Patent Publication Number: US-8531474-B2

Title: Methods, systems and apparatus for jointly calibrating multiple displays in a display ensemble

Description:
FIELD OF THE INVENTION 
     Embodiments of the present invention relate generally to methods, systems and apparatus for color-display calibration and, in particular, to methods, systems and apparatus for jointly calibrating multiple displays in a display ensemble. 
     BACKGROUND 
     In a display ensemble comprising multiple color display apparatus, wherein a color display apparatus, also referred to as a color display or a display, comprises a color display device and a set of R, G and B Gamma one-dimensional look-up tables (1D LUTs), it may be desirable to calibrate all of the color displays to the same gray-scale chromaticity values, tone response function, also referred to as gamma curve, and maximum luminance value in order to assure consistent image appearance across display boundaries. Without calibration, when the same Red-Green-Blue (RGB) signals are sent to different color displays, even of the same make and model, each color display will, generally, produce different output colors, thereby making display boundaries noticeable and visually displeasing. 
     An RGB input signal received by a color display apparatus may be modified according to the RGB Gamma 1D LUTs, and the modified signals may be used to drive the color display device. The Gamma 1D LUTs may be used to set the proportions of maximum R, G and B signals, actually sent to the color display device, to achieve the desired displayed luminance and chromaticity at the white point. In addition, the Gamma 1D LUTs may be used to set the R, G and B signal levels, actually sent to the color display device, along the gray scale to control the chromaticity and tone response produced for gray, also considered equi-RGB, signals received by the color display apparatus. 
     A model of a response function, of a color display device, that predicts the color output, in CIE XYZ, from an input RGB signal may be required to properly generate the data for the RGB Gamma 1D LUTs. A model of the display device response function may be obtained by measuring the colors actually displayed, on the display device, in response to a variety of different RGB signal inputs, presented to the display device, and inverting the measured relationship between the displayed colors and the RGB signal inputs. The model of an individual display device may be used to generate the data for that display&#39;s RGB Gamma 1D LUTs, which may be used to modify that display&#39;s input RGB signals to achieve the desired chromaticity along the gray scale, the desired tone response function and the desired maximum luminance. By loading appropriate data into each display&#39;s Gamma 1D LUTs, the gray scale chromaticity, tone response function and maximum luminance may be made the same for all the displays, provided the desired chromaticity and maximum luminance are achievable on each display. 
     A color-measurement device, for example, a colorimeter or a spectroradiometer, may be used to measure a display&#39;s color outputs. A more accurate calibration may require more measurements with different RGB input signals, especially around the gray scale, making more accurate calibrations more time consuming and hence, more costly. Methods, systems and apparatus for generating an accurate calibration, with a small number of color measurements made of the display using a color-measurement device, may be desirable. 
     SUMMARY 
     Some embodiments of the present invention comprise methods, systems and apparatus for calibration of multiple displays in a display ensemble. 
     According to a first aspect of the present invention, a camera-calibration model associated with a display, in a display ensemble, may be generated based on one or more color images, acquired using a digital color camera, of the display and a plurality of color measurements made of the display using a color-measurement device. 
     According to a second aspect of the present invention, a display-calibration model may be generated for a display, in a display ensemble, using a digital color camera and a previously determined camera-calibration model associated with the display. 
     According to a third aspect of the present invention, a display-calibration model may be generated in a two-pass process, wherein the first pass comprises an initial estimation of a display response function and the second pass comprises refinement of the initial estimate. 
     According to a fourth aspect of the present invention, an initial estimate of a display response function may be generated using a color-measurement device. 
     According to a fifth aspect of the present invention, an initial estimate of a display response function may be generated using a digital color camera and a previously determined camera-calibration model. 
     The foregoing and other objectives, features, and advantages of the invention will be more readily understood upon consideration of the following detailed description of the invention taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL DRAWINGS 
         FIG. 1  is a picture illustrating an exemplary display apparatus; 
         FIG. 2  is a picture illustrating exemplary embodiments of the present invention comprising an exemplary display ensemble, a digital color camera located on a tripod, a color-measurement device located on a support mechanism, a display-driver computer and a calibration computer; 
         FIG. 3  is a chart depicting exemplary embodiments of the present invention comprising camera calibration and display calibration; 
         FIG. 4  is a picture illustrating an exemplary display ensemble comprising four displays and illustrating exemplary measurement sites associated with each display in the display ensemble; 
         FIG. 5  is a picture illustrating an exemplary display ensemble comprising four displays and illustrating exemplary measurement sites associated with each display in the display ensemble; 
         FIG. 6  is a chart depicting exemplary embodiments of the present invention comprising specular-highlight detection in a dark-camera image, wherein a user may be prompted to adjust the imaging geometry to eliminate the detected specular highlights; 
         FIG. 7  is a chart depicting exemplary embodiments of the present invention comprising specular-highlight detection in a dark-camera image, wherein image portions contaminated by detected specular highlights may be synthesized or disregarded; 
         FIG. 8  is a chart depicting exemplary embodiments of camera calibration according to the present invention; 
         FIG. 9A  and  FIG. 9B  are a chart depicting exemplary embodiments of display calibration according to the present invention; 
         FIG. 10A  and  FIG. 10B  are a chart depicting exemplary embodiments of display calibration refinement according to the present invention; 
         FIG. 11  is a chart depicting exemplary embodiments of look-up-table construction according to the present invention; 
         FIG. 12  is a chart depicting exemplary embodiments, according to the present invention, of look-up-table construction comprising smoothing of the look-up-table entries; 
         FIG. 13  is a picture illustrating exemplary embodiments of the present invention comprising a display ensemble, a permanently mounted digital color camera, a color-measurement device located on a support mechanism, a display-driver computer and a calibration computer; 
         FIG. 14  is a picture illustrating exemplary embodiments of the present invention comprising a display ensemble, a permanently mounted digital color camera, a color-measurement device located on a support mechanism, a display-driver computer and a display-ensemble services solution in a cloud computing environment; 
         FIG. 15A  and  FIG. 15B  are a chart depicting exemplary embodiments of the present invention, wherein camera calibration and initial display model determination use color-measurement data and color images acquired using a digital color camera; 
         FIG. 16  is a chart depicting exemplary embodiments of the present invention, wherein dark-camera values may be obtained prior to camera calibration and prior to display calibration; and 
         FIG. 17  is a chart depicting exemplary embodiments of the present invention wherein dark-camera values may be obtained prior to camera calibration and initial display model estimation and prior to display model refinement. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Embodiments of the present invention will be best understood by reference to the drawings, wherein like parts are designated by like numerals throughout. The figures listed above are expressly incorporated as part of this detailed description. 
     It will be readily understood that the components of the present invention, as generally described and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of the embodiments of the methods, systems and apparatus of the present invention is not intended to limit the scope of the invention, but it is merely representative of the presently preferred embodiments of the invention. 
     Elements of embodiments of the present invention may be embodied in hardware, firmware and/or a non-transitory computer program product comprising a computer-readable storage medium having instructions stored thereon/in which may be used to program a computing system. While exemplary embodiments revealed herein may only describe one of these forms, it is to be understood that one skilled in the art would be able to effectuate these elements in any of these forms while resting within the scope of the present invention. 
     Although the charts and diagrams in the figures may show a specific order of execution, it is understood that the order of execution may differ from that which is depicted. For example, the order of execution of the blocks may be changed relative to the shown order. Similarly, for example, two or more blocks shown in succession in a figure may be executed concurrently, or with partial concurrence. It is understood by those with ordinary skill in the art that a non-transitory computer program product comprising a computer-readable storage medium having instructions stored thereon/in which may be used to program a computing system, hardware and/or firmware may be created by one of ordinary skill in the art to carry out the various logical functions described herein. 
     Some embodiments of the present invention may comprise a computer program product comprising a computer-readable storage medium having instructions stored thereon/in which may be used to program a computing system to perform any of the features and methods described herein. Exemplary computer-readable storage media may include, but are not limited to, flash memory devices, disk storage media, for example, a floppy disk, an optical disk, a magneto-optical disk, a Digital Versatile Disc (DVD), a Compact Disc (CD), a micro-drive and other disk storage media, a Read-Only Memory (ROM), a Programmable Read-Only Memory (PROM), an Erasable Programmable Read-Only Memory (EPROM), an Electrically Erasable Programmable Read-Only Memory (EEPROM), a Random-Access Memory (RAM), a Video Random-Access Memory (VRAM), a Dynamic Random-Access Memory (DRAM) and any type of media or device suitable for storing instructions and/or data. 
     Although embodiments of the present invention may be described in relation to a specific color space, it is understood that another color space may be used. 
     In a display ensemble comprising multiple color displays, it may be desirable to calibrate all of the color displays to the same gray-scale chromaticity values, tone response function, also referred to as gamma curve, and maximum luminance value in order to assure consistent image appearance across display boundaries. Target, also considered desired, gray-scale chromaticity values and a target, also considered desired, tone response function may be specified by a user. Exemplary tone response functions may include a power-law gamma curve specified by the exponent, for example, 2.2, an sRGB tone response curve as specified in the IEC 61966-2-1:1999 standard, and other gamma curves known in the art. A specific target, also considered desired, maximum luminance value may be specified by a user, or a user may specify that the desired maximum luminance value may be the maximum luminance value that is jointly achievable by all displays in the display ensemble. 
     Without calibration, when the same Red-Green-Blue (RGB) signals are sent to different color displays, even of the same make and model, each color display will, generally, produce different output colors, thereby making display boundaries noticeable and visually displeasing. 
       FIG. 1  illustrates an exemplary color display apparatus  100  comprising a color display device  102  and a set of R, G and B Gamma one-dimensional look-up tables (1D LUTs)  104 . An RGB input signal  106  received by the color display apparatus  100  may be modified according to the RGB Gamma 1D LUTs  104 , and the modified signals  108  may be used to drive the color display device  102 . The Gamma 1D LUTs  104  may be used to set the proportions of maximum R, G and B signals, actually sent  108  to the color display device  102 , to achieve the desired displayed luminance and chromaticity at the white point. In addition, the Gamma 1D LUTs  104  may be used to set the R, G and B signal levels, actually sent  108  to the color display device  102 , along the gray scale to control the chromaticity and tone response produced for gray, also considered equi-RGB, signals received  106  by the color display apparatus  100 . 
     A model of a response function, of a color display device  102 , that predicts the color output  110 , in CIE XYZ, from a a device input RGB signal  108  may be required to properly generate the data for the RGB Gamma 1D LUTs  104 . A model of the display device  102  response function may be obtained by measuring the colors actually displayed  110 , on the display device  102 , in response to a variety of different RGB signal inputs  108 , presented to the display device  102 , and inverting the measured relationship between the displayed colors  110  and the RGB signal inputs  108 , presented to the display device  102 . The model of an individual display device  102  may be used to generate the data for that display&#39;s RGB Gamma 1D LUTs  104 , which may be used to modify that display&#39;s input RGB signals  106  to achieve the desired chromaticity along the gray scale, the desired tone response function and the desired maximum luminance. By loading appropriate data into each display&#39;s Gamma 1D LUTs  104 , the gray scale chromaticity, tone response function and maximum luminance may be made the same for all the displays, provided the desired chromaticity and maximum luminance are achievable on each display. 
