaining S (i). According to the above procedure, the pixel arrangement S (i) uniquely corresponding to the given j and d can be obtained.

 This method will be further described using specific numerical examples.

FIG. 4 is a diagram showing a matrix determination method when n = 4, j = 3, and d = 15.

Each element S (i) of the 4 × 4 matrix is arranged as shown in FIG. First, three 1's are located at 16 pixel positions.
There are a total of ₁₆ C ₃ = 560 ways of arranging. this is,
₁₅ C ₂ = 105 cases with S (0) = 1 and S (0) = 0
_It is divided into ₁₅ C ₃ = 455 types (FIG. 7A). For the former, an integer of d = 0, 1, 2,..., 104 (= ₁₅ C ₂ -1), and for the latter, an integer of d = 105, 106,..., 559 (= ₁₆ C ₃ -1) Assign. Further, d and ₁₅ C ₂ are compared according to equation (7), and d = 15 < ₁₅
S (0) = 1 from C ₂ = 105. Since one pixel position with the value “1” has been determined, the same operation is repeated with j = 2.

That is, d and ₁₄ C ₁ are compared, and d = 15 ≧ ₁₄ C ₁ = 14 and S (1)
= 0 and d = 1 (FIG. 9B). Similarly, d = 1 < ₁₃ C ₁
= 13 to S (2) = 1 (FIG. 9 (c)). Where ₁₃ C ₁ =
₁₂ but C is ₀ + ₁₂ C _{1, 12} C ₀ Hatada 1 kinds, namely S
(4) = S (5) =... = S (15) = 0 (FIG. 4D). d = 1 ≧ ₁₂ C ₀ = 1 to d = 0 and S
(3) = 0. Similarly than _{12 C 1 = 11 C 0 +} 11 C 1, d = 0
The output pixel array corresponding to ₁₁ C ₀ is shown in FIG.
(E)).

With the above operation, all pixel arrays are obtained. The above procedure is summarized as follows.

(1) Encoding procedure The array for storing the result is represented by S (i) (i = 0, 1,..., 15).
And

Assign xCy to array COMB (x, y) (x, y = 0,1, ..., 16) Initial value setting x ← 15: x is a subscript of COMB y ← j: j is the number of 1 to be arranged i ← 0: i is a subscript of S (i) From the text data array [log ₂ ｛COMB (16, j) ｝] Set bit extraction d as IF y = 0 THEN S (i) ← 0 GO TO IF d <COMB (x, y-1) THEN S (i) ← 1 y ← y-1 ELSE S (i) ← 0 d ← d-COMB (x, y-1) x ← x-1 i ← i + 1 IF i ≦ 15 THEN GO TO ELSE end (2) Decoding procedure The binary array to be decoded is represented by S (i) (i = 0 , 1, ……, 1
5)

Assign xCy to array COMB (x, y) (x, y = 0,1, ..., 16) Initial value setting x ← 16: x is a COMB subscript y ← j: j is 1 in S (i) I ← 0: i is the subscript of S (i). The decoded data is stored in d ← 0: d. IF y = 0 THEN GO TO IF S (i) = 0 THEN d ← d + COMB (x, y-1 ELSE y ← y-1 x ← x-1 i ← i + 1 IF i ≦ 15 The lower [log ₂ {COMB (16, j)}] bit of THEN GO TO d is the decoding result. According to the generation method, the processing time can be greatly reduced, and since a memory for storing a matrix is not required, a device to be used can be simplified, and the trouble of creating a table can be omitted.

FIG. 5 is a block diagram showing an embodiment in which the present invention is applied to encryption communication means.

In FIG. 1, reference numeral 11 denotes an original image signal. A pixel signal extracted therefrom and a signal obtained by encrypting data 12 to be mixed with a scrambler 14 using an encryption key 13 are used in an encoding circuit 15. Dithered image synthesized by the method described above
16 is generated and transmitted to desired users 17,17. Upon receiving this, the user separates the original image signal 19 and the encrypted signal by the decryption circuit 18 based on a predetermined rule, and further deciphers the encrypted signal by the descrambler 20 using the predetermined encryption key 21. The data 22 is extracted.

Since each block in this system, for example, the scrambler 14, the descrambler 20, or the encryption method can be easily realized by using the existing technology, the detailed description is omitted.

When various experiments were performed based on the method described above, extremely good results were obtained.

For example, images of the standard image database SIDBA (256 x 25
(6 pixels x 8 bits), and when implemented with a binary image of n = 4, the density gradation becomes 17, so the original image is uniformly quantized to 17 levels, converted to ASCII code, and converted to 75,205 characters. As a result of the synthesis, there was almost no difference from the reproduced image using the conventional fixed pattern.

