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 
   Japanese patent application No. 2005-334994 is hereby incorporated by reference in its entirety. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an image correction apparatus and an image correction method for correcting gradation values in image data. 
   2. Description of the Related Art 
   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. 
   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. 
   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. 
   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. 
   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 . 
   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. 
   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. 
   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 
   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. 
   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. 
   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. 
   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. 
   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. 
   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. 
   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. 
   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. 
   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. 
   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. 
   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. 
   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 
       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. 
       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. 
       FIG. 3  is a flow chart of the correction process executed by the host computer  1 . 
       FIG. 4  is a flow chart of the process for calculating statistical counts of the gray levels and totaling the statistical counts. 
       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. 
       FIG. 6  shows a histogram generated from the statistical counts of the gray levels from the check. 
       FIGS. 7A-7F  show the luminance correction range defined by the resulting gamma curves. 
       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. 
       FIG. 9  shows the histogram generated from the statistical counts of the gray levels from the check shown in  FIG. 8 . 
       FIG. 10  shows a gamma curve when no image correction is applied. 
       FIG. 11  shows the gamma curves for f(x)=0 and f(x)=255. 
       FIG. 12  shows the gamma curves defining the correction range of the related art. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   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. 
   Internal Arrangement of the Host Computer and Printer 
     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. 
   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. 
   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 . 
   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 . 
   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 . 
   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. 
   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. 
   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 . 
   Image Correction Process 
   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. 
     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 . 
     FIG. 3  is a flow chart of the image correction process executed by the host computer  1  in this embodiment. 
   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 B1 and B2, and values C1 and C2 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. 
   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. 
   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. 
   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 ). 
   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. 
   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. 
   Process for Acquiring Statistical Counts for the Gray Level 
   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 B1 (B2).  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 B1 and B2, and values C1 and C2 for determining the correction range. 
   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. 
   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 B1 (the left side of Tables 1, 2, and 3, beginning with Table 1). Total B2 (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 ). 
   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. 
   Acquiring the Correction Range for Brightening the Image and the Correction Range for Darkening the Image 
   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. 
   Step S 3  for acquiring the correction range for brightening the image is described first. 
   The correction range controller  6  calculates value C1 for acquiring the correction range for brightening the image (step S 21 ). This value C1 for acquiring the correction range for brightening the image can be calculated using the following equation.
 
 C 1=(128 −n )* B 1/128
 
   where n is the gray level (0&lt;=n&lt;=127) and B1 is the cumulative total for n. 
   The gray level n where B1&gt;C1 is then stored (step S 22  returns Yes). 
   As indicated by arrow X in Table 2, the gray level n where B1&gt;C1 in the image of check  20  is n=80, and the value 80 is therefore stored. 
   The correction range value L1 for increasing image brightness from the stored gray level n is then calculated (step S 23 ). The correction range value L1 for increasing image brightness can be calculated using the following equation.
 
 L 1=128 −n  
 
   where n is the gray level at which B1&gt;C1. 
   In the check  20  image in this example L1=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. 
   The value C2 for determining the correction range for darkening the image can be determined using the following equation.
 
 C 2=( n− 127)* B 2/128
 
   where n is the gray level (128&lt;=n&lt;=255) and B2 is the cumulative total for n. 
   The gray level n where B2&gt;C2 is then stored. 
   As indicated by arrow Y in Table 1, B2&gt;C2 at gray n=233 in the image of this check  20 , and the value 233 is therefore stored. 
   The correction range value L2 for darkening the image can be calculated as follows.
 
 L 2 =n −127
 
   where n is the gray level at which B2&gt;C2. 
   In the check  20  image in this example L2=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. 
   In this embodiment of the invention the value C1 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 C2 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 . 
   By thus separately calculating the correction range value L1 for brightening the image from the cumulative total of the dark gray levels n=0 to 127, and the correction range value L2 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. 
     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. 
   As shown in  FIG. 7F , by separately calculating the correction range VALUE L1 for brightening the image and the correction range VALUE L2 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. 
   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  FIGS. 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. 
   Because the statistical counts of the gray level are biased in this example, the value C1 for determining the correction range for brightening the image and the value C2 for determining the correction range for darkening the image are weighted by totals B1 and B2, respectively, before taking the average, but other calculation methods can be used instead. 
   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 . 
   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. 
   More specifically, the correction range controller  6  can calculate the value C1 for determining the correction range for brightening the image as follows.
 
 C 1 =E 1/10
 
   where E1 is the sum of all n=0 to 127. 
   The luminance level n at which B1&gt;C1 where B1 is the total for a given n is then stored. 
   The correction range controller  6  can calculate the value C2 for determining the correction range for darkening the image as follows.
 
 C 2 =E 2/10
 
   where E2 is the sum of all n=255 to 128. 
   The luminance level n at which B1&gt;C1 where B1 is the total for a given n is then stored. 
   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. 
   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 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
           
         
             
                 
               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 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               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