EP1856905A1

EP1856905A1 - Color correction techniques for correcting color profiles

Info

Publication number: EP1856905A1
Application number: EP06720355A
Authority: EP
Inventors: Christopher Edge
Original assignee: Eastman Kodak Co
Current assignee: Eastman Kodak Co
Priority date: 2005-02-15
Filing date: 2006-02-01
Publication date: 2007-11-21
Also published as: JP4633806B2; JP2008530952A; WO2006088683A1

Abstract

According to an embodiment of the present invention, selective tristimulous corrections to device independent coordinates are applied using a piecewise linear correction function. The piecewise linear correction function is defined such that a maximum of the piecewise linear correction function occurs at a boundary condition of a corresponding device-dependent color space, and the piecewise linear correction function is linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different boundary condition or a neutral axis. By having the piecewise linear correction function reduce linearly to zero or approximately zero, corrections to one region of color smoothly diminish and blend into the other regions of color, thereby substantially preventing the introduction of artifacts or image corruption due to the corrections.

Description

COLOR CORRECTION TECHNIQUES FOR CORRECTING COLOR

PROFILES

FIELD OF THE INVENTION This invention relates to correcting device-independent color data in a color management profile in a manner that allows selective adjustment of one or more regions of color with substantially no risk of introducing artifacts or unwanted corruption of subsequently generated images. This invention is useful for, among other things, improving a color profile of a digital -image input device, such as a digital camera or a scanner.

BACKGROUND OF THE INVENTION A digital-image input device, such as a digital camera or a scanner, converts light reflected from an object into digital data representing an image of the object. Typically, the digital data is divided into units, each unit describing the color of a portion, or pixel, of the image. Accordingly, the image may be described as a two-dimensional array of pixels (x, y). Further, each unit of digital data typically describes the color of a pixel by describing the amount, or intensity, of each primary color red, green, and blue, present in the pixel. For example, the digital data may indicate that the pixel at x=0 and y=0 has a red intensity of 200, a green intensity of 134, and a blue intensity of 100, where the intensity of each primary color is represented by eight bits. (Eight bits allows 256 combinations, so each primary color may have a value of 0-255, in this example, where 255 indicates the highest level of intensity and zero indicates no intensity, or black.). The digital data produced by a digital-image input device is referred to herein as "device dependent data," because different digital-image input devices typically produce different digital data representing the same image acquired under the same conditions. For example, a first digital camera may indicate that a first pixel of an image has a red component of 200, whereas a second digital camera may indicate that the same pixel of an equivalent image taken under the same conditions has a red component of 202. For another example, the first digital camera may record the red in an apple as 200, and the second digital camera may record the red in the same part of the apple (as imaged under the same conditions) as 202. Because the device-dependent data generated by a digital-image input device typically specifies the red, green, and blue color components associated with each pixel, it is often referred to as "RGB" data.

The differences between device-dependent data from two different devices arise from minute differences in the imaging components in each device. These differences create problems when the images are output by a digital- image output device, such as a color ink-jet printer, a CRT monitor, or an LCD monitor. For example, the image of the apple taken by the first digital camera discussed above will appear differently than the image of the apple taken by the second digital camera when output to the same color ink-jet printer.

To further complicate matters, digital-image output devices also have the same types of discrepancies between each other that digital-image input devices have. For example, a user may want to view an image of a red square on one CRT monitor while a customer simultaneously views the same image on another CRT monitor. Assume that the digital-image input device used to image the red square recorded all pixels of the red square as red^OO, green=0, and blue=0. Commonly, when the two monitors display the same image, each monitor displays a slightly different red color even though they have received the same digital data from the input device. The same differences commonly exist when printing the same image to two different printers. However, it should be noted that the digital image data processed by printers typically describes each pixel in an image according to the amount, or intensity, of each secondary color cyan, magenta, and yellow, as well as black present in the pixel. Accordingly, the device-dependent digital image data processed by printers is referred to as "CMYK" data (as opposed to RGB device-dependent data associated with digital-image input devices.) (Monitors, on the other hand, display data in RGB format).

Color profiles provide a solution to the color discrepancies between devices discussed above. Each digital-image input device typically has its own color profile that maps its device-dependent data into device-independent data. Correspondingly, each digital-image output device typically has its own color profile that converts device-independent data into device-dependent data usable by the output device to print colors representative of the device-independent data. Device-independent data describes the color of pixels in an image in a universal manner, i.e., a device-independent color space. A device-independent color space assigns a unique value to every color, where the unique value for each color is determined using calibrated instruments and lighting conditions. Examples of device-independent color spaces are CIEXYZ, CIELAB, CIE Yxy, and CIE LCH, known in the art. Device-independent data is sometimes referred to herein as "device-independent coordinates." Device-independent data in the CIEXYZ color space is referred to herein as "XYZ data," or just "XYZ." Device-independent in the CIELAB color space is referred to herein as "LAB data," "CIELAB" or just "LAB."

Theoretically, color profiles allow a user to acquire an image of an object using any digital-image input device and to output an accurate representation of the object from a digital-image output device. With reference to FIG. 1, for example, an image of an object 101 is acquired using a digital-image input device 102. The image is represented in FIG. 1 as RGB 103. Then, the image RGB 103 is converted into device-independent data (XYZ 105, for example) using the digital-image input device's color profile 104. The device- independent data XYZ 105 is then converted using the output device's color profile 106 into device-dependent data (CMYK 107, for example) specific to the output device 108. The output device 108 uses its device-dependent data CMYK 107 to generate an accurate representation 109 of the object 101.

The usefulness of color profiles is limited by how accurately they convert device-dependent data to device-independent data, or vice versa. Currently, there is no way of generating a color profile that perfectly translates device-dependent data to device-independent data, or vice- versa. Errors in color profiles become apparent when comparing a displayed image, such as an image displayed on a CRT or LCD monitor, and a hard-copy printout of the image. Conventional methods exist that improve color profiles by correcting device-independent data associated with device-dependent data. However, these methods, while improving color profiles, still leave small but significant color errors on the order of 2-3 delta E in certain regions of color space. (The unit of 1 delta E, known in the art, refers to one unit of Euclidean distance in the CIELAB color space.) In other words, the translations or corrections performed by the conventional methods still introduce irregularities in the corrected color gamut and, particularly for large corrections, are not truly linear in all areas of color space.

Accordingly, a need in the art exists for a method for correcting color profiles or a device-independent color space with reduced errors.

