Abstract:
An image correction apparatus and method enable correcting an image so that the image is always discernible and at least text can be read regardless of user settings. A correction range that increases the gray level and a correction range that decreases the gray level are calculated for each image to calculate the correction range suitable for the particular image.

Description:
RELATED APPLICATIONS  
       [0001]     Japanese patent application No. 2005-334994 is hereby incorporated by reference in its entirety.  
       BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention relates to an image correction apparatus and an image correction method for correcting gradation values in image data.  
         [0004]     2. Description of the Related Art  
         [0005]     A digital image is an image in which the value of each pixel is represented as a single sample, typically composed of shades of gray, varying from black at the weakest intensity to white at the strongest. Gray-scale images intended for visual display are typically stored with 8 bits per sampled pixels, thereby allowing 256 intensities (i.e. shades of gray, or gray-scale levels, or gray levels) to be recorded. A color image may be recorded, for example, with 24 bits per pixel, e.g. RGB (red, green, blue) 8:8:8. The terms “gray-scale level” and “gray level” will be used interchangeably herein.  
         [0006]     Image correction methods that correct the gradation level (gray level) of digital images presented on a monitor or other type of image display device according to a user setting are known from the literature. Images can be corrected as needed by the user by adjusting the gray level of the value of the pixels forming the image. Various methods can be used to correct the brightness (value) information in digital images, and gamma correction is one method of correcting image brightness and contrast by adjusting the gamma curve. The gamma curve is a function representing the relationship between the gray level of the input signal on the x-axis and the gray level of the output signal on the y-axis. As shown in  FIG. 10 , for example, if the input signal on the x-axis and the output signal on the y-axis can range from 0 (dark) to 255 (light) and the gamma curve  50  is a ramp with a slope of 45°, the input value and the output value are the same and no gamma correction is applied. Image brightness and contrast can be precisely adjusted by adjusting this gamma curve.  
         [0007]     Referring to  FIG. 11  and Japanese Unexamined Patent Appl. Pub. 2005-77638, when the gamma curve  51  is in the domain under the ramp with a slope of 45° (such as when the gamma curve (called a “tone curve” in the cited application) is downwardly concave with a low slope on the low gray level side and a steep slope on the high gray level side), the range of gray scale values in the image is compressed into the low gray level domain and the overall image becomes darker. Conversely, when the gamma curve  52  is in the domain above the ramp (such as when the gamma curve is upwardly concave with a steep slope on the low gray level side and a gradual slope on the high gray level side), the range of gray scale values in the image expands into the high gray level domain and the overall image becomes brighter.  
         [0008]     The gamma function f(x) gives the curve of the brightness correction afforded by the gamma curve. The gamma function resulting in the lowest image brightness (black) is f(x)=0 as denoted by curve (straight line in this instance)  53  in  FIG. 12 , and the gamma function resulting in the greatest image brightness (white) is f(x)=255 as denoted by curve (straight line in this instance)  54  in  FIG. 12 . However, if gamma correction ranges from f(x)=0-255 and gamma is set to f(x)=0, gray level 0 will be output for all input values, the output image will be the darkest displayable image, that is, completely black, and no image details will be discernible. Likewise, if gamma correction is set to f(x)=255, gray level 255 will be output for all input values, the output image will be the brightest displayable image, that is, completely white, and no image details will be discernible.  
         [0009]     The correction range is therefore reduced to enable converting the input image to a usable output image and not output a completely black or a completely white image. More specifically, displaying a completely black or a completely white image is prevented by not applying gamma correction using specific functions including f(x)=0 and f(x)=255 indicated by the shaded areas (a) and (b) in  FIG. 11 .  
         [0010]     However, when the correction range is limited as described above, the correction range (c) in  FIG. 11  for brightening an image that is dark overall is the same size as the correction range (d) in  FIG. 11  for darkening an image that is bright overall regardless of the actual image brightness level because the correction range is limited so that the center of the correction range is a simple line with a slope of 45°, even though the correction needed to brighten (darken) an image that is dark (light) overall is greater than the correction needed to darken (brighten) the image.  
         [0011]     If the correction range for increasing image brightness and the correction range for decreasing image brightness are the same size, the correction process may needlessly brighten an image that is light overall (such as a source image that contains text) where the correction needed to further brighten the image is less than the correction needed to darken the image. More specifically, depending upon the user settings, conversion using a function f(x) that brightens the image more than the correction range that is actually appropriate to the image may be needlessly applied. This also applies to images that are dark overall. The resulting image may therefore not enable reading individual characters in a block of text, for example, due to image whiteout or blackout.  
         [0012]     The image correction apparatus and image correction method of this invention enable correcting images so that image recognition, and particularly reading text in the image, is possible regardless of the user settings.  
       SUMMARY OF THE INVENTION  
       [0013]     An image correction apparatus according to a first embodiment of the invention for correcting the gray level of pixels in an image includes a controller that computes a correction range for an image by separately calculating for the image a correction range for increasing the gray levels and a correction range for decreasing the gray levels.  
         [0014]     Preferably, the controller determines the correlation between the gray levels before correction and the gray levels after correction, and computes the correction range so that the correlation when the gray levels increase and the correlation when the gray levels decrease are asymmetric.  
         [0015]     Yet further preferably, the gray levels representing the pixels in the image include 256 gray levels ranging from 0 to 255 where the bit depth of each pixel is 8 bits. The controller calculates a statistical count of each of the 256 gray levels for a plurality of pixels, calculates a first total by accumulating the statistical counts starting from value 0 and a second total by accumulating the statistical counts starting from value 255, calculates a value for determining a correction range for increasing the gray levels and calculates a value for determining a correction range for decreasing the gray levels, calculates a correction range that decreases the gray level based on the value at which the first total exceeds the value for determining the correction range for increasing the gray levels, and calculates a correction range that increases the gray level based on the value at which the second total exceeds the value for determining the correction range for decreasing the gray level.  
