Abstract:
Systems and methods for determining the texture of the images to be processed are provided. An image data manager is provided that is capable of generating summed-area tables to be applied in texture mapping for texture that have no special direction or orientation, by generating summed-area tables for areas that best approximate circles. The image data manager uses the generated summed-area tables to process the image data. The summed-areas tables applied include a hexagon and an octagon. Accordingly, problems in processing images having textures that have no special direction or orientation, are reduced or eliminated.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     This invention is directed to methods and systems that process images using summed-area tables. 
     2. Description of Related Art 
     Digitally reproducing, transferring and/or displaying various types of images presently occurs using a variety of devices and systems in a variety of environments. A digital image may be input into a device, processed, and then output from the device, for example. In some applications, it may be necessary or desirable to process the image between the inputting at one device and outputting the data from that one device for the specific purpose of using the processed image data by another device. In other applications, it may be necessary or desirable to process the input image for some particular application within a device itself. 
     In image processing, images are represented in a wide variety of manners. Various techniques have been implemented in image processing. 
     SUMMARY OF THE INVENTION 
     In various exemplary embodiments of image processing, summed-area tables are used for processing the image. In these exemplary embodiments, a summed-area table has an entry for each pixel of the image. Each such entry is the sum of all values in the rectangular region with one corner of the region at the corner of the image, for example, the upper left corner, and the opposing corner of the region at the pixel. 
     This invention provides systems and methods that is generate non-rectangular summed-area tables. 
     This invention separately provides an image data manager that generates non-rectangular summed-area tables to process the image data. 
     In accordance with the systems and methods of this invention, the manager is capable of generating summed-area tables for areas that approximate circles. 
     Various exemplary embodiments of the summed areas usable with the summed-areas tables and systems and methods for generating and using these summed area tables according to this invention include non-rectangular regions. 
     In various exemplary embodiments of image processing systems using the systems and methods of this invention, problems in processing images having textures that have no special direction or orientation can be reduced or eliminated. 
     These and other features and advantages of the systems and methods of this invention are described in or are apparent from the following detailed description of the exemplary embodiments. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The exemplary embodiments of this invention will be described in detail, with reference to the following figures, wherein: 
     FIGS. 1 and 2 illustrate conventional rectangular regions used to generate summed-area tables; 
     FIGS. 3-8 show various exemplary embodiments of non-rectangular regions for summed-area tables used for processing the image in accordance with the methods and systems of this invention; 
     FIG. 9 is a functional block diagram of one exemplary embodiment of a image processing system in accordance with the systems and methods of this invention; 
     FIG. 10 shows in greater detail one exemplary embodiment of a functional block diagram of the memory of FIG. 9 in accordance with this invention; and 
     FIG. 11 shows in greater detail one exemplary embodiment of a functional block diagram of the image data manager of FIG. 9 in accordance with this invention; 
     FIG. 12 is a flowchart outlining one exemplary embodiment of a method for processing an image in accordance with the methods and systems of this invention; and 
     FIG. 13 is a flowchart outlining in greater detail one exemplary embodiment of a method for generating summed-area tables of FIG.  12 . 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 1 shows one exemplary embodiment of an area for summed-area tables used for processing the image. In this exemplary embodiment, a single table has an entry for each pixel of the image. Each such entry is the sum of all values in the rectangular region with one corner of the region at the corner of the image, for example, the upper left corner, and the opposing corner of the region at the pixel. The sum of all intensities in any rectangular region of the image may easily be recovered from such a table. Dividing the sum by the area of the rectangular region gives the average intensity over the rectangular region. 
     As shown in FIG. 1, the table entry at position (x,y) contains the sum of the values for all pixels in area A. The summed-area table entries are given by:                S        (     x   ,   y     )       =       ∑     j   =   0     y                       ∑     i   =   0     x                     I        (     i   ,   j     )                   (   1   )                                
     where: 
     x indicates the position of the current pixel along a row, 
     y indicates the row of the current pixel, 
     S(x,y) is the summed-area value for the pixel (x,y), and 
     I(i,j) is the image value of the pixel (i,j). 
     When the pixels of an image are read in a scanning order, i.e, the row direction, an intermediate sum T y (x) is used for all the pixels on the current row, or scan line, y. That is, T y (x) for each new pixel is determined as: 
     
       
           T   y ( x )= T   y ( x− 1)+ I ( x,y )  (2) 
       
     
     where: 
     I(x,y) is the image value of the pixel (x,y), 
     T y (x) is the intermediate sum for the pixel (x,y), and 
     T y (x−1) is the previous intermediate sum. 
     The summed-area table value for a particular pixel of interest in the image will be the value for the area above and left of that pixel plus the sum for the current scan line to that pixel. That is, the sum is determined as: 
     
