Method and system for toner reproduction curve linearization using least squares solution of monotone spline functions

Methods are presented for calibrating or characterizing a printing system with respect to at least one color, in which a toner reproduction curve (TRC) is measured and curve-fitted according to a least squares solution using a set of spline basis functions having high spline density in regions of high TRC curvature and/or high measurement noise, with the weights of the spline functions being restricted to positive values to maintain monotonicity of the TRC.

BACKGROUND

The present disclosure is generally related to the field of color image/text printing or display systems and to methods and systems for calibrating color output devices, such as color displays, printers and printing devices thereof. Color has become essential as a component of communication and facilitates the sharing of knowledge and ideas, and there are continuous efforts to improve the accuracy and total image quality of digital color output devices. Color images are commonly represented as one or more separations, each including color density signals for a single primary or secondary color. Color density signals are commonly represented as digital gray or contone pixels, varying in magnitude from a minimum to a maximum, with a number of gradients between corresponding to the bit density of the system, where a common 8-bit system provides 256 shades of each primary color. A color can therefore be considered the combination of magnitudes of each pixel, which when viewed together, present the combination color, with color printer signals typically including three subtractive primary color signals Cyan (C), Magenta (M), and Yellow (Y) and a Black signal (K), which together can be considered the printer colorant signals. Each color signal forms a separation and when combined together with the other separations, forms the color image. Color images, text, and other features in a given document or print job are generally specified as image data in a printer-independent form (color space) based on the characteristics of human vision to facilitate the exchange and reuse of documents.

The native control spaces of output devices in a printing system, however, are not printer-independent color spaces. Consequently, printing systems are characterized and calibrated by determining the device control values corresponding to specified printer-independent color values in order to print a given color. This is normally accomplished by a three-step procedure. Initially, a set of color patches with pre-determined device control values is output on the device and the color of each patch is measured in printer-independent color coordinates. This may include printing test patches on a sheet of paper and measuring the resulting patch colors or transferring toner or other marking material onto an intermediate medium (e.g., an intermediate transfer belt or photoreceptor in the system) and measuring the color of the transferred material. Next, a “forward device-response function” or forward transform is estimated using the device control values and the corresponding measured printer-independent color values, sometimes referred to as a measured toner response curve (TRC), which represents a mapping from device control values to the printer-independent-color values produced by the device in response to the control values. The forward response function is then inverted to obtain a “device-correction-function” or inverse transform that maps each printer-independent color to the device control values that produce the specified printer-independent color value on the output device, and this is stored in the printer. In operation, the printer-independent color values of a given print job are mapped through the “device correction-function” to obtain control values that are used by the rendering devices of the printer to produce the desired color. By this process, the printing system transfer function from input (device-independent) data to output (printed media) is calibrated and essentially linearized. An example of a calibration system is described in U.S. Pat. No. 5,305,119 to Rolleston et al, “Color Printer Calibration Architecture,” which issued on Apr. 19, 1994 and is assigned to Xerox Corporation, and which is generally directed toward a method of calibrating a response of a printer to an image described in terms of calorimetric values. Another example of a calibration method and system is described in U.S. Pat. No. 5,528,386 to Rolleston et al, “Color Printer Calibration Architecture”, which issued on Jun. 18, 1996 and is also assigned to Xerox Corporation, and which describes a conventional one-dimensional architecture. Both U.S. Pat. Nos. 5,305,119 and 5,528,386 are incorporated herein by reference.

Calibration and/or characterization of color printers is often subject to different forms of noise. In particular, digital correction of a printer TRC often requires measuring points along the TRC, and then projecting, for each desired density, how many pixels must be turned on to achieve that density. Typically a few points along the TRC are measured and a line is fit through the measured points using linear interpolation or other curve fitting techniques, or a parameterized function may be fit to the measured data. Conventional spline fitting can leave the fit too sensitive to measurement noise, which can induce contours. Parameterized functions are typically not flexible enough to cover the full range of TRC variation observed. Consequently, there remains a need for improved printing system calibration and characterization techniques to better fit measured TRCs to avoid or mitigate the effects of measurement noise while accurately characterizing the true machine performance.

BRIEF DESCRIPTION

Methods and systems are provided for color printer calibration or characterization and for determining the color response of a color printer in which spline basis functions are selected according to better fit the anticipated or observed curvature of the TRC, and a spline fitted TRC is generated using a least-squares solution, by which the above mentioned shortcomings of conventional TRC calibration and/or characterization can be mitigated. The disclosure presents techniques for fitting TRCs using a least-squares solution to a set of monotone spline basis functions to ensure that the output fit is monotonic, and the spline density can be selectively adjusted to provide flexibility in areas with known discontinuities, or areas where the slope is changing rapidly, while providing stiffness and noise reduction in smoothly varying sections of the TRC.

In accordance with one or more aspects of the present disclosure, a method is provided for calibrating and/or characterizing a printing system with respect to at least one color, which may be employed in connection with monotone printers, multi-color printers, etc. The method includes providing a set of spline basis functions as a vector [S], and providing a measured TRC that includes measured density values associated with a plurality of input density values, where the input density values are selected from values of a machine TRC. In certain preferred embodiments, the spline function density is set according to curvature and/or noise of the measured TRC, where the method may include defining high and low density regions in the machine TRC according to the measured TRC with the high density region(s) corresponding to an area of the measured TRC exhibiting higher measurement noise or higher curvature than the low density region(s), and providing a higher density of spline basis functions in the high density region(s) than in the low density region(s). In this manner, the resulting curve fit will be less susceptible to measurement noise and can provide better accuracy for high curvature portions of the machine TRC range. For multi-color systems, basis functions and measured TRCs may be provided for each color to be calibrated/characterized. The method further includes deriving a matrix [X] of weighting coefficients for the spline basis functions by determining a least-squares solution for the matrix equation [measured TRC]=[X]*[S], and constructing a spline fitted TRC based on the spline basis functions and the coefficient matrix. A binary dot file is formed according to the spline fitted TRC, and is loaded into the system for use in printing. In various implementations, a majority of the spline basis functions are of second or higher order. Moreover, an iterative curve fit can be employed in certain embodiments. In this case, if any of the weighting coefficients are negative, the solution is determined by setting the negative coefficients to zero, removing the corresponding function from the set of spline basis functions, and recalculating to determine an adjusted least-squares solution for the matrix equation to derive the weighting coefficients. In this manner, monotonicity is ensured in the fitted TRC. The binary dot file formation in certain embodiments may include forming a threshold array including a value corresponding to each value in the desired (or target) TRC, where the values of the threshold array indicate the number of pixels that must be turned on to achieve the target TRC value from the spline fitted TRC, providing a fill order list indicating the order in which each pixel of a digital pattern is turned on for the printer system, and forming the binary dot file including a value corresponding to each value in the fill order list, where the values of the binary dot file indicate the smallest index of the threshold array for which the threshold array value is greater than the value of the fill order list.

In accordance with further aspects of the disclosure, a method of calibrating or characterizing a printing system is provided, which includes providing a measured toner reproduction curve (TRC) including measured density values, defining at least one high density region and at least one low density region in the machine TRC where the high density region corresponds to an area of the measured TRC exhibiting higher measurement noise or higher curvature than the low density region, and providing a set of spline basis functions as a vector [S] having a higher density of spline basis functions in the high density region than in the low density region, and deriving a matrix of weighting coefficients for the basis functions by determining a solution for the matrix equation [measured TRC]=[X]*[S]. The method further includes constructing a spline fitted TRC based on the spline basis functions and the weighting coefficients, forming a binary dot file based at least in part on the spline fitted TRC, and loading the binary dot file into the printing system for use in printing.

DETAILED DESCRIPTION

Referring now to the drawings,FIG. 1illustrates an exemplary method2for characterizing and/or calibrating a printing or rendering system in accordance with one or more aspects of the present disclosure. Although the exemplary method2is illustrated and described below in the form of a series of acts or events, it will be appreciated that the various methods of the disclosure are not limited by the illustrated ordering of such acts or events except as specifically set forth herein. In this regard, except as specifically provided hereinafter, some acts or events may occur in different order and/or concurrently with other acts or events apart from those illustrated and described herein, and not all illustrated steps may be required to implement a process or method in accordance with the present disclosure. The illustrated method2and other methods of the disclosure may be implemented in hardware, software, or combinations thereof, whether in a single system or in distributed form in two or more components or systems, in order to characterize or calibrate a single or multi-color printing device or other device that renders single or multi-color images, and may be employed in any form of printing system including without limitation desktop printers, network printers, stand-alone copiers, multi-function printer/copier/facsimile devices, high-speed printing/publishing systems and digital printing presses, wherein the disclosure is not limited to the specific applications and implementations illustrated and described herein.

The method2includes providing a set of spline basis functions at10inFIG. 1, where multi-color implementations may (but need not) involve provision of a separate spline basis function set for each color. Referring also toFIGS. 2-4, an exemplary set of spline basis functions120are illustrated inFIG. 3, including spline functions S1through SK, where K is any integer greater than 2, such as 23 in the illustrated embodiment, and where the splines form a spline basis function vector [S] of dimension 23×72 in this example (FIG. 4). The basis functions S may be imported or calculated, for example, as described further in connection withFIGS. 2 and 3below. At20, a measured toner reproduction curve is provided (measured TRC121inFIGS. 4 and 6below), which may be acquired by any suitable means, including without limitation using a device such as an ETAC sensor included in a printing system (system202inFIG. 5below) to measure toner density on a photoreceptor intermediate transfer medium, or by using a spectrophotometer to measure marking material density on a final print medium (e.g., paper). Moreover, multiple measurements may be made at each point or at certain points of the TRC to increase the accuracy of the fit. The measured TRC121includes a plurality of measured density values121associated with a plurality of input density values for at least one color. In the illustrated examples, 72 points were used for the measured TRC121out of 256 possible values in an 8-bit machine TRC range for a given color.

The method2further includes deriving a matrix at30of weighting coefficients122(e.g., a 1×23 matrix [X] of weighting values122as in the example ofFIGS. 4 and 9below) for the spline basis functions120by determining a solution at32for the matrix equation [measured TRC]=[X]*[S]. In one example, the weighting coefficients are determined by finding a least-squares solution to the equation. The least-squares solution to this equation may be solved by any suitable techniques, such as using a QR factorization procedure commonly available in many linear-algebra libraries. A discussion of QR factorization and it's uses in least squares fitting is found in section 14.3: General Linear Least Squares in “Numerical Recipes, The Art of Scientific Computing” by Press, Teukolsky, Flannery and Vetterling [Cambridge University Press, c 1986]. This book also includes example code primarily for teaching purposes. A public domain implementation of QR factorization for FORTRAN77supported by the National Science Foundation is available as the subroutine xGEQRF in the LAPACK linear algebra library. Other Linear Algebra libraries are available in the public domain and commercially for most programming languages. In accordance with an aspect of the disclosure, the use of carefully selected spline basis functions120facilitates the use of a least-squares solution to be calculated quickly using standard linear algebra libraries with a minimum of coding effort, although any suitable computation technique may be employed within a printing system or in an external system. One exemplary least-squares solution at30provides the 23 weighting values122shown in the graph330ofFIG. 9, including the values 0.005141; 0; 0; 0; 0.013083; 0.053188; 0.060096; 0.079864; 0.09851; 0.045528; 0.110625; 0.06874; 0.05825; 0.063349; 0.044357; 0.075672; 0.07162; 0.048483; 0.025841; 0.004255; 0.01465; 0; 0.00203.

The determination of the weighting coefficients122at30, moreover, may involve one or more iterations in certain embodiments, in order to ensure monotonic fitting. As shown in the example ofFIG. 1, a determination is made at34as to whether any of the weighting coefficients122are negative. If not (NO at34), the process proceeds to construct the spline fitted TRC312at38using the spline basis functions120and the calculated weighting coefficients122. Otherwise (YES at34), the negative coefficients are set to zero at36and the function(s) corresponding to the negative coefficient is removed from the set of spline basis functions120. The weighting coefficients122are then recalculated at32by determining an adjusted solution for the matrix equation.

A spline fitted TRC (fitted curve312inFIG. 7below) is constructed at40based on the spline basis functions120and the matrix [X] of weighting coefficients122, where the resulting fitted TRC is a composite of the basis functions [S] weighted by the coefficients [X] to fit a curve according to the measured TRC values121. At40, a binary dot file210(FIG. 5) is formed at least partially based on the spline fitted TRC312, and the dot file210is loaded at50into the printing system202for use in machine controls, or for printing customer print jobs. In an alternate implementation, a look-up table can be generated which remaps input TRC levels to the output levels required to get the desired density, and the lookup table can be loaded onto the printer202. In this example, the method2may be employed in initial characterization of the printing system202, and/or may be employed thereafter for calibration, wherein the curve fitting techniques may be employed in computing components within the printer202and/or using external systems or devices wherein all such alternate implementations are contemplated as falling within the scope of the present disclosure.

The fitted TRC construction may be done by any suitable technique within the scope of the present disclosure. In the embodiment ofFIG. 1, the process40includes forming a threshold array at42that includes a value corresponding to each value in the machine TRC (e.g., 256 values in the illustrated 8-bit example), where the values of the threshold array indicate the number of pixels that must be turned on to achieve the measured value from the spline fitted TRC. The following Table 1 shows an exemplary 256 value threshold table formed for the exemplary 72-point measured TRC and the spline functions120above, where the printing system202is capable of generating over 13,312 possible density values for a given color, by turning on the laser in a halftone screen comprising 16 laser scanlines and 832 possible laser actuation time durations within each scanline.

The exemplary process ofFIG. 1also includes providing a fill order list at44indicating the order in which each pixel of a digital pattern is turned on for the printer system202, which may be any suitable fill order list associated with half-toning within the scope of the disclosure. At46, the binary dot file210(FIG. 5) is formed including a value corresponding to each value in the fill order list, with the values of the binary dot file210indicating the smallest index of the threshold array for which the threshold array value is greater than the value of the fill order list. In one implementation of this dot file generation procedure, for each element of the halftone screen, an integer would be read in from the fill order file, specifying the order in which that element would be turned on. This integer would be compared to each threshold value, starting at threshold 1. If the fill order value was greater than the threshold 1 value, it would be compared next to threshold 2, continuing until finally the fill order value was less than the value of the threshold. The index for this threshold (a byte between one and 255) would be written to an output halftone dot file. If no threshold value is greater than the fill order value (i.e. for the fill order value 13,312 in this example) then the byte255would be written to the output halftone dot file. The program would then continue onto the next integer in the fill order file, writing an output byte for each input integer, until the end of the fill file.

The dot file may include many more levels than required to define a customer TRC, for example, where the dot file in the illustrated embodiment may define the turn-on pattern for 13,312 levels for a 256 value customer TRC, wherein the graph340inFIG. 10illustrates a curve342depicting an exemplary dot file including values indicating the dot level (from 1 to above 13,000 in the illustrated system202) required to achieve a desired output density from the fitted TRC310, illustrated as a curve312inFIG. 7. In this example, 13,312 cells in a two dimensional grid are defined to accommodate a rendering mechanism in the printer202that generates 16 laser scan-lines in a slow scan direction and 832 fast-scan sub-pixels, where a sub-pixel represents the shortest amount of time (smallest distance) for which a laser actuator is turned on and then off again. For an example customer input of 100, all cells with values less than or equal to 100 will have the laser turned on, and will develop, while all cells with values greater than 100 will have the laser turned off, and will not develop toner. The threshold specifies how many additional cells are turned on for each level from 1 to 255, where the dot fill-in order file specifies the order in which each of the 13,312 cells should be turned on. In one example, if the threshold indicates 1000 cells should have a value of 34, the dot fill-in file specifies which 1000 sub-pixels should be turned on next. The dot file is loaded at50inFIG. 1into the printer system202or other rendering device that will use this to generate printed/rendered images based on 8-bit customer input data.

Referring toFIGS. 2 and 3, monotonic spline basis functions120are preferably used, and may be characterized by a set of discrete points (ti. . . tk+n), referred to as knots (23 splines120in the illustrated embodiment). Each spline Sihas a value of 0 at all x values below ti, and a value of 1 at all points above ti+n, and follows an s-shaped curve for intervening values, where n is the order of the spline S, and where there are n fewer splines than knots. In one embodiment, the function which determines the spline value in the s-shaped region is chosen so that the nthderivative is continuous, where the simplest possible monotone spline would have order zero. The spline would be 0 below a knot, and 1 above a knot, with a step transition between. A function fit with a 0thorder spline120would look like a staircase, in which case even the first derivative would be discontinuous. A piecewise linear fit would result from 1storder splines to yield a linear ramp between successive knots. Visually smooth splines are preferred, at least for the majority of the basis functions120having 2ndor higher orders to provide continuous second derivatives, and more preferably the majority of the selected splines120are of order 3 or higher within the scope of the present disclosure. The set of equations100inFIG. 2define an exemplary 3rdorder spline employed in the illustrated embodiments. The graph110inFIG. 3illustrates set of Spline Basis vectors S1through SKused for the magenta and black dots. Note that there are more vectors in the toe (highlight) area of the TRC, where density is changing rapidly, and fewer vectors in the shadow region, which is typically flat. These curves were generated from the set of knots: 0; 0; 0; 0; 2; 4; 8; 16; 32; 42; 44; 54; 62; 70; 78; 86; 96; 104; 104; 104. Duplicate knots are employed in this example at the beginning and end of the curve, moreover, to give smooth behavior at the boundaries. Although the exemplary implementations are illustrated and described in the context of third order spline basis functions, splines of other orders may be used and all such alternate embodiments are contemplated as falling within the scope of the present disclosure.

Various aspects of the disclosure provide for fitting a measured TRC in a smooth, monotonic way, using a least-squares error (LSE) approach and a set of 3rdorder spline basis functions120having a functional range [0,1] between the digital area coverage (percentage) range [ti, ∞] for set i. The weights of the spline functions, moreover, are preferably restricted to positive values in order to maintain monotonicity in the TRC, as is advantageous for image rendering applications involving marking material density (brightness and darkness). Splines with negative weights in this regard, are preferably removed from the set of basis functions120in the iterative LSE minimization process (e.g., at34and36inFIG. 1). The number of spline basis functions, moreover, is preferably adjusted to reflect known engine/dot pattern behavior. Subsequently, the print engine is linearized by the spline fitted TRC310by definition of a desired TRC for each of the values in the input data (e.g. 256 values of the machine TRC) such that the fitted TRC310determines the dot which will produce the desired response in rendering/printing a customer image, so as to produce a smooth, contour-free TRC for each of the color channels.

As shown in FIGS.3and6-8, moreover, the disclosure advantageously contemplates defining one or more high density regions (e.g., region112b) and at least one low density region (112c) in the 256 value range of the machine TRC, based at least partially on the measured TRC121in one example. Alternatively, the high density regions can be set to correspond to regions in the machine TRC expected to have high TRC curvature. The high density region(s) thus corresponds to an area of the measured TRC exhibiting higher curvature than the low density region(s). Decreasing spline density in the low density region(s) decreases the sensitivity of the fit to noise, in areas where the TRC slope is not expected to change rapidly. In this aspect of the disclosure, the set of spline functions120are selectively chosen so as to provide a higher density of spline basis functions in the high density region(s) than in the low density region(s). Accordingly, the spline spacing is tighter in the high density region112bthan in the region112c(FIG. 3), so as to accommodate high TRC curvature in the region112bof the measured TRC121(FIG. 6), while providing increased noise reduction in the region112c. For a particular half-tone dot design, moreover, the digital area coverage value in a machine TRC at which a new row of pixels has been started may be known in advance, and accordingly additional knots can be placed at this point to accommodate a discontinuity in the curve. Moreover, fewer knots can be placed in areas where the TRC is known to be smoothly varying. This type of selectivity in the spline functions120facilitates adjustability in the stiffness of the fit as well as selective use of discontinuities.

The above described techniques can be employed in calibrating and/or characterizing any form of image rendering device, including without limitation printing systems.FIG. 5illustrates an exemplary multi-color document processing or printing system202provided with a dot file210in accordance with one or more exemplary aspects of the disclosure. While illustrated in the context of a single print engine system2, the various aspects of the disclosure may be implemented in association with document processing systems having multiple print engines, one or more of which may be single-color rendering devices. The system202ofFIG. 5can be any form of commercial printing apparatus, copier, printer, facsimile machine, or other system which may include a scanner or other input device204that scans an original document text and/or images to create an image comprising pixel values indicative of the colors and/or brightness of areas of the scanned original, or receives images such as in a print job, and which has a marking engine or print engine206by which visual images, graphics, text, etc. are printed on a page or other printable medium, including xerographic, electro photographic, and other types of printing technology, wherein such components are not specifically illustrated inFIG. 5to avoid obscuring the various TRC fitting aspects of the present disclosure.

As shown inFIG. 5, the exemplary document processing system202includes a print engine206, which may be any device or marking apparatus for applying an image from a digital front end (DFE) printer job controller208to printable media (print media) such as a physical sheet of paper, plastic, or other suitable physical media substrate for images, whether precut or web fed, where the input device204, print engine206, and controller208are interconnected by wired and/or wireless links for transfer of electronic data therebetween, including but not limited to telephone lines, computer cables, ISDN lines, etc. The printing system202, moreover, includes an integral user interface210with a display and suitable operator/user controls such as buttons, touch screen, etc. The print engine206generally includes hardware and software elements employed in the creation of desired images by electrophotographic processes wherein suitable print engines206may also include ink-jet printers, such as solid ink printers, thermal head printers that are used in conjunction with heat sensitive paper, and other devices capable of printing or marking an image on a printable media.

The image input device204may include or be operatively coupled with conversion components for converting the image-bearing documents to image signals or pixels or such function may be assumed by the printing engine206. In the illustrated document processor202, the printer controller208provides the output pixel data from memory to a print engine206that is fed with a print media sheets212from a feeding source214such as a paper feeder which can have one or more print media sources or paper trays216,218,220,222, each storing sheets of the same or different types of print media212on which the marking engine206can print. The exemplary print engine206includes an imaging component244and an associated fuser248, which may be of any suitable form or type, and may include further components which are omitted from the figure so as not to obscure the various aspects of the present disclosure. In one example, the print engine206may include a photoconductive insulating member or photoreceptor which is charged to a uniform potential via a corotron and exposed to a light image of an original document to be reproduced via an imaging laser under control of a controller of the DFE208, where the exposure discharges the photoconductive insulating surface of the photoreceptor in exposed or background areas and creates an electrostatic latent image on the photoreceptor corresponding to image areas of the original document. The electrostatic latent image on the photoreceptor is made visible by developing the image with an imaging material such as a developing powder comprising toner particles via a development unit, and the customer image is then transferred to the print media212and permanently affixed thereto in the fusing process.

In a multicolor electrophotographic process, successive latent images corresponding to different colors can be formed on the photoreceptor and developed with a respective toner of a complementary color, with each color toner image being successively transferred to the paper sheet212in superimposed registration with the prior toner image to create a multi-layered toner image on the printed media212, and where the superimposed images may be fused contemporaneously, in a single fusing process. The fuser248receives the imaged print media from the image-forming component and fixes the toner image transferred to the surface of the print media212, where the fuser248can be of any suitable type, and may include fusers which apply heat or both heat and pressure to an image. Printed media from the printing engine206is delivered to a finisher230including one or more finishing output destinations232,234,236such as trays, stackers, pans, etc.

The document processing system202is operative to perform these scanning and printing tasks in the execution of print jobs, which can include printing selected text, line graphics, images, machine ink character recognition (MICR) notation, etc., on either or both of the front and back sides or pages of one or more media sheets212. An original document or image or print job or jobs can be supplied to the printing system202in various ways. In one example, the built-in optical scanner204may be used to scan an original document such as book pages, a stack of printed pages, or so forth, to create a digital image of the scanned document that is reproduced by printing operations performed by the printing system202via the print engine206. Alternatively, the print jobs can be electronically delivered to the system controller208via a network or other means, for instance, whereby a network user can print a document from word processing software running on a network computer284or286with a print job278being sent to the DFE208of the processing system202via a connection280to a digital network282thereby generating an input print job.

A print media transporting system or network or highway240of the document processing system202links the print media source214, the print engine206, and the finisher230via a network of flexible automatically feeding and collecting drive members, such as pairs of rollers242, spherical nips, air jets, or the like, along with various motors for the drive members, belts, guide rods, frames, etc. (not shown), which, in combination with the drive members, serve to convey the print media212along selected pathways at selected speeds. Print media212is thus delivered from the source214to the print engine206via a pathway246common to the input trays216,218,220,222, and is printed by the imaging component244and fused by the fuser248, with a pathway246from the print engine206merging into a pathway270which conveys the printed media212to the finisher230, where the pathways246,248,270of the network240may include inverters, reverters, interposers, bypass pathways, and the like as known in the art. In addition, the print engine206may be configured for duplex or simplex printing and a single sheet of paper212may be marked by two or more print engines206or may be marked a plurality of times by the same marking engine206, for instance, using internal duplex pathways.

As discussed above, the described TRC fitting techniques can be employed in either or both of calibration or device characterization operations in a rendering system. Referring briefly toFIGS. 11 and 12, a general device correction function may include both a calibration that immediately precedes the device and a characterization which addresses the device “through” the calibration function. This example is schematically illustrated inFIG. 11for the case of a CMYK printing system400, which partitions “device-correction function” into characterization and calibration. For example, system400includes a printer-independent-color which can be provided as input410to a characterization routine402whose output is fed to a calibration unit404, whose output in turn is fed to an output device406via output line414. Additionally, lines408and412indicate alternate CMYK paths used for fast reprint and fast emulation, respectively, which are fed to calibration unit404.

The purpose of the calibration transformation is to facilitate a trade-off. Unlike the full device-correction function, the calibration transformation provides control of the output device only in a limited fashion. However, in comparison to the full device-correction function the calibration transformation also offers significant advantages in that it requires substantially reduced measurement effort and also a substantially lower computational effort. The lower computational effort requirement allows it to be incorporated in high-speed real-time printing image-processing chains for which the full device-correction function may be too computation and/or memory intensive. For color output devices, particularly those utilized in the printing arts, calibration is typically performed for the Black channel (K) independently and for the Cyan (C), Magenta (M), and Yellow (Y) channels either independently or together.

In an exemplary three channel (CMY) color printer example, calibration may be used to determine a calibration transform from CMY to C′M′Y′ that maintains a desired printer response in selected regions of color space. Additionally, the calibration transform is preferably computationally efficient with a small memory requirement so that it can be incorporated in high-speed real-time printing paths. Traditionally, the calibration transform has been applied in the form of one-dimensional correction to the individual channels for the device. For CMY, the calibration is applied as three TRCs for each of the C, M, and Y channels.FIG. 12illustrates a traditional three-color one-dimensional calibration transformation system500with arrows502,504and506representing C, M, and Y inputs to transformations514,516, and518, respectively. Dashed line512generally indicates the boundaries of a calibration transformation, which is composed of individual transformations514,516, and518. Outputs are indicated by arrows508,510and511, which respectively represent C′, M′ and Y′. It can thus be appreciated that the following equation applies to system500ofFIG. 12:
C′=f1(C),M′=f2(M),Y′=f3(Y)

Furthermore, the techniques above can be employed in generating spline fitted TRCs for use in such calibration and/or device characterizations and in other applications for image rendering systems.

The above described examples are merely illustrative of several possible embodiments of the present disclosure, wherein equivalent alterations and/or modifications will occur to others skilled in the art upon reading and understanding this specification and the annexed drawings. In particular regard to the various functions performed by the above described components (assemblies, devices, systems, circuits, and the like), the terms (including a reference to a “means”) used to describe such components are intended to correspond, unless otherwise indicated, to any component, such as hardware, software, or combinations thereof, which performs the specified function of the described component (i.e., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the illustrated implementations of the disclosure. In addition, although a particular feature of the disclosure may have been disclosed with respect to only one of several embodiments, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application. Also, to the extent that the terms “including”, “includes”, “having”, “has”, “with”, or variants thereof are used in the detailed description and/or in the claims, such terms are intended to be inclusive in a manner similar to the term “comprising”. It will be appreciated that various of the above-disclosed and other features and functions, or alternatives thereof, may be desirably combined into many other different systems or applications, and further that various presently unforeseen or unanticipated alternatives, modifications, variations or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompassed by the following claims.