JP2006109394A - Color processing apparatus and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that image defects such as pseudo-contours occur, when tetrahedral interpolation is used for correction of color reproduction associated with color adjustment, because the surfaces of the tetrahedron satisfy boundary condition. <P>SOLUTION: Pixel positions of digital image data are calculated and RGB values in the pixel positions are obtained (S801). The obtained RGB values are displayed in the RGB value display region (S802). L*a*b* values are calculated by the basis function and coefficient value of B-spline solid for color calculation (S803). The calculated L*a*b* values are displayed in the L*a*b* value display region (S804). <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a color processing apparatus and method, for example, for creating a color process for calculating a color signal value of a second color system from a color signal value represented by a first color system, and creating a profile. The present invention relates to the calculation or prediction of color signal values.

  In recent years, with the spread of personal computers and workstations, desktop publishing (DTP) and digital image management have become widely used. In a computer system having a color monitor for DTP and a color printer, a color image is created / edited / processed on the monitor, an output image is checked by a preview, and a color image is output by the color printer. Alternatively, an image photographed by a digital camera is displayed on a color monitor or output by a color printer after color adjustment. In the field of such image processing, various color calculation methods are used depending on the purpose in order to realize desired color processing.

  In the print output preview in DTP, based on the color profile of the printing device, L * a * b * values are calculated to indicate what color reproduction will occur when an RGB image is printed, and this L * a * For example, the sRGB value is calculated from the b * value and previewed on the monitor. Here, a look-up table (LUT) is generally used for the color profile of the printing device. When calculating an L * a * b * value using this LUT, tetrahedral interpolation that performs linear interpolation calculation within a small region surrounded by four points is widely used. In particular, in tetrahedral interpolation using the LUT, a hexahedral area surrounded by eight adjacent colors is further divided into six tetrahedral areas, and linear interpolation is performed for each area. FIG. 1 is a diagram schematically showing six divisions into tetrahedrons.

  Further, in the color adjustment of the digital camera image, when a certain color is adjusted, the color reproduction is corrected so that the color around the adjusted color changes. There are various methods for correcting the color reproduction. As a typical method, a method of changing the gradation characteristics of RGB is known. However, such a method cannot limit the color reproduction correction to the local region. Therefore, as a further advanced correction method, a method using color gamut mapping is used. According to this method, the color reproduction can be corrected by changing the mapping parameter as in the technique disclosed in Japanese Patent Laid-Open No. 2002-33929, for example. As another correction method, there is a method in which color reproduction is approximated with a plurality of representative colors, and the change of the representative colors is combined with tetrahedral interpolation using the representative colors. According to this method, it is possible to limit the influence range only to the tetrahedron region including the adjustment color and correct the color reproduction.

  However, when tetrahedral interpolation is used, an image failure may occur due to switching of linear interpolation with the tetrahedral surface as a boundary. For example, in the preview of print output, there may be an image failure such as a decrease in preview display accuracy due to a decrease in L * a * b * value calculation accuracy or a pseudo contour due to switching of linear interpolation. In particular, when the lattice spacing of the LUT is coarse, the value changes abruptly with the surface of the tetrahedron as a boundary, and there is a tendency that an image defect appears remarkably.

  In addition, when tetrahedral interpolation is used in correction of color reproduction accompanying color adjustment, an image failure such as a pseudo contour may occur due to the surface of the tetrahedron becoming a boundary condition. In particular, when the rate of change in brightness varies with the surface of the tetrahedron as a boundary, smooth gradation changes such as gradation images are lost, and if the change in rate of change is steep, image disturbances such as pseudo contours appear more prominently. .

  Further, when color gamut mapping is performed in correction of color reproduction accompanying color adjustment, there is a problem that it is difficult to directly specify the color after adjustment. For example, according to a mapping method in which compression mapping is performed using a point on the L axis that is commonly used as a target point, the color change may become steep near the gamut boundary, and an image defect such as a pseudo contour may occur. . Figures 2 (a) and 2 (b) show how the color change becomes steep near the gamut boundary.Figure 2 (a) shows the monitor color reproduction, and Figure 2 (b) shows the solid line. The printer color reproduction after mapping is indicated by, and the printer color gamut is indicated by a dotted line in FIG.

  In the fields such as DTP and CAD described above, a color prediction technique for predicting actual physical stimulus values when a digital image is printed or displayed is essential.

  For example, there is color management as a technique in which this color prediction technique is indispensable. For example, when a color image is created, edited, or processed on a color monitor and output by a color printer, the color image on the monitor and the output image of the printer are perceived regardless of the color characteristics of the monitor or printer. Matching is required. As an example of a technique for realizing color management that satisfies such requirements, there is a CMS (Color Management System) that performs color management based on an ICC color profile defined by the ICC (International Color Consortium).

  CMS defines a device independent hub color space or PCS (Profile Connection Space) for color matching, and performs color conversion from the device color space to the hub color space (or PCS) on that color space. Color management is realized by using a source-side profile to be defined and a destination-side profile to define color conversion from the hub color space (or PCS) to the device color space.

  The processing system converts the input color signal value of the device color space depending on the input device into the color signal value of the hub color space (or PCS) by the source side profile, and further adapted to the output device by the destination side profile. It consists of two large conversion processes that convert the output color signal of the device color space. This system can deal with a wide range of flexibility, such as color matching from a scanner to a printer, and color matching from a monitor to a printer. For example, in a DTP system, if a monitor profile is specified as the source profile and a printer profile is specified as the destination profile, perceptual matching between the color image on the monitor and the output image of the printer becomes possible. .

  Here, since the quality of perceptual matching depends on the profile, it is necessary to create a profile that associates the color depending on the device with the color of the hub color space or the PCS as accurately as possible. Therefore, it is necessary to accurately perform color prediction that predicts a physical stimulus value when a device-dependent color is actually printed or displayed.

  As a color prediction technique, there is a table-type color prediction technique using patch colorimetric values and linear interpolation, and various interpolation methods such as tetrahedral interpolation, cube interpolation, and triangular prism interpolation have been proposed for the linear interpolation. However, the prediction accuracy by these interpolation methods depends on the grid density of the table. For this reason, when high accuracy is required, a great amount of labor is required to increase the number of grids and measure a very large number of patches.

JP 2002-33929 A

  An object of the present invention is to calculate a color with a smooth change reflecting a tendency of a color change when correcting the color reproduction.

  Another object of the present invention is to provide a color adjustment interface that can be easily controlled by the user.

  Another object of the present invention is to suppress the occurrence of vibration (see FIG. 23 (a)), which will be described later, when the coefficient value of the basis function is determined so as to pass a predetermined color coordinate value.

  Another object is to accurately predict the color signal value from the colorimetric results of a small number of patches.

  The present invention has the following configuration as one means for achieving the above object.

  In the first aspect of the present invention, when the color signal value of the second color system is calculated from the color signal value represented by the first color system, it is the same as the number of dimensions of the first color system. It is disclosed that a color signal value of the second color system is calculated using a multiple sum operation using a severe piecewise polynomial as a basis function.

  Further, in the second aspect of the present invention, the corrected value of the color is designated, the color reproduction is calculated according to the corrected value, and the change of the color reproduction is simulated according to the calculation result of the color reproduction. Generating data for original display is disclosed.

  In the third aspect of the present invention, when calculating a color signal value of a predetermined color system, a multiple sum having a piecewise polynomial of the same multiplicity as the number of dimensions of the first color system as a basis function. A conversion formula is set by calculation, and a plurality of color signal values represented by the first color system and a plurality of color signal values of the second color system to be calculated for these color signal values Based on the data that defines the combination, find the coefficients of the piecewise polynomial corresponding to the conversion formula that approximates the combination, or the conversion formula that smooths the curved surface set, polyhedron set, or hyperpolyhedron set connecting the combinations, and performs multiple summation Is used to calculate the color signal value of the second color system corresponding to the color signal value expressed in the first color system.

  According to a fourth aspect of the present invention, when calculating a color signal value of a predetermined color system, a multiple sum having a piecewise polynomial having the same multiplicity as the number of dimensions of the first color system as a basis function. Data indicating a combination of a plurality of color signal values represented by the first color system and a plurality of color signal values of the second color system, which is a colorimetric result for these color signal values, by setting an operation And calculating a plurality of color signal values of the second color system corresponding to the plurality of color signal values represented by the first color system using a multiple sum operation. Is disclosed.

  According to the present invention, when the color reproduction is corrected, the color can be calculated with a smooth change reflecting the tendency of the color change.

  In addition, it is possible to provide an interface for color adjustment that can be easily controlled by the user.

  In addition, when the coefficient value of the basis function is determined so as to pass a predetermined color coordinate value, it is possible to suppress the occurrence of vibration (see FIG. 23 (a)) described later.

  Further, the color signal value can be accurately predicted from the color measurement results of a few patches.

  Hereinafter, image processing according to an embodiment of the present invention will be described in detail with reference to the drawings.