SUMMARY OF THE INVENTION The above-described problems are addressed and a technical solution is achieved in the art by a system and a method for correcting color profiles or a device-independent color space that allow selective adjustment of one or more regions of color with substantially no risk of introducing artifacts or unwanted corruption of subsequently generated images. According to an embodiment of the present invention, selective tristimulous corrections to device-independent coordinates are applied using a piecewise linear correction function. The piecewise linear correction function is defined such that a maximum of the piecewise linear correction function occurs at a boundary condition of a corresponding device-dependent color space and the piecewise linear correction function is linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different boundary condition or a neutral axis. By having the piecewise linear correction function reduce linearly to zero or approximately zero, corrections to one region of color smoothly diminish and blend into the other regions of color, thereby substantially preventing the introduction of artifacts or image corruption due to the corrections.

BRIEF DESCRIPTION OF THE DRAWINGS The present invention will be more readily understood from the detailed description of preferred embodiments presented below considered in conjunction with the attached drawings, of which: FIG. 1 illustrates a conventional arrangement for acquiring and outputting an image; FIG. 2 illustrates a system for generating a color profile for a digital-image input device, according to an embodiment of the present invention;

FIG. 3 illustrates a method for generating a color profile for a digital-image input device, according to an embodiment of the present invention; FIG. 4 illustrates a method for calculating a parameter list used to calculate final device independent coordinates of the profile, which may be used as step 314 in FIG. 3, according to an embodiment of the present invention; and

FIG. 5 illustrates a method for performing selective adjustments to the device independent color space, which may be used independently or as part of step 406 in FIG. 4, according to an embodiment of the present invention.

It is to be understood that the attached drawings are for purposes of illustrating the concepts of the invention and may not be to scale.

DETAILED DESCRIPTION OF THE INVENTION

The present invention corrects one or more selected regions of color in a device-independent color space, such that the magnitude of the corrections diminish as colors in the color space move away from the selected region being corrected. Accordingly, adjustments to regions of color in a device- independent color space may be made, such that the adjustments pose substantially no risk of introducing artifacts or unwanted corruption of subsequently generated images. The present invention has been shown to be useful in correcting both small color discrepancies, i.e., on the order of 2-3 delta E, or large color discrepancies, i.e., on the order of 20-30 delta E.

FIG. 2 illustrates a system 200 for generating a color profile for a digital-image input device, according to an embodiment of the present invention. The system 200 may include a digital-image input device 202 communicatively connected to a computer system 204, which is communicatively connected to a data storage system 206. The computer system 204 may include one or more computers communicatively connected and may or may not require the assistance of an operator 208. The digital-image input device 202 acquires a test image of a color chart and optionally a scene outside of the color chart. Examples of the digital-image input device 202 include a digital camera or a scanner. The digital- image input device 202 transmits the test image to the computer system 204, 04123

which generates a color profile for the digital-image input device 202 based upon the test image and an estimated illumination of the color chart as discussed in more detail with reference to FIGS. 3 and 4. The color profile may be stored in the data storage system 206, output to other optional devices 210, or otherwise output from the computer system 204. It should be noted that the information needed by the computer system 204, such as the test image and information pertaining to the color chart, may be provided to the computer system 204 by any means, and not necessarily by the digital-image input device 202.

The data storage system 206 may include one or more computer- accessible memories. The data storage system 206 may be a distributed datastorage system including multiple computer-accessible memories communicatively connected via a plurality of computers, devices, or both. On the other hand, the data storage system 206 need not be a distributed data-storage system and, consequently, may include one or more computer-accessible memories located within a single computer or device.

The term "computer" is intended to include any data processing device, such as a desktop computer, a laptop computer, a mainframe computer, a personal digital assistant, a Blackberry, and/or any other device for processing data, and/or managing data, and/or handling data, whether implemented with electrical and/or magnetic and/or optical and/or biological components, and/or otherwise.

The phrase "computer-accessible memory" is intended to include any computer-accessible data storage device, whether volatile or nonvolatile, electronic, and/or magnetic, and/or optical, and/or otherwise, including but not limited to, floppy disks, hard disks, Compact Discs, DVDs, flash memories, ROMs, and RAMs.

The phrase "communicatively connected" is intended to include any type of connection, whether wired, wireless, or both, between devices, and/or computers, and/or programs in which data may be communicated. Further, the phrase "communicatively connected" is intended to include a connection between devices and/or programs within a single computer, a connection between devices and/or programs located in different computers, and a connection between devices not located in computers at all. In this regard, although the data storage system 206 is shown separately from the computer system 204, one skilled in the art will appreciate that the data storage system 206 may be stored completely or partially within the computer system 204. FIG. 3 illustrates a method 300 for generating a color profile for the digital-image input device 202, according to an embodiment of the present invention. The method 300 is executed as hardware, software, and/or firmware by the computer system 204, according to an embodiment of the present invention. At step 302, the computer system 204 receives device-dependent data from the digital-image input device 202 or from some other source. The device-dependent data received at step 302 is RGB data, according to an embodiment of the present invention. The device-dependent data represents a test image of at least a color chart. It should be noted that although this application is described in the context of using a color chart, any object that has known device- independent values associated with its colors may be used. It should also be noted that the device-dependent data received at step 302 need not include data pertaining to a scene outside of the color chart in the test image.

The operator 208, who also may operate the digital-image input device 202, may specify the location and orientation of the color chart in the test image. Alternatively, the orientation of the color chart may be determined automatically by the computer system 204. The average of the device-dependent RGB values received at step 302, for each color patch in the color chart may be determined, such that a single device-dependent RGB value for each color patch is output from step 302. Collectively, the device-dependent RGB values, each associated with a color patch, are referred to as an array of device-dependent RGB values represented as RGB 303.

At step 304, the array of RGB values, RGB 303, is associated with device-independent data XYZ 301 previously measured for the color chart used for the test image. The association of the device dependent data RGB 303 with the corresponding device-independent data XYZ 301 may be stored as a two- dimensional array, represented as "RGB-XYZ" 305 in FIG. 3. The array may include two columns, one for the device-dependent data and one for the device- independent data, where each row contains associated data for a single color patch in the color chart. For example, the following software code could be used to define such an array:

RGB rgbChartValue[i]

Lab labMeasuredValue[i], where 0<i<numPatches

rgbChart Value represents RGB 303 in FIG. 3. labMeasured Value represents the previously measured device-independent data XYZ 301 associated with the color chart, converted and stored as Lab data. numPatches represents the number of patches in the color chart. One skilled in the art will appreciate that any manner of representing the association of the device-dependent data RGB 303 and the device-independent data XYZ 301 may be used.

Although the device-independent data XYZ 301 is illustrated as being in the CIEXYZ device-independent color space, any device-independent color space may be used. Further, although FIGS. 3, 4, and 5 illustrate device- independent data as XYZ data, particular steps in FIGS. 3, 4, and 5 may operate on the device-independent data in other color spaces. Accordingly, conversions of XYZ data into other color spaces are implied by these steps and are not illustrated in the figures, because such conversions are well known to one of ordinary skill in the art.

