Patent Publication Number: US-9406005-B2

Title: Gamma correction table generation method, image processing device using the gamma correction table and control program thereof

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a Divisional of U.S. patent application Ser. No. 14/088,836 filed Nov. 25, 2013, which claims the benefit of priority from Japanese Patent Application No. 2012-261311 filed Nov. 29, 2012, each of which is hereby incorporated by reference herein in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present disclosure generally relates to gamma correction and, more particularly, to a method of creating a gamma correction table for forming an image on a recording medium based on digital image data or an image processing method using a gamma correction table. 
     2. Description of the Related Art 
     In image forming devices for forming images on a recording medium based on a digital image data, each of the image forming devices has a different output density characteristic. Therefore, when forming an image on a recording medium based on the same digital image data, the density output on the recording medium may be sometimes different. In order to output a desired digital image data on a recording medium, each of the image forming devices generally corrects the digital image data according to the characteristic of each image forming device. This is well-known as gamma correction. 
     Also, in many cases, the tone number available per pixel in an image forming device such as a printer is smaller than the tone number of a digital image data handled in a personal computer or the like. Therefore, the digital image data is subjected to low tone processing to convert the tone number of the digital image data into a tone number which the image forming device can output. Among low tone processing, the screen processing generally converts input digital image data into image data that represents the tone in a quasi-manner in a certain area. 
     On the other hand, when performing the screen processing on the image data, the resolution may sometimes degrade. In particular, it is known that, in an image drawn with characters and/or lines, the characters and/or lines may generate a discontinuation, resulting in a considerable detone of the image quality. Japanese Patent Application Laid-Open No. 2005-341249 discusses a method in which a contour portion of an image is detected and the detected image is subjected to an enhancing or reducing processing, and subsequently the image is subjected to a continuous tone processing before being output. Pixels which are not in the contour portion are output after being subjected to the screen processing. According to the Japanese Patent Application Laid-Open No. 2005-341249, a contour portion and an area other than the contour portion are subjected to a different gamma correction. 
     A gamma correction table used for gamma correction is generated based on the characteristic of the output density, which is obtained by measurement of the actual density recorded on a recording medium, with use of a sensor. 
     However, conventional methods have a problem that it is difficult to obtain a precise characteristic of the output density. In the method discussed in the Japanese Patent Application Laid-Open No. 2005-341249, the tone on a contour portion is represented by a single pixel. On the other hand, in a portion other than the contour portion, an area including a plurality of pixels represents the tone in a quasi-manner. Therefore, a plurality of gamma correction tables appropriate to the respective areas has to be generated. However, in the conventional methods, appropriate gamma correction table is hardly generated. 
     According to the Japanese Patent Application Laid-Open No. 2005-341249, since dot gain and bleeding of ink have to be considered, the output density in a contour portion corresponding to a pixel of interest is measured using a sensor having the resolution lower than the resolution of input image data. However, it is likely that different output densities corresponding to the respective input tone values appear in a mixed state around the pixel of interest forming the contour portion. Therefore, since it is impossible to relate the output densities measured by a sensor to the input tone values in a one-to-one relationship, it is impossible to obtain an appropriate characteristic of the output density. As a result, it is difficult to generate a gamma correction table. Thus, it is occasionally necessary to correct the measurement of the output density to calculate the characteristic of the output density based on a measurement result of the output density recorded on a recording medium measured by a sensor of an image forming device. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present disclosure is directed to an image processing method for creating a precise gamma correction table by appropriately correcting a measurement result of an output density on a recording medium measured by a sensor. 
     According to an aspect of the present disclosure, a gamma correction table generation method includes: obtaining density information by reading, with a reading sensor, a density patch output by an image forming device in a range wider than a cell, the density patch including a plurality of cells disposed such that a part of the cells as a unit representing a tone overlaps with each other and dots included in each of the cells are separated from each other to an extent that no influence is exerted on each other on a recording medium which the image forming device outputs; correcting the density information according to a number of the cells in the density patch; and generating a gamma correction table based on the corrected density information. 
     Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure. 
         FIG. 1  is a block diagram of an image forming device. 
         FIGS. 2A and 2B  illustrate examples of a density patch. 
         FIG. 3  illustrates a measurement range of a density sensor. 
         FIG. 4  is a block diagram illustrating a detailed image processing section. 
         FIGS. 5A and 5B  are flowcharts of image processing and image recording in the image forming device. 
         FIG. 6  illustrates fine line detection patterns and detection conditions. 
         FIGS. 7A-7D  illustrate examples of an input image, intermediate images, and an output image. 
         FIGS. 8A and 8B  illustrate screen processing. 
         FIG. 9  illustrates a low tone processing for a fine line. 
         FIGS. 10A and 10B  illustrate a generation of a gamma correction table. 
         FIG. 11  illustrates an example of an isolated point patch. 
         FIG. 12  is a block diagram illustrating a detailed image processing section. 
         FIGS. 13A and 13B  are flowcharts of an image recording operation and a gamma correction table creating operation. 
         FIG. 14  illustrates an isolated point detection condition. 
         FIG. 15  illustrates a measurement range of a high-resolution sensor. 
         FIG. 16  is a block diagram illustrating a detailed image processing section. 
         FIG. 17  illustrates an example of density patches. 
         FIG. 18  illustrates a creating method of a high-density patch. 
         FIGS. 19A and 19B  are flowcharts of an image recording operation and a gamma correction table creating operation. 
         FIGS. 20A and 20B  illustrate a generation of a gamma correction table. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Various exemplary embodiments, features, and aspects of the disclosure will be described in detail below with reference to the drawings. 
     The following exemplary embodiments are given only as examples. The exemplary embodiments do not limit the scope of the disclosure. 
     A first exemplary embodiment describes an example of a creating method of a gamma correction table for a plane portion and a fine line. More particularly, a gamma correction table is generated that is capable of appropriately correcting a measurement result of an output density of pixels constituting a fine line and is capable of appropriately performing gamma correction on pixels constituting the fine line. 