Experiments have also confirmed that image data generated by the method of the present invention can be restored to an image by a conventional fixed pattern or other methods by changing the pixel arrangement.

This will prove that the method of synthesizing data to an image according to the present invention does not change the image information itself, and therefore the original image information is preserved in perfect form.

Also, when mixing data into an image according to the present invention,
When a long input of bit 0 occurs as a data string, the value of d at this time becomes 0, so that black pixels are always concentrated at the front of the array regardless of the original image density. It is sufficient to add an operation such as inverting and inputting one bit at a time immediately before combining, and this has also been confirmed by experiments.

This method can be widely used not only in the case described above, but also when there is a possibility that a data string having a certain regularity may have an undesired effect on a reproduced image.

In the above description, the case of mainly using the binary dither method has been exemplified. However, the present invention is also applicable to the multi-value dither method, and the following description will briefly describe the density pattern in the image processing using the multi-value dither method. A method of mixing other data will be described.

Now, assuming that the output device is capable of displaying an L-level halftone, the number of pseudo tones that can be represented by one cell at this time
Leq is Leq = (L−1) × n ² +1 as shown in the equation (1).
However, as in the case of the binary dither method, Leq depends only on L and n, and has no relation to the pixel arrangement in the cell.

Therefore, if the one corresponding to the data to be mixed is selected from the multi-valued dither matrix representing the same gradation, other data can be mixed into the image as in the case of the binary dither method. In addition, since the degree of freedom in selecting a matrix is greater than that of the binary dither method, the amount of data that can be mixed dramatically increases.

That is, when the total number of pixel array combinations that can represent the density value j in one cell when the number of pseudo gradations j (j = 0, 1, 2,... Leq-1) is C (j), From data series to bj
The number of bits when extracting bits and selecting one from C (j) ways is bj = [log ₂ (C (j))] (bits)
(8) When the number of pixels of density level j included in one image is represented by W (j), the total number of bits B that can be combined in this image is It is represented by

For example, the output device can display ternary values of 0, 1, and 2.
Assuming that the cell size is n = 2, the number of pseudo gradations Leq that can be expressed at this time is 9 levels from Equation (1), and the density levels j that can be pseudo expressed are 0, 1, 2,. Become.

Each of these density levels is represented by a combination of each pixel shown in Table 1 below.
(J).

Table 1 Combinations of j pixel C (j) bj 0 (0,0,0,0 ) 4 C 0 = 1 0 1 (1,0,0,0) 4 C 1 = 4 2 2 (1,1, _{0,0) (2,0,0,0) 4 C 2} + 4 C 1 = 10 3 3 (1,1,1,0) (2,1,0,0) 4 C 3 + 4 C 1 · _{3 C 1 = 16 4 4 (} 1,1,1,1) (2,1,1,0) (2,2,0,0) 4 C 4 + 4 C 1 · 3 C 2 + 4 C 2 = 19 4 5 (2,1,1,1) (2,2,1,0 ) 4 C 1 + 4 C 2 · 2 C 1 = 16 4 6 (2,2,1,1) (2,2, _{2,0) 4 C 2 + 4 C} 3 = 10 3 7 (2,2,2,1) 4 C 3 = 4 2 8 (2,2,2,2) 4 C 4 = 1 0 each value of j Are assumed to be equal, C in the above Table-1
The average value b of the number of bits bj that can be extracted from (j) is Becomes

Similarly, for L = 2,3,4, n = 2,3,4, the information amount of data that can be synthesized is obtained for each cell and for each bit after encoding. Shown in

As is clear from this table and the above description, if the present invention is applied to the multi-value dither method, more data can be synthesized in the image.

In order to select the location required matrix, any of a method based on a table prepared in advance and a method based on calculation similar to the binary dither may be used.

The procedure for determining a matrix by calculation is L = 3, n =
This will be briefly described as 2.

Pixels of interest in the original image are represented by Leq = 9 levels (0,1,2, ...
…, 8). As a result, it is assumed that the density level is 3.

The number of bits b ₃ to be taken out from the text data in Table -1
To 4 bits. It is assumed that d = 12 as a result of taking out 4 bits and converting it into an integer representation.

First, suppose that only pixels of density level 1 are displayed, and d
With ₄ C ₁ . ₄ C ₁ = 4 <12 indicates that the combination is not (1,1,1,0). These four types are d = 0,1,2,
This is a combination corresponding to 3.

Since it is determined that it is not the first four of the twelve combinations, the remaining combinations may be searched for 12-8 = eighth. Compared to the number of the following (2,1,0,0) combinations, ₄ C ₁ × ₃ C
This combination can be determined from ₁ = 12> 8.