At step 306, the gray patches in the device-independent data XYZ 301 are identified. The gray patches may be identified using the device- independent data XYZ stored in the array RGB-XYZ 305. The identified gray patches output at step 306 are represented as GrayPatches 307. RGB-XYZ 305 may pass through step 306 to step 308 unmodified. Although not required, it may be advantageous to identify gray patches in the LAB color space as opposed to the XYZ color space. In particular, in the LAB color space, gray colors are associated with the coordinates "a" and "b" approximately equal to zero, thereby providing for a simple calculation. Accordingly, the device-independent data XYZ in the array RGB-XYZ 305 may be converted to LAB prior to performing step 306. The following software code illustrates a way of identifying the GrayPatches 307, as well as the benefits of operating in the LAB color space.

graylndex=θ; For (i=0; i<numPatches; i++)

{

If (labMeasuredValue[i] .a()<GrayRange && labMeasuredValue[i].b()<GrayRange)

{ LabGrayValue.lab[grayIndex]= labMeasuredValue[i] ; rgbGrayValues[grayIndex] = rgbChartValuesfi]; graylndex++;

} } nuniGrayPatches=grayIndex;

labMeasuredValue[i].a() is the "a" value (in LAB) of the current patch i. Similarly, labMeasuredValue[i].b() is the "b" value (in LAB) of the current patch i. GrayRange is the value used to determine if a color is gray. According to an embodiment of the present invention, GrayRange is 5 delta E. LabGrayValue.lab[], when output, contains the array of gray patches 307 in the CIELAB device-independent color space. rgbGrayValues[] represents the device dependent gray values extracted from the RGB image of the color chart. nuniGrayPatches is the total number of identified gray patches.

According to an embodiment of the present invention, GrayPatches 307 includes both the device-independent measured data array (referred to as LabGrayValue[] in the software code, above) as well as the corresponding device dependent gray values extracted from the RGB image of the chart (referred to as rgbGrayValues[] in the software code, above). It may be convenient to sort the array of LabGrayValue[i] and rgbGrayValues[i] where index i=0,..., numGrayPatches maps to lightest -> darkest, unless it is known in advance that the chart data is already sorted in this manner.

At step 308, the brightest within-range gray patch in GrayPatches 307 is identified and output as Brightest Patch 309. According to an embodiment of the present invention, the brightest within-range gray patch is the gray patch (in device-independent coordinates) that has associated device-dependent data of R<255, G<255, and B<255. Stated differently, the brightest gray patch having associated non-overexposed device-dependent data is identified. The device- independent data and the device-dependent data necessary for performing step 308 may be obtained from the array RGB-XYZ 305. GrayPatches 307 and RGB-XYZ 305 maybe passed through step 308 unchanged to step 310. The following software code illustrates a way to accomplish step 308, which assumes that the input GrayPatches 307, as well as the array RGB-XYZ 305, have been sorted in order of intensity (coordinate "L" in LAB) (from brightest to darkest):

int maxGrayPatchlndex = 0; float maxL=0.0;

For (i=0;i<numGrayPatches;i++)

{ if (LabGrayValue.lab[i]>maxL && rgbGrayValues[i].r() < 255&& rgbGrayValues [i].g() < 255&& rgbGrayValues [i].b() < 255)

{ maxL=LabgrayValue[i] ; maxGrayPatchlndex =i;

} }

maxGrayPatchlndex, upon completion of the above-code, is the location in the array labGrayValue.lab[] (GrayPatches 307) that stores the brightest in-range gray patch. maxL, upon completion of the above-code, is the L* value of the brightest in-range gray patch from labGrayValue.lab[] (GrayPatches 307). maxL is subsequently converted to Y_measured5 discussed below. rbgChartValuesf] represents the device-dependent data from the array RGB-XYZ 305, such that rgbChartValues[i].r() is the red component, rgbChartValues[i].g() is the green component, and rgbChartValues[i].b() is the blue component.

At steps 310 and 312, in order to compensate for the effects of over-illumination or underillumination of the color chart, the device-independent data of the color chart (stored in the array RGB-XYZ 305) is scaled by an illumination-correction factor (X_ILLCORR- OCILL_CORR, according to an embodiment of the present invention, is generated by comparing the illumination of the BrightestPatch 309 in device-independent coordinates and the illumination of the same patch as indicated by the associated device-dependent coordinates. In other words, the measured illumination of the BrightestPatch 309 is compared against the illumination of the same patch as recorded by the digital-image input device in the RGB data 303. According to an embodiment of the present invention, ctiLLCORR is generated as follows.

^ILLCORR ⁼ (Yestimated) ' (Yraeasured)

Yestimated is an estimated illumination of the RGB data 303 for the brightest in- range gray patch. Yestimated may be represented as follows.

^ estimated ⁼ J Y V^i₀ ' "/„ ' "i₀ )

where the index 'V refers to maxGrayPatchlndex. Y_measured is the illumination of the XYZ data 301 as identified by BrightestPatch 309. At step 312, according to an embodiment of the present invention, illumination-corrected device-independent data is generated by linearly scaling the device-independent data XYZ 301 by (XILL_CORR- Such illumination-corrected device-independent data is represented in FIG. 3 as XYZ_1LL_CORR- The one-to-one color-patch association between XYZ_1LLCORR and the RGB data 303 is represented as RGB-XYZ₁LLC_ORR 313. According to an embodiment of the present invention, XYZiLLcoRR is generated by multiplying all values of the XYZ data 301 by ctiLLcoRR, as illustrated below.

Y = a lllcoir Y

V JlLLCORR \ Z J 6 004123

The vector on the right represents the XYZ data 301 and the vector on the left represents XYZIL_LCORR. This correction assures that the brightest in-range gray patch continues to have a value that corresponds to the original RGB value for that patch assuming an initial camera gamma of 2.2. According to this embodiment of the present invention, it is assumed that values of gamma and RGB chromaticites have been initialized to the default digital-image input device profile settings, e.g., sRGB or Adobe RGB, known in the art.

At step 314, an optimized list of parameters 315 used to generate final device independent coordinates of the digital-image input device profile is calculated. FIG. 4, discussed below, illustrates an inventive method for generating such parameters, according to an embodiment of the present invention. However, any method for calculating these parameters, known in the art, may be used. The parameter list 315 is used at step 316, as well as RGB 303 and XYZ 301, to generate a profile 317 for the digital-image input device 202. FIG. 4 illustrates an exploded view of the substeps that may be performed at step 314, according to an embodiment of the present invention. The input to step 402 is the RGB-XYZ_ILL_CORR array 313 of associated device- dependent data RGB and illumination-corrected device-independent data XYZ_ILL_CORR- At step 402, optimal parameters arc 403 that describe the 1- dimensional tone curves R, G, and B of the device-dependent data RGB (in RGB- XYZΪLLCORR) are generated. RGB-XYZILLCORR 313 is passed unmodified through step 402 to step 404.