       FIG. 1  is a block diagram illustrating an example of a configuration of an image forming device applicable to the first exemplary embodiment. An image forming device  10  includes a patch recording section  101 , a density information obtaining section  102 , a density information correction section  103 , a gamma correction table generation section  104 , an image processing section  105 , and an image recording section  106 . The image forming device  10  obtains digital data of an input image from a central processing unit (CPU) or a memory connected to the outside via a bus. The image forming device  10  forms image data, in which various processing is made on multi-level image data, on a recording medium. The image forming device  10  also generates a gamma correction table where appropriate according to an instruction from a CPU or given by a user. In the first exemplary embodiment, a description will be made while taking an example of a case where the multi-level image data is 8-bit data (including 256 tones of 0-255). 
     The patch recording section  101  records a density patch on a recording medium (or on an intermediate recording medium when the correlation with an output density on the recording medium is known). The density patch is recorded to generate a gamma correction table.  FIGS. 2A and 2B  illustrate examples of density patches recorded by the patch recording section  101 . The size of each density patch according to the first exemplary embodiment is 10 pixels×10 pixels. Each of the density patches is previously determined according to the low tone processing performed by the image processing section  105 . According to the first exemplary embodiment, the density patches to be recorded include a plane portion density patch group  200 , a vertical fine line density patch group  201 , and a slant fine line density patch group  202 . Detailed description on each of the density patches will be given later. 
     The density information obtaining section  102  obtains density information of the density patch on a recording medium or an intermediate recording medium recorded by the patch recording section  101 . Herein, a density sensor is used to directly measure an output density on the recording medium and a measurement result is obtained as the density information. The measurement method of the output density can also be achieved by obtaining another kind of information such as a height of toner having a correlation with the density.  FIG. 3  illustrates a measurement range of a density sensor used by the density information obtaining section  102  according to the first exemplary embodiment. It is understood that the resolution of the density sensor used in the first exemplary embodiment is lower than the resolution of the image data. That is, the measurement result obtained by the density sensor is approximate to a value of an averaged density of the pixels constituting image data corresponding to the measurement range. 
     The density information correction section  103  corrects the density information obtained by the density information obtaining section  102 . Here, the density information is corrected when the density information is a measurement result obtained by recording the density of the vertical fine line density patch group  201  and the slant fine line density patch group  202 . The density information is corrected based on a relationship between the pixel value of each pixel in the density patch and the tone represented by the dot pattern constituting the density patch. Detailed description on the correction method made by the density information correction section  103  will be given later. The density information of the plane portion density patch group  200  is not subjected to the correction. 
     The gamma correction table generation section  104  generates a gamma correction table based on the characteristic of the output density obtained from the density information or corrected density information. According to the first exemplary embodiment, a gamma correction table for plane portion, a gamma correction table for vertical fine line, and a gamma correction table for slant fine line are generated. 
     The image processing section  105  performs an image processing on multi-level image data transmitted from the CPU or the memory.  FIG. 4  illustrates a detailed block diagram of the image processing section  105  according to the first exemplary embodiment. The image processing section  105  includes a fine line detection section  1051 , a fine line gamma correction section  1052 , a gamma correction section  1053 , a fine line low gradation processing section  1054 , a screen processing section  1055 , and selectors  1056  and  1057 . 
     The fine line detection section  1051  checks each of the pixels and performs a pattern matching to determine whether the pixel is the pixel constituting a fine line. 
     The fine line gamma correction section  1052  performs a gamma correction on a pixel (hereinafter referred to as pixel of fine line) which is detected as a fine line by the fine line detection section  1051 . The fine line gamma correction section  1052  uses either one or both of a gamma correction table for vertical fine line and a gamma correction table for slant fine line generated by the gamma correction table generation section  104 . 
     The gamma correction section  1053  performs a gamma correction on a pixel (hereinafter referred to as flat pixel) in a plane portion, which is output from the fine line gamma correction section  1052  and is not detected as a fine line by the fine line detection section  1051 . The gamma correction section  1053  uses the gamma correction table for plane portion generated by the gamma correction table generation section  104 . 
     The fine line low gradation processing section  1054  performs a low tone processing on a pixel value of a pixel of fine line output from the fine line gamma correction section  1052 . The fine line low gradation processing section  1054  performs the low tone processing to reduce the tone number of a pixel value representing a pixel of fine line according to the tone number per pixel, which the image recording section  106  can output. The image data input into the image processing section  105  is 8-bit data representing 256 tones. The fine line low gradation processing section  1054  performs a 9-valuation processing to convert a pixel value having 256 tones into 9 tones. 
     The screen processing section  1055  performs a screen processing on a pixel value of a flat pixel output from the gamma correction section  1053 . Here, the conversion of the tone number is made by a dither method using a threshold matrix. The screen processing section  1055  performs the processing for converting the pixel value of 256 tones into 9 values. 
     The selector  1056  sorts the image data for each pixel according to the detection result made by the fine line detection section  1051 . When a pixel to be processed is detected as a fine line, the pixel value of each pixel is output to the fine line gamma correction section  1052 . When any pixel to be processed is not detected as a fine line, the pixel value of each pixel is output to a gamma correction section  1053 . Likewise, the selector  1057  selects a result obtained by the fine line low gradation processing section  1054  as for a pixel detected as a fine line, and selects a result obtained by the screen processing section  1055  as for a pixel not detected as a fine line, as an output value respectively. The selector  1057  gives output image data. 
     The image recording section  106  records the output image data processed by the image processing section  105  on a recording medium. The image recording section  106  may be either an electrophotographic system or an inkjet system. 
     (Image Processing and Image Recording Operation) 
     The operation of the image forming device to record an image according to the first exemplary embodiment will be described below.  FIG. 5A  is a flowchart when the image recording section  106  records an image. 
     In step S 500 , the image forming device  10  determines whether any instruction to print image data is given from a CPU connected outside the device, or a user. As a determination result, when a printing instruction is detected (YES in step S 500 ), the process proceeds to step S 501 . 
     In step S 501 , the image forming device  10  obtains input image data to be recorded. The input image data is input from the CPU connected to the outside of the image forming device  10  or a memory. 
     In step S 502 , the fine line detection section  1051  performs fine line detection. According to the first exemplary embodiment, the fine line detection section  1051  detects a fine line of a one pixel width by performing a pattern matching.  FIG. 6  illustrates patterns of fine lines and detection conditions that the fine line detection section  1051  uses for detecting the fine line. The fine line detection section  1051  detects a vertical fine line, a horizontal fine line, a slant fine line, and other fine lines. 