[Constitution]
FIG. 3 is a block diagram illustrating a configuration example of the color processing apparatus according to the first embodiment.

  In FIG. 3, a CPU 101 is described later via a system bus (and PCI bus) 114 using the main memory 102 as a work memory according to a program stored in a main memory 102 or a hard disk drive (HDD) 105 including ROM and RAM. Various processes and controls to be described later are executed by controlling the configuration to be performed.

  A general-purpose parallel interface (I / F) 103 such as SCSI (Small Computer Standard Interface) interfaces the HDD 105 with the system bus 114. The graphic accelerator 106 interfaces the color monitor 107 and the system bus 114. The USB controller 108 interfaces the color printer 109 and the system bus 114. The keyboard / mouse controller 110 interfaces the input device such as the keyboard 111 and the mouse 112 with the system bus 114. Note that the HDD 105, the keyboard 111, and the mouse 112 may be interfaced with the system bus 114 by a serial bus interface such as the USB controller 108 or IEEE1394 instead of the SCSI I / F 103 and the keyboard / mouse controller 110. A network interface (I / F) 104 interfaces a local area network (LAN) 113 with a system bus.

[Preview operation]
A print image preview operation in the above configuration will be described. FIG. 4 is a diagram showing an example of a user interface for previewing.

  First, an image preview application stored in the HDD 105 is activated by a command from the CPU 101. Subsequently, the initial profile and initial digital image data stored in the HDD 105 in accordance with the processing of the image preview application are transferred to the main memory 102 via the SCSI I / F 103 and the system bus 114 based on a command from the CPU 101. . Then, the CPU 101 displays the window shown in FIG. The user confirms the color reproduction of the print image using the image preview 203 and the L * a * b * value display 205 in the displayed window.

  The window shown in FIG. 4 includes a button 201 for instructing reading of a profile, a button 202 for reading an image file for preview display, an image preview display area 203, an RGB value display area 204, L * a * b * A value display area 205 and an application end button 206 are provided.

  When the user clicks (or presses) the image file reading button 202 with the mouse 112 or the like and instructs to read the image, the digital image data stored in the HDD 105 according to the processing of the image preview application is sent to the CPU 101 command. Based on this, the data is transferred to the main memory 102 via the SCSI I / F 103 and the system bus 114. Alternatively, digital image data stored in a server connected to the LAN 113 or digital image data on the Internet is transferred to the main memory 102 via the network I / F 104 and the system bus 114 according to a command from the CPU 101. The The digital image data stored in the main memory 102 is appropriately processed and then newly stored as image data for preview display in the main memory 102 and displayed in the display area 203.

  Also, when the user clicks the profile load button 201 with the mouse 112 or the like and instructs to load the profile, the specified profile is read from the HDD 105 or via the network according to the processing of the image preview application, and the color Calculation processing is set. The digital image data stored in the main memory 102 is appropriately processed to generate image data for preview display. The image data for preview display is stored in the main memory 102 and displayed in the display area 203. Is done.

  Furthermore, when the user clicks an arbitrary position in the display area 203 with the mouse 112 to confirm color reproduction, the image preview application calculates the RGB value of the pixel corresponding to the click position from the digital image data stored in the main memory 102. Acquired and calculated L * a * b * value by the color calculation process described later, and displayed RGB value in RGB value display area 204 and L * a * b * value in L * a * b * value display area 205 To do.

  When the user clicks the end button 206 with the mouse 112 or the like, the image preview application releases the storage area and work area for the digital image data and preview display image data in the main memory 102 and ends the processing.

[Operation of image preview application]
FIG. 5 is a state transition diagram for explaining the operation of the image preview application.

  First, initialization such as securing various memory areas necessary for operation is performed (S301), an initial profile is read from the HDD 105 as an initial digital image file and a color calculation profile, and stored in the main memory 102 (S302). The digital image data held in the main memory 102 will be described as image data in which each RGB color signal is expressed by 8 bits without a sign. Further, the profile has a data structure as shown in FIG. 6B in which the correspondence between the color coordinate step of the grid point in the RGB color space and the coordinate value of the L * a * b * color space reproduced by the grid point is described. . The R / G / B value step is described at the head, and then L * a * b * color coordinates corresponding to each grid point are nested in the order of R, G, and B. FIG. 6A is a diagram schematically showing the data structure of the profile in the RGB color space.

  Next, using the stored profile, a coefficient and a basis function for a B-spline solid for color calculation (B-Spline Solid) are calculated by a process described later (S303), and a color calculation B is performed according to the process described later. The digital image data stored using the spline body is converted into image data for preview, displayed on the display area 203 (S304), and waiting for a user operation (S305).

  When the profile loading button 201 is pressed in the user operation waiting state (S305), a dialog for the user to specify a profile to be read is displayed. If a profile is specified, whether or not the profile can be opened. If it can be opened, the profile is read and stored in the main memory 102, and it is determined whether the profile format is correct (S306). If the format can be opened and is correct, the process proceeds to step S303. If the format is not open or illegal, the message is displayed and the process returns to step S305.

  When the image file reading button 202 is pressed, a dialog for the user to specify an image file to be read is displayed. When an image file is specified, it is determined whether the image file can be opened, If it can be opened, the image file is read and stored in the main memory 102, and it is determined whether or not the format of the image file is correct (S307). If the format can be opened and is correct, the process proceeds to step S304. If the format is not open or illegal, the fact is displayed and the process returns to step S305.

  When the mouse is clicked in the display area 203, the position of the mouse pointer on the display area 203 is stored, and then the RGB value of the pixel corresponding to the mouse pointer position is stored in the RGB value display area 204 according to the processing described later. The L * a * b * value when the RGB value is printed is displayed in the L * a * b * value display area 205 (S308), and the process returns to step S305.

  When the end button 206 is pressed, an end operation such as memory release is performed, and the image preview application is ended.

[Setting of B-spline body for color calculation (S303)]
The B-spline body for color calculation is defined by a multiple sum operation formula having the following piecewise polynomial as a basis function.
λ = Σ _i Σ _j Σ _k cλ _ijk N _ri (rr) N _gj (gg) N _bk (bb)
a = Σ _i Σ _j Σ _k ca _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (1)
b = Σ _i Σ _j Σ _k cb _ijk N _ri (rr) N _gj (gg) N _bk (bb)
Where rr, gg, and bb are RGB values
λ, a, b are L * a * b * values
Nr is the basis function in the R-axis direction
Ng is the basis function in the G-axis direction
Nb is the basis function in the B-axis direction
cλijk, caijk, cbijk are coefficients
Suffixes i, j, and k attached to Nr, Ng, and Nb
Basis function number in the basis

  FIG. 7 is a flowchart for explaining the coefficient and basis function calculation processing of the B-spline body for color calculation.

First, the correspondence between RGB values and L * a * b * values is acquired from the profile represented by the data structure shown in FIG. 6B (S401). The RGB value is calculated according to the order of nesting and the step value of the R / G / B value, and the L * a * b * value is a value described in the profile. Thereafter, the corresponding data of the RGB value and the L * a * b * value, the RGB value of the i-th editing color as rr _i , gg _i , bb _i , and the L * a * b * value as λ _i , a _i , b _This is described as _i .

Next, a basis function is calculated based on the R / G / B value step from the profile represented by the data structure shown in FIG. 6B, and stored in the main memory 102 (S402). A general DeBoor-Cox algorithm is used to calculate the basis function. If the steps of the R / G / B values are the same as shown in FIG. 6B, if the basis functions N _r , N _g , and N _b are all B-spline bases in the third place, all are shown in FIG. It becomes a four-node basis function of ξ0 to ξ3. Incidentally, FIG. 8 shows the basis functions N _r of R axis. In the following description, it is assumed that each basis function is a third-order B-spline basis.

  Next, using the calculated basis function and the correspondence relationship between the acquired RGB value and L * a * b * value, the matrix equation f = MC is changed to LU for each of the λ * component, the a * component, and the b * component. Each coefficient is calculated by solving using decomposition. Hereinafter, the coefficient calculation by the above equation will be described in detail.

First, the s-row t-column component m _st of the matrix M is calculated as follows.
m _st = N _ri (rr _s ) N _gj (gg _s ) N _bk (bb _s )… (2)
Where t = 25 (i-1) + 5 (j-1) + k
i, j, k are integers from 1 to 5

  Note that the relationship between t and i, j, k varies depending on the number of nodes and the order of basis functions. For example, in the case of a three-position B-spline basis and six nodes, the relationship is t = 49 (i-1) +7 (j-1) + k.