The process of generating optimized θχc 403 may be performed by selecting initial parameters for α-rc, according to an embodiment of the present invention, and applying the initially selected parameters for αγc to the device- dependent data RGB to generate predicted device-independent coordinate values. Then, an error between the generated predicted device-independent coordinate values and the measured device-independent coordinate values (XYZ₁L_LC_OR_R) is calculated. The process is repeated with newly selected parameters for arc until the calculated error is minimized. The parameters for α-rc 403 that produce the minimum error are output at step 402 as the optimal parameters OC_TC 403. The process of step 402, according to an embodiment of the present invention, may be represented as follows.

E/τ(α_rc)

The index "i" refers to the "n" gray patches on the color chart, where the index "io" refers to maxGrayPatchlndex, which is the location in the array labGrayValue.labQ (GrayPatches 307) that stores the brightest in-range gray patch. The (L*a*b*iLLcoRR) vector represents the LAB coordinate values corresponding to XYZI_LLCORR. The (F_LAB(RGBJ, α_Tc)) vector represents the function used to calculate the predicted device-independent coordinates corresponding to the device-dependent data RGB 303. Any function, known in the art, may be used for FL_AB(RGBJ, α-rc)- Using well-known methods, such as Newton's method or Powell's method, the parameters α-rc may be varied automatically in such a manner as to minimize the value of the least squared error function Εrr(ατc)- The resulting values of arc may, in some cases, be optimal values for use in predicting device independent coordinates from RGB 303.

According to an embodiment of the present invention, the following expression may be used as FLAB(RI, «TC) for the red tone channel.

fARΛ_M^_bias, γ_R,βc) =R_MΛ\Λ^~ R_b,-ΛfλR,βc)Y^« + R_bbuias

fR is a function that defines the one-dimensional response of the red tone channel, such that Riviax, Rwa_sj Y_R5 and β_c represent <xτc in the case where the digital-image input device is a digital camera. The above expression may be used similarly for the green and blue tone channels, where β₀ = 0 in the contrast function f_c(R) defined by:

/_c(x,/)_c) = x + /5_c(O.5 + O.5(2(x-O.5))³ -x). Note that for β_c = O, the contrast function f_c(x)=x. R._Max is a linear scaling factor and indicates the maximum red color recorded by the digital-image input device. R_bi_as, a black bias offset, indicates the darkest red color recorded by the digital- image input device 202. YR is the gamma, known in the art, of the digital-image input device associated with the red color. Alternatively, J_R may equal Y_G and JB, which all may equal the overall gamma of the device 202. β_c is a parameter for adjusting contrast, i.e., a means for reducing the output of the function f_o() for values 0.0<x<0.5 and increasing the output of function f_c() for 0.5<x<1.0. Many mathematical functions exist that can perform such an adjustment, e.g., 3^rd order polynomials, splines, etc. The concept of performing such an adjustment is well- known in the art (c.f. the "auto-contrast" feature in applications such as Adobe® PhotoShop®) although it is often in the context of an aesthetic improvement to an image rather than attempting to characterize a device with regard to color data.

The following software code illustrates how step 402 may be performed, according to an embodiment of the present invention. It is assumed in this software code that all GrayPatches represented in RGB-XYZILL_CORR 313 are sorted in order of brightest to darkest.

MinimizeError(sumSquareGrayDeltaE, parameterList,

NumParameters) where sumSquareGrayDeltaE() is defined as: for (i=brightestValidGray; i<nGray; i++)

{ xyzPred=evaluateModel(grayRGB[i]); labPred=mColMetric->XYZToLab(xyzPred); labMeas=grayLab [i] ; xyzMeas=mColMetric->LabToXYZ(labMeas); xyzMeas *=Y_IlluminationCorr; labMeas=mColMetric->XYZtoLab(xyzMeas); errSq=distanceSquaredLab(labPred, labMeas); sumSq+=errSq; 2006/004123

} retum(sumSq);

parameterList represents α-rc 403 output by step 402, and NumParameters represents the number of parameters in arc 403. brightestValidGray represents the location of the brightest in-range gray patch in XYZILLCORR- nGray represents the total number of gray patches. xyzPred is a predicted device independent value corresponding to a device-dependent value in RGB 303. evaluateModel() is a function that generates the predicted device independent value xyzPred, and is akin to FLA_B(RGBJ, OLT_C), discussed above. labPred represents the LAB version of xyzPred, such that xyzPred is converted to LAB space using the function mColMetric->XYZToLab(). labMeas represents the LAB device-independent values of the current gray patch (grayLab[]). xyzMeas represents the XYZ version of labMeas. xyzMeas* represents xyzMeas corrected by Y_IlluminationCorr, which represents (X_ILL_CORR- errSq is an individual squared error and sumSq is the total squared error.

The values of arc 403 should be adjusted to minimize the sum of the calculated squared errors (sumSq, for example). The mathematical model (evaluateModel(), for example) used to predict the device-independent coordinates associated with RGB (in RGB-XYZΪLLC_ORR) may be any model known in the art. However, it is important that a selected model provide smoothness (i.e., low values of second order derivatives and/or no unwanted visual banding or artifacts when the profile is used for characterizing images) and as few parameters as possible, while achieving accurate predictions. The following software code illustrates a mathematical model (evalGammaModel() used as FL_AB(RGB;, ατc)_> discussed above) that predicts device-independent coordinates for the device dependent data RGB, according to an embodiment of the present invention.

double evalGammaModel (double *RGBMax, double * gamma, double *blackBias, double filmContrastCorr, int rgblndex, const double& cVal) { double val, corrVal, result=O.O; corrVal=0.5+0.5*pow(2.0*(cVal-0.5),3.0)-cVal; val=cVal+filmContrastCorr*corrVal; if (rgblndex != iFixedMaxRGB) result=RGBMax[rgbIndex]*(1.0- blackBias[rgbIndex] ) * pow(val, gamma[rgblndex]) + blackBias [rgblndex]; else result=(1.0-blackBias[rgbIndex])* pow(val, gamma[rgblndex]) + blackBias[rgbIndex]; if(cVal<0.0) result=O.O; return(result);