       FIG. 7A  is an example of an input image data.  FIG. 7B  illustrates a detection result of fine lines obtained from the input image data. In  FIG. 7B , the pixels detected as a vertical fine line and a horizontal fine line are represented with black pixels; the pixels detected as a slant fine line are represented with light gray pixels; the pixels detected as other fine lines are represented with heavy gray pixels; and the pixels other than fine lines are represented with white pixels. 
     In step S 503 , the process branches based on the fine line detection result in step S 502 . When the pixel to be processed is not a pixel of fine line (NO in step S 503 ), the process proceeds to step S 504 , and when the pixel to be processed is a pixel of fine line (YES in step S 503 ), the process proceeds to step S 506 . For example, in the case of the fine line detection result illustrated in  FIG. 7B , since white pixels are not detected as pixels of fine line, the process proceeds to step S 504 . On the other hand, when the pixels are other than white pixels, since the pixels are detected as pixels of fine line, the process proceeds to step S 506 . According to the first exemplary embodiment, the image processing section  105  performs switching between the processing on the pixels of fine lines and the processing on the pixels other than fine lines. However, the image processing section  105  may be configured to perform both of the processing on the pixels of fine line and the processing on the pixels for other than fine lines and to select processing results based on the fine line detection result. 
     In step S 504 , the gamma correction section  1053  performs a gamma correction on flat pixels in the pixels constituting the input image data. According to the first exemplary embodiment, the gamma correction section  1053  performs a gamma correction by using a gamma correction table, which is generated using the plane portion density patch group  200 . 
     In step S 505 , the screen processing section  1055  performs a screen processing using a dither method.  FIGS. 8A and 8B  illustrate a dither method that the screen processing section  1055  performs. Each of the cells corresponding to the pixel groups stores a different index number. As illustrated in  FIG. 8A , the cells corresponding to the image data are periodically arranged without any space and each of the pixels is associated with any of index numbers. Each of the index numbers corresponds to a threshold value having a different level respectively as illustrated in  FIG. 8B . The screen processing section  1055  makes a comparison between the pixel value of each of the pixels constituting the input image data of 256 tones and the threshold value corresponding to the index number, to determine the output value of each pixel as any of 9 tones. The threshold value TH[n] is calculated using the formula shown below:
 
 TH[n]=X* 20+1.25+ n* 2.5
 
(X: index number).
 
     The processing result using the above dither method can express a quasi tone in a unit cell. Generally, in the dither method, (a tone number which the cell can express in a quasi manner)=(number of pixels in the cell)×(output tone number in the cell−1)+1. That is, in the example of the first exemplary embodiment, as a result of screen processing by the screen processing section  1055 , 105 tones can be expressed in a quasi manner. 
       FIG. 7C  illustrates a result of the screen processing made by the screen processing section  1055  on the input image data illustrated in  FIG. 7A . In  FIG. 7C , the processing is performed on all pixels constituting the input image data illustrated in  FIG. 7A . According to the first exemplary embodiment, the processing is practically performed only on the white pixels in the detection result illustrated in  FIG. 7B . 
     In step S 506 , the fine line gamma correction section  1052  performs a fine line gamma correction on the pixels of the fine line. The fine line gamma correction section  1052  performs the gamma correction on every fine line detected in step S 502  using a vertical fine line gamma correction table and a slant fine line gamma correction table. The gamma correction is performed using a dedicated gamma correction table on the pixels, which are determined as included in a vertical fine line or a slant fine line as a result of fine line detection in step S 502 . When a horizontal fine line is detected, the fine line gamma correction section  1052  performs a gamma correction using a vertical fine line gamma correction table which has characteristics similar to the output density of the image forming device. 
     As for other fine lines, it is estimated that the other fine lines have characteristics of the output density which are intermediate density characteristics between the characteristics of the output density of the vertical fine line or the horizontal fine line and the characteristics of the output density of the slant fine line. Therefore, a gamma correction value suitable to the pixel detected as other fine lines can be calculated using the vertical fine line gamma correction table along with the slant fine line gamma correction table. 
     In step S 507 , the fine line low gradation processing section  1054  performs a low tone processing on the pixels of fine line. 
       FIG. 9  illustrates a fine line low tone processing. As illustrated in  FIG. 9 , the fine line low gradation processing section  1054  has eight threshold values for one pixel. The fine line low gradation processing section  1054  compares sequentially the pixel values of the pixels constituting the input image data of 256 tones with the eight threshold values corresponding to the pixel, and outputs any of the 9 tones as an output value. In such low tone processing carried out by the fine line low gradation processing section  1054 , the tone number is represented in a pixel unit. Therefore, although the tone is lower than the quasi tone number represented by each cell obtained by the screen processing section  1055 , the resolution is maintained. 
     For human eyes, the resolution tends to have priority over the tone in a region where many high-frequency components are included like fine line. Accordingly, when the fine line low gradation processing section  1054  makes low tone processing, the reduction of the tone in the fine line portion is hardly perceived and a satisfactory low tone image can be obtained while maintaining the resolution. Although the low tone processing on the pixel of fine line is not necessarily processing according to the first exemplary embodiment, it is desirable that the low tone processing is the processing that places emphasis on the resolution rather than a low tone processing which is performed on the pixels in a plane portion. 
     In step S 508 , the image recording section  106  records output image data on a recording medium. In step S 505  or step S 507 , the tone number of each of the pixels is reduced to a tone number which the image recording section  16  can output. In the first exemplary embodiment, the input pixel data illustrated in  FIG. 7A  is converted into an output image data illustrated in  FIG. 7D  through the processing in step S 505  and step S 507 . Since each of the plane portion and the fine line portion have been subjected to an appropriate gamma correction, the image formed on the recording medium becomes an agreeable image in which the density of the plane portion matches up with the density of the fine line. 
     (Density Patch to be Employed in Creating Gamma Correction Table) 
     A detailed description will be given below on the density patch which is recorded by the patch recording section  101  to generate a gamma correction table. 
       FIGS. 2A and 2B  illustrate examples of density patches recorded according to the first exemplary embodiment. The patch recording section  101  records density patches of a plane portion density patch group  200 , a vertical fine line density patch group  201 , and a slant fine line density patch  202 . 
     The plane portion density patch group  200  includes a plurality of density patches for measuring the characteristic of the output density when an input image data representing plane tone including no lines is formed on the recording medium. The plane portion density patch group  200  includes dot patterns that the screen processing section  1055  obtains by performing a screen processing on a plane input image data. In this case, the tone value represented by all pixels are constant. 
     Here, all pixels in 10 pixels×10 pixels are the density patch which are the result of the screen processing that the image processing section  105  performs on a uniform input image data of an input tone value of 20, 38, 59, 79, 100, 123, 138, 159, 177, 197, 218, 236 and 255. The screen processing will be described below. 
     In the dot patterns obtained as a result of the screen processing, the ratio of the black pixels to the white pixels in the 100 pixels is, in the above-mentioned order, 8%, 15%, 23%, 31%, 39%, 46%, 54%, 62%, 69%, 77%, 85%, 92% and 100% respectively. 
     In the plane portion density patch, each of the cells is represented by a quasi tone. In the measurement range illustrated in  FIG. 3 , the result measured by the sensor is approximate to an average value of each pixel included in the density patch. Therefore, with respect to the characteristic of the output density of the plane portion, the input tone value can be associated with the output density without correcting measurement result obtained by the sensor. 
     The vertical fine line density patch group  201  includes density patches for measuring the characteristic of the output density when a vertical fine line is formed on a recording medium. It is desirable to measure the characteristic of the output density of one pixel included in a fine line that forms one vertical fine line having a width of one pixel. That is, measurement of the density at which a fine line having a target tone is output is used as the output density corresponding to the target tone. 
     However, when measuring the output density on the recording medium, it is difficult to measure the output density of a single vertical fine line without including any background (paper white) of the vertical fine line. Also, if the measuring position of the density sensor is displaced a little, the number of pixels of fine line included in the measurement range may change resulting in an alteration of the detected output density. 
     Therefore, according to the first exemplary embodiment, as illustrated in the vertical fine line density patch group  201 , an image in which a plurality of vertical fine lines are periodically arranged is used as the density patch. However, depending on the characteristic of the image forming device, the surrounding recorded dots may have influence on the density of the output dot. Therefore, in any of the density patches of the vertical fine line density patch group  201 , the vertical fine lines are arranged being separated from each other to an extent that no influence is exerted on the respective densities. 
     When the repeated dot patterns are used as a unit pattern, the density patch in the vertical fine line density patch group  201  is 10 pixels in a vertical direction×3 pixels in a horizontal direction. An image of a vertical fine line having black pixels at the left side becomes the unit pattern. By periodically arranging the unit patterns 10 pixels in the vertical direction×10 pixels in the horizontal direction necessary for the density patch, the output density is increased so that the density sensor can precisely measure even when the measurement position is altered. 
     The density patches in the vertical fine line density patch group  201  are constituted of pixels of fine line having vertical fine lines of tone 33, 69, 102, 136, 172, 205, 238 and 255. The measurement result of the density recorded on the recording medium measured by the density sensor is approximate to an average value of the density represented by the pixels constituting the image data corresponding to the measurement range. That is, the measurement result of a fine line density patch is approximate to an average value of the pixel values of the pixels included in the unit pattern. 
     It is desirable to measure the output density of one pixel constituting the fine line. However, the unit pattern includes also pixels (white pixel) in addition to the pixels constituting the fine line. Therefore, a correction is made on the measurement result using the ratio of the pixels of fine line in the unit pattern. Here, the density patch in the vertical fine line density patch group  201  uses a unit pattern in which the ratio of the pixels of fine line is ⅓. Therefore, by performing a correction by multiplying 3-fold the measurement result, the output density per pixel of fine line forming a vertical fine line can be calculated. 
     Likewise, the slant fine line density patch group  202  is density patches for measuring the output density when an input image data of a slant fine line is formed on a recording medium. The density patch is an image including a plurality of slant lines of 45°, which are disposed periodically to calculate the characteristic of the output density per pixel constituting one slant line of 45°. Here, a unit pattern of the density patch in the slant fine line patch group  202  includes 4 pixels×4 pixels. A diagonal line extending diagonally right-upward including four black pixels is an image of a slant fine line. The density patch includes four slant fine lines. The four slant fine lines are separated from each other at an extent that no influence is exerted on the respective densities. 
     In each of the density patches in the slant fine line density patch group  202 , the slant fine line includes pixels of fine line having a tone of 33, 69, 102, 136, 172, 205, 238, 255. Similar to the vertical fine line, also in the measurement result of the slant fine line density patch, the result has to be corrected based on the ratio of the pixels of fine line in a unit pattern to associate with the input tone value. Each of the density patches of the slant fine line density patch group  202  uses a unit pattern in which the ratio of the pixels of fine line is ¼. Therefore, the output density per pixel forming a slant fine line is calculated by performing a correction multiplying the measurement result by 4. 
     A distance that the density is not influenced each other, depends on the characteristic of the image recording section  106 . It is possible to calculate the necessary distance between the dots based on experiments. The unit pattern may be determined based on the necessary distance between the dots. For example, when the necessary distance between the dots is three pixels, the unit pattern of the density patch of fine line is 10 pixels in vertical direction×4 pixels in horizontal direction. An image of vertical fine line including a black pixel at the left side may become the unit pattern. 
     (Gamma Correction Table Generation) 
     The operation of the image forming device according to the first exemplary embodiment for creating a gamma correction table will be described below.  FIG. 5B  is a flowchart for creating a gamma correction table. 
     In step S 520 , the image forming device  10  determines whether the gamma correction table should be generated. The gamma correction table may be generated simultaneously when a calibration is made on the image forming device  10 . Also, the gamma correction table may be generated when an instruction is given from the CPU or a user; when the number of records exceeds a predetermined number; or when an environmental condition of the apparatus changes. The gamma correction table may be generated at any timing. When a gamma correction table is generated (YES in step S 520 ), the process proceeds to step S 524 . 
     In step S 524 , the patch recording section  101  selects a predetermined density patch group to generate a gamma correction table. According to the first exemplary embodiment, the image processing section  105  uses three kinds of gamma correction tables; i.e., a gamma correction table for plane portion, a gamma correction table for vertical fine line, and a gamma correction table for slant fine line. Therefore, the patch recording section  101  selects any one of the plane portion density patch group  200 , the vertical fine line density patch group  201 , and the slant fine line density patch group  202 . The density patches illustrated in  FIG. 2  are stored in a storage capacity such as a read-only memory (ROM) or a random access memory (RAM). According to the first exemplary embodiment, as a result of a low tone processing made by the low gradation processing section  1054 , the number of density patches included in the plane portion density patch group  200  is smaller than a quasi available number of tones. This is because a number of measurement density patches is to be reduced. 
     In step S 525 , the density information obtaining section  102  obtains density information of each of the density patches recorded on the recording medium. According to the first exemplary embodiment, a measurement result of an output density of a density patch corresponding to each tone, which is measured using the density sensor, is obtained as density information. The density sensor has a measurement range illustrated in  FIG. 3 . When the plane portion density patch group  200  is selected, the measurement values in  FIG. 3  are obtained as the density information. When the vertical fine line density patch group  201  or the slant fine line density patch group  202  is selected, eight measurement values corresponding to the target tone are obtained as the density information. According to the first exemplary embodiment, the resolution of the density sensor is lower than the resolution of the input image as described above. With this, an output density corresponding to a quasi tone expressed by a plurality of pixel groups can be measured. Also, when the tone is expressed in a pixel unit, the output density can be measured considering a bleeding of a dot (ink) or a dot gain on the recording medium. 
     In step S 526 , the process branches based on whether or not the selected density patch group is plane portion. When the dot pattern is a plane portion (YES in step S 526 ), the process proceeds to step S 529 , and when the dot pattern is a fine line (NO in step S 526 ), the process proceeds to step S 527 . 
     In step S 527 , when the selected density patch group is for vertical fine line or for slant fine line, the density information correction section  103  performs a correction on the density information obtained in step S 525  to calculate a precise output density characteristic. In the case of the vertical fine line density patch  201  or the slant fine line density patch  202  illustrated in  FIG. 2B , the output density in the measurement range tends to vary easily depending on the position of the measurement range. 
     However, when the measurement range of the density sensor is wider than the distance between the fine lines, or when a plurality of fine lines is included in a measurement range like the case of the first exemplary embodiment, the measurement result measured by the density sensor and the ratio of the pixels of fine lines included in the density patch are substantially identical to each other. 
     Here, the ratio of pixels of fine lines included in a density patch is defined as the ratio of the pixels of fine lines included in the unit patterns disposed in a repeated manner in the density patch. In the vertical fine line density patch group  201 , the ratio of the pixels of fine lines is ⅓; and in the slant fine line patch group  202 , the the ratio of the pixels of fine lines is ¼. As described above, by multiplying the density information corresponding to each input tone by an inverse number of the ratio of the pixels of fine lines, the output density corresponding to the input tone can be calculated more precisely. 
       FIG. 10A  illustrates a measurement result of the vertical fine line density patch group  202 . In the figure, a plot “●” represents a measurement value of the vertical fine line density patch group  201  measured by the sensor. The measurement value is held as density information. In step S 527 , when the density information correction section  103  performs a correction, a correction value indicated by a plot “×” is obtained. The correction value illustrated in  FIG. 10A  includes a region where the output density exceeds 100%. This is caused by a dot gain phenomenon on the recording medium in which dots are recorded in a range exceeding pixels of the input image data. 
     In step S 529 , the image forming device  10  calculates the characteristic of the output density based on the density information or the corrected density information to generate a gamma correction table. As an example, a case will be described where a vertical fine line gamma correction table is generated. In the case of the vertical fine line, a corrected value of the density information is the output density corresponding to each input tone value. Based on the obtained plurality of output densities, the output densities for the not-measured input tone values are interpolated. A solid line in  FIG. 10A  represents an interpolation result. The solid line in  FIG. 10A  represents the characteristic of the output density of the pixels constituting a vertical fine line. 
     In contrast to the solid line in  FIG. 10A , a broken line in  FIG. 10B , which is obtained by exchanging the coordinate axes of the input tone value and the output density, is the gamma correction table. A gamma correction table like the solid line illustrated in  FIG. 10B  may be generated by correcting the correction table in a region where the reliability of the measurement value is low such as a low density region and a high density region. 
     In step S 530 , the image forming device  10  determines whether all gamma correction tables have been generated. According to the first exemplary embodiment, when the generation of any gamma correction table is not completed with respect to the plane portion, the vertical fine line, and the slant fine line (NO in step S 530 ), the process proceeds to step S 520  to generate another gamma correction table. 
     As described above, in the gamma correction table generation method according to the first exemplary embodiment, the correction is made on density information measured by the sensor to precisely calculate the output density corresponding to the input tone. With this, precise characteristic of the output density is obtained and an appropriate gamma correction table can be generated. 
     Also, in the density patch to be measured by the density sensor, a plurality of fine lines is disposed by repeating a unit pattern of a fine line. With this, even when the measurement position of the density sensor is displaced due to an attachment error or the like, the ratio of the dots included within the measurement range is constant. That is, by using a density patch in which a unit pattern is disposed in a repeated manner according the first exemplary embodiment, a measurement value which varies little with respect to a relative position between the sensor and the density patch can be obtained. In the density patch, the dots included in the unit pattern are separated from each other to an extent that the density is not influenced by the dots included in another unit patterns. 
     According to the first exemplary embodiment, as described above, even when the tone is represented in a pixel unit by correcting a measurement result, the output density per pixel which represents an input tone can be calculated. In particular, the measurement result is corrected based on a relationship between the pixel value of each pixel in a dot pattern and the tone represented by the dot pattern. As a result, according to the first exemplary embodiment, appropriate output density of an image of fine lines can be obtained, which is hard to measure when a conventional density sensor having a low resolution is used. The first exemplary embodiment eliminates an extra cost for adding a new sensor to generate a fine line gamma correction table. 
     A second exemplary embodiment will describe a generation of a gamma correction table for an isolated point. Different from the above-described first exemplary embodiment, an example will be described in which a gamma correction table is generated by using a high resolution density sensor having the resolution similar to that of an image data. A configuration similar to the configuration of the first exemplary embodiment is given with the same reference numeral and detailed description thereof will be omitted. 