Next, calculation of the coefficients cλ _ijk , ca _ijk , and cb _ijk will be described. First, in order to calculate the coefficient cλ _ijk , the following matrix equation is solved using LU decomposition.
fλ = [λ ₁ , λ ₂ ,…, λ ₁₂₅ ]
cλ = [cλ ₁₁₁ , cλ ₁₁₂ ,…, cλ ₁₁₅ , cλ ₁₂₁ ,…, cλ ₁₅₅ , cλ ₂₁₁ ,…, cλ ₅₅₄ , cλ ₅₅₅ ]… (3)
fλ = M ・ cλ

Next, in order to calculate the coefficient ca _ijk , the following matrix equation is solved using LU decomposition.
fa = [a ₁ , a ₂ ,…, a ₁₂₅ ]
ca = [ca ₁₁₁ , ca ₁₁₂ ,…, ca ₁₁₅ , ca ₁₂₁ ,…, ca ₁₅₅ , ca ₂₁₁ ,…, ca ₅₅₄ , ca ₅₅₅ ]
fa = M ・ ca… (4)

Next, in order to calculate the coefficient cb _ijk , the following matrix equation is solved using LU decomposition.
fb = [b ₁ , b ₂ ,…, b ₁₂₅ ]
cb = [cb ₁₁₁ , cb ₁₁₂ ,…, cb ₁₁₅ , cb ₁₂₁ ,…, cb ₁₅₅ , cb ₂₁₁ ,…, cb ₅₅₄ , cb ₅₅₅ ]
fb = M ・ cb (5)

  Then, the calculated coefficient is stored in the main memory 102 (S404).

  By using the B-spline body calculated as described above, changes in L * a * b values relative to RGB values can be smoothly expressed as shown in the schematic diagram of FIG. In addition, FIG. 9 represents the calculation result of the B-spline body as a distribution in the L * a * b * space. A line other than the axis shown in FIG. 9 indicates the L when any one of the RGB values changes. Represents the trajectory of * a * b * values.

[Display of RGB value and L * a * b * value (S303)]
FIG. 10 is a flowchart for explaining the display processing of the RGB value and L * a * b * value at the designated image position.

First, the pixel position of the digital image data corresponding to the position of the mouse pointer is calculated, the RGB value of that pixel position is acquired (S801), and the acquired RGB value is displayed in the RGB value display area 204 (S802). Obtain the basis function and coefficient value of the B-spline body for color calculation from the memory 102, calculate the L * a * b * value using the following formula (S803), and use the calculated L * a * b * value as L * The data is displayed in the a * b * value display area 205 (S804).
λ = Σ _i ⁵ Σ _j ⁵ Σ _k ⁵ cλ _ijk N _ri (rr) N _gj (gg) N _bk (bb)
a = Σ _i ⁵ Σ _j ⁵ Σ _k ⁵ ca _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (6)
b = Σ _i ⁵ Σ _j ⁵ Σ _k ⁵ cb _ijk N _ri (rr) N _gj (gg) N _bk (bb)
Where rr, gg, and bb are RGB values
λ, a, b are L * a * b * values

[Generate preview image (S304)]
FIG. 11 is a flowchart for explaining the process of generating preview image data.

  First, an initialization operation such as discarding the existing preview image data and securing the work memory area for generating the preview image data and initializing variables is performed (S901). One pixel value (RGB value) is acquired from the digital image data stored in 102 (S902), the basis function and coefficient value of the B-spline body for color calculation are acquired from the main memory 102, and the same as step S803 Then, the L * a * b * value is calculated from the RGB value using the B-spline body for color calculation (S903).

  Next, the calculated L * a * b * value is converted into an RGB value based on sRGB (S904), and the RGB value is stored in the memory address (main memory 102) corresponding to the pixel position (S905). It is determined whether or not the above conversion has been performed on all the pixels of the data (S906), and steps S902 to S905 are repeated until the conversion is performed on all the pixels.

  When all the pixels are converted, the converted image data stored in the main memory 102 is stored as a preview image data in a predetermined area of the main memory 102 (S907), and the preview image data is displayed as an image preview. The display is displayed in the area 203 (S908), end processing such as releasing the working memory is performed (S909), and generation of the preview image is ended.

  As described above, when calculating a color from a plurality of representative colors, the color is calculated with a smooth change by naturally reflecting the tendency of the change in the value, so that it is possible to accurately calculate a color with a small number of representative colors. Furthermore, if this color calculation is applied to color adjustment, it is possible to limit the range of influence of color correction to the local area using the locality of the base, and to specify the adjusted color directly. It becomes possible. Along with the correction, the color changes smoothly, so that it is possible to correct a color with very good gradation.

  The image processing according to the second embodiment of the present invention will be described below. Note that in this embodiment, the same reference numerals as those in the first embodiment denote the same parts, and a detailed description thereof will be omitted.

  Example 2 describes a color processing apparatus that provides color correction and its user interface. The apparatus configuration is the same as that in FIG.

[Profile creation operation]
FIG. 12 is a diagram showing a user interface for creating a profile with color correction.

  First, a color reproduction editing application stored in the HDD 105 is activated by a user operation and a command from the CPU 101. Subsequently, the initial profile and initial edit color data stored in the HDD 105 are transferred to the main memory 102 via the SCSI I / F 103 and the system bus 114 based on the command of the CPU 101 in accordance with the processing of the color reproduction editing application. Is done. Then, the CPU 101 displays the window shown in FIG. The user edits the color reproduction by correcting the color to be edited with reference to the three-dimensional display of the color reproduction in the window.

  The window shown in FIG. 12 includes a button 1001 for instructing reading of editing color data, a button 1002 for instructing saving of editing color data, a button 1003 for saving editing results of color reproduction as a profile, and a color Reproduction 3D display area 1004, editing area 1005 for displaying or inputting the color number, RGB value, L * a * b * value for the color to be edited, check for instructing on / off of color gamut display A box 1006 has a check box 1007 for turning on / off the point display of the edit color, a check box 1008 for instructing on / off of the color reproduction display as the color reproduction editing result, and a three-dimensional display of the profile color distribution. There is a check box 1009 and an application end button 1010.

  When the user clicks (or presses) the edit color data read button 1001 with the mouse 112 or the like to instruct to read the edit color data, the edit color data stored in the HDD 105 according to the process of the color reproduction editing application is stored in the CPU 101. Is transferred to the main memory 102 via the SCSI I / F 103 and the system bus 114 based on the command. Alternatively, edit color data stored in a server connected to the LAN 113 or edit color data on the Internet is transferred to the main memory 102 via the network I / F 104 and the system bus 114 in accordance with a command from the CPU 101. The Then, a color reproduction calculation process is executed. The color reproduction calculation process is also executed when the user edits the color in the editing area 1005.

  The calculation process result of color reproduction is displayed in a pseudo three-dimensional manner in the three-dimensional display area 1004 for color reproduction according to the setting of each check box. When the color gamut display check box 1006 is checked, the three-dimensional shape of the color gamut of the edit color data is displayed. When the edit color display check box 1007 is checked, all the edit colors are displayed as points. When the color reproduction display check box 1008 is checked, color reproduction information configured according to the RGB value of the current edit color is displayed. If the profile distribution display check box 1009 is checked, the profile LUT value is displayed as a dot. Of course, when the check boxes 1006 to 1009 are turned on and off, the display area 1004 is updated to the display form as described above.

  Further, when the user presses the edit color data save button 1002 to instruct to save the edit color data, the color reproduction edit application saves the edit color data being edited in the HDD 105.

  When the user presses a profile save button 1003 to instruct profile saving, the color reproduction editing application saves the generated profile in the HDD 105.

  When the user presses the end button 1010, the color reproduction editing application releases all data storage areas and work areas used for the process, and ends the process.

[Operation of color reproduction editing application]
FIG. 13 is a state transition diagram for explaining the operation of the color reproduction editing application.

  First, initialization such as securing various memory areas necessary for operation is performed (S1101), initial color editing data is read from the HDD 105 and stored in the main memory 102 (S1102). The color editing data held in the main memory 102 represents a set of RGB values that specify colors in the RGB color space and L * a * b * color coordinates that represent reproduction colors at the time of printing, and a color gamut. It has a data structure shown in FIG. 14 composed of triangular patch data. The total number of data is described at the top, and then a set of RGB values and L * a * b * color coordinates is described for the total number of data. Subsequently, the total number of triangular patch data representing the color gamut is described, and thereafter triangular patch data composed of three L * a * b * values representing the three vertices of the triangle is described by the total number of patches.

  Next, using the color editing data stored in the main memory 102, the coefficient and basis function for the B-spline body for color calculation are calculated by the process described later (S1103), and the color calculation B is performed according to the process described later. -Create a profile using the spline body, store it in the main memory 102 (S1104), and calculate 3D object data for pseudo 3D display using the B-spline body for color calculation and the profile according to the processing described later (S1105). As 3D object data, solid data for color gamut display, point data for edit color display, solid data for color reproduction display, and point data for profile display are generated.

  Subsequently, the process waits for a user operation (S1106). In this state, when the edit color data read button 1001 shown in FIG. 12 is pressed, a dialog for the user to specify the color edit data file to be read is displayed. When the file is specified, the file can be opened. If it can be opened, the file is read and stored in the main memory 102, and it is determined whether or not the format of the color editing data is correct (S1108). If the format is open and correct, the process proceeds to step S1103. If the format is not open or illegal, the message is displayed and the process returns to step S1106.