} In this example, αxc 403 includes RGBMax, gamma, blackBias, and filmContrastCorr. RGBMax corresponds to the linear scaling factor R_Max, described above, as well as the GMA_X and B_MA_X counterparts. Gamma corresponds to Y_R, described above, as well as the γo and γe counterparts. blackBias corresponds to Rbi_aS5 described above, as well as the Gbi_as and Bbias counteφarts. filmContrastCorr corresponds to β_c. Note that rgblndex indicates which channel is being calculated (rgbIndex=0,l,2^:=>R,G,B) and cVal is the input color value (R₅G, or B) which is being converted to the corresponding output color value modified by the evalGammaModel() function. The value "result" is calculated to obtain R₅G₅B (out) for input index rgblndex=θ,l,2. The resultingRGB vector is multiplied by the RGB->XYZ matrix described below to obtain the calculated values of XYZ. The above calculation of the sum square error is repeated after methodically adjusting parameters α_TC 403 in the RGB- >XYZ calculation until the sum square error is minimized. Note that the above tone curve calculation begins with a contrast adjustment applied to the RGB input values. This contrast adjustment is a 3^rd order polynomial with constraints that no correction is applied to values RGB=O, 0.50, or 1.0 (assume RGB normalized to 1.0). The correction is multiplied by filmContrastCorr, default=0.0, which can be positive or negative (decreasing or increasing contrast, respectively) and added to the RGB value. The modified values are used to calculate a standard gamma function with a black bias offset (defined by blackBias[]), a linear scaling factor for each R, G, B channel (RGBMax[J) and a value of Gamma for each RGB channel (gamma[]). In this example, the total number of adjustable parameters axe 403 is ten: RGBMax, gamma for R, G, and B, blackBias for R, G, and B, and a single value of filmContrastCorr for all three channels. Note that if the number of data values for the color chart is 6 gray patches, there are 18 data points to calculate on (6 times 3 (for L*,a*,b*) = 18). In the event that the first two patches are overexposed, the number of data points is reduced to 4x3=12. One can optionally assume that gamma is identical for each of the three RGB channels and reduce the number of parameters <xχc 403 to 8. This approach is helpful for lower quality images that have noisy RGB data extracted from the color chart. Having determined optimal parameters arc 403 at step 402, step

404 generates optimal parameters <xc 405 that describe the RGB chromaticites of the device profile, arc 403 and RGB-XYZ_1LLCOR_R 313 are passed unmodified through step 404 to step 406. In step 404, standard Matrix/TRC formalism, as indicated in the description below, may be used to calculate the values of XYZ for R, G, and B for all the color chart values using tone response calculated in step 402. The error function is similar to that described above with respect to step 402. However, all data points may be used, and all squared errors added to the sum may be reduced by a predefined weighting factor if values of R, G, or B are equal to 0 or 255, implying that the image data was clipped and that the actual R, G, or B value is not known accurately.

In step 404, the adjusted parameter list αc 405 is the chromaticity value (xy, known in the art) for R, G, and B. According to an embodiment of the present invention, the mathematical description of the matrix portion of the XYZ function of RGB is as follows. Note that it is assumed that device-dependent data RGB (in RGB-XYZ,LL_CORR 313) has already been processed by the RGB tone curve functions defined above with respect to step 402. In other words, the new values of RGB are in linear RGB space. Thus, they can easily be converted to XYZ using a simple matrix:

The M matrix is uniquely determined by the (x,y) chromaticities of the RGB channels and the white point for the system, i.e., the (x,y) chromaticities resulting from the value of the XYZ at RGB=max.

M_c(x_n ,y_ιχ ,Z₁. ,x_gι ,y_g[ ,z_gι ,x_bi ,y_bι ,z_b[ ) = y,Jy_n y_sjy_gl y_bjy_h ^z _>Jy_n z_gjy_gι z_bι /y_bι

In this case, the formalism for defining the error function is identical to process of defining the tone curve described above with respect to step 402, with the differences that a) all color chart values can be used (as opposed to only the gray chart patches) and b) the parameters αc defined are the values of x and y for the R, G, B channels. The white point of model (x_Wp,y_wp) should correspond to the white point used for the measured data of the chart, typically D50, known in the art. At step 406, which is optional, optimal parameters CX_SA 407 that describe selective adjustments to the resulting device-independent color space values XYZ of the device profile. Parameters <XSA 407 may be optimized using the error minimization routines described above with respect to steps 402 and/or 404. According to an embodiment of the present invention, the selective adjustments performed by parameters <X_SA 407 at step 406 are made to one or more colors such that there is substantially no risk of introducing artifacts or unwanted corruption to images converted or rendered with profiles that have been modified with this approach. Although any method may be used at step 406, an inventive process of performing selective adjustments to a device-independent color space as part of step 406 is described below with respect to FIG. 5. The embodiment illustrated with FIG. 5 may be used to generate parameters (X_SA 407 that comprise a list of corrections ΔXYZj for i=0,..,5 corresponding to R, G₅B₃C₅M, Y. Such parameters may be optimized using the error minimization processes described above such that an adjusted device-independent color space XYZ_adj 505 is generated that minimizes sum squared error.

At step 408, also an optional step, a final optimization of some or all of the parameters in otxc 403, etc 405, and <X_SA 407 may be performed. These parameters may be optimized individually by repeating steps 402 and/or 404 and/or 406 and/or by optimizing most of the parameters as a group using the error minimization techniques mentioned above, such as Powell. For images that are not over-exposed, the total number of data points is 24x3=72. The total number of adjustable parameters is 10 for the tone curves (α-rc 403), 6 for the chromati cities (αc 405), and 18 for the selective XYZ adjustments (<X_SA 407). Since there is a strong correlation of the chromaticity values and the selective XYZ adjustments, it may be beneficial to perform a global optimization of the tone curve and selective chromaticities simultaneously, leaving the chromaticities fixed. The output of step 408 may include adjusted αc parameters αc' 409 , adjusted αxc parameters α-rc' 410, and adjusted αsA parameters αs_A' 411. αc' 409 , α-rc' 410 and αsA⁵ 411 are output from step 408 and included in ParameterList 315. RGB-XYZ _!LLCORR 313 need not be output from step 408, and, instead, (XILL_CO_RR 311 may be output from step 408 and added to the ParameterList 315 used to generate the profile 317 at step 316. In this regard, it should be noted that step 312 could be performed as part of step 316. In this scenario, (X_IL_LCORR 311 and RGB-XYZ 305, output from step 310, would be passed directly as input to step 314, instead of RGB-

XYZJLL_CORR 313. Anytime illumination-corrected device-independent data is needed to be operated on in step 314, (XI_LLC_ORR 311 could be applied to XYZ 301 (stored in RGB-XYZ 305) to generate XYZ_ILLCORR.

The above method of FIGS. 3 and 4 has been shown to provide good results on image with color checker, known in the art, that are either overexposed or less well-illuminated than the rest of a scene. In all cases, the extreme colors and overall white balance is improved. If desired, the measured chart values XYZ 301 can be modified to achieve the equivalent of a "look profile", i.e., images can be made more saturated or otherwise modified. Turning now to FIG. 5, a method 500, according to an embodiment of the present invention, for performing selective adjustments to a device independent color space is illustrated. The method 500 ensures an excellent visual match between an image displayed for viewing and the same image printed out in hard-copy form. The method 500 is useful for characterizing image data coming from input devices, rendering images to display devices, and converting images to output devices. The method 500 also is useful for improving the accuracy of a color profile for a digital-image input device, such as a digital camera or a scanner. Accordingly, the method 500 may be used as part of step 406 in FIG. 4. However, one skilled in the art will appreciate that the method 500 may be used completely independently of the method 300 illustrated with FIGS. 3 and 4.

