Patent Publication Number: US-2023137371-A1

Title: Reproducing out-of-gamut spot colors on a color printer

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application No. 63/273,254, filed Oct. 29, 2021, which is incorporated herein by reference in its entirety. 
     Reference is made to commonly assigned, co-pending U.S. Patent Application Serial No. __/______ (Docket K002373), entitled: “User-preferred reproduction of out-of-gamut spot colors,” by C.-H. Kuo et al., which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     This invention pertains to the field of electrographic printing and more particularly to a method for reproducing out-of-gamut spot colors. 
     BACKGROUND OF THE INVENTION 
     Electrophotography is a useful process for printing images on a receiver (or “imaging substrate”), such as a piece or sheet of paper or another planar medium (e.g., glass, fabric, metal, or other objects) as will be described below. In this process, an electrostatic latent image is formed on a photoreceptor by uniformly charging the photoreceptor and then discharging selected areas of the uniform charge to yield an electrostatic charge pattern corresponding to the desired image (i.e., a “latent image”). 
     After the latent image is formed, charged toner particles are brought into the vicinity of the photoreceptor and are attracted to the latent image to develop the latent image into a toner image. Note that the toner image may not be visible to the naked eye depending on the composition of the toner particles (e.g., clear toner). 
     After the latent image is developed into a toner image on the photoreceptor, a suitable receiver is brought into juxtaposition with the toner image. A suitable electric field is applied to transfer the toner particles of the toner image to the receiver to form the desired print image on the receiver. The imaging process is typically repeated many times with reusable photoreceptors. 
     The receiver is then removed from its operative association with the photoreceptor and subjected to heat or pressure to permanently fix (i.e., “fuse”) the print image to the receiver. Plural print images (e.g., separation images of different colors) can be overlaid on the receiver before fusing to form a multicolor print image on the receiver. 
     As the digital printing technology is beginning to gain a foothold in package printing, it is imperative for the digital printing system to satisfactorily match any predefined spot color. While it is more economical for the traditional high-volume package printing process to utilize premixed inks that match the intended custom spot colors, this solution is generally not suitable for short-run package print jobs. Typically, the printing systems used for such applications (e.g., electrophotographic printing systems) use a predefined set of colorants (e.g., cyan, magenta, yellow and black toners), and it would not be economical to change the colorants for short-run print jobs. Many spot colors do not fall within the color gamut associated with the predefined set of colorants. As a result, it is necessary to reproduce the spot colors using a color which falls within the color gamut. The determination of the optimal in-gamut colors for reproducing out-of-gamut spot colors is not a trivial process. Various “gamut-mapping algorithms” have been proposed for mapping out-of-gamut colors to appropriate colors on the surface of the device color gamut. One prior art gamut mapping algorithm finds the in-gamut color having the smallest color difference to the out-of-gamut color. Such algorithms are prone to introducing objectionable hue shifts. Another prior art gamut mapping algorithm operates by clipping the chroma to the color gamut while maintaining the hue and lightness of the out-of-gamut color. Such algorithms are prone to introducing objectionable chroma reductions. As a result of these deficiencies, many users choose to manually determine a preferred aim color for out-of-gamut spot colors. This typically requires a time-consuming iterative process to determine the preferred color reproduction given the complex shape of typical color gamuts and the fact that a plurality of control parameters (e.g., hue and lightness) must be adjusted to move around on the color gamut surface. This process needs to be repeated every time a new spot color is introduced. Furthermore, the preferred aim color may be customer-dependent so that the preferred aim color determined for one customer may not be the optimal solution for a different customer. 
     There remains a need for a user-friendly method to determine preferred aim colors for out-of-gamut spot colors in a color printing system. 
     SUMMARY OF THE INVENTION 
     The present invention represents a method for reproducing an out-of-gamut spot color on a color printer, including: 
     determining a color gamut for the color printer, the color gamut being defined by a color gamut surface in a three-dimensional color space representing the colors that can be printed by the color printer; 
     specifying a spot color by color coordinates in the three-dimensional color space, wherein the spot color is outside of the color gamut surface; 
     determining a first target color corresponding to a color on the color gamut surface having a minimum color difference to the specified spot color; 
     determining a second target color corresponding to a color on the color gamut surface having a hue value equal to a hue value of the specified spot color; 
     defining a path on the color gamut surface connecting the first target color and the second target color, wherein a control parameter having a control parameter value is used to specify a relative position along the defined path; 
     providing a control parameter prediction function which computes a predicted control parameter value as a function of color coordinates in the three-dimensional color space; 
     using the control parameter prediction function to compute a spot color control parameter value responsive to the specified color coordinates of the spot color; and determining an aim color for reproducing the spot color using the color printer, wherein the aim color has a relative position along the defined path corresponding to the computed spot color control parameter value. 
     This invention has the advantage that a control parameter prediction function can be used to automatically compute a control parameter value that can be used to determine a preferred aim color. 
     It has the additional advantage that an aim color corresponding to a preferred reproduction of a spot color can be determined using only a single control parameter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is an elevational cross-section of an electrophotographic printer suitable for use with various embodiments; 
         FIG.  2    is an elevational cross-section of one printing module of the electrophotographic printer of  FIG.  1   ; 
         FIG.  3    shows a processing path for producing a printed image using a pre-processing system coupled to a print engine; 
         FIGS.  4 A- 4 B  illustrate the CIELAB color space; 
         FIG.  5    shows an exemplary spot color which is outside the color gamut of a printing device; 
         FIG.  6    shows a flowchart for an exemplary method for determining a preferred aim color for reproducing a spot color in accordance with an embodiment of the invention; 
         FIG.  7    illustrates a path formed on the color gamut surface between two target colors; 
         FIGS.  8 A- 8 C  illustrate different user interface examples for use with the method of  FIG.  6   ; and 
         FIG.  9    is a flowchart of a method for determining a control parameter prediction function in accordance with an exemplary embodiment. 
     
    
    