  When the edit color data save button 1002 shown in FIG. 12 is pressed, the edit color data stored in the main memory 102 is saved in the HDD 105 in a predetermined format (S1109), and the process returns to step S1106.

  When the profile save button 1003 shown in FIG. 12 is pressed, the profile stored in the main memory 102 is saved in the HDD 105 in a predetermined format (S1110), and the process returns to step S1106.

  Also, if the color gamut display check box 1006 shown in FIG. 12 is operated and checked, the solid data for color gamut display is displayed, and if the check is removed, the solid data is not displayed (S1111). Return to step S1106. When the color gamut display is turned on, a figure in the three-dimensional display area 1004 shown in FIG. 12 is displayed. Note that FIG. 12 shows a single display example of solid data for color reproduction display, and other 3D object data may be superimposed and displayed.

  Also, the edit color display check box 1007 shown in FIG. 12 is operated, and if it is checked, the edit color display point data is displayed, and if the check is removed, the same point data is not displayed (S1112). Return to step S1106. When the edit color display is turned on, a figure as shown in the three-dimensional display area 1004 shown in FIG. 15 is displayed. Note that FIG. 14 shows a single display example of point data for editing color display, and other 3D object data may be superimposed and displayed.

  In addition, when the color reproduction display check box 1008 shown in FIG. 12 is operated and checked, the solid data for color reproduction display is displayed, and when the check is removed, the solid data is not displayed (S1113). Return to step S1106. When the color reproduction display is turned on, a figure as shown in the three-dimensional display area 1004 shown in FIG. 16 is displayed. FIG. 15 shows an example of single display of solid data for color reproduction display, and other 3D object data may be displayed in a superimposed manner.

  In addition, when the check box 1009 of the profile distribution display shown in FIG. 12 is operated and checked, the point data for profile display is displayed, and when the check is removed, the point data is not displayed (S1114), The process returns to step S1106. When the profile distribution display is turned on, a figure as shown in the three-dimensional display area 1004 shown in FIG. 17 is displayed. Note that FIG. 17 shows an example of single display of point data for profile display, and other 3D object data may be superimposed and displayed.

  Also, when any one of the color number, RGB value, and L * a * b * value of the editing area 1005 shown in FIG. 12 is input, the RGB value and L * a * of the specified color number are input based on the input. The b * value is corrected, and an L * a * b * value to be described later is corrected (S1107), and the process proceeds to step S1103.

  When an end button 1010 shown in FIG. 12 is pressed, an end operation such as memory release is performed, and the color reproduction editing application is ended.

[Setting of B-spline body for color calculation (S1103)]
Below, for the sake of simplicity, the expression of the B-spline body is expressed as follows. In the following equation, C _ijk is a three-dimensional column vector representing L * a * b * coefficients, and the coefficients cλ _ijk , ca _ijk , and cb _ijk described with reference to the flowchart of FIG. Are summarized in
┌ ┐
│λ│
│ a│ = Σ _i Σ _j Σ _k C _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (7)
│ b│
└ ┘

  FIG. 18 is a flowchart for explaining processing for calculating coefficients and basis functions for a B-spline body for color calculation.

First, from the edit color data represented by the data structure shown in FIG. 14, the correspondence relationship between the RGB value of the edit color and the L * a * b * value is acquired for all the sets (S1201). Are subjected to a gamma correction operation of γ = 2.2 (S1202), and a basis function is calculated and stored in the main memory 102 (S1203). However, from the edit color data the total number n ³ of edit color data, the number of nodes is n-1.

  Next, similarly to step S403 shown in FIG. 7, the matrix equation is calculated and the coefficient of the B-spline body is calculated using the equation (S1204), and the calculated coefficient is stored in the main memory 102 (S1205). ).

[Calculate profile (S1104)]
FIG. 19 is a flowchart for explaining the creation of a profile using a B-spline body for color calculation.

First, an initializing operation such as allocating a working memory area and initializing variables is performed (S1401), and one RGB value corresponding to the LUT lattice point of the profile is acquired according to the appropriate order (S1402). The basis function and coefficient value of the B-spline body for color calculation are acquired from the memory 102, and the L * a * b * value is calculated using the following equation (S1403). In the following equation, rr, gg, and bb are values obtained by performing a gamma correction operation of γ = 2.2 on the R value, G value, and B value acquired in step S1402, respectively.
┌ ┐
│λ│
│ a│ = Σ _i Σ _j Σ _k C _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (8)
│ b│
└ ┘

  Next, the calculated L * a * b * value is stored in the memory address (main memory 102) corresponding to the LUT grid point position (S1404), and whether or not the above conversion is applied to all the LUT grid points. (S1405), and steps S1402 to S1404 are repeated until the above conversion is applied to all the LUT lattice points.

  When conversion is performed on all LUT lattice points, the converted LUT data stored in the main memory 102 is stored as profile data in a predetermined area of the main memory 102 (S1406), and the work memory is released, etc. The operation is performed (S1407), and the profile creation process is terminated.

[3D object generation (S1105)]
The solid data for gamut display uses all the triangular patch data attached to the color edit data to generate solid data in polygon notation. The point data for editing color display uses the L * a * b * values of all editing data as points, and generates point data. Point data for profile display is generated using all L * a * b * table values in the LUT as points. The solid data for color reproduction display is generated as follows.

  First, generate a 5x5x5 grid with steps [0, 64, 128, 192, 255], with the vertex of the grid cube and the grid point adjacent to the editing color as the vertex, and the volume is maximized Get a cuboid. Next, for all grid points on the rectangular parallelepiped, L * a * b * values are calculated from the RGB values in the same manner as in step S1403, and finally, from the calculated set of L * a * b * values Generate solid data for color reproduction display in polygon notation.

[Edit Color Edit (S1107)]
FIG. 20 is a flowchart for describing processing for correcting the RGB value, the L * a * b * value, or both of the color editing data of the number designated in the editing area 1005 shown in FIG.

  First, it is determined whether or not the specified L * a * b * value is out of the color gamut (S1501). If it is out of the color gamut, the specified L * a * b * value and L * a * b * value are determined. An intersection point where a straight line connecting the colors (50, 0, 0) intersects the color gamut is calculated, and the calculated intersection value is set as a target color as shown in FIG. 21 (S1502). If it is not out of the gamut, the specified L * a * b * value is used as the target color. Then, the RGB value and the L * a * b * value of the target value are stored in the main memory 102 as the color editing data of the designated number (S1503).

  In this way, it is possible to provide an interface for color adjustment that can be easily controlled by the user.

  In each of the above embodiments, a basic calculation method in color calculation has been described, and an application example of the calculation method has been described. Therefore, the present invention can be applied not only to preview and color reproduction correction as shown in the embodiment, but also to various uses relating to image processing such as color gamut mapping, color separation from RGB to CMYK, profile creation, and calibration. .

[Modification]
In the above embodiment, an example in which B-splines are used as basis functions in the solid representation has been described. However, any piecewise function such as rational B-spline, non-uniform rational B-spline, Bezier, rational Bezier, etc. can be used as the basis function. Since it is more desirable that the locality of the basis function exists, the embodiment has been described using the most representative B-spline.

  In the above embodiment, the number of nodes on each base is assumed to be the same. However, the number of nodes can be changed for each base so that it can be easily guessed. However, in Example 1, if the number of nodes in the R-axis direction is l, the number of nodes in the G-axis direction is m, and the number of nodes in the B-axis direction is n, the number of profile data is (l + 1) x (m + 1 ) X (n + 1), and the number of profile nesting is "l + 1" for R, "m + 1" for G, and "n + 1" for B . Further, in Example 2, if the number of nodes in the R-axis direction is l, the number of nodes in the G-axis direction is m, and the number of nodes in the B-axis direction is n, the number of data of the color editing data is (l + 1) × (m + 1) x (n + 1).

In the above embodiment, L * a * b * three-dimensional was calculated from RGB three-dimensional. However, there is no restriction on the calculated dimension. For example, when calculating a gray value (scalar value) from an RGB value, it can be expressed as the following equation.
gray = Σ _i Σ _j Σ _k c _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (9)

Also, for example, when calculating the CMYK value from the RGB value, it can be expressed as the following equation.
┌ ┐
│c│
│m│ = Σ _i Σ _j Σ _k C _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (10)
│y│
│k│
└ ┘
Where C _ijk is a four-dimensional column vector representing the cmyk coefficient

In the above-described embodiment, solid representation by RGB three-dimensional is used as the color space given to the equation. However, as can be easily guessed, it can be extended to a two-dimensional surface representation such as xy chromaticity, or a four-dimensional representation such as cmyk. For example, when calculating one RGB value from xy chromaticity, the following equation may be used.
┌ ┐
│R│
│G│ = Σ _i Σ _j C _ij N _xi (x) N _yj (y)… (11)
│B│
└ ┘

Alternatively, when calculating the L * a * b * value from the CMYK value, the following equation may be used.
┌ ┐
│λ│
│ a│ = Σ _i Σ _j Σ _k Σ _l C _ijkl N _ci (c) N _mj (m) N _yk (y) N _bkl (bk)… (12)
│ b│
└ ┘

  However, as is clear from the above equation, the multiplicity of the sum operation must be equal to the color space given to the equation, that is, the number of dimensions of the input color signal value. In addition, in order to obtain the coefficients in the summation formula, the matrix equation must be changed as the solid representation is expanded.