The method 500 applies corrections in a linear manner in all or selected areas of device-independent data derived from device-dependent data with substantially no possibility of introducing artifacts. Selective adjustments may be made to the device-independent data to improve color in selected color regions, such as in the vicinity of red ("R"), green ("G"), blue ("B"), cyan ("C"), magenta ("M"), or yellow ("Y"), without degrading color in the unmodified color areas. Inputs used by the method 500 include device-dependent data "RGB" 501, device-independent data "XYZ" 502, other parameters 503, and changes to selected regions of color "ΔXYZj" 504 in device-independent coordinates, where "i" represents a local region of color. When the method 500 is used as part of step 406 in FIG. 4, ΔXYZ; 504 represents αs_A 407. The device- dependent data RGB 501 and the device-independent data XYZ 502 correspond, such that each piece of device-dependent data in RGB 501 corresponds to a piece of device-independent data in XYZ 502. For example, if the method 500 is used as step 406 in FIG. 4, the RGB data in RGB-XYZ_1LLCORR 313 may be input as RGB data 501 , and the associated device-independent data XYZ_ILL_CORR in RGB- XYZILLCORR 313 may be input as XYZ data 502.

When attempting to improve a profile for RGB device-dependent data, such as RGB data 501, it is desirable to perform a correction in a device- independent color space that is similar to the output of the mathematical expression characterizing the device associated with the RGB data. A common mathematical expression characterizing RGB-data-generating devices, such as digital cameras and scanners, is a modified version of the Matrix/TRC formalism described above, for example, in regard to step 402 in FIG. 4. This Matrix/TRC formalism inherently converts RGB to XYZ. Hence, for most devices, XYZ tristimulous space is the preferred space in which to perform corrections.

Therefore, the device-independent data 502 is shown as XYZ data, and the output of the method 500 is adjusted XYZ coordinates, illustrated as XYZ_adj 505. However, similar linear corrections to those described with reference to the method 500 may be performed with some degree of success for visually uniform color spaces, such as CIELAB, and the various CIECAM models such as CIECAM 98, known in the art.

ΔXYZj 504 represents changes (e.g., to saturation, hue, and brightness) to selected regions "i" of color in the device-independent color space. According to an embodiment of the present invention, 0 < i < 5, such that the values zero to five are associated with the colors red, green, blue, cyan, magenta, and yellow, respectively (referred to as R₀, Go, B₀, C₀, M₀, and Y₀, respectively). One skilled in the art will appreciate, however, that changes to different color regions may be used. The value R₀ is defined as R=R_max, G=O, B=O, C=O, M=O₅ and Y=O. The values of G₀, B₀, C₀, M₀, and Y₀ follow similarly. ΔXYZ; 504 may be generated manually or automatically. An example of manually generating ΔXYZj 504 is having an operator view a displayed image (such as on a CRT) or a hard copy print out of an image generated from the device-independent data XYZ

502 and then make changes to select colors of the displayed or printed image. For instance, if red in a displayed image looks too bright, the operator may specify a negative brightness value for ΔXYZo 504 to reduce the brightness of the red in the image. Alternatively, ΔXYZ; data 504 may be generated automatically through the use of an error minimization routine, such as that described with respect to steps 402 and/or 404 above. For example, if the method 500 is used as part of step 406 in FIG. 4, initial values for ΔXYZ; data 504 may be automatically generated. Then, the method 500 may be performed iteratively, such that different values of ΔXYZj data 504 are used in an effort to minimize the sum squared error between the resulting device-independent color space XYZadj 505 and a predicted device-independent color space. The values of ΔXYZj data 504 that result in the least sum squared error may be output at step 406 as α≤_A 407.

Step 506 of method 500 takes as input RGB 501 and other parameters 503 and generates linear RGB values (RGB)' 507. Alternatively, step 506 may take directly as input the linear values (RGB)' without the need for the other parameters 503 and step 506. Although any procedure for generating (RGB)' 507 may be used, (RGB)' 507 typically is calculated to be the corrected values of RGB 501 that achieve optimized predictions of XYZ 502 when multiplied by the appropriate RGB->XYZ matrix as described in the optimization processes above. In the case of a CRT, (RGB)' may be calculated by a form of gamma curve associated with the CRT, e.g., R^γ. In this case, the other parameters

503 are the parameters describing the gamma curve. More complex functions, beyond just using the gamma curve, may be required for greater accuracy or for LCD systems. In the case where the method 500 is used as step 406 in FIG. 4, the other parameters 503 may include one or more of the parameters in arc 403. For example, if the device-independent coordinates of a digital camera profile are to be adjusted, the camera's tone channel expressions f_R, fo, fβ (and associated α-rc 403 parameters as described with respect to step 402) may be used at step 506 to generate (RGB)' 507.

At step 508, correction factors β 509 are generated for each color i corresponding to ΔXYZj 504. According to an embodiment of the present invention, the correction factors β 509 are calculated using piecewise linear correction functions, such that a maximum of each of the piecewise linear correction functions occurs at a boundary condition of a corresponding device- dependent color space (RGB 501) and each piecewise linear correction function is linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different boundary condition or a neutral axis. Stated differently, the correction factors β 509 are calculated, according to an embodiment of the present invention, such that (a) the piecewise linear correction function for a correction factor (β) and a color i is at a maximum when the current device-dependent color being evaluated is at a maximum distance from all other colors capable of being associated with i and the neutral axis, and (b) the piecewise linear correction function for a correction factor correction factor (β) and a color i scales linearly to zero as the device-dependent colors being evaluated approach another color capable of being associated with i or the neutral axis. For an illustration of what is meant by "associated," consider a color at the boundary condition R_bG_bB_b . Assume, for example, that a boundary condition is defined as all values of R_bG_bB_b being either 0 or 1.0. An "adjacent" or "associated" color would be one in which only one of the colors is switched from 0 to 1 or from 1 to 0 from the current color. Thus, adjacent colors to R_bG_bB_b =(1,0,0) are (1,1,0) and (1,0,1). Adjacent colors to R_bG_bB_b =(1,1,0) are (1,0,0) and (0,1,0)

According to an embodiment of the present invention, βj 509 for i=0 to i=5 (i.e., for R₀, G₀, B₀, C₀, M₀, and Y₀) for values ΔXYZ; 504 are calculated as follows. According to this embodiment, R, G, and B are assumed to be normalized to 1.0 so that β is between zero and one, with maximum correction occurring at β= 1. 04123