     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. Identical reference numerals have been used, where possible, to designate identical features that are common to the figures. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The invention is inclusive of combinations of the embodiments described herein. References to “a particular embodiment” and the like refer to features that are present in at least one embodiment of the invention. Separate references to “an embodiment” or “particular embodiments” or the like do not necessarily refer to the same embodiment or embodiments; however, such embodiments are not mutually exclusive, unless so indicated, or as are readily apparent to one of skill in the art. The use of singular or plural in referring to the “method” or “methods” and the like is not limiting. It should be noted that, unless otherwise explicitly noted or required by context, the word “or” is used in this disclosure in a non-exclusive sense. 
     As used herein, “sheet” is a discrete piece of media, such as receiver media for an electrophotographic printer (described below). Sheets have a length and a width. Sheets are folded along fold axes (e.g., positioned in the center of the sheet in the length dimension, and extending the full width of the sheet). The folded sheet contains two “leaves,” each leaf being that portion of the sheet on one side of the fold axis. The two sides of each leaf are referred to as “pages.” “Face” refers to one side of the sheet, whether before or after folding. 
     As used herein, “toner particles” are particles of one or more material(s) that are transferred by an electrophotographic (EP) printer to a receiver to produce a desired effect or structure (e.g., a print image, texture, pattern, or coating) on the receiver. Toner particles can be ground from larger solids, or chemically prepared (e.g., precipitated from a solution of a pigment and a dispersant using an organic solvent), as is known in the art. Toner particles typically have a range of diameters (e.g., less than 8 on the order of 10-15 up to approximately 30 or larger), where “diameter” preferably refers to the volume-weighted median diameter, as determined by a device such as a Coulter Multisizer. 
     “Toner” refers to a material or mixture that contains toner particles, and that can be used to form an image, pattern, or coating when deposited on an imaging member including a photoreceptor, a photoconductor, or an electrostatically-charged or magnetic surface. Toner can be transferred from the imaging member to a receiver. Toner is also referred to in the art as marking particles, dry ink, or developer, but note that herein “developer” is used differently, as described below. Toner can be a dry mixture of particles or a suspension of particles in a liquid toner base. 
     As mentioned already, toner includes toner particles; it can also include other types of particles. The particles in toner can be of various types and have various properties. Such properties can include absorption of incident electromagnetic radiation (e.g., particles containing colorants such as dyes or pigments), absorption of moisture or gasses (e.g., desiccants or getters), suppression of bacterial growth (e.g., biocides, particularly useful in liquid-toner systems), adhesion to the receiver (e.g., binders), electrical conductivity or low magnetic reluctance (e.g., metal particles), electrical resistivity, texture, gloss, magnetic remanence, florescence, resistance to etchants, and other properties of additives known in the art. 
     In single-component or mono-component development systems, “developer” refers to toner alone. In these systems, none, some, or all of the particles in the toner can themselves be magnetic. However, developer in a mono-component system does not include magnetic carrier particles. In dual-component, two-component, or multi-component development systems, “developer” refers to a mixture including toner particles and magnetic carrier particles, which can be electrically-conductive or -non-conductive. Toner particles can be magnetic or non-magnetic. The carrier particles can be larger than the toner particles (e.g., 15-20 μm or 20-300 μm in diameter). A magnetic field is used to move the developer in these systems by exerting a force on the magnetic carrier particles. The developer is moved into proximity with an imaging member or transfer member by the magnetic field, and the toner or toner particles in the developer are transferred from the developer to the member by an electric field, as will be described further below. The magnetic carrier particles are not intentionally deposited on the member by action of the electric field; only the toner is intentionally deposited. However, magnetic carrier particles, and other particles in the toner or developer, can be unintentionally transferred to an imaging member. Developer can include other additives known in the art, such as those listed above for toner. Toner and carrier particles can be substantially spherical or non-spherical. 
     The electrophotographic process can be embodied in devices including printers, copiers, scanners, and facsimiles, and analog or digital devices, all of which are referred to herein as “printers.” Various embodiments described herein are useful with electrostatographic printers such as electrophotographic printers that employ toner developed on an electrophotographic receiver, and ionographic printers and copiers that do not rely upon an electrophotographic receiver. Electrophotography and ionography are types of electrostatography (printing using electrostatic fields), which is a subset of electrography (printing using electric fields). The present invention can be practiced using any type of electrographic printing system, including electrophotographic and ionographic printers. 
     A digital reproduction printing system (“printer”) typically includes a digital front-end processor (DFE), a print engine (also referred to in the art as a “marking engine”) for applying toner to the receiver, and one or more post-printing finishing system(s) (e.g., a UV coating system, a glosser system, or a laminator system). A printer can reproduce pleasing black-and-white or color images onto a receiver. A printer can also produce selected patterns of toner on a receiver, which patterns (e.g., surface textures) do not correspond directly to a visible image. 
     In an embodiment of an electrophotographic modular printing machine useful with various embodiments (e.g., the NEXFINITY Digital Press manufactured by Eastman Kodak Company of Rochester, N.Y.) color-toner print images are made in a plurality of color imaging modules arranged in tandem, and the print images are successively electrostatically transferred to a receiver adhered to a transport web moving through the modules. Colored toners include colorants, (e.g., dyes or pigments) which absorb specific wavelengths of visible light. Commercial machines of this type typically employ intermediate transfer members in the respective modules for transferring visible images from the photoreceptor and transferring print images to the receiver. In other electrophotographic printers, each visible image is directly transferred to a receiver to form the corresponding print image. 
     Electrophotographic printers having the capability to also deposit clear toner using an additional imaging module are also known. The provision of a clear-toner overcoat to a color print is desirable for providing features such as protecting the print from fingerprints, reducing certain visual artifacts or providing desired texture or surface finish characteristics. Clear toner uses particles that are similar to the toner particles of the color development stations but without colored material (e.g., dye or pigment) incorporated into the toner particles. However, a clear-toner overcoat can add cost and reduce color gamut of the print; thus, it is desirable to provide for operator/user selection to determine whether or not a clear-toner overcoat will be applied to the entire print. A uniform layer of clear toner can be provided. A layer that varies inversely according to heights of the toner stacks can also be used to establish level toner stack heights. The respective color toners are deposited one upon the other at respective locations on the receiver and the height of a respective color toner stack is the sum of the toner heights of each respective color. Uniform stack height provides the print with a more even or uniform gloss. 
       FIGS.  1  and  2    are elevational cross-sections showing portions of a typical electrophotographic printer  100  useful with various embodiments. Printer  100  is adapted to produce images, such as single-color images (i.e., monochrome images), or multicolor images such as CMYK, or pentachrome (five-color) images, on a receiver. Multicolor images are also known as “multi-component” images. One embodiment involves printing using an electrophotographic print engine having five sets of single-color image-producing or image-printing stations or modules arranged in tandem, but more or less than five colors can be combined on a single receiver. Other electrophotographic writers or printer apparatus can also be included. Various components of printer  100  are shown as rollers; other configurations are also possible, including belts. 
     Referring to  FIG.  1   , printer  100  is an electrophotographic printing apparatus having a number of tandemly-arranged electrophotographic image-forming printing subsystems  31 ,  32 ,  33 ,  34 ,  35 , also known as electrophotographic imaging subsystems. Each printing subsystem  31 ,  32 ,  33 ,  34 ,  35  produces a single-color toner image for transfer using a respective transfer subsystem  50  (for clarity, only one is labeled) to a receiver  42  successively moved through the modules. In some embodiments one or more of the printing subsystem  31 ,  32 ,  33 ,  34 ,  35  can print a colorless toner image, which can be used to provide a protective overcoat or tactile image features. Receiver  42  is transported from supply unit  40 , which can include active feeding subsystems as known in the art, into printer  100  using a transport web  81 . In various embodiments, the visible image can be transferred directly from an imaging roller to a receiver, or from an imaging roller to one or more transfer roller(s) or belt(s) in sequence in transfer subsystem  50 , and then to receiver  42 . Receiver  42  is, for example, a selected section of a web or a cut sheet of a planar receiver media such as paper or transparency film. 
     In the illustrated embodiments, each receiver  42  can have up to five single-color toner images transferred in registration thereon during a single pass through the five printing subsystems  31 ,  32 ,  33 ,  34 ,  35  to form a pentachrome image. As used herein, the term “pentachrome” implies that in a print image, combinations of various of the five colors are combined to form other colors on the receiver at various locations on the receiver, and that all five colors participate to form process colors in at least some of the subsets. That is, each of the five colors of toner can be combined with toner of one or more of the other colors at a particular location on the receiver to form a color different than the colors of the toners combined at that location. In an exemplary embodiment, printing subsystem  31  forms black (K) print images, printing subsystem  32  forms yellow (Y) print images, printing subsystem  33  forms magenta (M) print images, and printing subsystem  34  forms cyan (C) print images. 
     Printing subsystem  35  can form a red, blue, green, or other fifth print image, including an image formed from a clear toner (e.g., one lacking pigment). The four subtractive primary colors, cyan, magenta, yellow, and black, can be combined in various combinations of subsets thereof to form a representative spectrum of colors. The color gamut of a printer (i.e., the range of colors that can be produced by the printer) is dependent upon the materials used and the process used for forming the colors. The fifth color can therefore be added to improve the color gamut. In addition to adding to the color gamut, the fifth color can also be a specialty color toner or spot color, such as for making proprietary logos or colors that cannot be produced with only CMYK colors (e.g., metallic, fluorescent, or pearlescent colors), or a clear toner or tinted toner. Tinted toners absorb less light than they transmit, but do contain pigments or dyes that move the hue of light passing through them towards the hue of the tint. For example, a blue-tinted toner coated on white paper will cause the white paper to appear light blue when viewed under white light, and will cause yellows printed under the blue-tinted toner to appear slightly greenish under white light. 
     Receiver  42   a  is shown after passing through printing subsystem  31 . Print image  38  on receiver  42   a  includes unfused toner particles. Subsequent to transfer of the respective print images, overlaid in registration, one from each of the respective printing subsystems  31 ,  32 ,  33 ,  34 ,  35 , receiver  42   a  is advanced to a fuser module  60  (i.e., a fusing or fixing assembly) to fuse the print image  38  to the receiver  42   a . Transport web  81  transports the print-image-carrying receivers to the fuser module  60 , which fixes the toner particles to the respective receivers, generally by the application of heat and pressure. The receivers are serially de-tacked from the transport web  81  to permit them to feed cleanly into the fuser module  60 . The transport web  81  is then reconditioned for reuse at cleaning station  86  by cleaning and neutralizing the charges on the opposed surfaces of the transport web  81 . A mechanical cleaning station (not shown) for scraping or vacuuming toner off transport web  81  can also be used independently or with cleaning station  86 . The mechanical cleaning station can be disposed along the transport web  81  before or after cleaning station  86  in the direction of rotation of transport web  81 . 
     In the illustrated embodiment, the fuser module  60  includes a heated fusing roller  62  and an opposing pressure roller  64  that form a fusing nip  66  therebetween. In an embodiment, fuser module  60  also includes a release fluid application substation  68  that applies release fluid, e.g., silicone oil, to fusing roller  62 . Alternatively, wax-containing toner can be used without applying release fluid to the fusing roller  62 . Other embodiments of fusers, both contact and non-contact, can be employed. For example, solvent fixing uses solvents to soften the toner particles so they bond with the receiver. Photoflash fusing uses short bursts of high-frequency electromagnetic radiation (e.g., ultraviolet light) to melt the toner. Radiant fixing uses lower-frequency electromagnetic radiation (e.g., infrared light) to more slowly melt the toner. Microwave fixing uses electromagnetic radiation in the microwave range to heat the receivers (primarily), thereby causing the toner particles to melt by heat conduction, so that the toner is fixed to the receiver. 
     The fused receivers (e.g., receiver  42   b  carrying fused image  39 ) are transported in series from the fuser module  60  along a path either to an output tray  69 , or back to printing subsystems  31 ,  32 ,  33 ,  34 ,  35  to form an image on the backside of the receiver (i.e., to form a duplex print). Receivers  42   b  can also be transported to any suitable output accessory. For example, an auxiliary fuser or glossing assembly can provide a clear-toner overcoat. Printer  100  can also include multiple fuser modules  60  to support applications such as overprinting, as known in the art. 
     In various embodiments, between the fuser module  60  and the output tray  69 , receiver  42   b  passes through a finisher  70 . Finisher  70  performs various paper-handling operations, such as folding, stapling, saddle-stitching, collating, and binding. 
     Printer  100  includes main printer apparatus logic and control unit (LCU)  99 , which receives input signals from various sensors associated with printer  100  and sends control signals to various components of printer  100 . LCU  99  can include a microprocessor incorporating suitable look-up tables and control software executable by the LCU  99 . It can also include a field-programmable gate array (FPGA), programmable logic device (PLD), programmable logic controller (PLC) (with a program in, e.g., ladder logic), microcontroller, or other digital control system. LCU  99  can include memory for storing control software and data. In some embodiments, sensors associated with the fuser module  60  provide appropriate signals to the LCU  99 . In response to the sensor signals, the LCU  99  issues command and control signals that adjust the heat or pressure within fusing nip  66  and other operating parameters of fuser module  60 . This permits printer  100  to print on receivers of various thicknesses and surface finishes, such as glossy or matte. 
       FIG.  2    shows additional details of printing subsystem  31 , which is representative of printing subsystems  32 ,  33 ,  34 , and  35  ( FIG.  1   ). Photoreceptor  206  of imaging member  111  includes a photoconductive layer formed on an electrically conductive substrate. The photoconductive layer is an insulator in the substantial absence of light so that electric charges are retained on its surface. Upon exposure to light, the charge is dissipated. In various embodiments, photoreceptor  206  is part of, or disposed over, the surface of imaging member  111 , which can be a plate, drum, or belt. Photoreceptors can include a homogeneous layer of a single material such as vitreous selenium or a composite layer containing a photoconductor and another material. Photoreceptors  206  can also contain multiple layers. 
     Charging subsystem  210  applies a uniform electrostatic charge to photoreceptor  206  of imaging member  111 . In an exemplary embodiment, charging subsystem  210  includes a wire grid  213  having a selected voltage. Additional necessary components provided for control can be assembled about the various process elements of the respective printing subsystems. Meter  211  measures the uniform electrostatic charge provided by charging subsystem  210 . 
     An exposure subsystem  220  is provided for selectively modulating the uniform electrostatic charge on photoreceptor  206  in an image-wise fashion by exposing photoreceptor  206  to electromagnetic radiation to form a latent electrostatic image. The uniformly-charged photoreceptor  206  is typically exposed to actinic radiation provided by selectively activating particular light sources in an LED array or a laser device outputting light directed onto photoreceptor  206 . In embodiments using laser devices, a rotating polygon (not shown) is sometimes used to scan one or more laser beam(s) across the photoreceptor in the fast-scan direction. One pixel site is exposed at a time, and the intensity or duty cycle of the laser beam is varied at each dot site. In embodiments using an LED array, the array can include a plurality of LEDs arranged next to each other in a linear array extending in a cross-track direction such that all dot sites in one row of dot sites on the photoreceptor can be selectively exposed simultaneously, and the intensity or duty cycle of each LED can be varied within a line exposure time to expose each pixel site in the row during that line exposure time. 
     As used herein, an “engine pixel” is the smallest addressable unit on photoreceptor  206  which the exposure subsystem  220  (e.g., the laser or the LED) can expose with a selected exposure different from the exposure of another engine pixel. Engine pixels can overlap (e.g., to increase addressability in the slow-scan direction). Each engine pixel has a corresponding engine pixel location, and the exposure applied to the engine pixel location is described by an engine pixel level. 
     The exposure subsystem  220  can be a write-white or write-black system. In a write-white or “charged-area-development” system, the exposure dissipates charge on areas of photoreceptor  206  to which toner should not adhere. Toner particles are charged to be attracted to the charge remaining on photoreceptor  206 . The exposed areas therefore correspond to white areas of a printed page. In a write-black or “discharged-area development” system, the toner is charged to be attracted to a bias voltage applied to photoreceptor  206  and repelled from the charge on photoreceptor  206 . Therefore, toner adheres to areas where the charge on photoreceptor  206  has been dissipated by exposure. The exposed areas therefore correspond to black areas of a printed page. 
     In the illustrated embodiment, meter  212  is provided to measure the post-exposure surface potential within a patch area of a latent image formed from time to time in a non-image area on photoreceptor  206 . Other meters and components can also be included (not shown). 
     A development station  225  includes toning shell  226 , which can be rotating or stationary, for applying toner of a selected color to the latent image on photoreceptor  206  to produce a developed image on photoreceptor  206  corresponding to the color of toner deposited at this printing subsystem  31 . Development station  225  is electrically biased by a suitable respective voltage to develop the respective latent image, which voltage can be supplied by a power supply (not shown). Developer is provided to toning shell  226  by a supply system (not shown) such as a supply roller, auger, or belt. Toner is transferred by electrostatic forces from development station  225  to photoreceptor  206 . These forces can include Coulombic forces between charged toner particles and the charged electrostatic latent image, and Lorentz forces on the charged toner particles due to the electric field produced by the bias voltages. 
     In some embodiments, the development station  225  employs a two-component developer that includes toner particles and magnetic carrier particles. The exemplary development station  225  includes a magnetic core  227  to cause the magnetic carrier particles near toning shell  226  to form a “magnetic brush,” as known in the electrophotographic art. Magnetic core  227  can be stationary or rotating, and can rotate with a speed and direction the same as or different than the speed and direction of toning shell  226 . Magnetic core  227  can be cylindrical or non-cylindrical, and can include a single magnet or a plurality of magnets or magnetic poles disposed around the circumference of magnetic core  227 . Alternatively, magnetic core  227  can include an array of solenoids driven to provide a magnetic field of alternating direction. Magnetic core  227  preferably provides a magnetic field of varying magnitude and direction around the outer circumference of toning shell  226 . Development station  225  can also employ a mono-component developer comprising toner, either magnetic or non-magnetic, without separate magnetic carrier particles. 
     Transfer subsystem  50  includes transfer backup member  113 , and intermediate transfer member  112  for transferring the respective print image from photoreceptor  206  of imaging member  111  through a first transfer nip  201  to surface  216  of intermediate transfer member  112 , and thence to a receiver  42  which receives respective toned print images  38  from each printing subsystem in superposition to form a composite image thereon. The print image  38  is, for example, a separation of one color, such as cyan. Receiver  42  is transported by transport web  81 . Transfer to a receiver is effected by an electrical field provided to transfer backup member  113  by power source  240 , which is controlled by LCU  99 . Receiver  42  can be any object or surface onto which toner can be transferred from imaging member  111  by application of the electric field. In this example, receiver  42  is shown prior to entry into a second transfer nip  202 , and receiver  42   a  is shown subsequent to transfer of the print image  38  onto receiver  42   a.    
     In the illustrated embodiment, the toner image is transferred from the photoreceptor  206  to the intermediate transfer member  112 , and from there to the receiver  42 . Registration of the separate toner images is achieved by registering the separate toner images on the receiver  42 , as is done with the NexPress  2100 . In some embodiments, a single transfer member is used to sequentially transfer toner images from each color channel to the receiver  42 . In other embodiments, the separate toner images can be transferred in register directly from the photoreceptor  206  in the respective printing subsystem  31 ,  32 ,  33 ,  34 ,  25  to the receiver  42  without using a transfer member. Either transfer process is suitable when practicing this invention. An alternative method of transferring toner images involves transferring the separate toner images, in register, to a transfer member and then transferring the registered image to a receiver. 
     LCU  99  sends control signals to the charging subsystem  210 , the exposure subsystem  220 , and the respective development station  225  of each printing subsystem  31 ,  32 ,  33 ,  34 ,  35  ( FIG.  1   ), among other components. Each printing subsystem can also have its own respective controller (not shown) coupled to LCU  99 . 
     Various finishing systems can be used to apply features such as protection, glossing, or binding to the printed images. The finishing system scan be implemented as an integral components of the printer  100 , or can include one or more separate machines through which the printed images are fed after they are printed. 
       FIG.  3    shows a processing path that can be used to produce a printed image  450  with a print engine  370  in accordance with embodiments of the invention. A pre-processing system  305  is used to process a page description file  300  to provide image data  350  that is in a form that is ready to be printed by the print engine  370 . In an exemplary configuration, the pre-processing system  305  includes a digital front end (DFE)  310  and an image processing module  330 . The pre-processing system  305  can be a part of printer  100  ( FIG.  1   ), or may be a separate system which is remote from the printer  100 . The DFE  310  and an image processing module  330  can each include one or more suitably-programmed computer or logic devices adapted to perform operations appropriate to provide the image data  350 . 
     The DFE  310  receives page description files  300  which define the pages that are to be printed. The page description files  300  can be in any appropriate format (e.g., the well-known Postscript command file format or the PDF file format) that specifies the content of a page in terms of text, graphics and image objects. The image objects are typically provided by input devices such as scanners, digital cameras or computer generated graphics systems. The page description file  300  can also specify invisible content such as specifications of texture, gloss or protective coating patterns. 
     The DFE  310  rasterizes the page description file  300  into image bitmaps for the print engine to print. The DFE  310  can include various processors, such as a raster image processor (RIP)  315 , a color transform processor  320  and a compression processor  325 . It can also include other processors not shown in  FIG.  3   , such as an image positioning processor or an image storage processor. In some embodiments, the DFE  310  enables a human operator to set up parameters such as layout, font, color, media type or post-finishing options. 
     The RIP  315  rasterizes the objects in the page description file  300  into an image bitmap including an array of image pixels at an image resolution that is appropriate for the print engine  370 . For text or graphics objects the RIP  315  will create the image bitmap based on the object definitions. For image objects, the RIP  315  will resample the image data to the desired image resolution. 
     The color transform processor  320  will transform the image data to the color space required by the print engine  370 , providing color separations for each of the color channels (e.g., CMYK). For cases where the print engine  370  includes one or more additional colors (e.g., red, blue, green, gray or clear), the color transform processor  320  will also provide color separations for each of the additional color channels. The objects defined in the page description file  300  can be in any appropriate input color space such as RGB, CIELAB, PCS LAB or CMYK. In some cases, different objects may be defined using different color spaces. The color transform processor  320  applies an appropriate color transform to convert the objects to the device-dependent color space of the print engine  370 . Methods for creating such color transforms are well-known in the color management art, and any such method can be used in accordance with the present invention. Typically, the color transforms are defined using color management profiles that include multi-dimensional look-up tables. Input color profiles are used to define a relationship between the input color space and a profile connection space (PCS) defined for a color management system (e.g., the well-known ICC PCS associated with the ICC color management system). Output color profiles define a relationship between the PCS and the device-dependent output color space for the printer  100 . The color transform processor  320  transforms the image data using the color management profiles. Typically, the output of the color transform processor  320  will be a set of color separations including an array of pixels for each of the color channels of the print engine  370  stored in memory buffers. 
     The processing applied in digital front end  310  can also include other operations not shown in  FIG.  3   . For example, in some configurations, the DFE  310  can apply the halo correction process described in commonly-assigned U.S. Pat. No. 9,147,232 to Kuo entitled “Reducing halo artifacts in electrophotographic printing systems,” which is incorporated herein by reference. 
     The image data provided by the digital front end  310  is sent to the image processing module  330  for further processing. In order to reduce the time needed to transmit the image data, a compressor processor  325  is typically used to compress the image data using an appropriate compression algorithm. In some cases, different compression algorithms can be applied to different portions of the image data. For example, a lossy compression algorithm (e.g., the well-known JPEG algorithm) can be applied to portions of the image data including image objects, and a lossless compression algorithm can be applied to portions of the image data including binary text and graphics objects. The compressed image values are then transmitted over a data link to the image processing module  330 , where they are decompressed using a decompression processor  335  which applies corresponding decompression algorithms to the compressed image data. 
     A halftone processor  340  is used to apply a halftoning process to the image data. The halftone processor  340  can apply any appropriate halftoning process known in the art. Within the context of the present disclosure, halftoning processes are applied to a continuous-tone image to provide an image having a halftone dot structure appropriate for printing using the printer module  435 . The output of the halftoning can be a binary image or a multi-level image. In an exemplary configuration, the halftone processor  340  applies the halftoning process described in commonly assigned U.S. Pat. No. 7,830,569 to Tai et al., entitled “Multilevel halftone screen and sets thereof,” which is incorporated herein by reference. For this halftoning process, a three-dimensional halftone screen is provided that includes a plurality of planes, each corresponding to one or more intensity levels of the input image data. Each plane defines a pattern of output exposure intensity values corresponding to the desired halftone pattern. The halftoned pixel values are multi-level values at the bit depth appropriate for the print engine  370 . 
     The image enhancement processor  345  can apply a variety of image processing operations. For example, an image enhancement processor  345  can be used to apply various image enhancement operations. In some configurations, the image enhancement processor  345  can apply an algorithm that modifies the halftone process in edge regions of the image (see U.S. Pat. No. 7,079,281, entitled “Edge enhancement processor and method with adjustable threshold setting” and U.S. Pat. No. 7,079,287 entitled “Edge enhancement of gray level images,” both to Ng et al., and both of which are incorporated herein by reference). 
     The pre-processing system  305  provides the image data  350  to the print engine  370 , where it is printed to provide the printed image  450 . The pre-processing system  305  can also provide various signals to the print engine  370  to control the timing at which the image data  350  is printed by the print engine  370 . For example, the pre-processing system  305  can signal the print engine  370  to start printing when a sufficient number of lines of image data  350  have been processed and buffered to ensure that the pre-processing system  305  will be capable of keeping up with the rate at which the print engine  370  can print the image data  350 . 
     A data interface  405  in the print engine  370  receives the data from the pre-processing system  305 . The data interface  405  can use any type of communication protocol known in the art, such as standard Ethernet network connections. A printer module controller  430  controls the printer module  435  in accordance with the received image data  350 . In an exemplary configuration, the printer module  435  can be the printer  100  of  FIG.  1   , which includes a plurality of individual electrophotographic printing subsystems  31 ,  32 ,  33 ,  34 ,  35  for each of the color channels. For example, the printer module controller  430  can provide appropriate control signals to activate light sources in the exposure subsystem  220  ( FIG.  2   ) to expose the photoreceptor  206  with an exposure pattern. In some configurations, the printer module controller  430  can apply various image enhancement operations to the image data. For example, an algorithm can be applied to compensate for various sources of non-uniformity in the printer  100  (e.g., streaks formed in the charging subsystem  210 , the exposure subsystem  220 , the development station  225  or the fuser module  60 ). One such compensation algorithm is described in commonly-assigned U.S. Pat. No. 8,824,907 to Kuo et al., entitled “Electrophotographic printing with column-dependent tonescale adjustment,” which is incorporated herein by reference. 
     In some cases, the printing system can also include an image capture system  440 . The image capture system can be used for purposes such as system calibration. The image capture system  440  can use any appropriate image capture technology such as a digital scanner system, or a digital camera system. The image capture system  440  can be integrated into the printing system, or can be a separate system which is in communication with the printing system. 
     In the configuration of  FIG.  3   , the pre-processing system  305  is tightly coupled to the print engine  370  in that it supplies image data  350  in a state which is matched to the printer resolution and the halftoning state required for the printer module  435 . In other configurations, the print engine can be designed to be adaptive to the characteristics of different pre-processing systems  305  as is described in commonly-assigned, co-pending U.S. Pat. No. 10,062,017 to Kuo et al., entitled “Print engine with adaptive processing,” which is incorporated herein by reference. 
     As discussed earlier, the color transform processor  320  ( FIG.  3   ) will transform the image data to the color space required by the print engine  370 , providing color separations for each of the color channels (e.g., CMYK). The objects defined in the page description file  300  can include raster image data in any appropriate input color space such as RGB, CIELAB, PCS LAB or CMYK. In some cases, the page description file  300  can also include objects (e.g., graphics and text) specified as a named “spot color.” Such spot colors can be used to identify the colors to be used for content such as the company logos and product packaging. Examples of systems for naming spot colors would include the well-known Pantone Matching System, which is a proprietary color naming system for identifying colors used in graphic design. Other color naming systems include the RAL Color System, the Toyo Color Finder System and the DIC Color System. In other cases, a spot color can be identified using another named color system, or by simply specifying a color in a device-independent color space (e.g., CIELAB). When a spot color is specified using a color naming system, device-independent color values (e.g., CIELAB values) can be measured and stored in a look-up table for each of the named spot colors in the color naming system. Device independent color values can then be determined for any objects specified by named spot colors by looking up the associated color values in the look-up table. 
     The CIELAB color space is one of the most commonly used device-independent color spaces that is used for representing colors in color printing applications. A color space is said to be “device-independent” when it is tied to the color perceived by a human observer rather than to the device coordinates of an imaging device (e.g., RGB or CMYK). As is well-known in the art, the perception of a color by a human observer can be characterized by the CIE XYZ tristimulus values: 
         X=∫   λ   R (λ) I (λ)   x   (λ) dλ 
 
         Y=∫   λ   R (λ) I (λ)   y   (λ) dλ 
 
         Z=∫   λ   R (λ) I (λ)   z   (λ) dλ   (1)
 
     where R(λ) is the reflection spectrum of the printed color, I(λ) is the illumination spectrum,  x (λ),  y (λ) and  z (λ) are the CIE color matching functions, and the integration is performed over the visible spectrum, which is approximately 400≤λ≤700 nm. 
     While the CIE XYZ tristimulus values are device-independent, they are not uniformly related to the human perception of color. The CIELAB color space was developed to be a “uniform color space” which implies that geometric distances in the color space should be approximately proportional to perceived color differences. The CIELAB values are represent by three color coordinates L*, a* and b* which can be computed from the tristimulus values using the following equations: 
         L*= 116 f ( Y/Y   0 )−16
 
         a*= 500( f ( X/X   0 )− f ( X/X   0 ))
 
         b*= 200( f ( Y/Y   0 )− f ( Z/Z   0 ))  (2)
 
     where X 0 , Y 0 , Z 0  are the tristimulus values of a reference white, and 
     
       
         
           
             
               
                 
                   
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     As illustrated in  FIG.  4 A  which shows the CIELAB color space  460 , L* is a representation of the lightness of the color, a* is a representation of the greenness-redness of the color, and b* is a representation of the blueness-yellowness of the color. Colors that fall on neutral axis  461  (i.e., colors with a*=b*=0) are neutral colors ranging from black (L*=0) to white (L*=100). As illustrated in  FIG.  4 B , the hue h of a color can be represented by the angle in the a*-b* plane, and the chroma C* (i.e., the colorfulness) of a color can be represented by the radius in the a*-b* plane. In equation form: 
         C *=√{square root over ( a*   2   +b*   2 )}
 
         h =arctan( b*/a *)  (4)
 
     The perceived color difference ΔE* can be approximated by the distance between two colors in the CIELAB color space. In equation form: 
       Δ E *=√{square root over (Δ L*   2   +Δa*   2   +Δb*   2 )}  (5)
 
     Another device-independent color spaces that can be used in some applications is the well-known CIELUV color space, which represents the color in terms of L*, U* and V* color coordinates. The CIECAM 02  color appearance model can also be used to represent color. This model uses more complex models of the human visual system to compute J, a, b color values that correlate with human color appearance. Correlates of hue h and chroma C can also be calculated. A commonly-used derivative is the CAM 02  Uniform Color Space (CAM 02 -UCS), which is an extension of CIECAM 02  with tweaks to better match experimental data. Mathematical equations for computing color values in any of these color spaces are well-known to those skilled in the art. It will be obvious that any of these color spaces, as well as any other device-independent color space known in the art, can be used to represent color in accordance with the present invention. 
     Many commonly used spot colors are outside of the color gamut of typical printing systems that utilize CMYK colorants. The color gamut refers to the set of colors that are reproducible by a printing system, and can be defined by a volume in a three-dimensional device-independent color space such as CIELAB. The color gamut of a printing system will be a function of the colorants, the receiver media and the print mode. The outer surface of the color gamut represents the limiting colors that can be reproduced by the printing system and can be referred to as the gamut surface. The color gamut of a printing system is commonly represented by storing a representation of the gamut surface, for example as a three-dimensional object model defined by a mesh of interconnected points in a device-dependent color space.  FIG.  5    shows an example of a typical color gamut  500  represented in the CIELAB color space. 
     In high-volume printing applications, printing systems can be loaded with specialty colorants (e.g., inks or toners) to accurately reproduce the spot colors. However, this is an impractical solution for low- to mid-volume printing applications since it can be time-consuming and costly to change the colorants in the printing system. In such cases, it is preferable to compromise on the color accuracy and utilize an in-gamut color that can be printed using the standard colorant even though it is necessary to compromise on the color accuracy. The problem then is to determine the in-gamut color that most closely matches the desired appearance of the spot color. However, this is not a straight-forward problem to solve given the complex shape of device color gamuts and the subjective preferences of human observers. 
     An example spot color  502  is illustrated in  FIG.  5   , which falls outside the color gamut  500  of the printing system. In this example, the spot color  502  is a yellow color having a large b* value and a small a* value. In order to reproduce this color using the printing system, it is necessary to map it to a color which is within the reproducible color gamut  500 . Typically the chosen color will be a color on the color gamut surface  501 . Many “gamut mapping algorithms” exist in the art to perform the mapping of out-of-gamut colors. One such gamut mapping algorithm involves finding the target color  504  which has the minimum color difference (e.g., ΔE*) to the spot color  502 . While the target color  504  may be the closest visual match to the spot color  502 , it is frequently not the preferred reproduction of the spot color due to the fact that it can introduce significant hue shifts, particularly when the spot color  502  is near one of the sharp “corners” in the color gamut  500  corresponding to the printer&#39;s primary colors (C, M, Y) or secondary colors (R, G, B). These hue shifts are often objectionable to a user. For example, if a user specifies that their logo should be printed with a high-chroma lemon yellow spot color  502 , they would usually not want it to be reproduced with a greenish-yellow or orangish-yellow hue, and would instead want to compromise on the lightness and/or the chroma to keep the hue closer to the hue of the spot color  502 . 
     Other types of gamut mapping algorithms preserve the hue of the spot color  502  to avoid the objectionable hue shift problem associated with the minimum ΔE* algorithms. One simple algorithm of this type holds the lightness value (L*) and hue value (h) constant and clips the chroma value (C*) to the color gamut surface  501 . The often results in the reproduced color having significantly lower chroma than the spot color  502 . A more sophisticated hue-preserving gamut mapping algorithm involves finding the color on the color gamut surface  501  having the minimum color difference (e.g., ΔE*) to the specified spot color  502  subject to the constraint that the hue value is equal to the hue value of the spot color  502 . This tends to map the spot color  502  toward the high-chroma edges of the color gamut surface  501 .  FIG.  5    illustrates a target color  506  determined using a gamut mapping algorithm of this type. 
     While the hue-preserving target color  506  will preserve the hue of the spot color  502 , it will often have a significantly lower chroma than the minimum color difference target color  504 . Often, a particular user may not prefer either of these two extremes but will instead prefer to map the spot color  502  to some other location on the color gamut surface  502 . And frequently, the preferred color for one user may differ from that chosen by a different user. As a result, it is often necessary for users to perform a time-consuming iterative process to determine the preferred color reproduction for a particular spot color  501 . The method commonly involves making repeated adjustments to the target L*a*b* values (or to the printer CMYK values) until the preferred color reproduction is determined. This typically requires a complex search process given the high-dimensionality of the search space. 
     The present invention significantly simplifies the process of determining an aim color for reproducing an out-of-gamut spot color by reducing the dimensionality of the search process to provide a one-dimensional control parameter.  FIG.  6    shows a flowchart for an exemplary embodiment of the invention. The inputs to the process are a spot color  502  and a color gamut  500   
     In the following description, the spot color  502  will be referred to as C s  and is specified by color coordinates in a three-dimensional color space such as CIELAB. The color gamut  500  will likewise be referred to as G c , and can be represented by a color gamut surface  501  ( FIG.  5   ) in the three-dimensional color space representing the colors that can be printed by the color printing system, which will be referred to as δG c . The color gamut  500  is typically determined by printing color patches that span the range of input code values for the color channels of the color printing system. The color of the printed patches are then measured using a device such as a spectrophotometer or a colorimeter, and a color gamut surface  501  that contains all of the printable colors is determined using a fitting process as is well-known in the art. 
     If the spot color  502 , C s , is inside of the color gamut  500 , G c , (i.e., if C s  E G c ), then the spot color  502  can be used directly for the aim color  560 , C a , (i.e., C a =C s ). Otherwise, the method of  FIG.  6    is used to determine the aim color  560 , which will be a function of the spot color  502 , C s , and the color gamut  500 , G c . In the case, the resulting aim color  560  will preferably be a color on the surface of the color gamut  500  (i.e., C a  ∈δG c ). 
     A determine first target color step  520  is used to determine a first target color  504 , Cu. The quantity C t1  is a vector in the three-dimensional color space (e.g., [L t1 *, a t1 *, b t1 *]). In a preferred embodiment, the determine first target color step  520  determines the first target color  504  by finding the color on the surface of the color gamut  500  having the minimum color difference (e.g., ΔE*) to the spot color  502 . This corresponds to the first target color  504  shown in the example of  FIG.  5   . 
     A determine second target color step  530  is used to determine a second target color  506 , C t2 , having a hue value equal to the hue of the spot color  502 . The quantity C t2  is a vector in the three-dimensional color space (e.g., [L t2* , a t2* , b t2 *]). In a preferred embodiment, the second target color  506  is the color on the surface of the color gamut  500  having the minimum color difference (e.g., ΔE*) to the specified spot color  502  subject to the constraint that the hue value is equal to the hue value of the spot color  502 . This corresponds to the second target color  506  shown in the example of  FIG.  5   . In other embodiments, other hue preserving gamut mapping methods can be used to find the second target color  506 . For example, the second target color  506  can be found by clipping the chroma of the spot color  502  to the surface of the color gamut  500  while holding the hue and lightness constant. 
     The goal of the invention is to determine a preferred aim color  560  on the surface of the color gamut  500  for reproducing the spot color  502 . The generalized optimization problem would involve searching the entire surface of the color gamut  500  in the region near the spot color  502 . Since the computational complexity of the optimization process increases exponentially with respect to the dimension of the independent feature space (i.e., the curse of dimensionality), a constraint is introduced which limits the search space to a path  545  specified by a one-dimensional control parameter. In an exemplary embodiment, a define path step  540  is used to define the path  545  along the surface of the color gamut  500  connecting the first target color  504  and the second target color  506  as illustrated in  FIG.  7   . A control parameter, a, having a control parameter value  555  is used to specify a relative position along the path  545 , with α=0 corresponding to the first target color  504  and α=1 corresponding to the second target color  506 . The path  545  represents a limited search space for determining a preferred aim color  560  for reproducing the spot color  502 . 
     The define path step  540  can define the path  545  using a variety of methods. In an exemplary embodiment, the control parameter, a, specifies a hue, h α , using a linear relationship: 
         h   α   =h   1 +α( h   2   −h   1 )  (6)
 
     where h 1  is the hue of the first target color  504  and h 2  is the hue of the second target color  506 . The color C α  at a point along the path  545  corresponding to a particular control parameter value  555  can then be determined by finding the color on the surface of the color gamut  500  having the minimum color difference to the specified spot color  502  subject to the constraint that the hue value is equal to h α . 
     In another embodiment, the control parameter, a, specifies a relative position along a straight line connecting the first target color  504  and the second target color  506 . The color at this position is given by: 
         C   α   =C   t1 +α( C   t2   −C   t1 )  (7)
 
     The color, c α , does not generally lie on the color gamut surface  501 . Therefore, the path color, C a , can then be found by projecting the color c α  onto the color gamut surface  501  (for example at a constant lightness and hue). 
     A determine aim color step  550  is then used to determine aim color  560  corresponding a control parameter value  555  which specifies a position along the path  545  corresponding to a preferred reproduction of the spot color  502 . The control parameter value  555  can be determined using a variety of different methods. In an exemplary embodiment, a user interface  565  is provided which enables a user to adjust the control parameter value  555  to specify a preferred aim color  560 . 
     In one exemplary embodiment, a test target  600  is printed including a plurality of test patches  605  with sample colors at points along the defined color path corresponding to a plurality of control parameter values as illustrated in  FIG.  8 A . Patch identifiers  610  are included to label each of the printed test patches  605 . A user interface  565  is provided that includes features which enables the user to select one of the test patches  605  to be used as the aim color  560 . The exemplary user interface  565  includes user instructions  620 , patch selection features  625  (in this example radio buttons), and a done button  630 . In this embodiment, the number of test patches  605  should be large enough so that the color difference between the sample colors is relatively small (e.g., about 1-3 ΔE*). 
     In another exemplary embodiment, the user interface  565  walks the user through an iterative process to select the preferred aim color  560 . In a first step, a test target  600  is printed having three or more test patches  605  as shown in  FIG.  8 B . The first test patch  605  corresponds to the first target color  504  (α=0), the last test patch  605  corresponds to the second target color  506  (α=1), and the intermediate test patches  605  correspond to one or more intermediate control parameter values. In the illustrated example, a single intermediate test patch  605  is provided having α=0.5. A user interface  565  is provided which enables the user to either select one of the printed test patches  605  if the user judges that it represents a preferred reproduction of the spot color  502 , or to select two of the printed test patches  605  if the user judges that the preferred reproduction of the spot color  502  falls between them. To enable these features, the user interface  565  includes exemplary user interface  565  includes user instructions  620 , patch selection features  625  (in this example radio buttons), and a done button  630 . 
     If the user selects two of the printed test patches  605 , another test target  600  is printed having three or more test patches  605 , where the first and last test patches  605  correspond to the user selected test patches  605  in the previous iteration, and the intermediate test patches  605  correspond to one or more intermediate control parameter values. For example, if the user selected the test patches  605  corresponding to α=0 and α=0.5, the new test target would have patches with α=0, α=0.25 and α=0.5. The user then uses the user interface  565  as described above to either select one or two of the printed test patches  605 . This process is repeated with increasingly smaller color differences between the printed test patches  605  until the user indicates that one of the printed test patches  605  represents a preferred reproduction of the spot color  502 . While the illustrated example includes only a single intermediate test patch  605 , it will be obvious that a plurality of intermediate test patches  605  could be used in other embodiments. This would provide smaller color differences between the test patches  605 , and would enable the iterative process to converge with fewer iterations. 
     In some embodiments, the path  545  is comprised of colors that fall within the color gamut of a soft-copy display. In this case, the preferred reproduction of the spot color  502  can be selected based on previews of the reproduced color presented in an appropriate user interface  565  such as that shown in  FIG.  8 C . In this case, the user interface  565  includes user instructions  620 , together with a control feature  635  (e.g., a slide bar) that enables the user to adjust the control parameter, and a color patch  640  which displays a preview of the reproduced color corresponding to the control parameter selected using the control feature  635 . A done button  630  is provided to enable the user to indicate that the selection process is complete. This method can be used even if the path  545  includes colors that fall outside the color gamut of a soft-copy display. However, in this case, any out-of-gamut sample colors must be gamut-mapped to a color that can be displayed on the soft-copy display. This is preferably done using a hue-preserving gamut mapping algorithm. 
     The process of determining the preferred aim color  560  for a particular spot color  502  can be a time-consuming labor-intensive process that must be repeated for each different spot color  502 . However, the optimal control parameter value  555  determined for one spot color  502  should be similar to the value that would be determined for other similar spot colors  502 . Therefore, to aid in the optimization process a control parameter prediction function  570  can be determined (e.g., using a supervised learning algorithm) based on the values determined for previously evaluated spot colors  502 . The inputs to the control parameter prediction function  570  are the device-independent color values for a spot color, and the output of the control parameter prediction function  570  is a corresponding prediction of the optimal control parameter value  555 . 
       FIG.  9    shows a flowchart of an exemplary method for determining the control parameter prediction function  570 . A determine preferred control parameters step  575  is used to determine a set of control parameter values  585  corresponding to a set of spot colors  580 . The set of spot colors  580  preferably spans all parts of color space that are likely to be encountered in spot colors. In an exemplary embodiment, the determine preferred control parameters step  575  uses the method described with respect to  FIG.  6    to determine the control parameter values  555  for each of the spot colors  502  in the set of spot colors  580 . A fit mathematical function step  590  is used to fit an appropriate mathematical function to the set of spot colors  580  and the corresponding set of control parameter values  585  to determine the control parameter prediction function  570  having the form: 
         α = f   α ( c   s )  (8)
 