  As is clear from the above embodiments, the color space to be used is not limited, and color spaces such as CMYK, L * a * b *, JCH, XYZ, and xy can be used. Further, it can be applied to ink color separation, and a 6-dimensional color space obtained by adding light cyan and light magenta to CMYK can also be used. The color space given to the equation and the color space calculated from the equation may be the same color space.

  In the second embodiment, the gamma correction operation is performed on the equation before giving it to the B-spline body. However, this conversion can be replaced by other higher-order transformations or RGB → RGB affine transformations.

  Hereinafter, color processing according to the third embodiment of the present invention will be described. Note that the same reference numerals in the third embodiment denote the same parts as in the first and second embodiments, and a detailed description thereof will be omitted.

[Overview]
According to the technology that realizes the color calculation by the non-linear calculation described in the first and second embodiments, when the color is calculated from a plurality of representative colors, the trend of the color value change is naturally reflected in a smooth change. Since the color is calculated, it is possible to calculate the color accurately even with a small number of representative colors. If this technology is further applied to color adjustment, it is possible to naturally limit the range of influence of color correction to the local region using the locality of the base, and to directly specify the color after adjustment. . Furthermore, since the color changes smoothly with the correction, it is possible to correct the color with very good gradation. Of course, this technique can be applied to various uses relating to image processing, such as color gamut mapping, color separation from RGB to CMYK, profile creation, and calibration.

  However, when determining the non-linear calculation, the coefficient value of the basis function of the non-linear calculation is determined so as to pass a predetermined color coordinate value. According to such a calculation method, the non-linear calculation has smooth calculation characteristics, but on the other hand, vibration may occur so that it can be easily inferred from a one-dimensional spline function.

  FIGS. 23 (a) and 23 (b) are diagrams for explaining the vibration described above using a one-dimensional B-spline function as an example. To determine the coefficient value of the basis function so as to pass the predetermined color coordinate value is to determine the one-dimensional B-spline function so as to pass the predetermined value as shown in FIG. 23 (a) or (b). Correspondingly, as shown in FIG. 23 (a), even a slight vibration may occur. Such vibration may cause a problem depending on the calculated color signal. For example, vibration in the brightness signal appears as unevenness in the brightness (or density) of the image and is easily perceived as an image failure.

[Setting of B-Spline body for color calculation (S1103)]
First, the calculation processing (S1103) of the coefficients and basis functions of the B-spline body for color calculation in FIG. 13 will be described. Hereinafter, the B-spline body for color calculation is defined by the equation (13).
λ = Σ _i Σ _j Σ _k cλ _ijk N _ri (rr) N _gj (gg) N _bk (bb)
a = Σ _i Σ _j Σ _k ca _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (13)
b = Σ _i Σ _j Σ _k cb _ijk N _ri (rr) N _gj (gg) N _bk (bb)
Where rr, gg, and bb are RGB values
λ, a, b are L * a * b * values
N _r is the basis function in the R-axis direction
N _g is the basis function in the G-axis direction
N _b is the basis function in the B-axis direction
cλ _ijk , ca _ijk , cb _ijk are coefficients
Suffixes i, j, k attached to N _r , N _g , N _b are
Basis function number in the basis for each axis

  FIG. 22 is a flowchart for explaining the calculation processing (S1103) of the coefficients and basis functions of the B-spline body for color calculation.

First, correspondence data between the RGB value and L * a * b * value of the edit color is acquired for all sets from the edit color data represented by the data structure shown in FIG. 14 (S401). Thereafter, the corresponding data of the RGB value and the L * a * b * value, the RGB value of the i-th editing color as rr _i , gg _i , bb _i , and the L * a * b * value as λ _i , a _i , b _This is described as _i .

Next, after appropriately determining the nodes, a basis function is calculated based on the nodes and stored in the main memory 102 (S402). As a method for determining a node, the number of nodes and coordinates may be determined in advance, or the node may be determined from a change in L * a * b * value. A general DeBoor-Cox algorithm is used to calculate the basis function after the node is determined. For example, if the basis functions N _r , N _g , and N _b are all third-order B-spline bases and the number of nodes is 4, all four-node bases ξ0 to ξ3 as shown in FIG. Become a function. Incidentally, FIG. 8 shows the basis functions N _r of R axis. In the following, the basis functions will be described as B-spline bases with three positions of four nodes.

  Next, the calculated basis function and the correspondence data of RGB values and L * a * b * values obtained from the edit color data shown in Fig. 14 are approximated (or the polyhedron set connecting these correspondence data is smoothed) Each coefficient of the B-spline body having such characteristics is calculated (S403). For example, when viewed one-dimensionally, this corresponds to obtaining a B-spline function as shown in FIG. 23 (b) in which the vibration and ripple occurring in FIG. 23 (a) are suppressed.

  This process is performed by solving the matrix equation f = MC using LU decomposition for each of the L * component, the a * component, and the b * component, and calculating each coefficient. Hereinafter, the coefficient calculation by the above equation will be described in detail.

First, the s-row t-column component m _st of the matrix M is calculated as follows.
m _st = Σ _x (N _ri (rr _x ) N _gj (gg _x ) N _bk (bb _x )
・ N _rl (rr _x ) N _gm (gg _x ) N _bn (bb _x )}… (14)

  Here, s = 25 (I-1) + 5 (j-1) + k is established between i, j, and k with respect to s, and between l, m, and n with respect to t. t = 25 (l-1) + 5 (m-1) + n. This relationship varies depending on the number of nodes and the order of the basis function. For example, in the case of a six-node B-base spline at the third position, the relationship is t = 49 (I-1) +7 (j-1) + k.

Next, calculation of the coefficients cλ _ijk , ca _ijk , and cb _ijk will be described. First, in order to calculate the coefficient cλ _ijk , the s row component fλ _s of the column vector fλ is calculated as follows to determine the column vector fλ.
fλ _s = Σ _x N _ri (rr _x ) N _gj (gg _x ) N _bk (bb _x ) ・ λ _x … (15)

Again, as before, s = 25 (I-1) + 5 (j-1) + k stands for i, j, and k with respect to s. It depends on the order of the function. Then, using LU decomposition, the following matrix equation is solved to calculate the coefficient cλ _ijk .
cλ = [cλ ₁₁₁ , cλ ₁₁₂ ,…, cλ ₁₁₅ , cλ ₁₂₁ ,
…, Cλ ₁₅₅ , cλ ₂₁₁ ,…, cλ ₅₅₄ , cλ ₅₅₅ ]… (16)
fλ = M ・ cλ

Next, in order to calculate the coefficient ca _ijk , the s row component fa _s of the column vector fa is calculated as follows to determine the column vector fa.
fa _s = Σ _x N _ri (rr _x ) N _gj (gg _x ) N _bk (bb _x ) ・ a _x … (17)

After this, the following matrix equation is solved using LU decomposition.
ca = [ca ₁₁₁ , ca ₁₁₂ ,…, ca ₁₁₅ , ca ₁₂₁ ,
…, Ca ₁₅₅ , ca ₂₁₁ ,…, ca ₅₅₄ , ca ₅₅₅ ]… (18)
fa = M ・ ca

Next, in order to calculate the coefficient cb _ijk , the s row component fb _s of the column vector fb is calculated as follows to determine the column vector fb.
fb _s = Σ _x N _ri (rr _x ) N _gj (gg _x ) N _bk (bb _x ) ・ b _x … (19)

After this, the following matrix equation is solved using LU decomposition.
cb = [cb ₁₁₁ , cb ₁₁₂ ,…, cb ₁₁₅ , cb ₁₂₁ ,
…, Cb ₁₅₅ , cb ₂₁₁ ,…, cb ₅₅₄ , cb ₅₅₅ ]… (20)
fb = M ・ cb

  Then, the calculated coefficient is stored in the main memory 102 (S404). By using the above equations (15) and (17), the sum of squares of errors can be reduced. As a result, vibration and ripple can be suppressed.

[Calculate profile (S1104)]
Next, creation of a profile using a B-spline body for color calculation (S1104) will be described with reference to FIG.