RGB^_n =min(R,G,B) β₀ (R, G, B) = R- max(G, B) fori=0(R),R>G,R>B β_o(R,G,B) = O fori = 0(R),R<GorR<B

β_x (R, G, B) = G- max(i?, B) fori = l(G),G>R,G>B ft(R,G,B) = 0 fori = l(G),G<RorG<B

β₂ (R, G,B) = B- max(i?, G) fori = 2(B),B>G,B>R β₂(R,G,B) = 0 fori = 2(B),B<GorB<R

β₃(R,G,B) = min(G,B)-RGB_mkλ fori = 3(C),R<G,R<B β,(R,G,B) = O fori = 3(C),R>GorR>B

β₄ (R, G, B) = min(R, B) - RGB_ιrύa fori = 4(M),G<R,G<B β,(R,G,B) = 0 for i = 4(M), G > R or G > B

β₅(R,G,B) = min(R,G)~RGB^ fori = 5(Y),B<G,B<R β_s(R,G,B) = 0 fori = 5(Y),B>GorB>R

For example, when i=0 (associated with red), βo is at a maximum when the current device-dependent color being evaluated (from (RGB)' 507) is at a maximum distance from all other colors capable of being associated with i (that is, green, blue, cyan, magenta, and yellow) and the neutral axis. In other words, βo is at a maximum when the green and blue components of the current device-dependent color (from (RGB)' 507) being evaluated are zero. The piecewise linear correction function for β₀ linearly scales to zero as the device-dependent colors being evaluated (from (RGB)' 507) approach green, blue, cyan, magenta, yellow, or the neutral axis. In other words, the linear correction function associated with βo linearly scales to zero as the green and blue components of the current device- dependent color (from (RGB)' 507) being evaluated increase. At step 510, each of the individual device-independent changes

ΔXYZ; 504 is corrected by its corresponding correction factors β; 509. A total adjustment to be made to the device-independent data XYZ 502 is calculated as ΔXYZtotai 511. ΔXYZtotai 511 is calculated by summing each of the individually corrected device-independent changes ΔXYZj 504. According to an embodiment of the present invention, ΔXYZ_totai 511 is calculated as follows.

AXYZ_lolal(R,G,B) _^ %β_i{R,G,B)hXYZ_i

I=O At step 512, the device-independent data XYZ 502 is adjusted by

ΔXYZ_tot_ai 511, thereby generating XYZ_adj 505. According to an embodiment of the present invention, XYZ_adj 505 is calculated as follows.

XYZ_adJ = XYZ + AXYZ_lotal

The following software code illustrates an implementation of the method 500, according to an embodiment of the present invention.

#defme nRGBCMY 6 int iColor; deltaXYZ=XYZ(0.0,0.0,0.0); for (iColor=0; iColor<nRGBCMY; iColor++)

{ corrFactor=calcCorrFactor (rgbLinear, iColor); deltaX=corrFactor*mDeltaX[iColor] ; deltaY=corrFactor*mDeltaY[iColor]; deltaZ=corrFactor*mDeltaZ[iColor] ; deltaXYZtemρ.x(deltaX); deltaXYZtemρ.y(deltaY); deltaXYZtemp.z(deltaZ); deltaXYZ+=deltaXYZtemp;

} xyzResult+=deltaXYZ;

double CameraJVlodel: :calcCorrFactor(const vRGB<double>&rgbVal, int corrColor)

{ double corrFactor, minRGB; corrFactor=0.0;

minRGB=min(rgbVal.r(), min(rgbVal.g(), rgbVal.b())); 5 if(corrColor==iRED)

{ if (rgbVal.r()>rgbVal.g() && rgbVal.r()>rgbVal.b());

{

10 corrFactor=rgbVal.r() - max(rgbVal.g(), rgbValbO);

} else corrFactor=0.0

15 } else if (corrColor==iGRE)

{ if (rgbVal.g()>rgbVal.r() && rgbVal.g()>rgbVal.b()); 20 { corrFactor=rgbVal.g() - max(rgbVal.r(), rgbValbO);

} else

25 corrFactor=0.0

} else if (corrColor==iBLU)

{ if (rgbVal.b()>rgb VaLgO && 30 rgbVal.b()>rgbVal.r());

{ corrFactor=rgbVal.b() - max(rgbVal.r(), rgbVaLgO);

} else

5 corrFactor=0.0

} else if (corrColor==iCYAN)

{ if (rgbVal.g()>rgbVal.r() && 10 rgbVal.b()>rgbVal.r());

{ corrFactor=min(rgbVal.g(), rgbVal.b()) minRGB;

} 15 else corrFactor^O.O

} else if (corrColor^^iMAG)

{

20 if (rgbVal.r()>rgbVal.g() && rgbVal.b()>rgbVal.g());

{ corrFactor=min(rgbVal.r(), rgbVal.b()) - minRGB; 25 } else corrFactor=0.0

} else if (corrColoi^^iYELL) 30 { if (rgbVal.r()>rgbVal.bO && rgbVal.g()>rgbVal.b()); { corrFactor=min(rgbVal.r(), rgbVal.g()) - minRGB; } else corrFactor=0.0

} return(corrFactor); }

The method 500 may be used to improve the process of soft proofing on a display. In order to determine the desired corrections for achieving such improved soft proofing, the magnitude and direction of the corrections can be estimated by correcting a display profile A->display profile A' in the desired direction of improvement and then converting colors from the corrected display profile A'->display profile A. For example, if an operator desires to shift the hue of yellow in a displayed image towards red, a value of A(XYZ)₅ (yellow), which equates to a hue shift of 3 delta E towards red for saturated yellow, can be used. If the operator confirms that the desired result has occurred, the RGB profile of the display may now be corrected in an inverse manner to ensure that images rendered to the screen will have the desired red shift in the yellows. This may be accomplished to reasonable accuracy by adjusting the display profile A with a value of A(XYZ)₅ (yellow), which is the negative of the above correction. Similarly, the method 500 may be used to perform device independent color space correction. For instance, an original RGB profile (profile Al) may be modified according to the method 500 to generate a new profile (profile A2). XYZ corrections may be performed by following the standard color management path of XYZ->RGB(profileAl)->RGB(ρrofileA2)->(XYZ)'. Combining multiple conversions into a single conversion is well-known in the art and is called concatenation of profiles. The XYZ->(XYZ)' result is known as an abstract profile. Another application for the method 500, as discussed above with reference to FIGS. 3 and 4 is for digital-image input device (such as a scanner or a digital camera) profiling. The method 500 may permit adequate correction to be applied to a generic RGB profile for a digital camera or scanner in order to preserve gray balance and good overall image integrity, but also improvement to the predictive conversion of RGB->XYZ or L*a*b* for a specific object in an image having intense color. The values of the corrections to the angle, saturation, and luminance for RGBCMY may be automatically calculated by an error minimizing routine. Unlike other techniques, the method 500 uses piecewise linear functions that may be used to correct both small color discrepancies, i.e., on the order of 2-3 delta E, or large color discrepancies, i.e., on the order of 20-30 delta E.