     where a is the predicted control parameter value  555 , f α  (·) is the control parameter prediction function  570 , and C s  is the spot color  502 , which will generally be represented by three coordinates (e.g., L*, a*, b*). Any appropriate form of mathematical function can be used for the control parameter prediction function  570 . For example, the control parameter prediction function  570  can be a multi-dimensional polynomial function, a spline function, a multi-dimensional LUT, and a neural network function. Preferably, the output of the control parameter prediction function  570  should be constrained to provide predicted control parameter values  555  in the range of 0≤α≤1. In an exemplary embodiment the control parameter prediction function  570  is a neural network function where the inputs are the color coordinates of the spot color, the substrate and the illumination light source, and the output is the control parameter value. In some embodiments, the control parameter prediction function  570  can be determined by a particular user to represent the color reproduction preferences of that user. In other embodiments, a set of different users can each determine a set of color parameter values  585  according to their preferences, and the determined sets of color parameter values  585  can be pooled to determine a single control parameter prediction function  570  that is representative of the average preferences. 
     In some embodiments, each time a user determines a preferred aim color  560  for a new spot color  502  using the method of  FIG.  6   , the new data can be added to the set of spot colors  580  and the set of control parameter values  585 , and an updated control parameter prediction function  570  can be determined using the method of  FIG.  9   . 
     Generally, the control parameter prediction function  570  will be a function of the color gamut  500  of the printing system, and therefore different control parameter prediction functions  570  can be determined for each printer configuration (e.g., each set of different colorants, media, print modes, etc.). However, in some cases the control parameter prediction functions  570  may be similar enough that a single control parameter prediction function  570  can be used across at least some of the different configurations. Even when it is desirable to provide different control parameter prediction functions  570  for different printer configurations, it may be appropriate to use the control parameter prediction function  570  for one configuration as an initial guess at the control parameter prediction function  570  for a new configuration. The control parameter prediction function  570  can then be refined as new preferred aim colors are determined. 
     Once determined, the control parameter prediction function  570  can be used in the method of  FIG.  6    to provide an initial guess for the control parameter value  555  that will produce the preferred reproduction of the spot color  502 . The initial guess can be used in any of the methods described relative to  FIGS.  8 A- 8 C . For example, the predicted control parameter value  555  can be used to create the intermediate test patch  605  in first iteration of the method described relative to  FIG.  8 B , or can be used as the initial setting of the control feature  635  in the method described relative to  FIG.  8 C . 
     In some cases, the control parameter prediction function  570  can produce adequate reproductions of the spot colors  502  without the need for a user to utilize a manual selection process (such as those described relative to  FIGS.  8 A- 8 C ). In this case, the control parameter prediction function  570  can be used to automatically determine the preferred aim color  560  for any spot color  502  that comes into the printing system. In some embodiments, the printing system can provide an option to override the automatic aim color selection if a user desires to fine tune the reproduction of a particular spot color  502 . 
     Once the preferred aim color  560  is determined for a spot color  502  specified in an input page description file  300  ( FIG.  3   ), a color transform  320  is used to determine the corresponding device coordinates (e.g., CMYK values) that will produce the preferred aim color  560 . For example, in some embodiments the aim color  560  is specified in terms of the CIELAB color space. In this case, the color transform  320  can be an inverse device profile, for example in the format of an ICC profile, which transforms from the CIELAB values to the corresponding CMYK values. Once the device coordinates are determined and used by the pre-processing system  305  to provide the corresponding image data  350 , the print engine  370  is used to print the image data  350  to form a corresponding printed image  450 , wherein the spot colors  502  in the page description file  300  are reproduced as the preferred aim colors  560 . 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations, combinations, and modifications can be effected by a person of ordinary skill in the art within the spirit and scope of the invention. 
     PARTS LIST 
     
         
           31  printing module 
           32  printing module 
           33  printing module 
           34  printing module 
           35  printing module 
           38  print image 
           39  fused image 
           40  supply unit 
           42  receiver 
           42   a  receiver 
           42   b  receiver 
           50  transfer subsystem 
           60  fuser module 
           62  fusing roller 
           64  pressure roller 
           66  fusing nip 
           68  release fluid application substation 
           69  output tray 
           70  finisher 
           81  transport web 
           86  cleaning station 
           99  logic and control unit (LCU) 
           100  printer 
           111  imaging member 
           112  intermediate transfer member 
           113  transfer backup member 
           201  first transfer nip 
           202  second transfer nip 
           206  photoreceptor 
           210  charging subsystem 
           211  meter 
           212  meter 
           213  grid 
           216  surface 
           220  exposure subsystem 
           225  development station 
           226  toning shell 
           227  magnetic core 
           240  power source 
           300  page description file 
           305  pre-processing system 
           310  digital front end (DFE) 
           315  raster image processor (RIP) 
           320  color transform processor 
           325  compression processor 
           330  image processing module 
           335  decompression processor 
           340  halftone processor 
           345  image enhancement processor 
           350  image data 
           370  print engine 
           405  data interface 
           430  printer module controller 
           435  printer module 
           440  image capture system 
           450  printed image 
           460  CIELAB color space 
           461  neutral axis 
           462  a*-b* color plane 
           464  color coordinate 
           500  color gamut 
           501  color gamut surface 
           502  spot color 
           504  target color 
           506  target color 
           508  neutral axis 
           520  determine first target color step 
           530  determine second target color step 
           540  define path step 
           545  path 
           550  determine aim color step 
           555  control parameter value 
           560  aim color 
           565  user interface 
           570  control parameter prediction function 
           575  determine preferred control parameter values step 
           580  set of spot colors 
           585  set of control parameter values 
           590  fit mathematical function step 
           600  test target 
           605  test patches 
           610  patch identifiers 
           620  user instructions 
           625  patch selection feature 
           630  done button 
           635  control feature 
           640  color patch