     A color-measurement device, for example, a colorimeter or a spectroradiometer, may be used to measure a display&#39;s color outputs. A more accurate calibration may require more measurements with different RGB input signals, especially around the gray scale, making more accurate calibrations more time consuming and hence, more costly. Methods, systems and apparatus for generating an accurate calibration, with a small number of color measurements made of the display using a color-measurement device, may be desirable. 
     In some embodiments of the present invention, a plurality of displays, in a display ensemble, may be calibrated using a digital color camera and an instrument for measuring display color outputs, also referred to as a color-measurement device. Exemplary color-measurement devices include a colorimeter, a spectroradiometer and other instruments capable of measuring a color output on a display. 
       FIG. 2  depicts an exemplary system architecture  200  according to some embodiments of the present invention. A digital color camera  202  may be mounted on a tripod  204  located at a location whereat the digital color camera  202  may acquire a full view of a display ensemble  206 . In some embodiments of the present invention, a full view may be acquired as a single image, wherein the display ensemble  206  may be entirely contained in the digital color camera  202  field-of-view. In alternative embodiments of the present invention, a full view may be acquired through a panning, or other camera-movement, operation wherein multiple, partial views of the display ensemble  206  may be acquired, and wherein the partial views may be combined into a single, full-view image according to methods understood in the art. The display ensemble  206  may comprise multiple (four shown,  208 ,  210 ,  212 ,  214 ) color displays, each of which comprises a color display apparatus, comprising a color display device together with a set of downloadable Gamma 1D LUTs, wherein the Gamma 1D LUTs process RGB signals, also considered input RGB signals, received by the color display apparatus, and the processed RGB signals, also considered modified RGB signals, drive the color display device. A support mechanism  216  may be used for placing a colorimeter  218 , or other instrument for measuring display color outputs, so that the colorimeter  218 , or other instrument for measuring display color outputs, individually senses each color display  208 ,  210 ,  212 ,  214  to measure the respective display&#39;s output colors. Exemplary colorimeters include X-Rite&#39;s EyeOne Display 2 and Datacolor&#39;s Spyder 3. 
     The color displays  208 ,  210 ,  212 ,  214  in the display ensemble  206 , the digital color camera  202  and the colorimeter  218  may be connected to a calibration computer  220  via wired, wireless or other communication links  222 ,  224 ,  226 . A display-driver computer  228  may be used to drive, via a wired, wireless or other communication link  230  for graphics and video data transmission, the display ensemble  206 . In some embodiments of the present invention, the display-driver computer  228  may be a single computer. In alternative embodiments (not shown), the display-driver computer may comprise a computing system, wherein a plurality of driver computers may be supervised by a coordinating computer to drive all of the color displays. In some of these alternative embodiments, the computing system may comprise one, or more, set-top boxes. In some embodiments of the present invention (shown), the display-driver computer  228  and the calibration computer  220  may be distinct computer systems. In these embodiments wherein the display-driver computer  228  and the calibration computer  220  are distinct computer systems, the display-driver computer  228  and the calibration computer  220  may be linked via a wired, wireless or other communication link  232 . Exemplary communication links include a serial communication link via a serial port, a USB link, an Ethernet link and other wired and wireless communication links. In alternative embodiments of the present invention (not shown), one computer system may drive the display ensemble  206  and also function as the calibration computer. 
     A display-ensemble calibration program may reside on a non-transitory computer program product comprising a computer-readable storage medium having instructions stored thereon/in which may be used to program a calibration computer  220 . The display-ensemble calibration program may instruct the calibration computer  220  to generate and send a command to the digital color camera  202  effectuating the acquisition, by the digital color camera  202 , of an image of the display ensemble  206 . The display-ensemble calibration program may instruct the calibration computer  220  to generate and send a command to command the display-driver computer  228  to drive the display ensemble  206  to display a color patch of a particular color, from a plurality of color-patch colors, on a particular color display  208 ,  210 ,  212 ,  214 . The display-ensemble calibration program may instruct the calibration computer  220  to generate and send a command to the colorimeter  218  effectuating the acquisition of a color measurement on a particular color display  208 ,  210 ,  212 ,  214 . The display-ensemble calibration program may prompt a user to reposition the colorimeter  218  for subsequent color measurements. The display-ensemble calibration program may collect and process image and measurement data to generate a camera calibration model for each of the color displays  208 ,  210 ,  212 ,  214  in the display ensemble  206 ; to collect and process image data from the digital color camera  202  to generate data comprising the contents of a Red, a Green or a Blue Gamma 1D look-up table (LUT), collectively referred to as RGB Gamma 1D LUTs and gamma tables, for each color display  208 ,  210 ,  212 ,  214  in the display ensemble  206 ; and to download the RGB Gamma 1D LUTs associated with a particular color display to the color display  208 ,  210 ,  212 ,  214  in the display ensemble  206 . 
     Some embodiments of the present invention may be described in relation to  FIG. 3 . In these embodiments, a display-ensemble calibration program may initialize  302  the 
     RGB Gamma 1D LUTs in each color display to an identity function, wherein the RGB values sent to the display device are equal to the input RGB values received by the color display. In alternative embodiments, the RGB Gamma 1D LUTs in each color display may be initialized  302  to an alternative function and appropriate compensation may be performed based on the known alternative initialization function. In yet alternative embodiments (not shown), the RGB Gamma 1D LUTs in each color display may not be initialized, but may be known. In these embodiments, an appropriate compensation may be performed based on the known function. In some embodiments of the present invention, when the RGB Gamma 1D LUTs are known, but do not comprise a mapping from the complete domain to the complete range of values, then initialization may be required. The display-ensemble calibration program may instruct a calibration computer to generate and send a command to a digital color camera effectuating the acquisition  304 , by the digital color camera, of a dark-camera image of the display ensemble with all of the color displays in the display ensemble in a powered-down state under a normal lighting condition. In some embodiments of the present invention, the display-ensemble calibration program may provide a prompt to a user, for example, via a graphical user interface (GUI), via a textual user interface, or via another type of user interface, instructing the user to power down the display ensemble color displays and to set the lighting conditions to a normal lighting condition. In alternative embodiments, the display-ensemble calibration program may instruct the calibration computer to generate and send a command to a display-driver computer requesting the display-driver computer to power down the display ensemble displays. A summary dark-camera Red value, a summary dark-camera Green value and a summary dark-camera Blue value may be extracted from the acquired dark-camera image from a designated measurement site on each color display in the display ensemble. An exemplary summary value may be an average value of all respective values within a designated measurement site. In some embodiments of the present invention, a camera nonlinearity may be compensated for prior to determination of a summary value.  FIG. 4  illustrates an exemplary display ensemble  400  containing four color displays  402 ,  404 ,  406 ,  408 . An exemplary measurement site  410 ,  412 ,  414 ,  416  is illustrated on each of the color displays  402 ,  404 ,  406 ,  408 , respectively. In this example, a measurement site is a circular region located in the central portion of an associated color display.  FIG. 5  illustrates an alternative example of measurement sites  510 ,  512 ,  514 ,  516  for an exemplary display ensemble  500  containing four color displays  502 ,  504 ,  506 ,  508 . 
     These examples are for illustrative purposes and are not intended as a limitation. The display-ensemble calibration program may store measurement-site identification information that facilitates the extraction, from the dark-camera image or other image of the display ensemble, of the RGB values of the camera image pixels located within the measurement sites. In an exemplary embodiment of the present invention, the measurement-site identification information may comprise a mask image, wherein measurement-site pixel values are a first fixed value and non-measurement-site pixel values are a second fixed value. In an alternative embodiment, measurement-site identification information may comprise values associated with a parametric description identifying a measurement site, for example the centers and radii of circular sites, describing the measurement-site locations relative to a readily identifiable origin within the image. 
     Referring again to  FIG. 3 , after the dark-camera image is obtained  304 , camera calibration may be performed  306 , and display calibration may be performed  308 . 
     In alternative embodiments of the present invention described in relation to  FIG. 6 , after the dark-camera image is obtained  602 , specular highlight detection may be performed  604  to detect specular reflections of ambient lighting or bright objects that may appear in an image of the display ensemble. In some embodiments of the present invention, specular highlight detection may be performed  604  on the dark-camera image according to methods understood in the art. The detected specular highlight locations maybe examined  606  to determine if the specular highlights occur in a measurement site. If a specular highlight is detected in a measurement site  608 , then a user may be informed and/or instructed to adjust the imaging geometry, for example, to move the color digital camera, to block, to turn off, or to move a specular-highlight generating object, for example, a light source or other specular-highlight generating object, to change the measurement site to a location that is not contaminated by a specular highlight or to make other adjustments to the imaging geometry. A dark-camera image may be obtained  602 , and specular highlight detection may be performed  604  until a satisfactory dark-camera image is acquired  612 . Camera calibration may be performed  614 , and display calibration may be performed  616 . 
     In yet alternative embodiments of the present invention described in relation to  FIG. 7 , after the dark-camera image is obtained  702 , specular highlight detection may be performed  704  to detect specular reflections of ambient lighting or bright objects that may appear in an image of the display ensemble. In some embodiments of the present invention, specular highlight detection may be performed  704  on the dark-camera image according to methods understood in the art. The detected specular highlight locations maybe examined  706  to determine if the specular highlights occur in a measurement site. If a specular highlight is detected in a measurement site  708 , then camera data may be synthesized for the portion of the dark-camera image contaminated by the specular highlights. In some embodiments of the present invention, nearby non-contaminated image regions may be used to estimate the camera data in the contamination regions. Camera calibration may be performed  712 , and display calibration may be performed  714  after the data synthesis  710  or if there are no specular highlights detected in the measure sites. In alternative embodiments of the present invention, portions of the image contaminated by the specular highlights may be disregarded in subsequent processing. 
     Camera calibration, according to some embodiments of the present invention, may be understood in relation to  FIG. 8 . A next color patch, from a plurality of camera-calibration color patches, may be displayed  802  on each color display, wherein each color display may be fully warmed up to thermal equilibrium with the environment. In some exemplary embodiments of the present invention, eight color patches may be displayed, in turn, on each color display in the measurement site associated with the color display. In some exemplary embodiments, the eight color patches may be color patches associated with the eight colors corresponding to the corners of the Red-Green-Blue color cube: that is, color patches of black, white, red, green, blue, cyan, magenta and yellow. In alternative exemplary embodiments, the plurality of camera-calibration color patches may comprise colors corresponding to a rectilinear, for example, a 5×5×5 or other rectilinear, sampling of the RGB color cube. In yet alternative exemplary embodiments, the plurality of camera-calibration color patches may comprise a second plurality of color patches associated with a sampling of the display gray line from black to white with R=G=B. In some embodiments, the gray-line sampling may be a uniform sampling. In alternative embodiments, the gray-line sampling may be a non-uniform sampling. Alternative embodiments of the present invention may comprise alternative camera-calibration color-patch colors. 
     Measured CIE XYZ, also referred to as XYZ, values may be obtained from a color-measurement device, for example, a colorimeter, a spectroradiometer or other instrument for measuring display color outputs, appropriately positioned to make a measurement  804  at each measurement site. The color-measurement device measured XYZ values may be denoted:
 