First, an initialization operation is performed, such as allocating a working memory area and initializing variables (S1401). The base function and coefficient value of the B-spline body for color calculation are acquired from the memory 102, and the L * a * b * value is calculated using the following equation (S1403).
λ = Σ _{i = 1} ⁵ Σ _{j = 1} ⁵ Σ _{k = 1} ⁵ cλ _ijk N _ri (rr) N _gj (gg) N _bk (bb)
a = Σ _{i = 1} ⁵ Σ _{j = 1} ⁵ Σ _{k = 1} ⁵ ca _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (21)
b = Σ _{i = 1} ⁵ Σ _{j = 1} ⁵ Σ _{k = 1} ⁵ cb _ijk N _ri (rr) N _gj (gg) N _bk (bb)
Where rr, gg, and bb are RGB values
λ, a, b are L * a * b * values
N _r is the basis function in the R-axis direction
N _g is the basis function in the G-axis direction
N _b is the basis function in the B-axis direction
cλ _ijk , ca _ijk , cb _ijk are coefficients
Suffixes i, j, k attached to N _r , N _g , N _b are
Basis function number in the basis for each axis

  Next, the calculated L * a * b * value is stored in the memory address (main memory 102) corresponding to the LUT grid point position (S1404), and whether or not the above conversion is applied to all the LUT grid points. (S1405), and steps S1402 to S1404 are repeated until the above conversion is applied to all the LUT lattice points.

  When conversion is performed on all LUT lattice points, the converted LUT data stored in the main memory 102 is stored as profile data in a predetermined area of the main memory 102 (S1406), and the work memory is released, etc. The operation is performed (S1407), and the profile creation process is terminated.

[3D object generation (S1105)]
The generation of the solid data for displaying the color gamut in step S1105 is the same process as in the first embodiment, and thus detailed description thereof is omitted.

[Edit Color Edit (S1107)]
The editing of the editing color in step S1107 is the same process as in the first embodiment, and thus detailed description thereof is omitted.

  As described above, since the non-linear operation is performed so as to approximate / smooth the distributed color, it is possible to suppress the above-described non-linear operation vibration and ripple, and obtain a good color reproduction. That is, taking a one-dimensional B-spline function as an example, it is possible to calculate a smooth function in which vibration and ripple are suppressed as shown in FIG. Further, since the non-linear operation is determined so that the total sum of errors is minimized, good results can be obtained in the fidelity of color reproduction.

  Therefore, the third embodiment naturally reflects the change trend of the color signal value and can realize a smooth non-linear calculation that does not generate vibration and ripple, and is thus extremely useful for color calculation.

  In the above, a basic calculation method in color calculation has been described, and an application example of the calculation method has been described. However, the present embodiment is not limited to the above color reproduction correction, but includes color gamut mapping and calibration. It can be applied to various uses related to image processing.

  The color processing according to the fourth embodiment of the present invention will be described below. Note that the same reference numerals in the fourth embodiment denote the same parts as in the first to third embodiments, and a detailed description thereof will be omitted.

  In the fourth embodiment, the color calculation method using the B spline body is changed. Specifically, after performing a gamma correction operation on the RGB values, a color is calculated using a B-spline body. In the following, changes in the coefficient and basis function calculation process for the color calculation B spline body in step S1103 and the profile creation process in step S1104, which are differences from the third embodiment, will be described.

[Setting of B-Spline body for color calculation (S1103)]
Below, for the sake of simplicity, the expression of the B-spline body is expressed as follows. In the following equation, C _ijk is a three-dimensional column vector representing L * a * b * coefficients, and the coefficients cλ _ijk , ca _ijk , and cb _ijk described with reference to the flowchart of FIG. Are summarized in
┌ ┐
│λ│
│ a│ = Σ _i Σ _j Σ _k C _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (22)
│ b│
└ ┘

  Next, processing for calculating coefficients and basis functions for a B-spline body for color calculation will be described with reference to the flowchart shown in FIG.

  The sRGB formula stipulates that RGB values are converted into XYZ values by performing gamma calculation and matrix calculation. Therefore, the RGB reproduction colors in sRGB show a distribution with a certain tendency in the L * a * b * color space. Therefore, in order to improve the color calculation accuracy by the B-spline body, it is desirable to correct the RGB values in advance by gamma calculation.

  First, from the edit color data represented by the data structure shown in FIG. 14, the correspondence relationship between the RGB value of the edit color and the L * a * b * value is acquired for all the sets (S1201). The gamma correction operation of γ = 2.2 is performed on the RGB value in the set (S1202), and nodes are determined so as to be appropriate, then basis functions are calculated based on these nodes and stored in the main memory 102 (S1203). . In the following, the basis functions will be described as B-spline bases with three positions of four nodes.

  Next, in the same manner as in step S403 shown in FIG. 7, the matrix equation is calculated and the coefficient of the B spline body is calculated using the equation (S1204), and the calculated coefficient is stored in the main memory 102 (S1205). . However, the difference from step S403 is that the parametric value to be assigned to the basis function is not the RGB value itself but a value obtained by performing a gamma correction operation on the RGB value.

  Note that the gamma coefficient here is not directly related to the gamma equivalent value 2.2 in the sRGB formula. Accordingly, the color calculation accuracy may be further improved when a value such as 1.7 is used instead of 2.2.

[Calculate profile (S1104)]
The procedure for creating a profile using a B-spline body for color calculation is the same as the flowchart of the first embodiment shown in FIG. Therefore, an initialization operation such as securing a working memory area and initializing variables is performed (S1401), and one RGB value corresponding to the LUT lattice point of the profile is acquired according to the appropriate order (S1402). The basis function and coefficient value of the B-spline body for color calculation are acquired from the memory 102, and the L * a * b * value is calculated using the following equation (S1403). However, rr, gg, and bb in the following expression are values obtained by performing a gamma correction operation of γ = 2.2 on the R value, G value, and B value acquired in step S1402, respectively.
┌ ┐
│λ│
│ a│ = Σ _i Σ _j Σ _k C _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (23)
│ b│
└ ┘

  Next, the calculated L * a * b * value is stored in the memory address (main memory 102) corresponding to the LUT grid point position (S1404), and whether or not the above conversion is applied to all the LUT grid points (S1405), and steps S1402 to S1404 are repeated until the above conversion is applied to all the LUT lattice points.

[Modification]
Weighting approximation In Examples 3 and 4 described above, the B spline body was calculated so that the sum of the distance between the color calculated by the B spline body and the edit color was minimized without weighting. However, it is also possible to perform weighting for each editing color so that the sum of the weighted distances is minimized. At this time, when the matrix equation is, for example, the calculation of the lightness calculation coefficient in the first embodiment, the matrix element and the vector element on the left side of the equation are represented by the following expressions.
m _st = Σ _x (w _x N _ri (rr _x ) N _gj (gg _x ) N _bk (bb _x )
・ N _rl (rr _x ) N _gm (gg _x ) N _bn (bb _x )}… (24)
fλ _s = Σ _x (w _x N _ri (rr _x ) N _gj (gg _x ) N _bk (bb _x ) ・ λ _x

Here, w _x is a weight value for the x-th edit color, and the approximation of the color improves as the weight value increases.

  As a method for setting the weighting factor, for example, the user may manually specify the weighting factor for an editing color near the skin color. By adjusting the weighting coefficient, the user can improve color reproducibility in the vicinity of important colors such as skin color while observing the influence on the surroundings.

Alternatively, as another weighting factor setting method, for example, wx = 1 / √ (a ² + b ² ) may be automatically set according to the saturation of the editing color. As can be seen from the CIEΔE94 formula, human vision becomes insensitive near high saturation, so color reproduction is better when high color reproducibility is obtained with low saturation than when high saturation color is obtained. As effective. Therefore, as described above, by automatically setting the weight, it is possible to acquire high color reproducibility in the vicinity of low saturation and obtain more visually preferable color reproduction.

Replacement of B-spline basis functions with other piecewise polynomials in the solid representation In the third and fourth embodiments described above, examples of using B-splines as the basis functions in the solid representation have been described. However, as a basis function, any piecewise function such as rational B spline, non uniform rational B spline, Bezier, rational Bezier, etc. can be used. Since it is more desirable that the locality of the basis function exists, the embodiment has been described using the most typical B-spline.

Expansion of solid representation In the above-described Examples 3 and 4, solid representation by RGB three-dimensional was used as the color space given to the expression. However, it can be extended to a two-dimensional surface representation such as xy chromaticity, or a four-dimensional representation such as cmyk. For example, when calculating one RGB value from xy chromaticity, the following equation may be used.
┌ ┐
│R│
│G│ = Σ _i Σ _j C _ij N _xi (x) N _yj (y)… (25)
│B│
└ ┘

Alternatively, when the xy chromaticity value is calculated from the cmyk value, the following equation may be used.
┌ ┐
│x│
│ │ = Σ _i Σ _j Σ _k Σ _l C _ijkl N _ci (c) N _mj (m) N _yk (y) N _bkl (bk)… (26)
│y│
└ ┘

  However, as is apparent from the above equation, the multiplicity of the sum operation must be equal to the color space given to the equation, that is, the number of dimensions of the input color signal value.