         [0016]     Yet further preferably, the value for determining a correction range for increasing the gray levels and the value for determining a correction range for decreasing the gray levels are acquired by weighting using the total from value 0 to 127 and the total from value 255 to 128.  
         [0017]     An image correction method according to another embodiment of the invention has a first calculation step that calculates a correction range for increasing the gray levels and a correction range for decreasing the gray levels; and a second calculation step that calculates a correction range for the image based on the correction range for increasing the gray level and the correction range for decreasing the gray level that were calculated in the first calculation step.  
         [0018]     Preferably, each pixel in the image can be represented by one of 256 gray levels ranging from 0 to 255 where the bit depth of each pixel is 8 bits, and the first calculation step calculates a statistical count of the 256 gray levels for a plurality of pixels, calculates a first total by accumulating the statistical counts starting from value 0 and a second total by accumulating the statistical counts starting from value 255, calculates a value for determining a correction range for increasing the gray levels and calculates a value for determining a correction range for decreasing the gray levels, calculates a correction range that decreases the gray level based on the value at which the first total exceeds the value for determining the correction range for increasing the gray levels, and calculates a correction range that increases the gray levels based on the value at which the second total exceeds the value for determining the correction range for decreasing the gray level.  
         [0019]     Yet further preferably, the value for determining a correction range for increasing the gray levels and the value for determining a correction range for decreasing the gray levels are acquired by weighting using the total of value 0 to 127 and the total from value 255 to 128.  
         [0020]     By separately calculating for each image a correction range that increases the gray level and a correction range that decreases the gray level, the correction range can be adjusted to the gray levels in the original image.  
         [0021]     Furthermore, by calculating the correction range so that the curve on the side increasing the gray level and the curve on the side decreasing the gray level are asymmetrical, the correction range for increasing the gray level and the correction range for decreasing the gray level can be calculated according to the brightness (value) distribution in the original image.  
         [0022]     Furthermore, because the correction range for decreasing (increasing) the gray level is calculated from brightness (value) information with a high (low) gray level when the gray level of the original image overall is high (low), a gamma range that is appropriate to the correction required by the original image can be calculated. More specifically, because the correction range that is not required by the original image is cut off and correction is limited to the required correction range, an image that is always readable can be output with no whiteout or blackout.  
         [0023]     Furthermore, because the value for determining the correction range increasing the gray level and the value for determining the correction range decreasing the gray level are weighted before the correction range is determined, a correction range that is more appropriate to the original image data can be calculated even when the gray level of the original image is biased to a high gray level or a low gray level.  
         [0024]     Other objects and attainments together with a fuller understanding of the invention will become apparent and appreciated by referring to the following description and claims taken in conjunction with the accompanying drawings. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0025]      FIG. 1  is a block diagram showing the control structure of a host computer and printer according to a preferred embodiment of the present invention.  
         [0026]      FIG. 2A  shows the image of a deposit slip (check) inserted to the printer of the preferred embodiment, and  FIG. 2B  shows an enlarged portion of the check.  
         [0027]      FIG. 3  is a flow chart of the correction process executed by the host computer  1 .  
         [0028]      FIG. 4  is a flow chart of the process for calculating statistical counts of the gray levels and totaling the statistical counts.  
         [0029]      FIG. 5  is a flowchart of the process for acquiring the correction range for brightening the image and the correction range for darkening the image.  
         [0030]      FIG. 6  shows a histogram generated from the statistical counts of the gray levels from the check.  
         [0031]      FIGS. 7A-7F  show the luminance correction range defined by the resulting gamma curves.  
         [0032]      FIG. 8A  shows another example of a check inserted into the printer of the preferred embodiment, and  FIG. 8B  shows a portion of the check enlarged.  
         [0033]      FIG. 9  shows the histogram generated from the statistical counts of the gray levels from the check shown in  FIG. 8 .  
         [0034]      FIG. 10  shows a gamma curve when no image correction is applied.  
         [0035]      FIG. 11  shows the gamma curves for f(x)=0 and f(x)=255.  
         [0036]      FIG. 12  shows the gamma curves defining the correction range of the related art. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0037]     Preferred embodiments of an image correction apparatus and image correction method according to the present invention are described below with reference to the accompanying figures using by way of example a host computer connected to a printer that has an image reading function.  
         [0038]     Internal Arrangement of the Host Computer and Printer  
         [0039]      FIG. 1  is a block diagram showing the general structure of the host computer  1  and printer  10  according to this embodiment of the invention.  
         [0040]     The printer  10  in this embodiment of the invention is a hybrid printer that can print on both the front and back sides of slips such as checks and can also print on roll paper for issuing sales receipts, for example. The printer  10  is in communication with an external host computer  1 , and operates according to commands received from the host computer  1  to print and scan images.  
         [0041]     The host computer  1  also executes processes based on data output by the printer  10  and received through the communication interface  2  from the printer  10 .  
         [0042]     A scanner  8  located in a slip transportation path (not shown) in printer  10  scans checks conveyed through the slip transportation path. A data transmitter  9  then outputs the captured image data to the host computer  1 .  
         [0043]     The host computer  1  includes a receive buffer  3 , a gray level controller  5 , a correction range controller  6 , a display  7 , and a main controller  4  that controls host computer  1  operation. The communication interface  2  is an interface enabling communication with the printer  10 . All image data received from the printer  10  and all data sent from the host computer  1  to the printer  10  passes through this communication interface  2 . The receive buffer  3  is a temporary storage for temporarily storing image data sent by the data transmission unit  9  of the printer  10 .  
         [0044]     The gray level controller  5  calculates statistical counts of the gray levels of the pixels in the image scanned by the scanner  8 , and calculates a total of these statistical counts. The gray level of a pixel will be used in the present invention for lightening an image and for darkening the image. Each pixel in this embodiment is represented by eight bits and thus can be represented by one of 256 gray levels, ranging from 0 to 255.  