XYZ measured   (i, j) ,
 
where (i, j) may denote the ith display and the jth color patch, and XYZ measured   (i, j)  is a three-element vector containing the X, Y and Z values obtained by the color-measurement device.
 
     The three color component values in a three-element color vector, for example, the red component, the green component and the blue component in an RGB vector and the X component, the Y component and the Z component in a CIE XYZ vector, may be collectively referred to as a value, for example, an RGB value and an XYZ value. 
     A color-patch image may be acquired  806  of the display ensemble, wherein each color display in the display ensemble is displaying, in the associated measurement site, the color patch. A summary value associated with a measurement region of a color display may be extracted  808 . In an exemplary embodiment of the present invention, an average of the red (R) values, the green (G) values and the blue (B) values of the pixels located within a measurement site may be extracted  808  from the color-patch image. The summary values may be dark corrected  810  according to:
 
RGB CDC   (i, j) =RGB CP   (i, j) −RGB CD   (i, j) ,
 
where each RGB* (i, j)  is a three-element vector containing R, G and B values associated with the ith display and the jth color patch, and the identifiers CDC, CP and CD may denote the dark-corrected camera RGB values, the summary camera RGB values and the averaged dark camera RGB values, respectively.
 
     A determination  812  may be made as to whether or not all of the color patches in the plurality of camera-calibration color patches have been displayed and whether or not the resulting color measurements and acquired color-patch images have been processed. If there are patches remaining to be displayed  814 , then the next color patch may be displayed  802  on each color display, and the process may continue until there are no color patches remaining  816 . 
     A camera calibration model may be computed  818  for each of the color displays within the display ensemble. A camera calibration model, for a particular color display, may convert dark-corrected camera RGB values into camera-model generated XYZ values. A general model form may be:
 
 XYZ   C   (i)   =F   CM   (i) (RGB CDC   (i) ),
 
where RGB CDC   (i)  is a three-element vector containing dark-corrected camera RGB values associated with the ith display, X C   (i)  is a three-element vector containing camera-model generated XYZ values associated with the ith display and F CM   (i)  is a generic camera-calibration model function. In some exemplary embodiments, the camera-calibration model function may be a 3×3 matrix, which may be denoted M CM   (i)  for the ith display. In these exemplary embodiments, the model form may be written:
 
 XYZ   C   (i)   =M   CM   (i) RGB CDC   (i) ,
 
and in some exemplary embodiments, the matrix, M CM   (i) , may be determined according to:
 
               M   CM     (   i   )       =       [           X   measured     (     i   ,   1     )             X   measured     (     i   ,   2     )           …         X   measured     (     i   ,     N   C       )                 Y   measured     (     i   ,   1     )             Y   measured     (     i   ,   2     )           …         Y   measured     (     i   ,     N   C       )                 Z   measured     (     i   ,   1     )             Z   measured     (     i   ,   2     )           …         Z   measured     (     i   ,     N   C       )             ]     /             [           R   CDC     (     i   ,   1     )             R   CDC     (     i   ,   2     )           …         R   CDC     (     i   ,     N   C       )                 G   CDC     (     i   ,   1     )             G   CDC     (     i   ,   2     )           …         G   CDC     (     i   ,     N   C       )                 B   CDC     (     i   ,   1     )             B   CDC     (     i   ,   2     )           …         B   CDC     (     i   ,     N   C       )             ]     ,               
where N C  may denote the number of camera-calibration color patches, X measured   (i, j) , Y measured   (i, j)  and Z measured   (i, j)  may denote the X, Y and Z component values, respectively, of XYZ measured   (i, j)  for j=1, . . . , N  C  and R CDC   (i, j) , G CDC   (i, j)  and B CDC   (i, j)  may denote the R, G and B component values, respectively, of RGB CDC   (i, j)  for j=1, . . . , N  C  and •/• may denote a matrix right division function, for example, such as provided by the MATLAB programming language. Alternative regression methods may be used to estimate M CM   (i)  in alternative embodiments of the present invention. In alternative embodiments, the camera may not be modeled by a linear model, and a generic camera-calibration model function, F CM   (i) , may be estimated.
 