In addition, in order to obtain the coefficients in the summation formula, the matrix equation must be changed as the solid representation is expanded. For example, in the case of two-dimensional surface expression, when calculating from the xy chromaticity, the matrix equation for the R value coefficient must be defined as a matrix M and a vector f as shown in the following equation.
m _st = Σ _a N _xi (x _a ) N _yj (y _a ) N _xl (x _a ) N _ym (y _a )… (27)
fr _s = Σ _a N _xi (x _a ) N _yj (y _a ) ・ r _a

  Here, when the number of nodes is 5, s = 5 (i-1) + j between i and j with respect to s, and t = 5 (l-1) + m stands.

Also, for a four-dimensional representation such as cmyk, the matrix equation for the x-value coefficient must define a matrix M and a vector f as in the following equation.
m _st = Σ _aci (c _a ) N _mj (m _a ) N _yk (y _a ) N _bkl (bk _a )
・ N _co (c _a ) N _mp (m _a ) N _yq (y _a ) N _bkr (bk _a )}… (28)
fx _s = Σ _a N _ci (c _a ) N _mj (m _a ) N _yk (y _a ) N _bkl (bk _a ) ・ x _a

  Here, when the number of nodes is 5, s = 125 (i-1) + 25 (j-1) + 5 (k-1) + l between i, j, k, and l However, t = 125 (o-1) + 25 (p-1) + 5 (q-1) + r similarly holds between o, p, q, and r with respect to t.

  Of course, if the number of dimensions is five or more, the matrix equation must be changed as well.

Color Space to be Used In Examples 3 and 4, there is no limitation on the color space, and a CMYK color space, an L * a * b * color space, a JCH color space, an XYZ color space, an xy color space, and the like can be used. Further, the present invention can be applied to ink color separation, and a 6-dimensional color space obtained by adding light cyan and light magenta to CMYK, and an 8-dimensional color space obtained by adding red ink and green ink can also be used. Further, the color space given to the equation and the color space calculated from the equation may be the same color space.

  The color processing according to the fifth embodiment of the present invention will be described below. Note that the same reference numerals in the fifth embodiment denote the same parts as in the first to fourth embodiments, and a detailed description thereof will be omitted.

[Configuration and operation]
FIG. 24 is a block diagram illustrating the configuration of the color processing apparatus according to the fifth embodiment. The difference from the color processing apparatus shown in FIG.

  A series of operations for creating a profile by predicting L * a * b * values for RGB values based on the results of printing a color patch and measuring the color patch in the above configuration will be described.

  First, a profile creation application stored in the HDD 105 is activated by a command from the CPU 101. The profile application displays the user interface shown in FIG.

  The user interface shown in FIG. 25 includes a patch print button 2201 for the user to instruct color patch printing, a patch colorimetry button 2202 for instructing color measurement of the color patch, and a profile for saving the profile. There is a save button 2203 and an end button 2204 for ending the profile creation application.

  The profile creation application causes the printer 109 to print a patch image when the user presses the patch print button 2201. Subsequently, when the user sets the patch image at an appropriate position on the colorimeter 115 and then presses the colorimeter button 2202, the spectral reflectance of the color patch measured by the colorimeter 115 is changed to the main via the USB controller 108. Stored in the memory 102.

  The profile creation application converts the spectral reflectance of the color patches stored in the main memory 102 into L * a * b * values, and combines the converted L * a * b * values with the RGB values of the color patches. Store in 102. FIG. 26 is a diagram showing a data format example of a combination of L * a * b * values and RGB values of colorimetric data. Thereafter, the profile creation application enables the profile saving button 2203 (a state that the user can press). When the user presses the profile creation button 2203 after enabling the profile save button 2203, the profile of the printer 109 is created according to the procedure described later.

  When the user presses the end button 2204, the profile creation application ends processing, and the working memory area and application memory area of the main memory 102 are cleared.

[Profile creation operation]
FIG. 27 is a flowchart showing a process for calculating coefficients and basis functions of a B-spline body for color prediction. Note that the B-spline body for color prediction is expressed by the above-described equation (13).

First, from the colorimetric data represented by the data structure shown in FIG. 26, the correspondence between RGB values and L * a * b * values is acquired for all sets (S2401). Hereinafter, the correspondence between RGB values and L * a * b * values is described as i-th RGB values as rr _i , gg _i , bb _i , and L * a * b * values as λ _i , a _i , and b _i. To do.

Then, the number of nodes and n-1 with respect to the total number of data (patches total) n ³ of colorimetric data, calculates the basis functions on the basis of the node is stored in the main memory 102 (S2402). Since the example shown in FIG. 26 has 125 patches, the number of nodes is 4. As described in the first embodiment, a general DeBoor-Cox algorithm is used to calculate the basis function after the node is determined. In the following, the basis functions will be described as B-spline bases with three positions of four nodes.

  Next, using the calculated basis function and the correspondence data indicating the correspondence between the RGB value and the L * a * b * value obtained from the color measurement data shown in FIG. 26, the matrix equation f = MC is expressed as L * Each component, a * component, and b * component are solved using LU decomposition, and each coefficient of the B-spline body is calculated (S2403). Hereinafter, the coefficient calculation by the above equation will be described in detail.

First, the s-row t-column component m _st of the matrix M is calculated as follows.
m _st = N _ri (rr _s ) N _gj (gg _s ) N _bk (bb _s )… (29)
Where t = 25 (I-1) + 5 (j-1) + k
i, j, k are integers from 1 to 5

  Note that the relationship between t and i, j, k varies depending on the number of nodes and the order of basis functions. For example, in the case of a six-node B-base spline at the third position, the relationship is t = 49 (I-1) +7 (j-1) + k.

Next, calculation of the coefficients cλ _ijk , ca _ijk , and cb _ijk will be described. First, in order to calculate the coefficient cλ _ijk , the following matrix equation is solved using LU decomposition.
fλ = [λ ₁ , λ ₂ ,…, λ ₁₂₄ , λ ₁₂₅ ]
cλ = [cλ ₁₁₁ , cλ ₁₁₂ ,…, cλ ₁₁₅ , cλ ₁₂₁ ,
…, Cλ ₁₅₅ , cλ ₂₁₁ ,…, cλ ₅₅₄ , cλ ₅₅₅ ]… (30)
fλ = M ・ cλ

Next, in order to calculate the coefficient ca _ijk , the following matrix equation is solved using LU decomposition.
fa = [a ₁ , a ₂ ,…, a ₁₂₄ , a ₁₂₅ ]
ca = [ca ₁₁₁ , ca ₁₁₂ ,…, ca ₁₁₅ , ca ₁₂₁ ,
…, Ca ₁₅₅ , ca ₂₁₁ ,…, ca ₅₅₄ , ca ₅₅₅ ]… (31)
fa = M ・ ca

Next, in order to calculate the coefficient cb _ijk , the following matrix equation is solved using LU decomposition.
fb = [b ₁ , b ₂ ,…, b ₁₂₄ , b ₁₂₅ ]
cb = [cb ₁₁₁ , cb ₁₁₂ ,…, cb ₁₁₅ , cb ₁₂₁ ,
…, Cb ₁₅₅ , cb ₂₁₁ ,…, cb ₅₅₄ , cb ₅₅₅ ]… (32)
fb = M ・ cb

  Then, the calculated coefficient is stored in the main memory 102 (S2404).

  FIG. 28 is a flowchart for explaining a process for creating a profile by predicting a reproduction color using a B-spline body for color prediction.

  First, an initializing operation such as allocating a working memory area and initializing variables is performed (S601), and one RGB value corresponding to the LUT grid point of the profile is acquired according to the appropriate order (S602). Obtain the basis function and coefficient value of the B-spline body for color prediction from the memory 102, and use the following formula to determine what color it will be when the color given by the RGB value is printed L * a * b * Predicted as a value (S603).

λ = Σ _{i = 1} ⁵ Σ _{j = 1} ⁵ Σ _{k = 1} ⁵ cλ _ijk N _ri (rr) N _gj (gg) N _bk (bb)
a = Σ _{i = 1} ⁵ Σ _{j = 1} ⁵ Σ _{k = 1} ⁵ ca _ijk N _ri (rr) N _gj (gg) N _bk (bb)… (33)
b = Σ _{i = 1} ⁵ Σ _{j = 1} ⁵ Σ _{k = 1} ⁵ cb _ijk N _ri (rr) N _gj (gg) N _bk (bb)
Where rr, gg, and bb are RGB values
λ, a, b are L * a * b * values
N _r is the basis function in the R-axis direction
N _g is the basis function in the G-axis direction
N _b is the basis function in the B-axis direction
cλ _ijk , ca _ijk , cb _ijk are coefficients
Suffixes i, j, k attached to N _r , N _g , N _b are
Basis function number in the basis for each axis

  Next, the predicted L * a * b * value is stored in the memory address (main memory 102) corresponding to the LUT grid point position (S604), and it is determined whether all the LUT grid points have been predicted. (S605), steps S602 to S604 are repeated until all of the LUT lattice points are predicted.

  When all the LUT lattice points are predicted, the LUT data stored in the main memory 102 is stored as profile data in a predetermined area of the main memory 102 (S606), and the termination operation such as releasing the working memory is performed (S607). Then, the profile creation process ends.