         [0045]     The correction range controller 6 calculates the correction range for increasing image brightness (brightening the image) and the correction range for decreasing image brightness (darkening the image) based on the gray levels received from the gray level controller  5 . The correction range for increasing image brightness and the correction range for decreasing image brightness do not have the same area in this invention, and the correction ranges are more particularly calculated so that the content of the image data presented on the display  7  is discernible regardless of the user setting. The display  7  displays image data corrected within these correction ranges.  
         [0046]     The main controller  4  is the central controller of the host computer  1  and includes the gray level controller  5  and correction range controller  6 , which execute specific operations. The main controller  4  controls certain operations of the host computer  1  based on the results of calculations performed by the gray level controller  5  and correction range controller  6 . In this embodiment the controller  4  also corrects the image data within the correction range calculated by the correction range controller  6  and displays the corrected image data on the display  7 .  
         [0047]     Image Correction Process  
         [0048]     The general image correction process executed by the host computer  1  in this embodiment of the invention is described next with reference to  FIG. 2 ,  FIG. 3 , and Tables 1 to 3. Tables 1 to 3 are appended to the end of the specification.  
         [0049]      FIG. 2A  shows a typical deposit slip (check)  20  that is inserted into the printer  10 , and  FIG. 2B  shows an enlarged portion  21  of the check in  FIG. 2A .  
         [0050]      FIG. 3  is a flow chart of the image correction process executed by the host computer  1  in this embodiment.  
         [0051]     Tables 1 to 3 show the statistical count A that is calculated for the 256 gray levels 0 to 255 in the image data of the check  20 , cumulative totals B 1  and B 2 , and values C 1  and C 2  for determining the correction range. Note that images in this embodiment are represented using an 8-bit 256-level gray scale ranging from 0 (dark (black)) to 255 (bright (white)). The gray level is referred to a “luminance level” in the tables.  
         [0052]     The invention can also be applied to color images. If color images are processed, the color image data is preferably first converted to gray scale image data where BW=0.2999R+0.587G+0.114B, and the gray scale image data is then processed.  
         [0053]     When a user inserts a check  20  into the insertion slot (not shown) of the printer  10 , the scanner  8  scans the check  20  and the data transmission unit  9  sends the captured image data to the host computer  1 . As shown in  FIG. 2B , the scanner  8  resolves the check  20  image to R pixels as defined by a preset image resolution R and reads the gray level (the luminance value of pixel  22  shown in  FIG. 2B  is 254) of the R pixels to convert the scanned image to image data.  
         [0054]     When image data is received through the communication interface  2  (step S 1  returns Yes), the host computer  1  temporarily stores the image data in the receive buffer  3 . The gray level controller  5  then calculates statistical counts for each of the 256-level gray scale levels for all pixels, and adds the calculated statistical counts to calculate the total (step S 2 ).  
         [0055]     This embodiment is described as calculating statistical counts of each gray level for every pixel in the check  20  image where resolution R=162,074. It is not always necessary to acquire the gray level for all pixels, however, as long as there are enough gray levels to determine a uniform statistical distribution of gray levels in the entire image. For example, pixels in the check  20  image could be sampled in a checkered pattern to acquire the gray level of every other pixel instead of every pixel.  
         [0056]     The correction range controller  6  then calculates a correction range for brightening the image and a correction range for darkening the image based on the statistical counts of the 256 gray levels (step S 3  and step S 4 ), and calculates a luminance correction range. The controller  4  then corrects the image data in the calculated correction range according to the user-defined luminance setting, and displays the image on the display  7  (step S 5 ). Note that steps S 3  and S 4  can be reversed so that the correction range for darkening the image is calculated before the correction range for brightening the image.  
         [0057]     Process for Acquiring Statistical Counts for the Gray Level  
         [0058]     The process for calculating the totals of the gray levels in step S 2  in  FIG. 3  is described next with reference to  FIG. 4 ,  FIG. 6 , and Tables 1 to 3.  FIG. 4  is a flow chart of the process for calculating statistical count A and total B 1  (B 2 ).  FIG. 6  shows a histogram generated from the statistical counts of the gray levels from the check  20 . Tables 1 to 3 show the statistical count A that is calculated for every n luminance (gray) level ranging from 0 to 255, cumulative totals B 1  and B 2 , and values C 1  and C 2  for determining the correction range.  
         [0059]     The gray level controller  5  reads the 8-bit gray level (luminance value) of the first pixel (x=1) read from the gray levels for the R=162,074 pixels stored in the receive buffer  3  to acquire gray level n (steps S 11 , S 12 ). The counter for the gray level n of the first pixel in gray level 0-255 is then increased by 1. The gray level n of the pixel read second (x=x+1=2) is then acquired and the counter for the gray level n of this second pixel is incremented 1 (step S 14  returns No, step S 15 , step S 12 , step S 13 ). For example, because the gray level n of pixel  22  in  FIG. 2  ( b ) is 254, a bright gray level, the gray level controller  5  increments the counter (not shown) for gray level 254 (of gray levels 0 to 255) corresponding to the gray level n of pixel  22  by one. As a result, the statistical count A for gray level n=254 in Table 1 is increased by 1.  
         [0060]     Once these steps repeat and statistical count A (that is, the count) is obtained from the gray level for all pixels (when x=R), statistical count A is accumulated sequentially from gray level n=0 (black) to gray level n=127 to calculate total B 1  (the left side of Tables 1, 2, and 3, beginning with Table 1). Total B 2  (the right side of Tables 1, 2, and 3, beginning with Table 3) is likewise calculated by accumulating statistical count A sequentially from gray level n=255 (white) to gray level n=128 (step S 14  returns Yes, step S 16 ).  
         [0061]     As shown by the histogram in  FIG. 6 , if the gray levels 0 (black) to 255 (white) are plotted on the x-axis and statistical count A is on the y-axis, there is substantially no dark gray level, the curve starts to rise from approximately gray level n=230, and the curve peaks at gray level n=254. This means that the image data for the check  20  overall contains little dark gray levels and contains mostly bright gray levels.  
         [0062]     Acquiring the Correction Range for Brightening the Image and the Correction Range for Darkening the Image  
         [0063]     Step S 3  in  FIG. 3  for determining the correction range for brightening the image and step S 4  for determining the correction range for darkening the image are described in further detail below with reference to  FIG. 5  and Tables 1 to 3.  FIG. 5  is a flow chart describing the process for determining the correction range for brightening the image or correction range for darkening the image.  
         [0064]     Step S 3  for acquiring the correction range for brightening the image is described first.  
         [0065]     The correction range controller  6  calculates value C 1  for acquiring the correction range for brightening the image (step S 21 ). This value C 1  for acquiring the correction range for brightening the image can be calculated using the following equation.
 