     After a camera calibration is performed and a camera model is computed for each color display, a display calibration may be performed. 
     Display calibration, according to some embodiments of the present invention, may be understood in relation to  FIG. 9A  and  FIG. 9B . A next color patch, from a plurality of display-calibration color patches, may be displayed  902  on each color display in a display ensemble, wherein each color display may be fully warmed up to thermal equilibrium with the environment. In some exemplary embodiments of the present invention, twelve color patches may be displayed, in turn, on each color display in the measurement site associated with the color display. In some exemplary embodiments of the present invention, of the twelve color patches, nine color patches may correspond to a sampling of the gray line from black to white with R=G=B. In some embodiments, the gray-line sampling may be a uniform sampling. In alternative embodiments, the gray-line sampling may be a non-uniform sampling. In these exemplary embodiments, the other three color patches may be the pure red, pure green and pure blue primaries of the display device, at their maximum signal levels. 
     A color-patch image may be acquired  904  of the display ensemble, wherein each color display in the display ensemble is displaying the color patch. A summary value associated with a measurement region of a color display may be extracted  906 . In an exemplary embodiment of the present invention, an average of the red (R) values, the green (G) values and the blue (B) values of the pixels located within a measurement site may be extracted  906  from the color-patch image. The summary values may be dark corrected  908  according to:
 
RGB CDC   (i, j) =RGB CP   (i, j)−RGB   CD   (i, j) ,
 
where each RGB* (i, j)  is a three-element vector containing R, G and B values associated with the ith color display and the jth color patch, and the identifiers CDC, CP and CD may denote the dark-corrected camera RGB values, the summary camera RGB values and the averaged dark camera RGB values, respectively.
 
     For each color display, the previously computed camera calibration model, F CM   (i) , may be applied  910  to the dark-corrected camera RGB values, thereby generating camera-model generated XYZ values according to:
 
 XYZ   C1 =F CM   (i, j) (RGB CP   (i, j) −RGB CD   (i) ),
 
where XYZ C1   (i, j)  denotes a three-element vector containing the camera-model generated XYZ values for the ith color display and the jth color patch associated with a first display-calibration pass, RGB CP   (i, j)  denotes a three-element vector containing the summary RGB values, for the measurement region of the ith color display, for the jth color patch, and RGB CD   (i)  denotes a three-element vector containing the dark camera RGB values for the ith color display, thus making (RGB CP   (i, j) −RGB CP   (i) ) the dark-camera corrected, summary values.
 
     A determination  912  may be made as to whether, or not, all of the color patches in the plurality of display-calibration color patches have been displayed and the resulting color image processed. If there are patches remaining to be displayed  914 , then the next color patch may be displayed  902  on each color display, and the process may continue until there are no color patches remaining  916 . 
     When all of the color patches in the plurality of display-calibration color patches have been displayed and the resulting camera-acquired images have been processed to obtain camera-model generated XYZ values, then the RGB values of the nine gray patches and the corresponding camera-model generated Y values may be used to estimate  918  the nonlinearity of each display response, thereby generating 1-Dimensional (1D) display tone response functions, which may be used to compute  920  linear RGB values from the input display RGB values, with respect to the camera measured Y values. In the exemplary embodiments of the present invention wherein nine gray patches with R=G=B may be used to estimate the nonlinear luminance (Y) response of the display device to input gray signals with R=G=B, all three functions, F RL   (i) (•), F GL   (i) (•), F BL   (i) (•), may be the same function. The linear RGB values, therefore, may be determined, from the input display RGB values, which may be denoted R P   j , G P   j  and B P   j  for the jth color patch, according to:
 
 R   L   (i, j)   =F   RL   (i) ) R   P   j ),  G   L   (i, j)  and  B   L   (i, j   =F   BL   (i) ( B   P   (j) ),
 
where R L   (i, j) , G hu (i, j)  and B L   (i, j)  may denote the linear Red, Green and Blue values, respectively, associated with the ith color display and the jth color patch.
 
     In alternative embodiments of the present invention, the nonlinear response of the display device may be estimated with respect to alternative components of the XYZ triad. In yet alternative embodiments of the present invention, colorimeter-measured XYZ values along the gray line obtained during the camera-calibration process may be used to estimate the nonlinear response of a display device. 
     In some exemplary embodiments of the present invention, an initial display response function may be computed  922 , using the camera-model generated XYZ values and the linear display RGB values, wherein the initial display response function may be modeled as the application of a 3×3 matrix, which may be denoted M DM   (i)  for the ith color display, to the linear display RGB values. The model form may be written:
 
 XYZ   C1   (i)   =M   DM   (i) RGB L   (i) ,
 
and in some exemplary embodiments, the matrix, M DM   (i) , may be determined according to:
 
     
       
         
           
             
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     where N D  may denote the number of display-calibration color patches, X C1   (i, j) , Y C1   (i, j)  and Z C1   (i, j)  may denote the X, Y and Z components, respectively, of XYZ C1   (i, j)  for j=1, . . . , N D  and R L   (i, j) , G L   (i, j)  and B L   (i, j)  may denote the R, G and B components, respectively, of RGB L   (i, j)  for j=1, . . . , N D  and •/• may denote a matrix right division function, for example, such as is provided by the MATLAB programming language. Alternative regression methods may be used to estimate M DM   (i)  in alternative embodiments of the present invention. In alternative embodiments, a display may not be modeled by a linear model, and a generic display model function, F DM   (i) , may be estimated. In some embodiments of the present invention, a display model function, F DM   (i) , may be formulated as a color separation model followed by an n-primaries-to-XYZ model to more accurately model an n-channel display device. In some of these embodiments, the color separation model may be known from a display manufacturer. In alternative of these embodiments, the color separation model may be estimated. 
     With a computed initial display response, F DM   (i) , given a linear RGB value, a display XYZ value may be estimated for the ith color display according to: 
               [           X   C     (   i   )                 Y   C     (   i   )                 Z   C     (   i   )             ]     =       F   DM     (   i   )       ⁡     (     [           R   L     (   i   )                 G   L     (   i   )                 B   L     (   i   )             ]     )             
and, given a displayed XYZ value, a linear RGB value may be estimated for the ith color display according to:
 
     
       
         
           
             
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     The initial display response function for each color display may be refined  924 . In some embodiments of the present invention, the refinement of an initial display response for a color display may be described in relation to  FIG. 10A  and  FIG. 10B . In some embodiments of the present invention, a desired white point chromaticity for each display may be specified by user input. In alternative embodiments, a default white point chromaticity may be used. The camera-model generated Y value obtained in the first pass for the equi-RGB white patch may be combined with the desired (x, y) white point chromaticity to obtain  1002  a display-specific target white XYZ, which may not necessarily be realizable, for each color display, which may be denoted XYZ W   (i) =[X W   (I) Y W   (i) Z W   (i) ] T  for the ith color display, where T denotes the vector transpose operation. 
     The display-specific target white XYZ for each color display may be used to obtain  1004  linear RGB values for a plurality of refinement color patches defined in a particular color space. In some embodiments of the present invention, the plurality of color patches may be defined in a perceptually uniform color space. In some embodiments, described herein, an Lab color space may be used. In alternative embodiments of the present invention, an alternative perceptually uniform color space may be used. In yet alternative embodiments, a perceptually non-uniform color space may be used. In some embodiments of the present invention, the plurality of refinement color patches may comprise forty-seven color patches. Fifteen of the forty-seven refinement color patches may be obtained by uniformly sampling the neutral Lab gray line with a=b=0. These Lab coordinates are calculated with respect to the display-specific target white XYZ for each display, not with respect to the native XYZ produced by the display device in response to the equi-RGB white signal. Eight of the forty-seven refinement color patches may be obtained by uniformly sampling L with a=10 and b=0. Eight of the forty-seven refinement color patches may be obtained by uniformly sampling L with a=10 and b=0. Eight of the forty-seven refinement color patches may be obtained by uniformly sampling L with a=0 and b=10. Eight of the forty-seven refinement color patches may be obtained by uniformly sampling L with a=0 and b=10. The linear RGB values for the jth color patch and for the ith color display may be determined according to: 
                 [           R   L     (     i   ,   j     )                 G   L     (     i   ,   j     )                 B   L     (     i   ,   j     )             ]     =         (     F   DM     (   i   )       )       -   1       ⁢     (       F     Lab   →   XYZ       ⁡     (       [           L     (   j   )                 a     (   j   )                 b     (   j   )             ]     ,     [           X   W     (   i   )                 Y   W     (   i   )                 Z   W     (   i   )             ]       )       )         ,         
where F Lab→XYZ  (•,•) denotes the standard CIE Lab-to-XYZ conversion function.
 
     Since the display-specific target white point may be different from the native device white point of a display, the linear RGB values may be examined  1006  to determine if a linear RGB value is out of range. If a linear RGB value is out of range  1008 , then the linear RGB value may be clipped  1010 . In some embodiments of the present invention, an out-of-gamut linear RGB value may be clipped to the boundary of the gamut while substantially preserving the hue of the color. In some embodiments of the present invention, clipping may be performed according to: 
                 [           R   CL     (     i   ,   j     )                 G   CL     (     i   ,   j     )                 B   CL     (     i   ,   j     )             ]     =       F   Clip     ⁡     (     [           R   L     (     i   ,   j     )                 G   L     (     i   ,   j     )                 B   L     (     i   ,   j     )             ]     )         ,         
where R CL   (i, j) , G CL   (i, j)  and B CL   (i, j)  may denote the clipped RGB values and F Clip  may denote a clipping function that clips a point that falls outside the unit cube to a point on the surface of the unit cube, wherein the point on the surface of the unit cube is on a line that passes through the center of the unit cube and the point that falls outside the unit cube. In alternative embodiments of the present invention, F Clip  may denote a clipping function that may clip a point that falls outside the unit cube to a point on the surface of the unit cube, wherein the point on the surface of the unit cube is on a line that passes through the unit-cube vertex corresponding to black (R=G=B=0) and the point that falls outside the unit cube. In yet alternative embodiments of the present invention, other clipping functions known in the art may be used to clip an out-of-gamut linear RGB value to the boundary of the gamut while substantially preserving the hue of the color.
 
     The in-range, realizable RGB values, either those resulting from clipping  1010  or those initially in-range  1012 , may be converted  1014  to device RGB values for display by applying the inverse of the display tone response function obtained in the determination of the initial display model:
 
 R   P   (i, j) =( F   RL   (i) ) −1 ( R   CL   (i, j ), G P   (i, j) =( F   GL   (i) ) −1 ( G   CL   (i, j) ) and  B   P   (i, j) =( F   BL   (i) ) −1 ( B   CL   (i, j) ),
 
where R P   (i, j) , G P   (i, j)  and B P   (i, j)  denote the RGB, respectively, device values for the ith color display and the jth refinement color patch.
 
     The next color patch may be displayed  1016  on each color display in the display ensemble, and a color-patch image, associated with the jth refinement color patch, may be acquired  1018 . A summary value associated with a measurement region of a color display may be extracted  1020 . In an exemplary embodiment of the present invention, an average of the red (R) values, the green (G) values and the blue (B) values of the camera-image pixels located within a measurement site may be extracted  1020  from the color-patch camera image. The summary values may be dark corrected  1022  according to: 
       RGB   CDC   (i, j) =RGB CP   (i, j) −RGB CD   (i, j) , 
     where each RGB* (i, j)  is a three-element vector containing R, G and B values associated with the ith color display and the jth color patch, and the identifiers CDC, CP and CD may denote the dark-corrected camera RGB values, the summary camera RGB values and the averaged dark camera RGB values, respectively. 
     For each color display, the previously computed camera calibration model, F CM   (i) , may be applied  1024  to the dark-corrected camera RGB values, thereby generating camera-model generated XYZ values according to:
 
 XYZ   C2   (i, j)   =F   CM   (i) (RGB CP   (i, j) −RGB CD   (i) ),
 
where XYZ C2   (i, j)  denotes a three-element vector containing the camera-model generated XYZ values for the ith color display and the jth color patch associated with the refinement display-calibration pass, RGB CP   i, j)  denotes a three-element vector containing the summary RGB values, for the measurement region of the ith color display, for the jth refinement color patch, and RGB CD   (i)  denotes a three-element vector containing the dark camera RGB values for the ith color display, thus making (RGB CP   (i, j) −RGB CD   (i) ) the dark-camera corrected, summary values.
 
     A determination  1026  may be made as to whether, or not, all of the color patches in the plurality of refinement color patches have been displayed and the resulting color image processed. If there are patches remaining to be displayed  1028 , then the next color patch may be displayed  1016  on each color display, and the process may continue until there are no color patches remaining  1030 . 
     When all of the color patches in the plurality of refinement color patches have been displayed and the resulting camera-acquired images have been processed  1030  to obtain camera-model generated XYZ values for the refinement display-calibration pass, then the camera-model generated XYZ values may be used to model  1032  display functions around the gray scale. In some embodiments of the present invention, due to the irregularity of the camera-model generated XYZ points, the XYZ points, associated with a display, may be tessellated into tetrahedra for the display. In some embodiments of the present invention the Delaunay tessellation algorithm may be used to form the tetrahedra. In some of these embodiments, the MATLAB function “delaunayn” may be used to effectuate the Delaunay tessellation. 
     For each of a plurality of desired neutral colors, with XYZ specified, the tetrahedra associated with a particular color display may be searched to determine if the color is within one of the tetrahedra. If the color is in one of the tetrahedra, then the color is within the display gamut of the color display. If the color is not in one of the tetrahedra, then the color is not within the display gamut of the color display, and is thus, not realizable by the color display. If the color is within the display gamut of the color display, then tetrahedral (barycentric) interpolation may be used to obtain the linear RGB value for the color. By applying the inverse of the display tone response functions, the display RGB values may be obtained from the linear RGB values. 
     In alternative embodiments of the present invention, XYZ values may be converted to an alternative color space, and tessellation may occur in the alternative color space, for example, an Lab color space. 
     Referring again to  FIG. 9B , the RGB Gamma 1D LUTs for each color display may be constructed  926  and loaded  928  into the respective color display. In some embodiments of the present invention described in relation to  FIG. 11 , a maximum achievable display-ensemble luminance (Y) value, may be determined  1102 , wherein the maximum achievable display-ensemble luminance is the maximum display luminance value, that may be jointly achievable on all of the color displays in the display ensemble, having the desired chromaticity. 
     In some embodiments of the present invention, the maximum achievable display-ensemble luminance value may be determined  1102  by gradually increasing the luminance value with the white point chromaticity fixed, and using the XYZ, or other color-space, tessellation obtained, for each display, in the refinement display-calibration pass to test whether, or not, the color is realizable, on each color display. In some embodiments, a starting point from which the luminance value may be gradually increased may be a point associated with a color with the desired white/gray chromaticity that is close to the black point. 
     In alternative embodiments, the maximum achievable display luminance value may be determined  1102  by gradually moving down the gray line from a point outside the gamut, for example, the native white luminance, of the display, at the desired chromaticity, until the gamut is just entered. 
     Alternative embodiments may comprise a Digital Differential Analyzer (DDA) approach, a clipping-divider approach or another approach known in the art. 
     After the maximum achievable display-ensemble luminance value has been determined  1102 , then the luminance (Y) scale may be sampled  1104 , in some embodiments of the present invention, according to the desired tone response function, or other desired display response curve shape, from zero to the maximum achievable display-ensemble luminance value using the number of look-up-table points desired for the 1D look-up tables. In alternative embodiments, a number of sample points less than the total number of look-up-table points desired may be used, and points at locations not corresponding to sample points may be interpolated or approximated to achieve the desired number of look-up-table points. In some embodiments of the present invention, the look-up-table indices may be mapped uniformly onto the interval zero to one. The desired tone response function may be sampled based on the mapped indices, thereby producing a plurality of sample locations for sampling the zero-to-maximum-achievable-display-ensemble-luminance range. The sampled luminance values may be combined with the desired white-point chromaticity, and tetrahedral interpolation using the XYZ, or other color-space, tessellation obtained, for each display, in the refinement display-calibration pass may be used to obtain  1106  the corresponding linear RGB values for each display. By applying  1108  the inverse of the display tone response functions, the display RGB values may be obtained from the linear RGB values. The entries of the RGB Gamma 1D LUTs for each display are the display RGB values constructed for the associated display. 
     In some embodiments of the present invention described in relation to  FIG. 12 , the display RGB values may be smoothed  1202 . 
       FIG. 13  depicts an exemplary alternative system architecture  1300  according to some embodiments of the present invention. A digital color camera  1302  may be mounted on a permanent mounting fixture  1304  located at a fixed location relative to the digital color camera  1302 , whereat the digital color camera  1302  may acquire a full view of a display ensemble  1306 . 
     In some embodiments of the present invention, a full view may be acquired as a single image, wherein the display ensemble  1306  may be entirely contained in the digital color camera  1302  field-of-view. In alternative embodiments of the present invention, a full view may be acquired through a panning, or other camera-movement, operation wherein multiple, partial views of the display ensemble  1306  are acquired, and wherein the partial views may be combined into a single, full-view image according to methods understood in the art. In some exemplary embodiments, the digital color camera  1302  may be mounted from the ceiling. The display ensemble  1306  may consist of multiple (four shown,  1308 ,  1310 ,  1312 ,  1314 ) color displays, each of which may comprise a color display apparatus, comprising a color display device together with a set of downloadable Gamma 1D LUTs, wherein the Gamma 1D LUTs process RGB signals received by the color display apparatus, and the processed RGB signals drive the color display device. A support mechanism  1316  may be used for placing a colorimeter  1318 , or other instrument for measuring display color outputs, so that the colorimeter  1318 , or other instrument for measuring display color outputs, individually senses each color display  1308 ,  1310 ,  1312 ,  1314  to measure the respective display&#39;s output colors. Exemplary colorimeters include X-Rite&#39;s EyeOne Display 2 and Datacolor&#39;s Spyder 3. 
     The color displays  1308 ,  1310 ,  1312 ,  1314  in the display ensemble  1306 , the digital color camera  1302  and the colorimeter  1318  may be connected to a calibration computer  1320  via wired, wireless or other communication links  1322 ,  1324 ,  1326 . A display-driver computer  1328  may be used to drive, via a wired, wireless or other communication link  1330  for graphics and video data transmission, the display ensemble  1306 . In some embodiments of the present invention, the display-driver computer  1328  may be a single computer. In alternative embodiments (not shown), the display-driver computer may comprise a computing system, wherein a plurality of driver computers may be supervised by a coordinating computer to drive all of the color displays. In some of these alternative embodiments, the computing system may comprise one, or more, set-top boxes. In some embodiments of the present invention (shown), the display-driver computer  1328  and the calibration computer  1320  may be distinct computer systems. In these embodiments wherein the display-driver computer  1328  and the calibration computer  1320  are distinct computer systems, the display-driver computer  1328  and the calibration computer  1320  may be linked via a wired, wireless or other communication link  1332 . Exemplary communication links include a serial communication link via a serial port, a USB link, an Ethernet link and other wired and wireless communication links In alternative embodiments of the present invention (not shown), one computer system may drive the display ensemble  1306  and function as the calibration computer. 
     A display-ensemble calibration program may reside on a non-transitory computer program product comprising a computer-readable storage medium having instructions stored thereon/in which may be used to program the calibration computer  1320 . The display-ensemble calibration program may instruct the calibration computer  1320  to generate and send a command to the digital color camera  1302  effectuating the acquisition, by the digital color camera  1302 , of an image of the display ensemble  1306 . The display-ensemble calibration program may instruct the calibration computer  1320  to generate and send a command to the colorimeter  1318  effectuating the acquisition of a color measurement on a particular color display  1308 ,  1310 ,  1312 ,  1314 . The display-ensemble calibration program may prompt a user to reposition the colorimeter  1318  for subsequent color measurements. The display-ensemble calibration program may instruct the calibration computer  1320  to generate and send a command to instruct the display-driver computer  1328  to drive the display ensemble  1306  to display one color patch of a plurality of color patches on a particular color display  1308 ,  1310 ,  1312 ,  1314 . The display-ensemble calibration program may collect and process image data and measurement data to generate camera calibration models for all, or some, of the color displays  1308 ,  1310 ,  1312 ,  1314  in the display ensemble  1306 ; to collect and process image data from the digital color camera  1302  to generate a Red, a Green or a Blue Gamma 1D look-up table (LUT), collectively referred to as RGB Gamma 1D LUTs, for one, or more, of the color displays  1308 ,  1310 ,  1312 ,  1314  in the display ensemble  1306 ; and to download the RGB Gamma 1D LUTs associated with a particular color display to the color display  1308 ,  1310 ,  1312 ,  1314  in the display ensemble  1306 . 
       FIG. 14  depicts an alternative exemplary system architecture  1400  according to some embodiments of the present invention. A digital color camera  1402  may be mounted on a permanent mounting fixture  1404  located at a fixed location relative to the digital color camera  1402 , whereat the digital color camera  1402  may acquire a full view of a display ensemble  1406 . In some embodiments of the present invention, a full view may be acquired as a single image, wherein the display ensemble  1406  may be entirely contained in the digital color camera  1402  field-of-view. In alternative embodiments of the present invention, a full view may be acquired through a panning, or other camera-movement, operation wherein multiple, partial views of the display ensemble  1406  are acquired, and wherein the partial views may be combined into a single, full-view image according to methods understood in the art. In some exemplary embodiments, the digital color camera  1402  may be mounted from the ceiling. The display ensemble  1406  may consist of multiple (four shown,  1408 ,  1410 ,  1412 ,  1414 ) color displays. A support mechanism  1416  may be used for placing a colorimeter  1418 , or other instrument for measuring display color outputs, onto the surface of each color display  1408 ,  1410 ,  1412 ,  1414  to measure the respective display&#39;s output colors. Exemplary colorimeters include X-Rite&#39;s EyeOne Display 2 and Datacolor&#39;s Spyder 3. 
     The color displays  1408 ,  1410 ,  1412 ,  1414  in the display ensemble  1406 , the digital color camera  1402  and the colorimeter  1418  may be connected to a cloud-based display-ensemble service solution  1420  via wired, wireless or other communication links  1422 ,  1424 ,  1426 . A display-driver computer  1428  may be used to drive, via a wired, wireless or other communication link  1430  for graphics and video data transmission, the display ensemble  1406 . In some embodiments of the present invention, the display-driver computer  1428  may be a single computer. In alternative embodiments (not shown), the display-driver computer may comprise a computing system, wherein a plurality of driver computers may be supervised by a coordinating computer to drive all of the color displays. In some of these alternative embodiments, the computing system may comprise one, or more, set-top boxes. In some embodiments of the present invention (shown), the display-driver computer  1428  and the cloud-based display-ensemble service solution  1420  may be distinct computing systems. In these embodiments wherein the display-driver computer  1428  and the cloud-based display-ensemble service solution  1420  are distinct computing systems, the display-driver computer  1428  and the cloud-based display-ensemble service solution  1420  may be linked via a wired, wireless or other communication link  1432 . Exemplary communication links include a serial communication link via a serial port, a USB link, an Ethernet link and other wired and wireless communication links In alternative embodiments of the present invention (not shown), one computing system, for example, a cloud-based system, may drive the display ensemble  1406  and also function as the calibration computer. In yet alternative embodiments of the present invention (not shown), a display ensemble may be driven by a cloud service. 
     A display-ensemble calibration program may reside on a non-transitory computer program product comprising a computer-readable storage medium having instructions stored thereon/in which may be used to program the cloud-based display-ensemble services solution  1420 . The display-ensemble calibration program may instruct the cloud-based display-ensemble services solution  1420  to generate and send a command to the digital color camera  1402  effectuating the acquisition, by the digital color camera  1402 , of an image of the display ensemble  1406 . The display-ensemble calibration program may instruct the cloud-based display-ensemble services solution  1420  to generate and send a command to the colorimeter  1418  effectuating the acquisition of a color measurement on a particular color display  1408 ,  1410 ,  1412 ,  1414 . The display-ensemble calibration program may prompt a user to reposition the colorimeter  1418  for subsequent color measurements. The display-ensemble calibration program may instruct the cloud-based display-ensemble services solution  1420  to generate and send a command to command the display-driver computer  1428  to drive the display ensemble  1406  to display one color patch of a plurality of color patches on a particular color display  1408 ,  1410 ,  1412 ,  1414 . The display-ensemble calibration program may collect and process image and measurement data to generate camera calibration models for all, or some, of the color displays  1408 ,  1410 ,  1412 ,  1414  in the display ensemble  1406 ; to collect and process image data from the digital color camera  1402  to generate a Red, a Green or a Blue Gamma 1D look-up table (LUT), collectively referred to as RGB Gamma 1D LUTs, for one, or more, of the color displays  1408 ,  1410 ,  1412 ,  1414  in the display ensemble  1406 ; and to download the RGB Gamma 1D LUTs associated with a particular color display to the color display  1408 ,  1410 ,  1412 ,  1414  in the display ensemble  1406 . 
     In some embodiments of the present invention wherein a digital color camera may be mounted on a permanent mounting fixture located at a fixed location relative to the display ensemble, whereat the digital color camera may acquire a full view of a display ensemble, camera calibration may be performed less frequently than display calibration due to the fixed camera-display ensemble geometry. In some embodiments of the present invention, a camera-calibration frequency may be based on a known drift rate associated with the camera. In some embodiments of the present invention, a camera-calibration frequency may be based on a known drift rate associated with a display. In some embodiments of the present invention, a display-calibration frequency may be based on a known drift rate associated with the camera. In some embodiments of the present invention, a display-calibration frequency may be based on a known drift rate associated with a display. In some embodiments of the present invention, display calibration may be performed according to a display-calibration schedule. In some of these embodiments, camera recalibration may occur when changes in ambient lighting occur, when changes in object reflections occur or when other changes occur which may impact the camera model. The display calibration schedule may effectuate automatic display-ensemble calibrations during periods when the display ensemble is not otherwise in use. In some embodiments of the present invention, the display calibration schedule may effectuate automatic display-ensemble calibrations according to a fixed-frequency schedule. 
     In alternative embodiments of the present invention described in relation to  FIG. 15A  and  FIG. 15B , camera calibration and determination of an initial display response function may use both colorimetric measurements and color images acquired by a digital camera. In some embodiments of the present invention, a next color patch, from a plurality of color patches, may be displayed  1502  on each color display, wherein each color display may be fully warmed up to thermal equilibrium with the environment. In some exemplary embodiments of the present invention, twelve color patches may be displayed, in turn, on each color display in the measurement site associated with the color display. In some exemplary embodiments, of the twelve color patches, nine color patches may correspond to a sampling of the gray line from black to white with R=G=B. In some embodiments of the present invention, the gray-line sampling may be a uniform sampling. In alternative embodiments, the gray-line sampling may be a non-uniform sampling. In these exemplary embodiments, the other three color patches may be the pure red, pure green and pure blue primaries of the display device, at their maximum signal levels. 
     Measured CIE XYZ, also referred to as XYZ and colorimeter-measured XYZ, values may be obtained from a color-measurement device, for example, a colorimeter, a spectroradiometer or other instrument for measuring display color outputs, appropriately positioned to make a measurement  1504  at each measurement site. The colorimeter-measured XYZ values may be denoted:
 
XYZ measured   (i, j) ,
 
where (i, j) may denote the ith display and the jth color patch, and XYZ measured   (i, j)  is a three-element vector containing the X, Y and Z values obtained by the color-measurement device.
 
     The three color component values in a three-element color vector, for example, the red component, the green component and the blue component in an RGB vector and the X component, the Y component and the Z component in a CIE XYZ vector, may be collectively referred to as a value, for example, an RGB value and an XYZ value. 
     A color-patch image may be acquired  1506  of the display ensemble, wherein each color display in the display ensemble is displaying, in the associated measurement site, the color patch. A summary value associated with a measurement region of a color display may be extracted  1508 . In an exemplary embodiment of the present invention, an average of the red (R) values, the green (G) values and the blue (B) values of the pixels located within a measurement site may be extracted  1508  from the color-patch image. The summary values may be dark corrected  1510  according to:
 
RGB CDC   (i, j) =RGB CP   (i, j −RGB CD   (i, j) ,
 
where each RGB* (i, j)  is a three-element vector containing R, G and B values associated with the ith display and the jth color patch, and the identifiers CDC, CP and CD may denote the dark-corrected camera RGB values, the summary camera RGB values and the averaged dark camera
 
     RGB values, respectively. 
     A determination  1512  may be made as to whether or not all of the color patches in the plurality of color patches have been displayed and whether or not the resulting color measurements and acquired color-patch images have been processed. If there are patches remaining to be displayed  1514 , then the next color patch may be displayed  1502  on each color display, and the process may continue until there are no color patches remaining  1516 . 
     A camera calibration model may be computed  1518  for each of the color displays within the display ensemble. A camera calibration model, for a particular color display, may convert dark-corrected camera RGB values into camera-model generated XYZ values. A general model form may be:
 
 XYZ   C   (i)   =F   CM   (i) (RGB CDC   (i) ),
 
where RGB CDC   (i)  is a three-element vector containing dark-corrected camera RGB values associated with the ith display, XYZ C   (i)  is a three-element vector containing camera-model generated XYZ values associated with the ith display and F CM   (i)  a generic camera-calibration model function. In some exemplary embodiments, the camera-calibration model function may be a 3×3 matrix, which may be denoted M CM   (i)  for the ith display. The model form may be written:
 
XYZ C   (i)   =M   CM   (i) RGB CDC   (i) ,
 
and in some exemplary embodiments, the matrix, M CM   (i) , may be determined according to:
 
               M   CM     (   i   )       =       [           X   measured     (     i   ,   1     )             X   measured     (     i   ,   2     )           …         X   measured     (     i   ,     N   C       )                 Y   measured     (     i   ,   1     )             Y   measured     (     i   ,   2     )           …         Y   measured     (     i   ,     N   C       )                 Z   measured     (     i   ,   1     )             Z   measured     (     i   ,   2     )           …         Z   measured     (     i   ,     N   C       )             ]     /             [           R   CDC     (     i   ,   1     )             R   CDC     (     i   ,   2     )           …         R   CDC     (     i   ,     N   C       )                 G   CDC     (     i   ,   1     )             G   CDC     (     i   ,   2     )           …         G   CDC     (     i   ,     N   C       )                 B   CDC     (     i   ,   1     )             B   CDC     (     i   ,   2     )           …         B   CDC     (     i   ,     N   C       )             ]     ,               
where N C  may denote the number of color patches, X measured   (i, j) , Y measured   (i, j)  and Z measured   (i, j)  may denote the X, Y and Z component values, respectively, of XYZ measured   (i, j)  for j=1, . . . , N C  and R CDC   (i, j) , G CDC   (i, j)  and B CDC   (i, j)  may denote the R, G and B component values, respectively, of RGB CDC   (i, j)  for j=1, . . . , N  C  and •/• may denote a matrix right division function, for example, such as the one provided by the MATLAB programming language. Alternative regression methods may be used to estimate M CM   (i)  in alternative embodiments of the present invention. In alternative embodiments, the camera may not be modeled by a linear model, and a generic camera-calibration model function, F CM   (i) , may be estimated.
 
     After a camera calibration is performed and a camera model is computed for each color display, a display calibration may be performed. 
     The RGB values of the nine gray patches and the corresponding colorimeter-measured Y values may be used to estimate  1520  the nonlinearity of each display response, thereby generating 1-Dimensional (1-D) display tone response functions, which may be used to compute  1522  linear RGB values from the input display RGB values, with respect to the colorimeter-measured Y values. In the exemplary embodiments of the present invention wherein nine gray patches with R=G=B may be used to estimate the nonlinear luminance (Y) response of the display device in response to input gray signals with R=G=B, all three functions, F RL   (i) (•), F GL   (i) (•), F BL   (i) (•), may be the same function. The linear RGB values, therefore, may be determined, from the input display RGB values, which may be denoted R P   j , G P   j  and B P   j  for the jth color patch, according to:
 
 R   L   (i, j)   =F   RL   (i) ( R   P   j ),  G   L   (i, j)   =F   GL   (i) ( G   P   (j) ) and  B   L   (i, j)   =F   BL   (i) ( B   P   (j) ),
 
where R L   (i, j) , G L   (i, j)  and B L   L   (i, j)  may denote the linear Red, Green and Blue values, respectively, associated with the ith color display and the jth color patch.
 
     In alternative embodiments of the present invention, the nonlinear response of the display device may be estimated with respect to alternative components of the XYZ triad. 
     In some exemplary embodiments of the present invention, an initial display response function may be computed  1524 , using the colorimeter-measured XYZ values and the linear display RGB values, wherein the initial display response function may be modeled as the application of a 3×3 matrix, which may be denoted M DM   (i)  for the ith color display, to the linear display RGB values. The model form may be written:
 
 XYZ   measured   (i)   =M   DM   (i) RGB L   (i) ,
 
and in some exemplary embodiments, the matrix, M DM   (i) , may be determined according to:
 
               M   DM     (   i   )       =       [           X   measured     (     i   ,   1     )             X   measured     (     i   ,   2     )           …         X   measured     (     i   ,     N   C       )                 Y   measured     (     i   ,   1     )             Y   measured     (     i   ,   2     )           …         Y   measured     (     i   ,     N   C       )                 Z   measured     (     i   ,   1     )             Z   measured     (     i   ,   2     )           …         Z   measured     (     i   ,     N   C       )             ]     /             [           R   L     (     i   ,   1     )             R   L     (     i   ,   2     )           …         R   L     (     i   ,     N   C       )                 G   L     (     i   ,   1     )             G   L     (     i   ,   2     )           …         G   L     (     i   ,     N   C       )                 B   L     (     i   ,   1     )             B   L     (     i   ,   2     )           …         B   L     (     i   ,     N   C       )             ]     ,               
where N C  may denote the number of color patches, X measured   (i, j) , Y measure   (i, j)  and Z measured   (i, j)  may denote the X, Y and Z components, respectively, of XYZ measured   (i, j)  for j=1, . . . , N C  and R L   (i, j) , G L   (i, j)  and B L   (i, j)  may denote the R, G and B components, respectively, of RGB L   (i, j)  for j=1, . . . , N C  and •/• may denote a matrix right division function, for example, such as is provided by the MATLAB programming language. Alternative regression methods may be used to estimate M DM   (i)  in alternative embodiments of the present invention. In alternative embodiments, a display may not be modeled by a linear model, and a generic display model function, F DM   (i) , may be estimated.
 
     With a computed initial display response, M DM   (i) , given a linear RGB value, a display XYZ value may be estimated for the ith color display according to: 
               [           X   C     (   i   )                 Y   C     (   i   )                 Z   C     (   i   )             ]     =       M   DM     (   i   )       ⁡     [           R   L     (   i   )                 G   L     (   i   )                 B   L     (   i   )             ]             
and, given a displayed XYZ value, a linear RGB value may be estimated for the ith color display according to:
 
     
       
         
           
             
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     The initial display response function for each color display may be refined  1526 . In some embodiments of the present invention, the refinement of an initial display response for a color display may be as described above in relation to  FIG. 10A  and  FIG. 10B . 
     Referring again to  FIG. 15B , the RGB Gamma 1D LUTs for each color display may be constructed  1528  and loaded  1530  into the respective color display, according to methods previously described herein. 
     Some embodiments of the present invention may be described in relation to 
       FIG. 16 . In these embodiments, a display-ensemble calibration program may initialize  1602  the RGB Gamma 1D LUTs in each color display to an identity function, wherein the RGB values sent to the display device are equal to the input RGB values received by the color display. In alternative embodiments, the RGB Gamma 1D LUTs in each color display may be initialized  1602  to an alternative function and appropriate compensation may be performed based on the known alternative initialization function. In yet alternative embodiments (not shown), the RGB Gamma 1D LUTs in each color display may not be initialized, but may be known. In these embodiments, an appropriate compensation may be performed based on the known function. In some embodiments of the present invention, when the RGB Gamma 1D LUTs are known, but do not comprise a mapping from the complete domain to the complete range of values, then initialization of the RGB Gamma 1D LUTs may be required. The display-ensemble calibration program may instruct a calibration computer to generate and send a command to a digital color camera effectuating the acquisition  1604 , by the digital color camera, of an initial dark-camera image of the display ensemble with all of the color displays in the display ensemble in a powered-down state under a normal lighting condition. In some embodiments of the present invention, the display-ensemble calibration program may provide a prompt to a user, for example, via a graphical user interface (GUI), via a textual user interface, or via another type of user interface, instructing the user to power down the display ensemble color displays and to set the lighting conditions to a normal lighting condition. In alternative embodiments, the display-ensemble calibration program may instruct the calibration computer to generate and send a command to a display-driver computer requesting the display-driver computer to power down the displays of the display ensemble. An initial summary dark-camera Red value, an initial summary dark-camera Green value and an initial summary dark-camera Blue value may be extracted from the acquired initial dark-camera image from a designated measurement site on each color display in the display ensemble. An exemplary summary value may be an average value of all respective values within a designated measurement site. The display-ensemble calibration program may store measurement-site identification information that facilitates the extraction, from the dark-camera image or other image of the display ensemble, of the RGB values of the camera image pixels located within the measurement sites. In an exemplary embodiment of the present invention, the measurement-site identification information may comprise a mask image, wherein measurement-site pixels values are a first fixed value and non-measurement-site pixel values are a second fixed value. In an alternative embodiment, measurement-site identification information may comprise values associated with a parametric description identifying a measurement site, for example the centers and radii of circular sites, describing the measurement-site locations relative to a readily identifiable origin within the image. After the initial dark-camera image is obtained  1604 , camera calibration may be performed  1606  using the initial summary dark-camera RGB values. 
     Updated dark-camera RGB values may be obtained  1608  after camera calibration, and display calibration may be performed  1610 . 
     Some embodiments of the present invention may be described in relation to  FIG. 17 . In these embodiments, a display-ensemble calibration program may initialize  1702  the RGB Gamma 1D LUTs in each color display to an identity function, wherein the RGB values sent to the display device are equal to the input RGB values received by the color display. In alternative embodiments, the RGB Gamma 1D LUTs in each color display may be initialized  1702  to an alternative function and appropriate compensation may be performed based on the known alternative initialization function. In yet alternative embodiments (not shown), the RGB Gamma 1D LUTs in each color display may not be initialized, but may be known. In these embodiments, an appropriate compensation may be performed based on the known function. In some embodiments of the present invention, when the RGB Gamma 1D LUTs are known, but do not comprise a mapping from the complete domain to the complete range of values, then initialization may be required. The display-ensemble calibration program may instruct a calibration computer to generate and send a command to a digital color camera effectuating the acquisition  1704 , by the digital color camera, of an initial dark-camera image of the display ensemble with all of the color displays in the display ensemble in a powered-down state under a normal lighting condition. In some embodiments of the present invention, the display-ensemble calibration program may provide a prompt to a user, for example, via a graphical user interface (GUI), via a textual user interface, or via another type of user interface, instructing the user to power down the display ensemble color displays and to set the lighting conditions to a normal lighting condition. In alternative embodiments, the display-ensemble calibration program may instruct the calibration computer to generate and send a command to a display-driver computer requesting the display-driver computer to power down the display ensemble displays. An initial summary dark-camera Red value, an initial summary dark-camera Green value and an initial summary dark-camera Blue value may be extracted from the acquired initial dark-camera image from a designated measurement site on each color display in the display ensemble. An exemplary summary value may be an average value of all respective values within a designated measurement site. The display-ensemble calibration program may store measurement-site identification information that facilitates the extraction, from the dark-camera image or other image of the display ensemble, of the RGB values of the camera image pixels located within the measurement sites. In an exemplary embodiment of the present invention, the measurement-site identification information may comprise a mask image, wherein measurement-site pixel values are a first fixed value and non-measurement-site pixel values are a second fixed value. In an alternative embodiment, measurement-site identification information may comprise values associated with a parametric description identifying a measurement site, for example the centers and radii of circular sites, describing the measurement-site locations relative to a readily identifiable origin within the image. After the initial dark-camera image is obtained  1704 , camera calibration and initial display model estimation may be performed  1706  using the initial summary dark-camera RGB values. 
     Updated dark-camera RGB values may be obtained  1708  after camera calibration, and the initial display model estimates may be refined  1710 . 
     The terms and expressions which have been employed in the foregoing specification are used therein as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding equivalence of the features shown and described or portions thereof, it being recognized that the scope of the invention is defined and limited only by the claims which follow.