     (Device Configuration) 
     According to the second exemplary embodiment, an image processing section  105  uses a gamma correction table for plane portion and a gamma correction table for isolated point. A gamma correction table generation section  104  generates two kinds of gamma correction tables for plane portion and for isolated point. In the case of plane portion, the dot pattern that a patch recording section  101  records for creating the gamma correction table is the plane portion density patch group  200  illustrated in  FIG. 2A . On the other hand, an isolated-point density patch group  203  illustrated in  FIG. 11  is used when creating a gamma correction table for isolated point. 
       FIG. 12  illustrates a detailed block diagram of an image processing section  105  applicable to the second exemplary embodiment. The image processing section  105  according to the second exemplary embodiment includes a gamma correction section  1053 , a screen processing section  1055 , an isolated point detection section  1058 , an isolated point gamma correction section  1059 , and selectors  1060  and  1061 . 
     According to the second exemplary embodiment, the gamma correction section  1059  performs a gamma correction and the screen processing section  1055  performs screen processing on all pixels irrespective of characteristics of each pixel. 
     The isolated point detection section  1058  detects a pixel which is an isolated point based on the processing result of the screen processing section  1055 . 
     The selector  1060  outputs information on each pixel to either the selector  1061  or the isolated point gamma correction section  1059  based on the determination result of the isolated point detection section  1058 . 
     The isolated point gamma correction section  1059  further performs a gamma correction using an gamma correction table for isolated point, on the result processed by the screen processing section  1055  with respect to the pixel which is detected by the isolated point detection section  1058  as the isolated point. 
     The selector  1061  selects an value output from the isolated point gamma correction section  1059  for the pixel detected as the isolated point; and a value output from the screen processing section  1055  for the other pixels to output an output image data. 
     The image recording operation and the gamma correction table creating operation in the image forming device according to the second exemplary embodiment will be described below.  FIG. 13A  illustrates a flowchart of the image recording operation.  FIG. 13B  illustrates a flowchart of the gamma correction table creating operation. 
     (Image Recording Operation) 
     According to the second exemplary embodiment, when the image recording operation starts, input image data is obtained in step S 501 . In step S 504 , the gamma correction section  1053  performs a plane portion gamma correction on all pixels. In step S 505 , the screen processing section  1055  performs screen processing. 
     In step S 509 , the isolated point detection section  1058  detects an isolated point from the screen processing result.  FIG. 14  illustrates conditions for detecting an isolated point. The isolated point obtained as a result of the screen processing is a pixel having an output value larger than 0, and the output values of the pixels around the isolated point are all 0. 
     In step S 510 , the process branches on each pixel based on the isolated point detection result in step S 509 . When the pixel to be processed is determined as an isolated point (YES in step S 510 ), the process proceeds to step S 511 , and when the pixel to be processed is determined as not-isolated point (NO in step S 510 ), the process proceeds to step S 508 . 
     In step S 511 , the isolated point gamma correction section  1059  performs an isolated point gamma correction on the pixel at the isolated point. The isolated point gamma correction section  1059  according to the second exemplary embodiment performs a gamma correction using a gamma correction table for isolated point. The pixel value of the pixel to be processed, which is input to the isolated point gamma correction section  1059 , has been already subjected to the plane portion gamma correction by the gamma correction section  1053 . The image data has been converted to match up with the output density of screen processing in the plane portion. Therefore, the gamma correction table for isolated point used here is generated to match up with the output density at the isolated point after cancelling the effect of the plane portion gamma correction. 
     In step S 508 , the output image data output from the selector  1061  is recorded. Generally, the formation of the isolated point tends to be unstable particularly when the image recording section  106  records the image on a recording medium using electro-photography. Therefore, as the processing flow described above illustrates, the gamma correction is made by detecting the isolated point from the result of the screen processing; thereby output density of the isolated point can be precisely adjusted. 
     (Isolated Point Density Patch) 
       FIG. 11  illustrates a density patch group to be recorded to generate a gamma correction table for isolated point. An isolated-point density patch group  203  according to the second exemplary embodiment has 3 pixels×3 pixels. Here, the measurement of the density patch at the isolated point is carried out using a high-resolution sensor. To measure the output density considering bleeding of ink and dot gain, it is desirable that the measurement is carried out including the pixel of the isolated point and eight pixels around the isolated point. Compared to the case of the density patch of the plane portion density patch group  200 , in the case of the density patch of the isolated point, the time for creating the gamma correction table can be reduced by reducing a size of the patch group  200  to the minimum necessary for the measurement. For example, to generate a gamma correction table for isolated point, same as the first exemplary embodiment, it is assumed that density patches of 10 pixels×10 pixels for the tone number are sequentially detected with a low resolution sensor to obtain the density information. In the case that a high-resolution sensor is used according to the second exemplary embodiment, since the size of the density patch requires 3 pixels×3 pixels, the time required for recording the density patch is reduced to 3/10. Further, the area used for recording the patch is reduced to 9/100. The high-resolution sensor may include a plurality of density sensors so that entire area to be measured illustrated in  FIG. 15  can be detected simultaneously. Alternatively, the density information of an entire area to be measured may be obtained by increasing the measurement times using fewer sensors than the number of points to be measured. 
     (Gamma Correction Table Generation) 
     According to the second exemplary embodiment, the gamma correction table to be generated includes two kinds; i.e., a gamma correction table for plane portion and a gamma correction table for isolated point.  FIG. 13B  illustrates a flowchart of processing for creating the gamma correction tables. 
     In step S 531 , the patch recording section  101  branches the process depending on whether the gamma correction table should be generated for all dot patterns. When a gamma correction table for entire dot pattern should be generated (YES in step S 531 ), the process proceeds to step S 5244 , and the patch recording section  101  selects a plane portion density patch group  200  or the isolated-point density patch group  203  illustrated in  FIG. 11 . The patch recording section  101  records a density patch of the selected density patch group on the recording medium. 
     In step S 532 , the process branches depending on the generation of correction table for plane portion or for isolated point. When the gamma correction table to be generated is for plane portion (YES in step S 532 ), the process proceeds to step S 533 ; and when the gamma correction table to be generated is for isolated point (NO in step S 532 ), the process proceeds to step S 534 . 
     In step S 533 , the density information of the density patch recorded in step S 524  is obtained by a density information obtaining unit using a low resolution density sensor to generate a gamma correction table for plane portion. Same as the density information obtaining unit in step S 525 , which has been described in the first exemplary embodiment, this is a measurement result of the plane portion density illustrated in  FIGS. 2A and 2B . The patch group  200  is measured by a low resolution density sensor which has a measurement range illustrated in  FIG. 3 . 
     In step S 534 , to generate a gamma correction table for isolated point, the density patch recording an isolated point patch group illustrated in  FIG. 11  is measured by a high resolution density sensor having a measurement range illustrated in  FIG. 15 . When measuring the density patch with the high resolution density sensor, since the measurement range is smaller than the pixel area of the image data, after obtaining measurement values corresponding to the pixels included in the density patch illustrated in  FIG. 15 , a plurality of measurement values are averaged to obtain the density information. This is because, in the case that the dot pattern is an isolated point, since the dot recorded on the recording medium also bleeds to the surrounding as described above, the density information of the pixels surrounding the isolated point is detected. 
     In step S 527 , the density information obtained in step S 534  is corrected using the ratio of pixels constituting the isolated points in a dot pattern included in the measurement range. The measurement range by the high-resolution sensor illustrated in  FIG. 15  is an area of 3 pixels×3 pixels. In the measurement range, the dot pattern of the isolated point is the only one pixel as illustrated in  FIG. 11 . The ratio of the dot pattern included in the range that obtains the density information is 1/9. By multiplying the inverse number of 1/9, the density information is corrected. 
     In step S 529 , a gamma correction table for each dot pattern is generated based on the input tone of the isolated point corresponding to the density information. The image processing section  105  according to the second exemplary embodiment performs a gamma correction for isolated point on the image data, which has been subjected to a gamma correction for plane portion. Therefore, a gamma correction table for isolated point is generated by combining a degamma correction table, which is generated by inversely converting a gamma correction table for plane portion to cancel a gamma correction for plane portion, and a correction table for performing a gamma correction for isolated point. In order to prevent a discontinuity of the density between the plane portion and the isolated point region, the output range is adjusted so that the value of the tone 100% of the combined correction table constantly remains 100%. 
     In step S 530 , the process returns to step S 524  to repeat the above processing low until the gamma correction tables for the plane portion and for the isolated point have been generated. 
     When the processing flow for creating only a gamma correction table for isolated point is selected in step S 535  (YES in step S 535 ), the processing flow is similar to that of the above-described generation of the gamma correction table for isolated point. 
     In the description of an example made above, the processing flow chart for simultaneously creating a correction table for isolated point and a correction table for plane portion, and the processing flow chart for creating only a correction table for isolated point are carried out at a different timing. In the image forming device, the isolated point varies largely. Accordingly, with the configuration as described above, a gamma correction table for isolated point is generated more frequently than in a conventional generation of a gamma correction table. With this, a precise correction table matching up with the condition of the image forming device can be generated. Also, by using a high-resolution sensor for creating a correction table for isolated point, which is generated frequently, the time for creating a correction table and the area on a recording medium can be reduced. 
     A description will be made on a third exemplary embodiment of the gamma correction table generation method according to the invention below. According to the third exemplary embodiment, the accuracy of a gamma correction table for plane portion is increased by appropriately correcting a measurement result of a high-density patch for plane portion in a low density portion. 
     (Device Configuration) 
     Since the configuration of an image forming device according to the third exemplary embodiment is similar to the image forming device according to the first exemplary embodiment illustrated in  FIG. 1 , a part of description of image forming device according to the third exemplary embodiment will be omitted. 
       FIG. 16  illustrates a detailed block diagram of an image processing section  105  according to the third exemplary embodiment. The image processing section  105  according to the third exemplary embodiment includes a gamma correction section  1053  and a screen processing section  1055 . 
     The gamma correction section  1053  performs a gamma conversion of an image data based on a gamma correction table for plane portion. 
     The screen processing section  1055  performs screen processing illustrated in  FIG. 8 . As described above, a dot pattern, which is obtained by performing the screen processing, represents the tone in a unit cell of a plurality of pixels, in a quasi manner. 
     As described above, the image processing section  105  according to the third exemplary embodiment performs a gamma correction using only a single gamma correction table. The patch recording section records a density patch on a recording medium using a density patch group illustrated in  FIG. 17  to measure the density. A gamma correction table generation section  104  generates a gamma correction table based on the measurement result. In the density patch group illustrated in  FIG. 17 , low density patches included in the plane portion density patch group  200  illustrated in  FIG. 2A  are replaced with a high-density patch group  1700 . The low density patches here replaced with the high-density patch groups  1700  are dot patterns representing a tone  20  and a dot pattern representing a tone  38 . Each of the high-density patches has a density patch in which the dot density is higher than the resolution of the corresponding low density patches illustrated in  FIG. 2A . 
     The dot pattern representing a low density tone in the plane portion density patch group  200  illustrated in  FIG. 2A  has a small dot density. When the measurement range of the low resolution sensor illustrated in  FIG. 3  is displaced, the number of the dots included in the measurement range changes and the measured density changes. 
     Therefore, a high-density patch having a high dot density is recorded on the recording medium. Even when the measurement position of the low resolution sensor is slightly displaced, almost the same number of dots is included in the measurement range. With this, measurement result, which is little influenced by a positional displacement of the density sensor, can be obtained. 
     The measurement result obtained by the density sensor includes sensor noises or noises due to a roughness of the base surface of the recording medium or unevenness of the density. Therefore, in a density patch corresponding to a low density tone, since the output density is small and the influences due to the noises relatively get larger, it may be hard to obtain an effective measurement value. According to the third exemplary embodiment, a high-density patch is used in a low density portion; thereby the influences due to the noises are relatively reduced. The measured result is corrected by the density information correction section  103 . Thus, a high accurate gamma correction table can be generated. 
     The method for creating a high-density patch will be described in detail below. The dot patterns included in the plane portion density patch group  200  illustrated in  FIG. 2A  are formed based on the result of the screen processing illustrated in  FIG. 8  on a plane image having a uniform tone. Therefore, in the density patch, the number and the appearance position of dots are identical in each of the cells. 
     In the high-density patch group, dots are disposed with a higher density while maintaining the configuration of the dots in the low density dot pattern. In particular, as illustrated in  FIG. 18 , the distance L 0  and L 0 ′ between the dots in the adjacent cells is reduced to L 1  and L 1 ′; thus, a high-density patch group is generated. By reducing the distance among the dots, a part of the cells forming the dot pattern has a region overlapping with each other. Therefore, the ratio of the dots included in the density patch increases to be higher than the resolution of the original density patch. 
     The ratio of the dots included in the density patch can be calculated based on the ratio of the distance between the dots; i.e., (L 0 ×L 0 ′/L 1 ×L 1 ′). That is, the dot density in a high-density patch is (L 0 ×L 0 ′/L 1 ×L 1 ′) times the dot density in an ordinary density patch. For example, the dot density in a high-density patch corresponding to the tone  20  is approximately 2.6 times density patch corresponding to the tone  20 ; and approx. 1.6 times the density patch corresponding to the tone  38  illustrated in  FIG. 2A . 
     However, when the distance between the dots is too close to each other in creating a high-density patch, the output density of the respective dots is influenced. In the high-density patch, the dots are separated from each other to an extent that the output density is not influenced. According to the third exemplary embodiment, the dot pattern of the high-density patch is generated with the dots separated from each other by 2 pixels or more. The distance between the disposed dots can be obtained based on an experimental result. 
     As described above, in the high-density patch, the cells as a unit dot pattern are periodically disposed and overlap with each other to increase the output density. Further, since the dots are separated from each other to an extent that no influence is exerted on each other, a desired output density of the density patch can be calculated by performing a correction. 
       FIGS. 19A and 19B  illustrate processing flowcharts in the image forming device according to the third exemplary embodiment. In the process illustrated in  FIGS. 19A and 19B , since a process which has a the same name and reference numeral is a similar process as the process in the processing flowchart illustrated  FIGS. 5A, 5B, 13A and 13B , the description thereof will be omitted. 
     (Image Recording Operation) 
     In the image recording operation according to the third exemplary embodiment, after obtaining an image data, the image data is subjected to a gamma correction and a screen processing and hen record. The description of each stage will be omitted. 
     (Gamma Correction Generation Operation) 
     Referring to a processing flowchart illustrated in  FIG. 19B , a gamma correction table creating operation according to the third exemplary embodiment will be described below. 
     In step S 520 , a generation of a gamma correction table starts. 
     In step S 524 , a patch recording section  101  selects a density patch group and records the density patch on a recording medium. According to the third exemplary embodiment, a density patch group illustrated in  FIG. 17  is selected. Density patches  1700  corresponding to a low density tone are high-density patches in which dots are disposed at a high density. In step S 525 , a density information obtaining section  102  obtains a density patch recorded on the recording medium as density information based on a measurement result measured by a density sensor. According to the third exemplary embodiment, a density sensor having a measurement range illustrated in  FIG. 3  is used. Here, 13 pieces of density information corresponding to different tones are obtained. 
     In step S 536 , the density information correction section  103  determines whether the density information should be corrected on each obtained density information. The determination is made based on the tone value corresponding to the density information to be processed; i.e., whether the value is equal to or smaller than a predetermined value. Here, the predetermined value means a tone value corresponding to a previously generated high-density patch. 
     In step S 527 , the density information correction section  103  corrects density information, the tone value of which is determined to be equal to or smaller than the predetermined value in step S 536  (YES in step S 536 ); i.e., corrects the density information obtained by measuring a high-density patch. In the case of the high-density patch group  1700 , the dots are disposed at a density higher than the resolution of a desired dot pattern to be measured. The desired dot pattern to be measured means a dot pattern obtained through a screen processing made by the screen processing section  1055 . Therefore, it is necessary to correct the obtained density information. 
     As described above, the dot density in the high-density patch corresponding to the tone  20  is approximately 2.6 times, and approximately 1.6 times the density patch corresponding to the tone  38  illustrated in  FIG. 2A . Also, each of high-density patches does not influence the output density of the respective dots. 
     As for the density information corresponding to the tone  20 , the output density to be obtained can be calculated by multiplying the density information by an inverse number of 2.6. As for the density information corresponding to the tone  38 , the output density to be obtained can be calculated by multiplying the density information by an inverse number of 1.6.  FIG. 20A  illustrates a measurement value for each tone value obtained by the density information obtaining section  102  and a correction value obtained by the density information correction section  103 . 
     When the measurement for each tone is completed in step S 528  (YES in step S 528 ), the gamma correction table generation section  104  generates a gamma correction table in step S 529 . A solid line illustrated in  FIG. 20A  represents a characteristic of the output density obtained based on the measurement value and the correction value. As for the tone of the output density which is not measured, a curve is obtained by performing an interpolation. By performing an inverse conversion on the characteristic of the output density, an appropriate gamma correction table can be generated.  FIG. 20B  illustrates a gamma correction table generated according to the third exemplary embodiment. 
     In the third exemplary embodiment, a creating method of a gamma correction table has been described which can enhance the accuracy in a low density portion in the gamma correction table by correcting the density information based on the ratio of the dot pattern in a range for obtaining the density information. 
     In the third exemplary embodiment, an example of a dot concentrated type screen processing has been described. However, a similar effect can be also obtained through a dot dispersion type screen processing. 
     In the above-described exemplary embodiments, the patch recording section  101  is provided separate from the image recording section  106 . However, when the density patch on a recording medium is measured, the image forming device may be configured such that the image recording section  106  records a density patch. 
     The present disclosure can be achieved by supplying a storage medium storing computer program code of software that executes the functions described in the above exemplary embodiments, to a system or an apparatus. In this case, the functions described in the above exemplary embodiments are achieved by a computer (CPU, micro processing unit (MPU), or the like) in the system or apparatus that reads out the computer program code stored in a computer readable storage medium. 
     According to the disclosure, the output density on a recording medium is measured by a sensor, and the measurement result is appropriately corrected; thereby an accurate gamma correction table is generated. 
     Other Embodiments 
     Embodiments of the present disclosure can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions recorded on a storage medium (e.g., a non-transitory computer-readable storage medium) to perform the functions of one or more of the above-described embodiment(s) of the present disclosure, and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiment(s). The computer may comprise one or more of a CPU, MPU, or other circuitry, and may include a network of separate computers or separate computer processors. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, a memory card, and the like. 
     While the present disclosure has been described with reference to exemplary embodiments, it is to be understood that the disclosure is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.