 C 1=(128 −n )* B 1/128
 
         [0066]     where n is the gray level (0&lt;=n&lt;=127) and B 1  is the cumulative total for n.  
         [0067]     The gray level n where B 1 &gt;C 1  is then stored (step S 22  returns Yes).  
         [0068]     As indicated by arrow X in Table 2, the gray level n where B 1 &gt;C 1  in the image of check  20  is n=80, and the value 80 is therefore stored.  
         [0069]     The correction range value L 1  for increasing image brightness from the stored gray level n is then calculated (step S 23 ). The correction range value L 1  for increasing image brightness can be calculated using the following equation.
 
 L 1=128 −n 
 
         [0070]     where n is the gray level at which B 1 &gt;C 1 .  
         [0071]     In the check  20  image in this example L 1 =128−80=48 is obtained as the correction range value for brightening the image. The resultant correction range for brightening the image is expressed in gray value levels as 128&lt;=n&lt;=176 (176=128+48). Thus, for this generally bright image, the brightening range does not extend to gray level values at the brightest end of the scale.  
         [0072]     The value C 2  for determining the correction range for darkening the image can be determined using the following equation.
 
 C 2=( n− 127)* B 2/128
 
         [0073]     where n is the gray level (128&lt;=n&lt;=255) and B 2  is the cumulative total for n.  
         [0074]     The gray level n where B 2 &gt;C 2  is then stored.  
         [0075]     As indicated by arrow Y in Table 1, B 2 &gt;C 2  at gray n=233 in the image of this check  20 , and the value 233 is therefore stored.  
         [0076]     The correction range value L 2  for darkening the image can be calculated as follows.
 