Next, find the eighth of these 12 ways. It is considered that there are ₃ C ₁ = 3 patterns that determine the position of the pixel with the density value 1 for each of the ₄ C ₁ = 4 patterns that determine the position of the pixel with the density value 2. Then _{8/3 C 1 = 8/} 3 = 2 remainder 2 is because the position of the pixel density values 2 the third from the left, the density value 1
Can be determined as the third position from the left of the remaining three positions, that is, (0, 2, 0, 1).

The decoding process is based on the pixel arrangement of (0,2,0,1).
, Which can be easily realized as an inverse calculation of the above procedure.

As described above, various methods of using the means for transmitting or storing other data in an image in a concealed manner are conceivable. For example, a system for synthesizing personal information of a person with personal photograph data of the person and managing the data collectively is proposed. If constructed, only a person having a matching encryption key that is recognized as a facial photograph and can be known to a third party can know the confidential data, and a system that ensures the confidentiality can be obtained.

Also, irrespective of the presence or absence of the encryption means, if the present invention is applied to facsimile or other image signal transmission which is used daily, data relating to the image can be transmitted together with the image, so that the transmission processing can be unified. I can do it. Further, it is obvious that the data to be mixed is not limited to simple characters, but may be any signal such as an audio signal or an image signal.

In the above-described embodiment, the case of a binary image has been described for simplicity of description. However, the present invention is not limited to this and can be applied to a multi-valued image or a color image and the like. Obviously, various modifications may be made to the configuration of the device and system at that time.

(Effects of the Invention) As described above, the present invention mixes desired data in the dither image processing process as a means for expressing the gray scale of an image. This is very effective in providing a means for synthesizing an extremely large amount of data in an image without being difficult and deteriorating the image quality.

Further, according to the present invention, the image signal and other data can be handled by the same means, so that the information medium can be greatly simplified. It is also effective in concealing and storing important data for transmission and storage, and when combined with other encryption means, can be an encryption method that is more resistant to attacks.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, and FIG. 2 is a diagram for explaining a general dither method. FIG. 1 (a) shows a case where an original image and a dither matrix correspond one-to-one, and FIG. ) Is a diagram corresponding to one-to-four, FIG. 3 is a matrix diagram showing an example of a dither matrix determining method according to the present invention, and FIG. 4 is an example of a dither matrix determining method by calculation according to the present invention. FIG. 5 and FIG. 5 are block diagrams showing procedures when the present invention is applied to cryptographic communication. 1 ... original picture, 2 ... threshold matrix, 3 ... dither image, 5 ... quantization block, 6 ... density gradation comparison block, 7
…… Matrix selection block, 9 …… Encoding block, 10
...... Dither matrix.

Claims (5)

(57) [Claims] When quantizing a density pattern of density information of an original image using a dither method to represent a pseudo gradation, an arrangement of each element in a dither matrix is determined based on data to be mixed. A method for synthesizing data to the featured image. 2. A data synthesizing method according to claim 1, wherein other data to be mixed is specified by a combination of the number of specific values arranged in said dither matrix and the arrangement thereof. Method. 3. A table in which the number and arrangement of specific values in a dither matrix and their required numbers are associated with each other on a one-to-one basis is stored in advance, and each density information of an original image is represented based on the table. Desired data is mixed into the image signal by selecting a dither matrix that corresponds to the numeral corresponding to the other data to be mixed. 4. The data synthesizing method for an image according to claim 2, wherein other mixed data is specified based on the table. 4. The arrangement order of each element of an n × n matrix is i
(I = 0, 1, 2,..., N ² -1), the values stored in these elements are S (i), and when S (i) takes each value of the L-value dither, Element density information In the method of selecting one dither matrix corresponding to each of the values from the dither matrix representing an integer to an integer d that can be represented by bj bits, when each element of the n × n matrix is determined, the remaining matrices are selected. Are arranged in the form of a tree sequentially, and a numerical value up to the integer d is assigned to each of the terminal node matrices of the tree. 3. The method according to claim 1, further comprising tracing to a terminal node corresponding to the numerical value and determining a desired matrix based on the route. 5. In the case where the dither method is binary (L = 2), when d <n ² ₋₁ Cj ₋₁ , S (0) = 1 and d ≧ n ² ₋₁ Cj ₋₁ . At this time, S (0) = 0 is set, and if S (0) = 1, 1 is subtracted from j to compare a new j with n ² ₋₂ Cj ₋₁ and S (0) = If it is 0, the value of d is reduced by n ² _-1 Cj _{-1 to} obtain a new d, and this and n ² _-2
The desired matrix was determined by comparing Cj- ₁ and repeating the process until j = 0 until the value of S (i) was determined to be "0" or "1" according to the magnitude relational expression until j = 0. 5. The method for synthesizing data to an image according to claim 4, wherein: