JP2008136242A - Method for reversibly transforming data format, image processing apparatus, program for reversibly transforming data format, and storage medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To attain completely restorable invertible transform in mutually direct-and inverse-transforming data between unit systems different in resolution levels, particularly, different in color spaces. <P>SOLUTION: In a method for inversibly transforming a data format, a forward transformation and a backward transformation are reciprocally conducted for data between unit systems having different resolution levels, and in the forward transformation and the backward transformation, a first unit system having a lower resolution level is used as a common unit system and an inversible data conversion is conducted by an integer operation for data in the first unit system having the lower resolution level and data in a second unit system having a higher resolution level than the first unit system. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a data format reversible conversion method, an image processing apparatus, a data format reversible conversion program, and the like, which handle image data conversion processing, particularly color space conversion processing in a reversible / irreversible compression / decompression system using a color space. The present invention relates to a storage medium.

  A color space is a region in a three-dimensional or higher dimensional vector space. A color coordinate system is defined by some basis, for example, three primary independent three-dimensional vectors. A commonly used color coordinate system is defined by R (red), G (green) and B (blue) defined by their center wavelengths. When a certain three-dimensional color coordinate system is given, other three-dimensional linear color coordinate systems can be represented by a reversible (regular) 3 × 3 matrix.

  By the way, various color coordinate systems (color spaces) are defined for various reasons. For example, when displaying data on a monitor, most digital color images use an R, G, B coordinate system, for example, a fixed range of, for example, 8 bits / coordinate. For applications that require color decorrelation, such as compression, R, G, B are far from optimal and other color coordinates such as Y, I, Q are more appropriate. Other color coordinates include YUV and YCrCb. All of these opposite color coordinate systems seek to improve the separation of luminance and chrominance, ie the separation of the appearance of chrominance changes at the same luminance as the change in characteristics or color appearance in the associated brightness.

  For images for printing, a subtractive color mixing system such as CMY (cyan, magenta, yellow) is sometimes used. Depending on the application, a super-complete four-dimensional color such as CMYK (cyan, magenta, yellow, black) is used. Space is used.

  By the way, data compression is a very useful means for storing and transmitting a large amount of data. For example, the time required for image transmission such as facsimile transmission of a document is significantly shortened by using compression to reduce the number of bits necessary for reproducing the image.

  Conventionally, many different data compression methods exist. The compression methods can be roughly classified into two categories, namely lossy encoding and lossless encoding. Lossy coding is coding in which loss of information occurs and thus complete reproduction of the original data is not guaranteed. The goal of lossy compression is to keep the change from becoming uncomfortable or noticeable even if it changes from the original data. In lossless compression, all information is stored and the data is compressed in a fully recoverable manner.

  In lossless compression, input symbols or luminance data are converted into output codewords. Examples of input include image data, audio data, one-dimensional data (for example, data that changes over time), two-dimensional data (for example, data that changes in two spatial axis directions), or multidimensional / multispectral data. is there. If compression is successful, the codeword is represented with a smaller number of bits than the number of input symbols (or luminance data). The lossless encoding method includes a dictionary encoding method (for example, Lempel-Ziv method), a run length encoding method, an arithmetic encoding method, and an entropy encoding method. In the case of lossless image compression, the basis of compression is prediction or context and coding. The JBIG standard for facsimile compression and DPCM for continuous tone images (differential pulse code modulation—an option of the JPEG standard) are examples of lossless compression for images. In lossy compression, input symbols or luminance data are quantized and then converted to output codewords. The purpose of quantization is to remove data of low importance while preserving important features of the data. Lossy compression systems often use transformations to concentrate energy prior to quantization. Baseline JPEG is an example of a lossy encoding method for image data.

  Conventionally, conversion between color coordinates has been used together with quantization for lossy compression. In some reversible and reversible / irreversible systems, the main requirement is the reversibility and efficiency of the conversion. In other reversible / irreversible systems, in addition to the efficiency of reversible conversion, color decorrelation is also a factor, and for example, a 3 × 3 matrix can only be used for lossy compression. This is because the component is a non-integer, so that an error is added between compression and decompression when non-correlation is required.

  When performing color space conversion, a problem of calculation accuracy occurs. For example, when 8 bits are input, the necessary conversion space is usually 10 bits or 11 bits, and higher accuracy is required for the internal calculation, so that finally a stable color space can be obtained. Applying a process repeatedly with sufficient accuracy, converting the image from the RGB color space, compressing it, then decompressing it back to RGB, the result is a cumulative error, so the original color And the final color may not match. This is called color misregistration and is caused by the unstable color space.

  For this reason, there is a proposal example in which reversible color space conversion is possible by integer arithmetic with predictable accuracy (see, for example, Patent Documents 1 and 2).

In addition, as a color conversion processing method that can convert an image compressed in JPEG format into a full color image at high speed and low cost, the input color image is separated into a brightness component and a chrominance component, and the chrominance component Is used to calculate the number of color conversions with the brightness component as input and the output color space value as output, and by applying the brightness component to the color conversion function and performing color conversion, the input color in a predetermined color space is obtained. There is a proposal example that can be converted into an output color of another color space (for example, see Patent Document 3).
JP-A-9-6952 Japanese Patent Laid-Open No. 11-219428 JP 2000-175061 A

  In the case of Patent Documents 1 and 2, reversible color conversion by integer arithmetic is performed, and even if conversion and reverse conversion are repeated, no error is accumulated, but reversible color conversion is performed with predictable accuracy. Data conversion.

  In Patent Document 3, color conversion processing can be performed at high speed and low-cost color conversion processing with a small amount of computation can be realized, but the conversion accuracy is not increased.

  That is, in JPEG and JPEG2000, as described above, the image to be compressed is treated with YCbCr (Y: luminance, Cb: B system color difference, Cr: R system color difference) data, and in screen display and print development processing. Are often handled by RGB and YMC (or YMCK), and compatibility between the two is a major issue. In particular, when embedding a digital watermark for preventing tampering or a digital watermark as a cipher, it is necessary that both data conversions do not disappear, and maintaining the compatibility of image data conversion is the key to the solution. Holding. In particular, even in JPEG2000 capable of lossless compression encoding / decompression, RGB / YCbCr color conversion, which is color space conversion, is considered as irreversible color conversion. No fundamental color conversion is indispensable for image quality assurance.

  In addition to such color space conversion, there may be a problem of conversion regarding the length of image data. For example, while PCs handle data in mm units, printers often handle data in inches. If the conversion between the two data is not reversible, the page position will shift. It may happen.

  An object of the present invention is to realize a reversible conversion that can be completely restored when data is forward-converted and reverse-converted between unit systems having different resolution levels, particularly between unit systems having different color spaces.

  An object of the present invention is to reversibly improve JPEG2000 color conversion, which is irreversible color conversion.

  The data format reversible conversion method according to the first aspect of the present invention is a data format reversible conversion method for performing forward conversion and reverse conversion of data between unit systems having different resolution levels. Using a low first unit system as a common unit system, between the data of the first unit system having a low resolution level and the data of the second unit system having a higher resolution level than the first unit system Forward conversion from the second data to the third data of the first unit system after reverse conversion from the first data of the first unit system to the second data of the second unit system When performing the above, reversible data conversion is performed by integer arithmetic rounded off to the nearest decimal point so that the first data and the third data match.

  According to a second aspect of the present invention, the first unit system is a BMU unit system using inch system units, and the second unit system is a unit system represented by 1/100 mm using metric system units. , Using the first unit system as a common unit system, the first data of the first unit system is the β system data and the second unit system of the second unit system When the second data is expressed as α-system data, the inverse conversion from the β-system data to the α-system data and the forward conversion from the α-system data to the β-system data are:

の関係で結ばれるようにした整数演算により、前記第一のデータとしてのβ系データと逆変換後に順変換して得られた前記第三のデータとしてのβ系データとが一致するように前記整数演算により可逆変換を行わせるようにした。

By the integer operation connected in the relationship, the β data as the first data and the β data as the third data obtained by forward conversion after inverse transformation are matched with each other. Added reversible conversion by integer arithmetic.

  According to a third aspect of the present invention, the integer operation is:

による２のべき乗演算を用いて可逆なデータ変換を行うようにした。

Reversible data conversion is performed using power-of-two operation by 2.

  According to a fourth aspect of the present invention, the power of 2 is calculated by bit shift.

によって可逆なデータ変換を行うようにした。

According to the reversible data conversion.

The invention according to claim 5 is a data format reversible conversion method for performing forward conversion and reverse conversion of data between unit systems having different resolution levels.
Using the first unit system having a low resolution level for the forward conversion and the reverse conversion as a common unit system, the data of the first unit system having a low resolution level and the second having a resolution level higher than that of the first unit system Inverse conversion from the first data of the first unit system to the second data of the second unit system is performed by integer arithmetic rounded to the nearest decimal point. By performing forward conversion from the second data to the third data of the first unit system by an integer operation with the decimal point rounded off, the first data and the third data match each other. Data conversion was performed.

According to a sixth aspect of the present invention, the first unit system is a BMU unit system using inch units, and the second unit system is a unit system indicated by 1/100 mm using metric units. ,
Using the first unit system as a common unit system, the first data of the first unit system is the β system data and the second of the second unit system with the second unit system. When the data is expressed as α data,
The inverse transformation from the β-system data to the α-system data and the forward transformation from the α-system data to the β-system data,

の関係で結ばれるようにした整数演算により、前記第一のデータとしてのβ系データと逆変換後に順変換して得られた前記第三のデータとしてのβ系データとが一致するように前記整数演算により可逆変換を行わせるようにした。

By the integer operation connected in the relationship, the β data as the first data and the β data as the third data obtained by forward conversion after inverse transformation are matched with each other. Added reversible conversion by integer arithmetic.

  Therefore, in the case of forward conversion and reverse conversion, the unit system with the lower resolution level is used as the common unit system, and the data conversion is performed by integer calculation of the data between the unit systems with different resolution levels. Since the unit system can cope sufficiently, a reversible transformation that can be completely restored can be realized.

  As means for solving the above-described problems, the present invention provides an image processing apparatus that realizes processing by the data format reversible conversion method, a computer-executable program storing processing by the data format reversible conversion method, and the program Can also be used as a storage medium. Here, the image processing apparatus is not limited to a single machine such as a digital camera, a digital copying machine, and an MFP (multifunction machine), but also includes a system configuration such as a server / client system.

  According to the present invention, since the unit system having the lower resolution level is used as the common unit system in the forward conversion and the reverse conversion, the data conversion is performed by the integer operation of the data between the unit systems having different resolution levels. Since the unit system with the higher resolution level can sufficiently cope with it, a reversible transformation that can be completely restored can be realized.

  In particular, regarding digital color conversion by quantization of analog Y, Cb, and Cr signals between a unit system of color space RGB and a unit system of color space YCbCr, a unit system of low-resolution color space YCbCr is used as a common unit system. Since the unit system of the color space RGB having the higher resolution level can sufficiently cope with the above, it is possible to realize reversible conversion of the color space that can be completely restored.

  In addition, a reversible conversion of a color space that can be completely restored can be realized by a predetermined color conversion function.

  Further, even when a printing unit system of the color space YMC is targeted, reversible conversion of the color space that can be completely restored can be realized.

  In particular, regarding color conversion according to an international standard that defines a data format for converting an analog video signal between a unit system of color space RGB and a unit system of color space YCbCr into digital data, a unit system of low-resolution color space YCbCr is used. Since it is used for the common unit system, the unit system of the color space RGB having the higher resolution level can sufficiently cope with it, so that it is possible to realize a reversible conversion of the color space that can be completely restored.

  In particular, for color conversion of the original color based on luminance and color difference between the unit system of color space RGB and the unit system of color space YCbCr, the unit system of low-resolution color space YCbCr is used as the common unit system. Therefore, since the unit system of the color space RGB having the higher resolution level can sufficiently cope with it, the reversible conversion of the color space that can be completely restored can be realized.

  In addition, if the usage range of R (o) G (o) B (o) data and Y (o) Cb (o) Cr (o) data is unlimited, the range of the color conversion function is exceeded and cannot be completely restored. Although a case may occur, a restriction that restricts the maximum value and the minimum value is imposed, so that compatible conversion that completely restores can be performed.

  In particular, regarding the length conversion between BMU data using an inch system unit and 1/100 mm system data using a metric unit between a personal computer and a printer, a BMU system having a low resolution is used as a common unit system. Therefore, since the 1/100 mm system having the higher resolution level can sufficiently cope with it, it is possible to realize reversible conversion of length data that can be completely restored.

  An embodiment of the present invention will be described with reference to the drawings. The present invention is applied to color television broadcasting, digital video, digital cameras, digital copying machines, MFPs (multifunction peripherals), various image processing application software in personal computers, various image processing systems such as printers and scanners, image processing devices, and the like. Although possible, in order not to make the present invention unnecessarily difficult, explanations and illustrations regarding these various image processing systems, image processing devices, etc. shall be kept to the minimum necessary. In addition, the data format reversible conversion method according to the present invention can be realized by a program executed by a computer included in these various image processing systems or image processing devices, and various storage media in which the program is stored and readable by the computer. Of course.

[System configuration example]
As an example, the present invention can be incorporated into a compression / decompression system having an encoding unit and a decoding unit included in an image processing apparatus (various image processing systems or image processing devices). An example of such a system configuration is shown in FIG. The encoding unit 1 functions to generate the compressed data by encoding the input data, and the decoding unit 2 functions to generate the restored data of the original input data by decoding the encoded data. In the encoding unit 1, prior to compression 5, color space conversion 4 from one color coordinate system 1 to another color coordinate system 2 is performed. Similarly, in the decoding unit 2, after the decompression 6, the color space conversion 7 from the color coordinate system 2 to the color coordinate system 1 is performed again.

  Input data to the compression / decompression system may be in various data formats such as images (still images or moving images), graphics data, and the like. In one example, the input data is digital signal data, but it can also be digitized analog data or other forms. The source of the data may be a memory or a communication path 9 for the encoding unit 1 and / or the decoding unit 2. Such a system can be a reversible compression / decompression system or can be configured to perform lossy compression / decompression.

  As described above, the components of the encoding unit and / or the decoding unit may be realized by hardware, software, or a combination of both. The color space conversions 4 and 7 are executed as follows as the data format reversible conversion means or its function.

[Example of application to analog compatible color conversion]
As one embodiment of the present invention, an application example to digital color conversion by quantization of analog Y, Cb, and Cr signals (Y: luminance, Cb: B system color difference, Cr: R system color difference) will be described. In the present embodiment, a unit system of low-resolution color space YCbCr is commonly used for digital color conversion by quantization of analog Y, Cb, and Cr signals between a unit system of color space RGB and a unit system of color space YCbCr. The unit system is used to maintain compatibility with the unit system of the color space RGB by integer arithmetic. That is, the unit system of the color space YCbCr is used as the common unit system, and the unit system of the display system of the color space RGB is
YCbCr data → RGB data → Y'Cb'Cr 'data When performing reverse conversion and forward conversion data conversion sequentially, reversible by integer arithmetic so that Y = Y', Cb = Cb ', Cr = Cr' is satisfied. RGB data → Y′Cb′Cr ′ data in performing reverse conversion and forward conversion data conversion such as YCbCr data → RGB data → Y′Cb′Cr ′ data. Are a color conversion function that performs forward conversion on the side and a color conversion function that performs reverse conversion on the YCbCr data → RGB data side. Note that the component values R, G, and B of the color space RGB used in the present embodiment can independently take values of 2 to 253 (8 bits).

  First, as RGB data → YCbCr data conversion, ITU-R BT., Which is an international standard that defines a data format for converting an analog video signal defined in color television broadcasting or the like into digital data. An example of application to a digital color conversion equation based on quantization of analog Y, Cb, and Cr signals described in 601. Regarding this digital color conversion formula,

で示す実数演算による変換処理が用いられていた。しかしながら、コンピュータで数９を演算処理した場合、四則演算によるオーバーフローによって誤差が生じてしまう。これに対して、本実施の形態では、ＲＧＢデータ→ＹＣｂＣｒデータ変換に関しては、数９に代えて、

The conversion process by the real number calculation shown in FIG. However, when Equation 9 is arithmetically processed by a computer, an error occurs due to overflow caused by four arithmetic operations. On the other hand, in this embodiment, regarding the RGB data → YCbCr data conversion, instead of Equation 9,

で示す色変換関数の整数演算により行わせるものである。

The color conversion function shown in FIG.

  In Equation 10, addition and multiplication processing that does not cause an error if overflow does not occur is performed first, and division processing that is likely to generate overflow and also causes error is performed last. . In addition, rounding is performed by executing an arithmetic process of adding half of the denominator and rounding down the fractional part.

  That is, in the Y data conversion formula of Formula 10, 255 × 1000/2 indicating 1/2 of the denominator is added to the numerator, and then divided by 255 × 1000 of the denominator, and the fractional part is rounded down. In the Cb and Cr data conversion formula of Formula 10, 255 × 1000 × 1000/2 indicating 1/2 of the denominator is added to the numerator, and then the operation result in the numerator is divided by 255 × 1000 × 1000 of the denominator. Truncate part.

  In the arithmetic processing according to Equation 10, arithmetic processing can be performed with an integer, and the arithmetic result can be acquired with an integer.

  On the other hand, YCbCr data ← RGB data conversion can also be performed using international standard ITU-R BT. An example of application to a digital color conversion equation based on quantization of analog Y, Cb, and Cr signals described in 601. Regarding this digital color conversion formula,

で示す実数演算による変換処理が用いられていた。しかしながら、コンピュータで数１１を演算処理した場合、四則演算によるオーバーフローによって誤差が生じてしまう。これに対して、本実施の形態では、ＹＣｂＣｒデータ←ＲＧＢデータ変換に関しては、数１１に代えて、

The conversion process by the real number calculation shown in FIG. However, when Formula 11 is arithmetically processed by a computer, an error occurs due to overflow caused by four arithmetic operations. On the other hand, in the present embodiment, YCbCr data ← RGB data conversion, instead of Equation 11,

数１２では、オーバーフローが起きなければ誤差が生じない加算及び乗算処理をなるべく最初に行うようにし、オーバーフローを発生し易く、また、誤差を生じ易い除算処理をなるべく最後に行うように工夫してある。また、分母の半分を加算した後に小数部切捨てる演算処理を実行することによって四捨五入をしている。

In equation (12), the addition and multiplication processes that do not cause an error if overflow does not occur are performed first, and the division process that easily generates an overflow and also generates errors is performed as much as possible. . In addition, rounding is performed by executing an arithmetic process of adding half of the denominator and rounding down the fractional part.

  That is, after adding 713 × 224 × 219/2 indicating 1/2 of the denominator to the numerator in the R data conversion formula of Formula 12, the result of operation in the numerator is divided by 713 × 224 × 219 of the denominator, Truncate part. In the G data conversion formula of Formula 12, after adding to 219 × 713 × 224 × 587 × 564/2 numerator indicating 1/2 of the denominator, the calculation result in the numerator is 219 × 713 × 224 × 587 × 564. Divide by and round down the fractional part. In the B data conversion formula of Formula 12, after adding to 564 × 224 × 219/2 numerator indicating 1/2 of the denominator, the operation result in the numerator is divided by 564 × 224 × 219 of the denominator, and the fractional part is rounded down. Do.

  In the arithmetic processing according to Equation 12, arithmetic processing can be performed with an integer, and the arithmetic result can be acquired with an integer.

  Therefore, using the color space YCbCr as a common unit system, YCbCr data → RGB data side inverse conversion and YCbCr data → RGB data → Y′Cb′Cr ′ data, the inverse conversion on the YCbCr data → RGB data side Table 1 shows the result of performing the forward conversion on the RGB data → Y′Cb′Cr ′ data side using the color conversion function using the color conversion function.

この表１に示す色変換結果によれば、Ｙ＝Ｙ'，Ｃｂ＝Ｃｂ'，Ｃｒ＝Ｃｒ'が維持され、色変換に関するデータ互換性（可逆性）が保証されることが判る。

According to the color conversion results shown in Table 1, it can be seen that Y = Y ′, Cb = Cb ′, and Cr = Cr ′ are maintained, and data compatibility (reversibility) regarding color conversion is guaranteed.

[Examples of application to printing color space YMC]
In the above description, the application example to the unit system of the display system of the color space RGB has been described, but the present invention can be similarly applied to the unit system of the printing system of the color space YMC. In this case, an integer operation may be performed by replacing Y, M, and C in Equations 10 and 12 with Y = MAX-B, M = MAX-G, and C = MAX-R. Here, MAX indicates the maximum resolution level. For example, with 256 gradations, MAX = 256.

[Example of application to digital compatible color conversion]
As another embodiment of the present invention, an international standard ITU-R BT. An example of application to the color conversion formula described in 601 will be described. Also in this embodiment, the unit system of the color space YCbCr is used as the common unit system, and the unit system of the display system of the color space RGB is
YCbCr data → R (d) G (d) B (d) data → Y′Cb′Cr ′ data Y = Y ′, Cb = Cb ′, Cr = In order to satisfy Cr ′, reversible data conversion is performed by integer arithmetic, and such YCbCr data → R (d) G (d) B (d) data → Y′Cb′Cr ′ data , R (d) G (d) B (d) data → color conversion function for performing YCbCr data conversion and color conversion function for performing forward conversion of YCbCr data ← R (d) G (d) B (d) data And a color conversion function for performing an inverse conversion of R (d) G (d) B (d) data → Y′Cb′Cr ′ data.

First, the original original color conversion formula is the international standard ITU-R BT. The color conversion formula described in 601 is used. Regarding this color conversion formula,
a. Conversion formula from analog RGB (R (a), G (a), B (a)) signal to quantized digital (R (d), G (d), B (d)) where 0 ≦ R (a ) ≦ 256, 0 ≦ G (a) ≦ 256, 0 ≦ B (a) ≦ 256

ｂ．デジタルＲＧＢ信号からデジタルＹ，Ｃｂ，Ｃｒ信号への変換式

b. Conversion formula from digital RGB signal to digital Y, Cb, Cr signal

なる演算による変換処理が用いられていた。これに対して、本実施の形態では、
Ｒ（ａ）Ｇ（ａ）Ｂ（ａ）→ＹＣｂＣｒ変換に関しては、

A conversion process using the following calculation was used. In contrast, in the present embodiment,
Regarding R (a) G (a) B (a) → YCbCr conversion,

で示す色変換関数の演算により行い、ＹＣｂＣｒ→Ｒ（ｄ）Ｇ（ｄ）Ｂ（ｄ）変換に関しては、

For the YCbCr → R (d) G (d) B (d) conversion,

で示す色変換関数の整数演算により行い、Ｒ（ｄ）Ｇ（ｄ）Ｂ（ｄ）→Ｙ'Ｃｂ'Ｃｒ'変換に関しては、

The R (d) G (d) B (d) → Y′Cb′Cr ′ conversion is performed by integer calculation of the color conversion function indicated by

で示す色変換関数の整数演算により行わせるものである。

The color conversion function shown in FIG.

  Therefore, using the color space YCbCr as a common unit system, with respect to the reverse conversion and forward conversion of YCbCr data → R (d) G (d) B (d) data → Y′Cb′Cr ′ data, R ( a) G (a) B (a) → YCbCr conversion is performed using the color conversion function of Formula 15, and YCbCr → R (d) G (d) B (d) conversion is performed using the color conversion function of Formula 16. Table 2 shows the result of performing the R (d) G (d) B (d) → Y′Cb′Cr ′ conversion using the color conversion function of Equation 17.

この表２に示す色変換結果によれば、ＹＣｂＣｒが復元、即ち、Ｙ＝Ｙ'，Ｃｂ＝Ｃｂ'，Ｃｒ＝Ｃｒ'が維持され、色変換に関するデータ互換性（可逆性）が保証されることが判る。

According to the color conversion results shown in Table 2, YCbCr is restored, that is, Y = Y ′, Cb = Cb ′, and Cr = Cr ′ are maintained, and data compatibility (reversibility) regarding color conversion is guaranteed. I understand that.

[Original color conversion formula based on luminance and color difference; application example to JPEG2000]
In the JPEG2000 algorithm, RGB data is converted into YCbCR data based on luminance and color difference, or color space conversion processing for reverse conversion is performed, but this processing is irreversible color as described in the prior art. It has been converted.

A. In other words, as a color conversion formula conventionally performed by the JPEG2000 algorithm,
a. Conversion from RGB signal (R (o), G (o), B (o) signal to YCbCr signal (Y (o), Cb, (o) Cr (o))

なる変換式が用いられている。この式中のＡは行列であって、

The following conversion formula is used. A in this equation is a matrix,

で示される。なお、ｘ：Ｒｅｄの加重係数、ｙ：Ｂｌｕｅの加重係数、１−ｘ−ｙ：Ｇｒｅｅｎの加重係数である（ただし、０≦ｘ＜１，０≦ｙ＜１，かつ、ｘ＋ｙ＜１）。

Indicated by Note that x: Red weighting factor, y: Blue weighting factor, and 1-xy: Green weighting factor (where 0 ≦ x <1, 0 ≦ y <1, and x + y <1).

b. Conversion from YCbCr signal (Y (o), Cb, (o) Cr (o)) to RGB signal (R (o), G (o), B (o))

なる変換式が用いられている。この式中のＡは行列であって、数１９中に示した通りである。

The following conversion formula is used. A in this equation is a matrix, as shown in Equation 19.

  Here, specific examples of the transformation matrix A shown in Equation 19 include x = 299/1000 = Red weighting factor, y = 114/1000 = Blue weighting factor, 1-xy = 587/1000 = Green If the weighting factor is

で示される。以上が、ＪＰＥＧ２０００アルゴリズムにおいて、非可逆な色変換として使用されている変換行列式である。

Indicated by The above is a transformation determinant used as irreversible color transformation in the JPEG2000 algorithm.

  B. On the other hand, in the present embodiment, also for color conversion by the JPEG2000 algorithm, as in the case of the above-described embodiment, compatible conversion by integer values is enabled, and all variables and coefficients are converted to integers. The calculation result is also an integer.

x: Red weighting factor, y: Blue weighting factor, 1-xy: Green weighting factor is expressed as x = x _M / D, y = y _M / D (where x _M , y _M , D are all integers, and the subscript M is just a part of the variable name (for example, for distinguishing between “x” and “x _M ”).

となる。

It becomes.

  In the present embodiment, the following color conversion processing is performed using the coefficients related to such determinants. Note that “(o)” of R (o), G (o), B (o), Y (o), Cb (o), and Cr (o) is “brightness and luminance”. An expression added to distinguish it from general variable names such as R, G, B, Y, Cb, and Cr used in other conversion formulas as described above, from the intention of representing "original color based on color difference". Method, just part of the variable name.

a. Conversion from RGB signal (R (o), G (o), B (o) signal to YCbCr signal (Y (o), Cb, (o) Cr (o))

で示す色変換関数の整数演算により行う。

It is performed by integer calculation of the color conversion function indicated by.

MAX _RGB represents the number of gradations (integer), except for the first limitation on inputs R (o), G (o), and B (o) for realizing restoration compatibility described later by conversion processing.

なる関係となる。

It becomes a relationship.

For example, in accordance with the JPEG2000 algorithm, x = 299/1000 = Red weighting factor, y = 114/1000 = Blue weighting factor, 1-xy = 587/1000 = Green weighting factor, MAX _RGB = 256 floors As a key, RGB signal (R (o), G (o), B (o) signal → YCbCr signal (Y (o), Cb, (o) Cr (o))) Expression 13

で示す色変換関数に書換えることができる。

It can be rewritten to the color conversion function indicated by.

  By combining this conversion formula and the conversion formula shown in Equation 32, which will be described later, the color conversion formula, which was an irreversible color conversion scheme in the JPEG2000 algorithm, can be improved to a reversible color conversion formula.

  Further, by applying a bit shift to the color conversion function of Formula 25, the calculation speed can be further increased. For example, since the number of gradations of RGB is 256 and the range of use is 0 to 255, MAX_KAICHO = 255 as the maximum gradation value, bitSHIFT = 12 (bit shift number) (= 4096) as an exponent of the power of 2 R (0), G (0), and B (0) by bit shift are iR0RS, iG0RS, and iB0RS, respectively, and Y (0), Cb (0), and Cr (0) by bit shift are iY0RS and iCbRS, respectively. , ICrRS, and describing this change in C,

のように記述でき、これらの記述を簡潔にすると、

If these descriptions are simplified,

更に、数５７は、

Furthermore, Equation 57

のように簡潔に記述できる。

It can be described briefly as follows.

  In addition, when Expression 58 is expressed as a power of 2, when

のように表現される。

It is expressed as

  By the way, regarding such color conversion, it is necessary to limit the use range of input R (o) G (o) B (o) data in order to realize restoration compatibility. That is, in order to realize restoration compatibility, the limit range of data R (o) G (o) B (o) data newly input in Equation 23 is

であり、境界値を超えるものは境界値の値に変更することが必要である。この範囲を超えて入力すると、後述の数３２の変換式によって逆変換した場合に、上述の数２３の条件範囲を超えることがあり、その時は、詰まるところ、Ｙ（ｏ）Ｃｂ（ｏ）Ｃｒ（ｏ）が復元できない状態に陥るからである。

It is necessary to change the value exceeding the boundary value to the value of the boundary value. If the input exceeds this range, it may exceed the condition range of the above-mentioned equation 23 when it is inversely converted by the conversion equation of the later-described equation 32. At that time, Y (o) Cb (o) Cr This is because (o) falls into a state where it cannot be restored.

  In addition, as a limited range of the input data R (o) G (o) B (o) when restoring the original Y (o) Cb (o) Cr (o), When R (o) G (o) B (o) that has already been created is used and Y (o) Cb (o) Cr (o) is simply restored, there is no special limitation, and the following numbers If R (o) G (o) B (o) created by 31 conversion formulas is used as it is (without processing) as input data for the above conversion formulas, the restored Y (o) Cb (o) Cr (O) is obtained.

b. Compatible conversion from Y (o) Cb (o) Cr (o) to an integer value of R (o) G (o) B (o)

で示す色変換関数の整数演算により行う。

It is performed by integer calculation of the color conversion function indicated by.

For example, as in the case of Equation 25, x = 299/1000 = Red weighting factor, y = 114/1000 = Blue weighting factor, 1-xy = 587/1000 = Green according to the JPEG2000 algorithm. Assuming that the weighting coefficient, MAX _RGB = 256 gradations, Equation 31 relating to Y (o) Cb (o) Cr (o) → R (o) G (o) B (o) conversion is

で示す色変換関数に書換えることができる。

It can be rewritten to the color conversion function indicated by.

  Further, by applying a bit shift to the color conversion function of Equation 32, the calculation speed can be further increased. For example, since the number of gradations of RGB is 256 and the range of use is 0 to 255, MAX_KAICHO = 255 as the maximum gradation value, bitSHIFT = 12 (bit shift number) (= 4096) as an exponent of the power of 2 R (0), G (0), and B (0) by bit shift are iR0RS, iG0RS, and iB0RS, respectively, and Y (0), Cb (0), and Cr (0) by bit shift are iY0S and iCbS, respectively. , ICrS, and describing this change in C,

のように記述でき、これらの記述を簡潔にすると、

If these descriptions are simplified,

iR0RS=((((257 + (iY0S<<1)) << 11) + 5743*iCrS) >> 12) - 128;
更に、数３４は、

iR0RS = ((((257 + (iY0S << 1)) << 11) + 5743 * iCrS) >>12)-128;
Furthermore, the number 34 is

のように簡潔に記述できる。

It can be described briefly as follows.

  In addition, when Expression 35 is expressed as a power of 2,

のように表現される。

It is expressed as

  In order to realize restoration compatibility by various operations described above, it is necessary to limit the use range of input Y (o) Cb (o) Cr (o) data. First, the input data Y (o) Cb (o) Cr (o) used for this conversion equation is Y (o) Cb (o) Cr (o) originally created by the conversion equation of Equation 23 described above. It is assumed that there is. Y (o) "Cb (o)" Cr (o) obtained by adding editing processing such as image modification and digital watermarking to Y (o) Cb (o) Cr (o) created by the conversion equation of Equation 23 In order to make "" as compatible conversion target data, it becomes a source of Y (o) Cb (o) Cr (o) created in advance by the conversion equation of Formula 23 based on the maximum displacement difference with respect to the original value. The R (o) G (o) B (o) data may be changed from the boundary value to the inside of the allowable range.

Here, a description will be given of changing the boundary value to the inside of the allowable range before image modification so that the image data does not exceed the boundary value by image modification. The degree of influence of each displacement value ΔY, ΔCb, ΔCr of Y (o), Cb (o), Cr (o) on R (o) G (o) B (o) data is as follows: ΔR: ΔY: ΔCr = 1: 1: (2 (D−X _M ) / D)
_{ΔG: ΔY: ΔCr: ΔCb =} 1: 1: (2x M (D-x M) / ((D-x M -y M) * D)):
_{(2y M (D-y M} ) / ((D-x M -y M) * D))
ΔB: ΔY: ΔCb = 1: 1: (2 (D−Y _M ) / D)
Indicated by For example, if D = 1000, x _M = 299, y _M = 114,
ΔR: ΔY: ΔCr ≈ 1: 1: 1.40
ΔG: ΔY: ΔCr: ΔCb≈1: 1: 0.71: 0.34
ΔB: ΔY: ΔCb≈1: 1: 1.77
is there. For example, changes of ΔY = 1, ΔCb = 1, and ΔCr = 1 on the G data are affected by a displacement of 2.05 (= 1 + 0.34 + 0.71). Therefore, if the allowable range of G is changed to 4 ≦ G ≦ 251 before the editing process is started (in the case of MAX _RGK = 256 gradations), the original allowable range 1 ≦ when the displacement is newly added. It can be set so as not to exceed G ≦ 254.

  Using R (o) G (o) B (o) having undergone the above boundary value change, Y (o), Cb (o), Cr (o) are calculated according to the conversion equation of Equation 23. Y (o), Cb (o), Cr (o) calculated by adding the displacement within the allowable range and performing RGB conversion using the conversion equation of Formula 31, the Y (o), Cb (o, Cr (o) data can be restored.

  These transformations are linked with (Y (o) Cb (o) Cr (o) → R (o) G (o) B (o) → Y (o) ′ Cb (o) ′ Cr (o) ′). As a result, Y (o) Cb (o) Cr (o) is restored. That is, Y (o) ′ Cb (o) ′ Cr (o) ′ = Y (o) Cb (o) Cr (o).

Specifically, when x _M = 299, y _M = 114, D = 1000, and MAX _RGB = 256 gradations, the conversion is performed as follows. That is,
(1) Y (o) Cb (o) Cr (o) Tolerable range of original RGB to be generated: Input of conversion formula of Expression 23 1 ≦ R (o) ≦ 254, 1 ≦ G (o) ≦ 254,1 ≦ B (o) ≦ 254
(2) Conversion result range of Y (o) Cb (o) Cr (o) generated by the above (1): Input of conversion formula of Equation 31 1 ≦ Y (o) ≦ 254, −126 ≦ Cb (o) ≦ 127,
−126 ≦ Cr (o) ≦ 127
(3) R, G, and B conversion result range generated by equation (31) in equation (2): Input of equation (23) 0 ≦ R (o) ≦ 255, 0 ≦ G (o) ≦ 255, 0 ≦ B (O) ≦ 255
(4) Conversion result range of Y (o) Cb (o) Cr (o) restored by the conversion formula of Equation 23 in (3) above:
1 ≦ Y (o) ≦ 254, −126 ≦ Cb (o) ≦ 127,
−126 ≦ Cr (o) ≦ 127
It becomes.

  Table 3 shows the results obtained using such a color conversion function.

この表３に示す色変換結果によれば、ＹＣｂＣｒが復元、即ち、Ｙ＝Ｙ'，Ｃｂ＝Ｃｂ'，Ｃｒ＝Ｃｒ'が維持され、色変換に関するデータ互換性（可逆性）が保証されることが判る。

According to the color conversion results shown in Table 3, YCbCr is restored, that is, Y = Y ′, Cb = Cb ′, and Cr = Cr ′ are maintained, and data compatibility (reversibility) regarding color conversion is guaranteed. I understand that.

  As a result, for example, the color conversion generally positioned as the irreversible conversion process in the JPEG2000 algorithm schematically shown in FIG. 2 can be changed to the reversible color conversion by applying this embodiment. FIG. 2 shows an example of a compression / decompression system similar to the case of FIG. 1. In the compression system, after performing RGB → YCbCr color conversion by color space minimum error forward conversion, wavelet conversion, entropy encoding, etc. The encoded data is stored in a memory or an external storage device or distributed via a communication channel such as the Internet. In the decompression system, the compressed code data read from the memory or the like or supplied via the communication channel is reversibly decompressed in the reverse procedure, and YCbCr → RGB color conversion is performed by color space minimum error inverse transform. Restore as image data.

  By applying the color conversion of this embodiment described above to these color space error minimum forward conversion and reverse conversion, reversible conversion becomes possible. As a result, for JPEG2000 reversible conversion, color conversion can also be completely reversible, so image quality is guaranteed. The same applies to the analog compatible color conversion algorithm and the digital compatible color conversion algorithm.

  Now, an application example that requires reversible color conversion will be described with reference to the schematic diagram shown in FIG. 3 as an application example when an editing process such as tampering is added in the JPEG2000 algorithm.

  (1) First, a procedure for generating 4: 2: 2YCbCr from RGB base data to realize a mechanism of 4: 2: 2YCbCr → RGB → 4: 2: 2 complete restoration YCbCr data conversion from RGB base data explain.

  Assuming that two neighboring pixels as RGB base data are R0G0B0 and R1G1B1, color conversion of several 12 based on R = (R0 + R1) / 2, G = (G0 + G1) / 2, and B = (B0 + B1) / 2 Cb and Cr are calculated using the function. Y0 and Y1 are calculated by the color conversion function of Formula 12 using R0G0B0 and R1G1B1, respectively.

  Next, R0G0B0 and R1G1B1 are calculated again by performing inverse transformation from the above calculated Y0, Y1, Cb, and Cr. If any of R0G0B0 and R1G1B1 calculated again is not less than 0 and not less than 255, Y0 and Y1 are recalculated based on the above R, G and B (average values of R0G0B0 and R1G1B1).

  (2) Next, change the input 4: 2: 2YCbCr base data to realize the mechanism of the input (arbitrary) 4: 2: 2YCbCr base data → RGB → 4: 2: 2 complete restoration YCbCr data conversion. The procedure will be described.

  RGB can take an arbitrary value independently of R, G, B within the range of 0 ≦ R, G, B ≦ 255. However, the YCbCr data is not only limited to 16 ≦ Y ≦ 235, 16 ≦ Cb ≦ 240, 16 ≦ Cr ≦ 240, but also when calculating R, G, B from Y, Cb, Cr, 0 ≦ R, G, A condition that it is not effective unless the conversion result falls within the range of B ≦ 255 is added. Therefore, first, the RGB base data R0G0B0 and R1G1B1 of the above (1) are calculated by using the YCbCr → RGB conversion formula based on the color conversion function shown in Equation 16 for the input 4: 2: 2 YCbCr base data. In this case, the value exceeding the boundary value (0, 255) is changed to the value of the boundary value.

  As a result, R0G0B0 and R1G1B1 become values that do not exceed the boundary value, and 4: 2: 2YCbCr calculated by applying the R0G0B0 and R1G1B1 to the method (1) becomes YCbCr that can be completely restored. The value stable for color conversion described in FIG. 3 means a value having reversibility that restores the original value when the color-converted value is further inversely converted.

  (3) Next, a method for guaranteeing the 4: 2: 2YCbCr base data → RGB → 4: 2: 2 complete restoration YCbCr data conversion with editing (image modification, digital watermarking, etc.) will be described.

  The RGB base data R0G0B0 and R1G1B1 of the above (1) are calculated by using the YCbCr → RGB conversion formula (12) for the 4: 2: 2 YCbCr base data before the editing process is applied. Anything exceeding the boundary value is changed to the boundary value. At that time, the influence on the image value by the editing process (image modification) is taken into consideration. Based on the maximum displacement difference with respect to the original value, the boundary value is changed from the boundary value of the R0G0B0 and R1G1B1 data to the inside of the allowable range.

Here, a description will be given of changing the boundary value to the inside of the allowable range before image modification so that the image data does not exceed the boundary value by image modification. The influences of the displacement values ΔY, ΔCb, ΔCr of Y, Cb, Cr on the R0G0B0, R1G1B1 data are as follows:
ΔR: ΔY: ΔCr ≈ 1: 1.17: 1.60
ΔG: ΔY: ΔCr: ΔCb≈1: 1.17: 0.82: 0.40
ΔB: ΔY: ΔCb≈1: 1.17: 2.02
It is a ratio. For example, for the G data, changes of ΔY = 1, ΔCb = 1, and ΔCr = 1 each have a displacement of 2.39 (= 1.17 + 0.82 + 0.40). Therefore, if the G allowable range is changed to 3 ≦ G ≦ 252 before the editing process is started, the original allowable range 0 ≦ G ≦ 255 can be set even if a new displacement is added. .

  4: 2: 2 YCbCr is calculated by the method (1) above using R0G0B0 and R1G1B1 that have undergone the above boundary value changes. Even if the calculated 4: 2: 2 YCbCr is subjected to RGB conversion by adding an allowable range of displacement, 4: 2: 2 YCbCr data to which the allowable range of displacement is added can be restored.

[Reversible color conversion when using bit shift]
Next, reversible color conversion (YCbCr → RGB → YCbCr) when using bit shift will be considered. Here, the process of converting the original image RGB → YCbCr → RGB → Y′Cb′Cr ′ → R′G′B ′ will be considered.

  YCbCr (iY0S, iCbS, iCrS) = Y′Cb′Cr ′ (iY0RS, iCbRS, iCrRS), that is, iY0S = iY0RS, iCbS = iCbRS, iCrS = iCrRS. In this case, RGB = R′G′B ′.

  The original image RGB in the range of 0 ≦ R, G, B ≦ 255 is converted in the range of 0 ≦ Y ≦ 255, −128 ≦ Cb ≦ 128, −128 ≦ Cr ≦ 128 by YCbCr conversion, and by RGB conversion, -1 ≦ R, G, B ≦ 256, converted to Y′Cb′Cr ′, and converted to 0 ≦ Y ′ ≦ 255, −128 ≦ Cb ′ ≦ 128, −128 ≦ Cr ′ ≦ 128. Will be converted.

On the other hand, the specified range as an effective color that can be expressed in 8 bits / color is
In the RGB system,
0 ≦ R ≦ 255, 0 ≦ G ≦ 255, 0 ≦ B ≦ 255
In the YCbCr system,
0 ≦ Y ≦ 255, −128 ≦ Cb ≦ + 127, −128 ≦ Cr ≦ + 127
It is.

  The effective data range that can be reversibly converted within these specified ranges is 1 ≦ R, G, B ≦ 254 in the original image RGB, and 1 ≦ Y ≦ 254, −126 ≦ Cb ≦ 127, − in the YCbCr conversion. In the range of 126 ≦ Cr ≦ 127, in the RGB conversion, the range of 0 ≦ R, G, B ≦ 255, and in the Y′Cb′Cr ′ conversion, 1 ≦ Y ′ ≦ 254, −126 ≦ Cb ′ ≦ 127, −126 ≦ Cr ′ ≦ 127.

  That is, since all RGB original images in the range of 1 ≦ R, G, and B ≦ 254 can be converted within the specified range, reversible conversion can be performed.

  However, when the original image RGB is R or G or B = 0 or R or G or B = 255, the original image RGB → YCbCr → RGB → Y′Cb′Cr ′ → R′G′B ′ YCbCr, RGB may exceed the specified range. For example, there are one case where Cb = 128, one case where Cr = 128, and many cases where R, G, B = (− 1) or 256.

  Therefore, RGB → YCbCr conversion is performed after changing the original image RGB to values of 1 to 254 so that the conversion result is within the range of the specified value. For example, it is conceivable to prepare in advance a conversion table for conversion to a predetermined value.

  Next, regarding the capacity for holding the conversion table, the A state, the B state, and the C state will be considered below with reference to boundary values in the conversion process.

-State A Focusing on the boundary of YCbCr (Y <0 or 254 ≦ Y, Cb ≦ −127 or 127 <Cb, Cr ≦ −127 or 127 <Cr) when converting the original image RGB → YCbCr, and exceeding the specified range When considering the case of invalid data,

となる。

It becomes.

-B state Only YCbCr → RGB conversion is performed (correction processing is not performed), and in the same way as above, paying attention to the boundary between RGB and considering the case of invalid data exceeding the specified range,
R <0: 11,783 cases / (256 x 256 x 256) color ≒ 0.07%
R> 255: 11,883 / (256 × 256 × 256) color ≒ 0.07%
G <0: 6,171 cases / (256 x 256 x 256) Color ≒ 0.04%
G> 255: 6,117 cases / (256 × 256 × 256) color ≒ 0.04%
B <0: 14,408 cases / (256 x 256 x 256) Color ≒ 0.09%
B> 255: 14,529 / (256 × 256 × 256) color ≒ 0.09%
It was found that a total of 64,891 cases / (256 × 256 × 256) colors≈0.39% became invalid data.

・ C state When YCbCr → RGB conversion is performed and correction processing is performed, paying attention to the boundary between RGB and invalid data exceeding the specified range, and a countermeasure (change) method in such a case are considered. did. The results are shown in Table 4.

表４に示されるように、Ｃ状態では、合計８、０３１件が無効データとなることが分かった。

As shown in Table 4, it was found that a total of 8,031 cases became invalid data in the C state.

  When the conversion table is used as an exception process for data that cannot be reversibly converted within the specified range by Equation 28 and Equation 34 by bit shift, the C state (8) is applied rather than the B state (64,891 cases). , 031) is more efficient since the memory area can be reduced to 1/8.

  In this way, by applying the conversion table to the C state (8, 031 cases), reversible conversion can be realized for 16 million colors including Example 1 to Example 5 shown in Table 3.

[Concrete example]
When an arbitrary value from 0 to 255 is substituted for RGB basic data in the case of analog color conversion using Equation 10, Equation 12, etc. (here, R = 104, G = 112, B = 134) The conversion result is schematically shown in FIG. It can be seen that the reconstruction is performed so that Y = Y ′, Cb = Cb ′, and Cr = Cr ′.

  An ITU-R BT. FIG. 5 shows the conversion result when an arbitrary value from 0 to 255 is substituted for RGB basic data in the case of digital color conversion using 601 (here, R = 104, G = 112, B = 134). Is shown schematically. It can be seen that the reconstruction is performed so that Y = Y ′, Cb = Cb ′, Cr = Cr ′, R ′ = R ′, G ′ = G ′, and B ′ = B ′.

  In a reversible color conversion example using JPEG2000 using Equation 25, Equation 31, etc., when an arbitrary value from 1 to 254 is substituted for RGB basic data (here, R = 1, G = 254, B = 254) 6) is schematically shown in FIG. 6 together with a conventional irreversible conversion example as comparison information. Whereas the conventional irreversible conversion example is in a non-restoration state, in the case of the present embodiment, Y = Y ′, Cb = Cb ′, Cr = Cr ′, R ′ = R ′, G ′. It can be seen that the data is restored so that = G ′ and B ′ = B ′.

[Modification]
In the above description, only the color conversion is focused. However, as a general theory, this is a conversion method that performs forward conversion and reverse conversion of data between unit systems having different resolution levels. The same applies to the case where the lower unit system is used as a common unit system and reversible data conversion is performed by integer arithmetic between the data of the unit system with the lower resolution level and the data of the unit system with the higher resolution level. Applicable to.

  Therefore, it will be proved below that it can be completely restored by continuous conversion of the lower resolution unit system → the higher unit system → the lower unit system.

  In general, two resolutions α and β (where α> β> 0. For example, in the case of mm ← → BMU conversion, 1 inch is expressed in units of α = 2540: 1/100 mm and β = 1200 BMU. System), once converted from β unit system to α unit system, and converted back to β unit system using the converted data, the conversion formula is

の関係で結ばれている場合には、
α×（β系データ）／β−０．５ ……小数点以下の数も含む：有理数
＜ β→α変換関数（引数：β系データ）……上記定義より整数である
≦ α×（β系データ）／β＋０．５ ……小数点以下の数も含む：有理数
＜ α×（β系データ＋１）／β−０．５……小数点以下の数も含む：有理数
＜ β→α変換関数（引数：β系データ＋１）……上記定義より整数である
≦ α×（β系データ＋１）／β＋０．５……小数点以下の数も含む：有理数
であることから、
β→α変換関数（引数：β系データ＋１）−β→α変換関数（引数：β系データ）＞ α／β−１ ＞ ０であるので、元のβ系の隣り合うデータ（＋１又は−１した整数と元の整数）をα系に変換したもの同士は、重なることが無く、また（β系データ）−１
＜ （β系データ）−０．５×β／α−０．５
＜ β×β→α変換関数（引数：β系データ）／α−０．５
＜ α→β変換関数（引数：β→α変換関数（引数：β系データ））
≦ β×β→α変換関数（引数：β系データ）／α＋０．５
≦ （β系データ）＋０．５×β／α＋０．５
＜ （β系データ）＋１
である。

If you are tied in a relationship
α × (β system data) /β−0.5 …… Including numbers after the decimal point: rational number <β → α conversion function (argument: β system data) …… It is an integer from the above definition ≦ α × (β system Data) /β+0.5 ... includes numbers after the decimal point: rational number <α × (β system data + 1) /β-0.5……includes numbers after the decimal point: rational number <β → α conversion function (argument: β system data +1) …… It is an integer from the above definition ≦ α × (β system data + 1) /β+0.5……Includes numbers after the decimal point:
β → α conversion function (argument: β system data + 1) −β → α conversion function (argument: β system data)> α / β−1> 0, so the adjacent data of the original β system (+1 or − (Integer integer and original integer) converted to α system do not overlap each other, and (β system data) -1
<(Β data) -0.5 × β / α-0.5
<Β × β → α conversion function (argument: β system data) /α-0.5
<Α → β conversion function (argument: β → α conversion function (argument: β system data))
≦ β × β → α conversion function (argument: β system data) /α+0.5
≦ (β data) + 0.5 × β / α + 0.5
<(Β data) + 1
It is.

  In short, since α → β conversion function (argument: β → α conversion function (argument: β system data)) = (β system data) representing an integer value, the original beta system data is completely restored.

After all, using the unit system BMU as the common unit system, with the unit system 1/100 mm,
When performing the data conversion of BMU data → 1/100 mm data → BMU data, reversible conversion is performed by integer arithmetic so that the BMU data match each other.

なる整数演算により行わせればよいものである。

What is necessary is just to perform by the integer calculation.

  By changing the power-of-two operation of Equation 39 to bit shift, the operation speed can be made faster.

数４０において、下線の部分は、固定値であるので、予め計算しておくことにより、更に高速に演算処理を行うことができる。また、ビットシフト数（bitSHIFT）＝１２の場合、０≦（ＢＭＵ系データ）≦２４００の範囲で誤差なく変換できる。

In the equation 40, the underlined portion is a fixed value, so that the calculation process can be performed at a higher speed by calculating in advance. When the bit shift number (bitSHIFT) = 12, conversion can be performed without error in the range of 0 ≦ (BMU system data) ≦ 2400.

  Therefore, the resolution is also low especially for length conversion between BMU data using inch system units (inch, yards, feet, etc.) and 1/100 mm system data using metric system units between a personal computer and a printer. By using the BMU system as a common unit system, the higher resolution level 1/100 mm system can sufficiently cope with it, so that reversible conversion of length data that can be completely restored can be realized.

  Table 5 shows the results obtained using such a conversion function.

この表５に示す色変換結果によれば、ＢＭＵ系データが復元され、長さ変換に関するデータ互換性（可逆性）が保証されることが判る。

According to the color conversion results shown in Table 5, it can be seen that BMU data is restored and data compatibility (reversibility) regarding length conversion is guaranteed.

  In the following, a color conversion (YCbCr → RGB → YCbCr) method for further ensuring reversibility will be described.

[Color conversion (YCbCr → RGB → YCbCr) method to further ensure reversibility]
(1) Preparation (1-A) Representation method of rounding down to the next decimal point Division by normal fixed-point data of a normal computer is to perform the rounding down processing for the decimal point. In mathematics, this is expressed as a result of rounding off the decimal part of the real number A using an expression in which the real number A is enclosed by a Gaussian symbol. Accordingly, the division result of the fixed points of the computer is expressed by the following equation when expressed in modulo (representing the remainder of the division, abbreviated as “mod”).

数４１にて、コンピュータによる固定小数点データＶをＵで割った結果が表現される。
（１−Ｂ）小数以下四捨五入処理の表現方法
上記（１−Ａ）と同様に、コンピュータの正の固定小数点データ同士による割り算（Ｙ／Ｘ）結果における、小数部四捨五入による結果以下に示す等式となる。

In Formula 41, the result of dividing the fixed-point data V by the computer by U is expressed.
(1-B) Representation method for rounding to the nearest decimal point Similar to (1-A) above, the result obtained by rounding off the fractional part in the result of division (Y / X) by the positive fixed-point data of the computer. It becomes.

（１−Ｃ）小数以下五捨六入処理の表現方法
更に、数４２において、コンピュータの正の固定小数点データ同士による割り算（Ｚ／Ｗ）結果における、小数部五捨六入による結果以下に示す等式となる。

(1-C) Representation method of rounding and rounding off of decimal point Furthermore, in the formula 42, the result of rounding off the decimal part in the division (Z / W) result between the positive fixed-point data of the computer is shown below. It becomes an equation.

上記（１−Ａ）、（１−Ｂ）、及び、（１−Ｃ）での説明に基づいて、可逆性を更に保証する色変換の方法について以下に説明する。つまり、片方の変換を小数以下四捨五入で変換し、その逆方向の変換を小数以下五捨六入で変換することによって、可逆性を完全に保証できることを示すものである。
（２）低い分解能→高い分解能→低い分解能の連続変換によって完全復元を可能にする方法
２つの分解能α、βとし、β単位系からα単位系に変換し、その変換後のデータを使って、更にβ単位系に変換し戻すこととする。ただし、α＞β＞０とする。この場合、ｍｍ←→ＢＭＵ変換の場合、１ｉｎｃｈを、分解能α＝２５４０：１／１００ｍｍの単位、又は、分解能β＝１２００ＢＭＵの単位で表現するものとする。

Based on the description in (1-A), (1-B), and (1-C) above, a color conversion method that further guarantees reversibility will be described below. That is, it is shown that reversibility can be completely guaranteed by converting one of the conversions by rounding off the decimals and converting the conversion in the opposite direction by rounding off the decimals.
(2) Method to enable complete restoration by continuous conversion of low resolution → high resolution → low resolution. Two resolutions α and β are converted from β unit system to α unit system, and the converted data is used. Furthermore, it is supposed to convert back to the β unit system. However, α>β> 0. In this case, in the case of mm ← → BMU conversion, 1 inch is expressed in units of resolution α = 2540: 1/100 mm or in units of resolution β = 1200 BMU.

の関係で結ばれている場合には、

If you are tied in a relationship

とすると、

Then,

であるので、演算の内容から結果は整数であることより、Ｆ（α、β）となる。

Therefore, the result is F (α, β) because the result is an integer from the content of the calculation.

That is, since α → β conversion function (argument: β → α conversion function (argument: β system data)) = (β system data) representing an integer value, the original β system data is completely restored, and Even if α = β, complete restoration can be guaranteed.
(3) A color conversion method that guarantees reversibility (3-A) A color conversion formula that enables re-display (a personality equation based on a rational formula)
Based on the above [Original Color Conversion Formula Based on Luminance and Color Difference; Application Example to JPEG2000], the original color conversion formula can be expressed by an accurate equation using rational numbers.

  YCbCr → RGB → YCbCr conversion formula is

数４７において、Ａは行列であり詳しくは、

In Equation 47, A is a matrix.

のように表現される。従って、可逆性が保証される。
（３−Ｂ）整数（固定小数点演算）による色変換式
（ａ）小数以下五捨六入を適用したＹＣｂＣｒ→ＲＧＢ変換
上記（３−Ａ）にて示される数４７及び数４８に基づいて、上記（１−Ｃ）にて示される数４５を適用することによって、ＲＧＢは、ＹＣｂＣｒによって次のように表される。

It is expressed as Therefore, reversibility is guaranteed.
(3-B) Color conversion formula by integer (fixed-point arithmetic) (a) YCbCr → RGB conversion using rounding to the nearest decimal number Based on Equations 47 and 48 shown in (3-A) above, By applying the number 45 shown in (1-C) above, RGB is represented by YCbCr as follows.

（ｂ）小数以下四捨五入を適用したＹＣｂＣｒ→ＲＧＢ変換
上記（３−Ａ）にて示される数４７及び数４８に基づいて、上記（１−Ｂ）にて示される数４２を適用し、更に、数４９を代入することによって、ＲＧＢは、ＹＣｂＣｒによって次のように表される。以下の数式において、Ｘｍｏｄ（ｘ）＝０〜（ｘ−１）、即ち、最小値が０（ゼロ）であって、最大値が（ｘ−１）であるので、ｍｏｄ演算を"０〜（ｘ−１）"で表現している。

(B) YCbCr → RGB conversion with rounding to the nearest decimal number Based on the number 47 and the number 48 shown in the above (3-A), the number 42 shown in the above (1-B) is applied. By substituting Equation 49, RGB is represented by YCbCr as follows: In the following mathematical formula, Xmod (x) = 0 to (x−1), that is, the minimum value is 0 (zero) and the maximum value is (x−1). x-1) ".

とすると、

Then,

であるが、Ｙ'は整数であるので、Ｚ_ｙは０（ゼロ）になる。従って、Ｙ＝Ｙ'が導き出される。同様に、

However, since Y ′ is an integer, Z _y becomes 0 (zero). Therefore, Y = Y ′ is derived. Similarly,

とすると、

Then,

であるが、Ｃｂ'は整数であるので、Ｚ_ｂは０（ゼロ）になる。従って、Ｃｂ＝Ｃｂ'が導き出される。また、

Although, Cb 'is because an integer, _{Z b} is 0 (zero). Therefore, Cb = Cb ′ is derived. Also,

とすると、

Then,

であるが、Ｃｒ'は整数であるので、Ｚ_ｒは０（ゼロ）になる。従って、Ｃｒ＝Ｃｒ'が導き出される。

Although, Cr 'because an integer, _{Z r} is 0 (zero). Therefore, Cr = Cr ′ is derived.

  Such color conversion guarantees reversibility even for image data of 256 gradations or more.

1 is a schematic system configuration diagram showing an embodiment of the present invention. It is a schematic model diagram which shows the example of application to JPEG2000 color conversion. It is a schematic diagram which shows the example of application to the use which requires reversible color conversion. It is a schematic diagram which shows the example of a result of analog type color conversion. It is a schematic diagram which shows the example of a result of digital type | mold color conversion. It is a schematic diagram which shows the example of a result of the color conversion applied to JPEG2000.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Encoding part 2 Decoding part 4 Color space conversion (color coordinate system 1-> 2)
5 Compression 6 Expansion 7 Color space conversion (Color coordinate system 2 → 1)

Claims (8)

A data format reversible conversion method for forward conversion and reverse conversion of data between unit systems having different resolution levels,
Using the first unit system having a low resolution level for the forward conversion and the reverse conversion as a common unit system, the data of the first unit system having a low resolution level and the second having a resolution level higher than that of the first unit system Between the first data of the first unit system and the second data of the second unit system, after the inverse conversion from the first data of the first unit system to the second data of the second unit system When performing the forward conversion to the third data, reversible data conversion is performed by rounding off the decimal point so that the first data and the third data match. Data format reversible conversion method. The first unit system is a BMU unit system using inch units, and the second unit system is a unit system indicated by 1/100 mm using metric units,
Using the first unit system as a common unit system, the first data of the first unit system is the β system data and the second of the second unit system with the second unit system. When the data is expressed as α data,
The inverse transformation from the β-system data to the α-system data and the forward transformation from the α-system data to the β-system data,

By the integer operation connected in the relationship, the β data as the first data and the β data as the third data obtained by forward conversion after inverse transformation are matched with each other. 2. The data format reversible conversion method according to claim 1, wherein reversible conversion is performed by integer arithmetic. The integer arithmetic is

3. The reversible data format conversion method according to claim 2, wherein reversible data conversion is performed using a power-of-two operation of 2. The power of 2 is calculated by bit shift

4. The reversible data format conversion method according to claim 3, wherein reversible data conversion is performed by the method. A data format reversible conversion method for forward conversion and reverse conversion of data between unit systems having different resolution levels,
Using the first unit system having a low resolution level for the forward conversion and the reverse conversion as a common unit system, the data of the first unit system having a low resolution level and the second having a resolution level higher than that of the first unit system Inverse conversion from the first data of the first unit system to the second data of the second unit system is performed by integer arithmetic rounded to the nearest decimal point. By performing forward conversion from the second data to the third data of the first unit system by an integer operation with the decimal point rounded off, the first data and the third data match each other. A data format reversible conversion method characterized by carrying out various data conversions. The first unit system is a BMU unit system using inch units, and the second unit system is a unit system indicated by 1/100 mm using metric units,
Using the first unit system as a common unit system, the first data of the first unit system is the β system data and the second of the second unit system with the second unit system. When the data is expressed as α data,
The inverse transformation from the β-system data to the α-system data and the forward transformation from the α-system data to the β-system data,

By the integer operation connected in the relationship, the β data as the first data and the β data as the third data obtained by forward conversion after inverse transformation are matched with each other. 6. The data format reversible conversion method according to claim 5, wherein reversible conversion is performed by integer arithmetic. A data format conversion inverse conversion device comprising a data format reversible conversion means for performing forward conversion and reverse conversion of data between unit systems having different resolution levels,
Using the first unit system having a low resolution level for the forward conversion and the reverse conversion as a common unit system, the data of the first unit system having a low resolution level and the second having a resolution level higher than that of the first unit system Between the first data of the first unit system and the second data of the second unit system, after the inverse conversion from the first data of the first unit system to the second data of the second unit system When performing the forward conversion to the third data, reversible data conversion is performed by rounding off the decimal point so that the first data and the third data match. Data format reversible conversion device. A data format conversion inverse conversion device comprising a data format reversible conversion means for performing forward conversion and reverse conversion of data between unit systems having different resolution levels,
Using the first unit system having a low resolution level for the forward conversion and the reverse conversion as a common unit system, the data of the first unit system having a low resolution level and the second having a resolution level higher than that of the first unit system Inverse conversion from the first data of the first unit system to the second data of the second unit system is performed by integer arithmetic rounded to the nearest decimal point. By performing forward conversion from the second data to the third data of the first unit system by an integer operation with the decimal point rounded off, the first data and the third data match each other. A data format reversible conversion device characterized in that a simple data conversion is performed.

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