PARTS LIST

101 object

102 input device

103 device-dependent data RGB

104 color profile

105 device-independent data XYZ

106 output device color profile

107 device-independent data CMYK

108 output device

109 representation of object 101

200 system

202 input device

204 computer system

206 data storage system

208 operator

210 optional devices/computers

300 method

301 XYZ data

302 step

303 RGB data

304 step

305 RGB-XYZ

306 step

307 GrayPatches

308 step

309 Brightest Patch

310 step

311 αiLLCORR

312 step

313 RGB-XYZ_ILLC0RR I

314 step

315 parameters

316 step

317 profile

5 402 step

403 parameters arc

404 step

405 parameters αc

406 step

.0 407 parameters otsA

408 step

409 adjusted αc parameters αc'

410 adjusted αxc parameters arc'

411 adjusted αsA parameters αsA'

.5 500 method

501 device-dependent data "RGB"

502 device-independent data "XYZ"

503 other parameters

504 changes to selected regions of color "ΔXYZj"

10 505 adjusted device-independent data XYZ_a(1j

506 step

507 adjusted device-dependent data (RGB)'

508 step

509 correction factors β

»5 510 step

511 total changes to device-independent data ΔXYZ_tot_ai

512 step

Claims

1. A method performed at least in part by a computer, the method comprising applying a selective tristimulous correction to device-independent coordinates using a piecewise linear correction function, wherein the piecewise linear correction function is defined such that a maximum of the piecewise linear correction function occurs at a boundary condition of a corresponding device-dependent color space and the piecewise linear correction function is linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different boundary condition or a neutral axis.

2. The method of claim 1 , wherein the piecewise linear correction function is dependent on linear device-dependent coordinates associated with an RGB profile.

3. The method of claim 1 , further comprising applying a combination of piecewise linear correction functions, each correction function corresponding to a different region of color in a device-dependent coordinate space associated with an RGB profile, wherein each of the piecewise linear correction functions is defined such that a maximum of each of the piecewise linear correction functions occur at a respective boundary condition corresponding to the device-dependent color space and the piecewise linear correction functions are each linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different respective boundary condition or the neutral axis.

4. The method of claim 1 , further comprising adjusting a color space by applying the selective tristimulous corrections to the device-independent coordinates of an RGB profile using the piecewise linear correction function and concatenating the original and the modified profile in order to create an abstract profile.

5. The method of claim 1 , further comprising modifying an RGB profile by applying the selective tristimulous corrections to the device-independent coordinates using the piecewise linear correction function.

6. The method of claim 5, wherein the RGB profile comprises a profile of a digital camera or a scanner.

7. The method of claim 1 , further comprising adjusting an appearance of an image by applying the selective tristimulous corrections to the device-independent coordinates using the piecewise linear correction function.

8. The method of claim 1 , wherein the device-independent coordinates define colors in a visually non-uniform color space.

9. A method performed at least in part by a computer, the method comprising: determining tristimulous corrections to device-independent coordinates corresponding to each of a plurality of regions of color in a device- dependent coordinate space based at least on linear device-dependent coordinates; and applying the tristimulous corrections to the device-independent coordinates in the corresponding regions of color to obtain corrected device- independent coordinates, wherein the tristimulous corrections are defined such that a maxima of the tristimulous corrections occur at a boundary condition of a corresponding device-dependent color space and tristimulous corrections are linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different boundary condition or a neutral axis.

10. The method of claim 9, wherein determining tristimulous corrections further comprises calculating correction factors corresponding to each region of color.

11. The method of claim 10, wherein the linear device- dependent coordinates comprise linear RGB coordinates.

12. The method of claim 9, wherein the regions of color in the device-dependent coordinate space comprise red, green, blue, cyan, magenta and yellow.

13. A method comprising: determining a correction level based at least on desired changes in saturation, hue and brightness for chromatic colors of a device-dependent color space associated with a display device; calculating a correction factor based at least on a linear correction function associated with the display device; and applying the correction factor and the correction level to device- independent coordinates that define chromatic colors of a printing device to produce chromatically corrected device-independent coordinates, wherein the correction factor is defined such that a maxima of the correction factor occurs at a boundary condition of the device-dependent color space and the correction factor is linearly reduced to zero or approximately zero as values in the device- dependent color space approach either a different boundary condition or a neutral axis.

14. The method of claim 13, wherein calculating the correction factor further comprises calculating a piecewise linear correction function of linear device-dependent coordinates.

15. The method of claim 14, wherein the linear device- dependent coordinates are linear RGB coordinates.

16. The method of claim 14, further comprising: calculating a group of piecewise linear correction functions, each piecewise linear correction function corresponding to a different region of color; and applying each piecewise linear correction function in the group to the device-independent coordinates in the corresponding regions of color.

17. A computer-accessible memory containing instructions for causing a processor to apply selective tristimulous corrections to device-independent coordinates using a piecewise linear correction function, wherein the piecewise linear correction function is defined such that a maxima of the piecewise linear correction function occurs at a boundary condition of a corresponding device-dependent color space and the piecewise linear correction function is linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different boundary condition or a neutral axis.

18. The computer-readable medium of claim 17, wherein the piecewise linear correction function operates on linear device-dependent coordinates associated with an output device.

19. The computer-readable medium of claim 17, further comprising instructions that cause the processor to: generate a group of piecewise linear correction functions, each group corresponding to a different region of color in a device-dependent coordinate space associated with an output device; and apply each group of piecewise linear correction functions to the device-independent coordinates in the corresponding regions of color to perform tristimulous corrections to the device-independent coordinates, wherein each of the piecewise linear correction functions is defined such that a maxima of each of the piecewise linear correction functions occur at a respective boundary condition corresponding the device-dependent color space and the piecewise linear correction functions are each linearly reduced to zero or approximately zero as values in the corresponding device-dependent color space approach either a different respective boundary condition or the neutral axis.

20. The computer-readable medium of claim 17, further comprising instructions that cause the processor to adjust a color space by applying the selective tristimulous corrections to the device-independent coordinates using the piecewise linear correction function.

21. The computer-readable medium of claim 17, further comprising instructions that cause the processor to modify an RGB profile by applying the selective tristimulous corrections to the device-independent coordinates using the piecewise linear correction function.

22. The computer-readable medium of claim 21 , wherein the RGB profile comprises a profile of a digital camera or a scanner.

23. The computer-readable medium of claim 17, further comprising instructions that cause the processor to adjust the appearance of an image by applying the selective tristimulous corrections to the device-independent coordinates using the piecewise linear correction function.