  FIG. 29 is a diagram showing the data structure of the profile, and shows the correspondence between the color coordinates of the grid points in the RGB color space and the coordinate values of the L * a * b * color space reproduced by the grid points. The R / G / B value step is described at the beginning of the data structure, and the color coordinates of the L * a * b * values corresponding to each grid point are nested and described in the order of R, G, B. Has been.

  In this way, accurate color prediction is realized even with color measurement with a small number of color patches by applying the B-spline, which can naturally reflect the trend of value changes and calculate colors with smooth changes. can do.

[Modification]
Replacement of B-spline basis functions with other piecewise polynomials in solid representation In the fifth embodiment, an example in which B-splines are used as basis functions in solid representation has been described. However, as a basis function, any piecewise function such as rational B spline, non uniform rational B spline, Bezier, rational Bezier, etc. can be used.

In the fifth embodiment, the number of nodes in each base is described as being the same. However, the number of nodes in each base may be changed.

In the fifth embodiment, the physical stimulus value in the L * a * b * three-dimensional space is predicted from the RGB three-dimensional space, but there is no restriction on the predicted color dimension.

Expansion of Solid Representation In Example 5, the solid representation of the RGB three-dimensional color space was used as the color space of the prediction source, but there is no restriction on the number of dimensions of the color space of the prediction source.

[Other embodiments]
Note that the present invention can be applied to a system including a plurality of devices (for example, a host computer, an interface device, a reader, and a printer), and a device (for example, a copying machine and a facsimile device) including a single device. You may apply to.

  Also, an object of the present invention is to supply a storage medium (or recording medium) on which a program code of software that realizes the functions of the above-described embodiments is recorded to a system or apparatus, and the computer (or CPU or Needless to say, this can also be achieved by the MPU) reading and executing the program code stored in the storage medium. In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiments, and the storage medium storing the program code constitutes the present invention. Further, by executing the program code read by the computer, not only the functions of the above-described embodiments are realized, but also an operating system (OS) running on the computer based on the instruction of the program code. It goes without saying that a case where the function of the above-described embodiment is realized by performing part or all of the actual processing and the processing is included.

  Furthermore, after the program code read from the storage medium is written into a memory provided in a function expansion card inserted into the computer or a function expansion unit connected to the computer, the function is determined based on the instruction of the program code. Needless to say, the CPU of the expansion card or the function expansion unit performs part or all of the actual processing and the functions of the above-described embodiments are realized by the processing.

  When the present invention is applied to the storage medium, the storage medium stores program codes corresponding to the flowcharts described above.

A diagram schematically showing six divisions into tetrahedrons, A figure showing how the color change becomes steep near the gamut boundary, Block diagram showing a configuration example of a color processing device, A diagram showing an example of a user interface when previewing, State transition diagram explaining the operation of the image preview application, A diagram schematically showing the profile data structure in RGB color space, A diagram explaining the data structure of the profile, A flowchart for explaining the calculation processing of the coefficient and basis function of the B-spline body for color calculation, A diagram showing the R axis basis function N _r , A figure showing how the B-spline calculation results are expressed as a distribution in L * a * b * space. A flowchart for explaining display processing of RGB values and L * a * b * values at a specified image position; A flowchart for explaining a process of generating preview image data; Figure showing a user interface for color correction and creating a profile State transition diagram explaining the operation of the color reproduction editing application, The figure explaining the data structure of color edit data, The figure which shows the figure displayed on a three-dimensional display area according to operation of a user interface, The figure which shows the figure displayed on a three-dimensional display area according to operation of a user interface, The figure which shows the figure displayed on a three-dimensional display area according to operation of a user interface, A flowchart for explaining processing for calculating coefficients and basis functions for a B-spline body for color calculation; A flowchart for explaining creation of a profile using a B-spline body for color calculation; Flowchart explaining processing for correcting RGB values, L * a * b * values, or both for color editing data, A diagram explaining how to set the target color when an L * a * b * value outside the color gamut is specified, Flowchart explaining the calculation processing of the coefficient and basis function of the B-spline body for color calculation in Example 2, A diagram explaining vibrations that occur in a one-dimensional spline function, Block diagram showing a configuration example of a color processing device of Example 5, The figure which shows an example of the user interface which a profile creation application displays, A diagram showing the data format of the combination of L * a * b * values and RGB values of colorimetric data, A flowchart showing processing for calculating coefficients and basis functions of a B-spline body for color prediction, A flowchart for explaining a process of creating a profile by predicting a reproduction color using a B-spline body for color prediction; It is a figure which shows the data structure of a profile.

Claims (18)

A color processing method for calculating a color signal value of a second color system from a color signal value represented by a first color system,
A first calculation step of calculating a color signal value of the second color system using a multiple sum operation having a piecewise polynomial as a basis function and having the same number of dimensions as the first color system; The color processing method characterized by the above-mentioned.   2. The color processing method according to claim 1, wherein the basis function is a B-spline, a rational B-spline, a non-uniform rational B-spline, a Bezier, or a rational Bezier.   3. The color processing method according to claim 1, wherein the summation operation number of each summation term in the multiple summation operation is the same.   4. The color processing method according to claim 1, wherein at least one sum operation number of each sum term in the multiple sum operation is different. A second calculation step of calculating a basis function value of the multiple sum operation defined on each dimension of the first color system from a value of each dimension of the first color system;
5. The method according to claim 1, further comprising a third calculation step of calculating a color signal value of the second color system by the multiple sum operation using the calculated basis function value. The color processing method described in any one. A first conversion step for converting the color signal value represented by the first color system;
A second calculation step of calculating a basis function value of the multiple sum calculation defined on a basic axis of the space of the color signal value after the conversion from the color signal value after the conversion;
5. The method according to claim 1, further comprising a third calculation step of calculating a color signal value of the second color system by the multiple sum operation using the calculated basis function value. The color processing method described in any one.   For a plurality of color signal values represented by the first color system, a coefficient of the multiple sum operation is obtained from a set that defines the color signal values represented by the second color system to be calculated. 6. The color processing method according to claim 5, wherein the color processing method is obtained. Further, the first table of a set of color signal values represented by the second color system to be calculated for a plurality of color signal values represented by the first color system A second conversion step for performing the conversion on a plurality of color signal values represented by a color system;
7. The color processing method according to claim 6, wherein a coefficient of the multiple sum calculation is obtained from a set of color signal values converted in the second conversion step.   8. The color processing method according to claim 7, wherein the coefficient of the multiple sum calculation has a dimension corresponding to the second color system.   A sum operation scalar coefficient set is provided for each dimension of the second color system, and when calculating the color signal value of the second color system, the sum operation is performed for each dimension of the second color system. 9. The color processing method according to claim 8, wherein: A color processing device that calculates a color signal value of a second color system from a color signal value represented by a first color system,
It has a calculation means for calculating a color signal value of the second color system using a multiple sum operation having a piecewise polynomial as a basis function and having the same number of dimensions as the first color system. Color processing device. A color processing method for calculating a color signal value of a predetermined color system,
A setting step for setting a conversion formula by a multiple sum operation using a piecewise polynomial of the same multiplicity as the number of dimensions of the first color system as a basis function;
Based on data defining a combination of a plurality of color signal values represented by the first color system and a plurality of color signal values of the second color system to be calculated for the color signal values A first calculation step for obtaining a coefficient of the piecewise polynomial corresponding to a conversion equation that approximates the combination of the combinations, or a conversion equation that smoothes a curved surface set, polyhedron set, or hyperpolyhedron set connecting the combinations;
A second calculation step of calculating a color signal value of the second color system corresponding to a color signal value expressed in the first color system using the multiple sum operation. Color processing method.   13. The color processing method according to claim 12, wherein the coefficient is calculated by assigning a weight to each combination of the plurality of color signal values.   14. The color processing method according to claim 12, wherein the basis function is any one of a B spline, a rational B spline, a non-uniform rational B spline, a Bezier, and a rational Bezier.   15. The color processing method according to claim 12, wherein the coefficient has a dimension corresponding to the second color system. A color processing device for calculating a color signal value of a predetermined color system,
A setting means for setting a conversion formula by multiple sum operation with a piecewise polynomial having the same multiplicity as the number of dimensions of the first color system as a basis function;
Based on data defining a combination of a plurality of color signal values represented by the first color system and a plurality of color signal values of the second color system to be calculated for the color signal values A first calculation means for obtaining a coefficient of the piecewise polynomial corresponding to a conversion equation that approximates the combination of the combinations, or a conversion equation that smoothes a curved surface set, polyhedron set, or hyperpolyhedron set connecting the combinations;
And second calculating means for calculating a color signal value of the second color system corresponding to a color signal value expressed in the first color system using the multiple sum operation. Color processing device.   16. A program that controls an image processing apparatus to execute the color processing according to any one of claims 1 to 10 and claims 12 to 15.   18. A recording medium in which the program according to claim 17 is stored.

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