 L 2 =n −127
 
         [0077]     where n is the gray level at which B 2 &gt;C 2 .  
         [0078]     In the check  20  image in this example L 2 =233−127=106 is obtained as the correction range value for darkening the image. The resultant correction range for darkening the image is expressed in gray value levels as 21&lt;=n &lt;=127 (21=128−106). Thus, for this generally bright image, the darkening range does not extend to gray level values at the darkest end of the scale.  
         [0079]     In this embodiment of the invention the value C 1  for determining the correction range for brightening the image is weighted by the cumulative total for low gray levels n=0 to 127, the value C 2  for determining the correction range for darkening the image is weighted by the cumulative total for high gray levels n=255 to 128, and the average is then calculated. As a result, a correction range that more appropriately reflects the actual image data read can be determined even if the scanned image contains a biased gray level distribution with mostly bright gray level as shown by the histogram in  FIG. 6 .  
         [0080]     By thus separately calculating the correction range value L 1  for brightening the image from the cumulative total of the dark gray levels n=0 to 127, and the correction range value L 2  for darkening the image from the cumulative total of the bright gray levels n=255 to 128, the correction range for brightening the image is reduced (from the maximum, brightest, gray level value 255) and the correction range for darkening the image is increased (from the minimum, darkest, gray level value 0) when the scanned image is light overall, and a correction range appropriate to the correction required for the image of the check  20  can be calculated. More specifically, because the correction range that is unsuitable for the check  20  image is dropped and correction is limited to the appropriate correction range, a readable image can be consistently presented without whiteout or blackout.  
         [0081]      FIG. 7  shows the gamma curves of the luminance correction range acquired from this process with the gray level input values on the x-axis and the output values of the corrected gray level on the y-axis.  FIG. 7A  shows the gamma curve  31  when the image correction value set by the user using the host computer  1  is 127,  FIG. 7B  shows the curve  32  when the image correction setting is 192,  FIG. 7C  shows the curve  33  when the image correction setting is 255,  FIG. 7D  shows the curve  34  when the image correction setting is 64,  FIG. 7E  shows the curve  35  when the image correction setting is 0, and  FIG. 7F  shows the curves when the gamma correction curves for image correction settings of 0 and 255 are plotted together.  
         [0082]     As shown in  FIG. 7F , by separately calculating the correction range VALUE L 1  for brightening the image and the correction range VALUE L 2  for darkening the image, the gamma curve  33  for a correction setting of 0 and the gamma curve  35  for a correction setting of 255 defining the correction range  36  are asymmetric.  
         [0083]     As described above, by removing more of the correction range that results in excessive image brightness than the correction range that results in excessive image darkness when the scanned image is light overall, a usable readable image can be consistently displayed without causing whiteout regardless of the correction level set by the user as shown in  FIG. 7A , B, and C. Likewise, by removing more of the correction range that results in excessive image darkness than the correction range that results in excessive image brightness when the scanned image is dark overall, a usable readable image can be consistently displayed without causing blackout regardless of the correction level set by the user.  
         [0084]     Because the statistical counts of the gray level are biased in this example, the value C 1  for determining the correction range for brightening the image and the value C 2  for determining the correction range for darkening the image are weighted by totals B 1  and B 2 , respectively, before taking the average, but other calculation methods can be used instead.  
         [0085]     For example, if the check  40  is dark overall as shown in  FIG. 8A  and the luminance level n of pixel  42  is a dark gray level of 10 as shown in  FIG. 8B , in the group of counters (not shown) for gray levels n=0 to 255 the gray level controller  5  increments the counter for n=10 by one (step S 13 ), and the histogram generated from the counts of the gray level for all pixels (step S 14  returns Yes) appears as shown in  FIG. 9 .  
         [0086]     If the gray levels 0 (dark) to 255 (bright) are on the x-axis and the statistical count totals are on the y-axis, there is substantially no dark gray level, the peak is at an intermediate luminance level between n=127 and n=140, and the curve gradually decreases from luminance level n=140 to n=255. When the distribution of statistical counts is not particularly biased and the distribution is wide, the simple average can be taken.  
         [0087]     More specifically, the correction range controller  6  can calculate the value Cl for determining the correction range for brightening the image as follows.
 
 C 1 =E 1/10
 
         [0088]     where E 1  is the sum of all n=0 to 127.  
         [0089]     The luminance level n at which B 1 &gt;C 1  where B 1  is the total for a given n is then stored.  
         [0090]     The correction range controller  6  can calculate the value C 2  for determining the correction range for darkening the image as follows.
 
 C 2 =E 2/10
 
         [0091]     where E 2  is the sum of all n=255 to 128.  
         [0092]     The luminance level n at which B 1 &gt;C 1  where B 1  is the total for a given n is then stored.  
         [0093]     This embodiment of the invention is described using a pixel depth of 8 bits and 256 gray levels, but the invention is not so limited and can be used with an m-bit pixel depth, that is, 2 m  gray levels. In this case a first total accumulated from 0 and a second total accumulated from 2 m−1  are calculated. Further preferably, the totals from 0 to 2 m−1 −1 and from 2 m −1 to 2 m−1  are used for weighting.  
         [0094]     While the invention has been described in conjunction with several specific embodiments, it is evident to those skilled in the art that many further alternatives, modifications and variations will be apparent in light of the foregoing description. Thus, the invention described herein is intended to embrace all such alternatives, modifications, applications and variations as may fall within the spirit and scope of the appended claims.  
                                                                                     TABLES 1                       n   A           n   A                   LUMINANCE   STATISTICAL   B1       LUMINANCE   STATISTICAL   B2       LEVEL   COUNT   TOTAL   C1   LEVEL   COUNT   TOTAL   C2                                0   0   0   8839.0   250   0   0   153235.0           1   0   0   8769.9   254   70309   70309   152037.9       2   0   0   8700.9   253   4183   74492   150840.7       3   0   0   8631.8   252   4110   78602   149643.6       4   0   0   9562.8   251   447   79049   148446.4       5   0   0   8493.7   250   4177   83226   147249.3       6   0   0   8424.7   249   4201   87427   146052.1       7   0   0   8355.6   248   2254   89681   144855.0       8   0   0   8286.6   247   2743   92424   143657.8       9   0   0   8217.5   246   3770   9194   142460.7       10   0   0   8148.5   245   3058   99252   141263.5       11   0   0   8079.4   244   2691   101943   140066.4       12   0   0   8010.3   243   3210   105153   138869.2       13   0   0   7941.3   242   2754   107967   137672.1       14   0   0   7872.2   241   2719   110626   136474.9       15   0   0   7803.2   240   2826   113452   135277.8       16   0   0   7734.1   269   2519   115971   134080.6       17   0   0   7665.1   238   2247   118218   132883.5       18   0   0   7596.0   237   2241   120459   131686.3       19   0   0   7527.0   236   2450   122909   130489.2       20   0   0   7457.9   235   1898   124807   129292.0       21   0   0   7388.9   234   1667   126474   128094.9       22   0   0   7319.8   233   1790   128264   126897.7             Y       23   0   0   7250.7   232   1626   129890   125700.6       24   0   0   7181.7   231   1438   131328   124503.4       25   0   0   7112.6   230   1199   132527   123306.3       26   0   0   7043.6   229   1163   133690   122109.1       27   0   0   6974.5   228   1136   134826   120912.0       28   0   0   6900.5   227   947   135773   119714.8       29   0   0   6834.4   226   817   136590   118517.7       30   0   0   6767.4   225   851   137441   117320.5       31   0   0   6698.3   224   779   138220   116123.4       32   0   0   6629.3   223   710   138930   114926.3       33   0   0   6560.2   222   572   139502   113729.1       34   1   1   6491.1   221   657   140159   112532.0       35   2   3   6422.1   220   464   140623   111334.8       36   2   5   6353.0   219   511   141134   110137.7       37   1   6   6284.0   218   449   141583   108940.5       38   9   15   6214.9   217   409   141992   107743.4       39   5   20   6145.9   216   323   142315   106546.2       40   7   27   6076.8   215   387   142702   105349.1       41   29   56   6007.8   214   298   143000   104151.9       42   28   84   5938.7   213   26   143276   102954.8       43   14   98   5869.6   212   264   143540   101757.6       44   33   131   5800.6   211   250   143790   100560.5       45   51   182   5731.5   210   235   144025   99363.3       46   49   231   5662.5   209   227   144252   98166.2       47   57   288   5593.4   208   180   144432   96969.0       48   92   380   5524.4   207   207   144639   95771.9       49   54   434   5455.3   206   179   144808   74574.7                  
 
         [0095]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLES 2 
               
               
                   
                   
               
               
                   
                   
               
               
                   
                 n 
                 A 
                   
                   
                 n 
                 A 
                   
                   
               
               
                   
                 LUMINANCE 
                 STATISTICAL 
                 B1 
                   
                 LUMINANCE 
                 STATISTICAL 
                 B2 
               
               
                   
                 LEVEL 
                 COUNT 
                 TOTAL 
                 C1 
                 LEVEL 
                 COUNT 
                 TOTAL 
                 C2 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 50 
                 89 
                 523 
                 5386.3 
                 205 
                 163 
                 144981 
                 93377.6 
               
               
                   
                 51 
                 83 
                 606 
                 5317.2 
                 204 
                 157 
                 145138 
                 92180.4 
               
               
                   
                 52 
                 88 
                 694 
                 5248.2 
                 203 
                 131 
                 145269 
                 90983.3 
               
               
                   
                 53 
                 108 
                 802 
                 5179.1 
                 202 
                 174 
                 145443 
                 89786.1 
               
               
                   
                 54 
                 111 
                 913 
                 5110.0 
                 201 
                 136 
                 145579 
                 88589.0 
               
               
                   
                 55 
                 61 
                 974 
                 5041.0 
                 200 
                 151 
                 145730 
                 87391.8 
               
               
                   
                 56 
                 156 
                 1130 
                 4971.9 
                 199 
                 135 
                 145865 
                 86194.7 
               
               
                   
                 57 
                 136 
                 1266 
                 4902.9 
                 198 
                 128 
                 145993 
                 84997.5 
               
               
                   
                 58 
                 75 
                 1341 
                 4833.8 
                 197 
                 160 
                 146153 
                 93800.4 
               
               
                   
                 59 
                 118 
                 1459 
                 4764.8 
                 196 
                 113 
                 146266 
                 82603.2 
               
               
                   
                 60 
                 116 
                 1575 
                 4695.7 
                 195 
                 106 
                 146372 
                 81406.1 
               
               
                   
                 61 
                 95 
                 1670 
                 4626.7 
                 194 
                 100 
                 146472 
                 80208.9 
               
               
                   
                 62 
                 103 
                 1773 
                 4557.6 
                 193 
                 120 
                 146592 
                 79011.8 
               
               
                   
                 63 
                 106 
                 1879 
                 4488.6 
                 192 
                 106 
                 146698 
                 77814.6 
               
               
                   
                 64 
                 83 
                 1962 
                 4419.5 
                 191 
                 131 
                 146829 
                 76617.5 
               
               
                   
                 65 
                 99 
                 2061 
                 4350.4 
                 190 
                 77 
                 146906 
                 75420.4 
               
               
                   
                 66 
                 104 
                 2165 
                 4281.4 
                 189 
                 110 
                 147016 
                 74223.2 
               
               
                   
                 67 
                 78 
                 2243 
                 4212.3 
                 188 
                 90 
                 147106 
                 73026.1 
               
               
                   
                 68 
                 84 
                 2327 
                 4143.3 
                 187 
                 99 
                 147205 
                 71828.9 
               
               
                   
                 69 
                 91 
                 2418 
                 4074.2 
                 186 
                 107 
                 147312 
                 70631.8 
               
               
                   
                 70 
                 88 
                 2506 
                 4005.2 
                 185 
                 97 
                 147409 
                 69434.6 
               
               
                   
                 71 
                 104 
                 2610 
                 3936.1 
                 184 
                 88 
                 147497 
                 68237.5 
               
               
                   
                 72 
                 92 
                 2702 
                 3867.1 
                 183 
                 98 
                 147595 
                 67040.3 
               
               
                   
                 73 
                 101 
                 2803 
                 3798.0 
                 182 
                 101 
                 147696 
                 65843.2 
               
               
                   
                 74 
                 93 
                 2896 
                 3729.0 
                 181 
                 95 
                 147791 
                 64646.0 
               
               
                   
                 75 
                 90 
                 2986 
                 3659.9 
                 180 
                 89 
                 147880 
                 63448.9 
               
               
                   
                 76 
                 96 
                 3082 
                 3590.8 
                 179 
                 120 
                 147800 
                 62251.7 
               
               
                   
                 77 
                 87 
                 3169 
                 3521.8 
                 178 
                 101 
                 148101 
                 61054.6 
               
               
                   
                 78 
                 103 
                 3272 
                 3452.7 
                 177 
                 102 
                 148203 
                 59857.4 
               
               
                   
                 79 
                 101 
                 3373 
                 3383.7 
                 176 
                 78 
                 148281 
                 58660.3 
               
               
                 X→ 
                 80 
                 113 
                 3486 
                 3314.6 
                 175 
                 97 
                 148378 
                 57463.1 
               
               
                   
                 81 
                 78 
                 3564 
                 3245.6 
                 174 
                 87 
                 148465 
                 56266.0 
               
               
                   
                 82 
                 93 
                 3657 
                 3176.5 
                 173 
                 93 
                 148558 
                 55068.8 
               
               
                   
                 83 
                 119 
                 3776 
                 3107.5 
                 172 
                 90 
                 148648 
                 53871.7 
               
               
                   
                 84 
                 122 
                 3898 
                 3038.4 
                 171 
                 105 
                 148753 
                 52674.5 
               
               
                   
                 85 
                 112 
                 4010 
                 2969.4 
                 170 
                 78 
                 148831 
                 51477.4 
               
               
                   
                 86 
                 78 
                 4088 
                 2900.3 
                 169 
                 87 
                 148918 
                 50280.2 
               
               
                   
                 87 
                 93 
                 4181 
                 2831.2 
                 168 
                 84 
                 149002 
                 49083.1 
               
               
                   
                 88 
                 144 
                 4325 
                 2762.2 
                 167 
                 81 
                 149083 
                 47885.9 
               
               
                   
                 89 
                 105 
                 4430 
                 2693.1 
                 166 
                 100 
                 149183 
                 46688.8 
               
               
                   
                 90 
                 116 
                 4546 
                 2624.1 
                 165 
                 91 
                 149274 
                 45491.6 
               
               
                   
                 91 
                 150 
                 4696 
                 2555.0 
                 164 
                 84 
                 149358 
                 44294.5 
               
               
                   
                 92 
                 127 
                 4823 
                 2486.0 
                 163 
                 111 
                 149469 
                 43097.3 
               
               
                   
                 93 
                 109 
                 4932 
                 2416.9 
                 162 
                 109 
                 149578 
                 41900.2 
               
               
                   
                 94 
                 159 
                 5091 
                 2347.9 
                 161 
                 96 
                 149674 
                 40703.0 
               
               
                   
                 95 
                 122 
                 5213 
                 2278.8 
                 160 
                 122 
                 149796 
                 39505.9 
               
               
                   
                 96 
                 115 
                 5328 
                 2209.8 
                 159 
                 119 
                 149915 
                 38308.8 
               
               
                   
                 97 
                 133 
                 5461 
                 2140.7 
                 158 
                 88 
                 150003 
                 37111.6 
               
               
                   
                 98 
                 141 
                 5602 
                 2071.6 
                 157 
                 121 
                 150124 
                 35914.5 
               
               
                   
                 99 
                 123 
                 5725 
                 2002.6 
                 156 
                 119 
                 150243 
                 34717.3 
               
               
                   
               
             
          
         
       
     
         [0096]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLES 3 
               
               
                   
               
               
                   
               
               
                 n 
                 A 
                   
                   
                 n 
                 A 
                   
                   
               
               
                 LUMINANCE 
                 STATISTICAL 
                 B1 
                   
                 LUMINANCE 
                 STATISTICAL 
                 B2 
               
               
                 LEVEL 
                 COUNT 
                 TOTAL 
                 C1 
                 LEVEL 
                 COUNT 
                 TOTAL 
                 C2 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 100 
                 119 
                 5844 
                 1933.5 
                 155 
                 124 
                 150367 
                 33520.2 
               
               
                 101 
                 119 
                 5963 
                 1864.5 
                 154 
                 98 
                 150465 
                 32323.0 
               
               
                 102 
                 120 
                 6083 
                 1795.4 
                 153 
                 107 
                 150572 
                 31125.9 
               
               
                 103 
                 114 
                 6197 
                 1726.4 
                 152 
                 124 
                 150696 
                 29928.7 
               
               
                 104 
                 130 
                 6327 
                 1657.3 
                 151 
                 108 
                 150804 
                 28731.6 
               
               
                 105 
                 92 
                 6419 
                 1588.3 
                 150 
                 101 
                 150905 
                 27534.4 
               
               
                 106 
                 127 
                 6546 
                 1519.2 
                 149 
                 119 
                 151024 
                 26337.3 
               
               
                 107 
                 136 
                 6682 
                 1450.1 
                 148 
                 119 
                 151143 
                 25140.1 
               
               
                 108 
                 100 
                 6782 
                 1381.1 
                 147 
                 115 
                 151258 
                 23943.0 
               
               
                 109 
                 102 
                 6884 
                 1312.0 
                 146 
                 113 
                 151371 
                 22745.8 
               
               
                 110 
                 117 
                 7001 
                 1243.0 
                 145 
                 106 
                 151477 
                 21548.7 
               
               
                 111 
                 84 
                 4085 
                 1173.9 
                 144 
                 98 
                 151575 
                 20351.5 
               
               
                 112 
                 122 
                 7207 
                 1104.9 
                 143 
                 106 
                 151681 
                 19154.4 
               
               
                 113 
                 110 
                 7317 
                 1035.8 
                 142 
                 111 
                 151792 
                 17957.2 
               
               
                 114 
                 89 
                 7406 
                 966.8 
                 141 
                 108 
                 151900 
                 16760.1 
               
               
                 115 
                 94 
                 7500 
                 897.7 
                 140 
                 100 
                 152000 
                 15562.9 
               
               
                 116 
                 105 
                 7605 
                 828.7 
                 139 
                 117 
                 152117 
                 14365.8 
               
               
                 117 
                 88 
                 7693 
                 759.6 
                 138 
                 87 
                 152204 
                 13168.6 
               
               
                 118 
                 106 
                 7799 
                 690.5 
                 137 
                 95 
                 152299 
                 11971.5 
               
               
                 119 
                 118 
                 7919 
                 621.5 
                 136 
                 109 
                 152408 
                 10774.3 
               
               
                 120 
                 99 
                 8016 
                 552.4 
                 135 
                 106 
                 152514 
                 95772 
               
               
                 121 
                 90 
                 8106 
                 483.4 
                 134 
                 108 
                 152662 
                 8380.0 
               
               
                 122 
                 128 
                 8234 
                 414.3 
                 133 
                 99 
                 152721 
                 7182.9 
               
               
                 123 
                 101 
                 8335 
                 345.3 
                 132 
                 120 
                 152841 
                 5985.7 
               
               
                 124 
                 82 
                 8417 
                 276.2 
                 131 
                 109 
                 152950 
                 4788.6 
               
               
                 125 
                 131 
                 8548 
                 207.2 
                 130 
                 83 
                 153033 
                 3591.4 
               
               
                 126 
                 77 
                 8625 
                 138.1 
                 129 
                 127 
                 153160 
                 2394.3 
               
               
                 127 
                 214 
                 8839 
                 69.1 
                 128 
                 75 
                 153235 
                 1197.1