       
           S ( x,y )= S ( x,y− 1)+ T   y ( x )  (3) 
       
     
     where: 
     S(x,y) is the summed-area value for the pixel (x,y), 
     T y (x) is the intermediate sum for the pixel (x,y), and 
     S(x,y—1) is the summed-area value for the pixel (x, y−1), i.e., the image value for the area above and left of the pixel (x,y). 
     The summed-area table allows the sum of values for any rectangular area of pixels to be determined. This is done by adding or subtracting the summed-area table values at the rectangle corners. As shown in FIG. 2, the area of the rectangle a, b, c, d is: 
     
       
           S ( x   d   , y   d )− S ( x   c   , y   c )− S ( x   b   , y   b )+ S ( x   a   , y   a )  (4) 
       
     
     where: 
     S(x d , y d ) is the summed-area value at point (x d , y d ), 
     S(x c , y e ) is the summed-area value at point (x c , y c ), 
     S(x b , y b ) is the summed-area value at point (x b , y b ), and 
     S(x a , y a ) is the summed-area value at point (x a , y a ). 
     In other words, starting with the table entry at the lower right corner of the area, the table entry at the lower left is subtracted and then the entry at the upper right is subtracted. This removes all area above the rectangle of interest then all area to the left. The area lying above and to the left of the rectangle has been subtracted twice. This area must be restored by adding back in the table entry at the upper left of the rectangle. 
     For image processing, if, for example, the value of a pixel is to be replaced with the average value of a region surrounding it, the summed-area table can give the sum of the values for a rectangular region surrounding the pixel. Dividing this sum by the size of the area yields the desired average value. 
     However, rectangular regions are often not the ideal shaped regions for various image processing functions, such as, for example, creating and processing textures in an image. In the exemplary embodiment of texture creating and processing, as an electronic image is synthesized, a pair of texture coordinates is determined for each pixel representing a textured surface. Textures coordinates may be determined for the corners of each region, and pixel intensity, for example, can be determined from the average of all texture elements bounded by the corners of the region. 
     For such image processing functions, regions that more closely approximate a circular region are often more useful. However, previously, only rectangularly-shaped regions were available. In various exemplary embodiments of this invention, summed-area tables that enable regions having more than four sides to be used. Using summed-area tables that enable such non-rectangular regions enables more effective image processing for some types of image processing functions. In particular, the following discussion refers to hexagonal and octagonal regions. However, it should be appreciated that the techniques described herein are readily extendible to polygonal regions having any number, even or odd, of sides. Using hexagonal regions takes about twice the storage and effort of the rectangular regions. The octagonal regions take about three times the storage and processing. To use hexagonal regions, two summed-area tables are used, and the areas involved are triangles rather than rectangles. 
     FIGS. 3A and 3B show in detail one exemplary embodiment of two types of triangular regions usable to create non-rectangular summed-area regions. In this exemplary embodiment, triangular regions having hypotenuses that have a slope of ±½ are used. Corresponding angles occur in hexagonal regions. However, it should be appreciated that other slopes may be used, corresponding to shapes having different numbers of sides. The type  1  triangular region shown in FIG. 3A has a hypotenuse that slants upwardly while the hypotenuse of the type triangular region  2  shown in FIG. 3B slants downwardly. The values for the entries in these summed-area tables can be defined as follows:                    S1        (     x   ,   y     )       =       ∑     j   =   0     y                       ∑     i   =   x       x   +     2        (     y   -   j     )                           I        (     i   ,   j     )             ;              and          
              S2        (     x   ,   y     )       =       ∑     j   =   0     y            ∑     i   =     x   -     2        (     y   -   j     )           x                     I        (     i   ,   j     )             ;             (   5   )                                
     where: 
     S 1 (x,y) is the summed-area value at the pixel (x,y) for a type  1  triangular region, 
     S 2 (x,y) is the summed-area value at the pixel (x,y) for a type  2  triangular region, and 
     I(i,j) is the image value at the pixel (i,j). 
     As with the summed area tables for the rectangular regions, these two summed-area tables for the triangular regions shown in FIGS. 3A and 3B can be constructed incrementally in the scanning direction. To do so, an array of column sums is maintained. The value in this array C y (x) is the sum of entries from row zero to y in column x. This requires a scanline worth of table entries that are updated as each new row is processed. With these column sums, the areas are given by: 
     
       
           S   1 ( x,y )= I ( x,y )+ C   y−1 ( x )+ C   y−1 ( x+ 1)+ S   1 ( x+ 2,  y− 1);  (6) 
       
     
     
       
           S   2 ( x,y )= I ( x,y )+ C   y−1 ( x )+ C   y−1 ( x− 1)+ S   2 ( x− 2,  y− 1); and  (7) 
       
     
     
       
           C   y ( x )= C   y−1 ( x )+ I ( x,y ),  (8) 
       
     
     where: 
     S 1 ( ) is the summed-area value at the pixel ( ) of a type  1  triangular region, 
     S 2 ( ) is the summed-area value at the pixel ( ) of a type  2  triangular region, 
     I( ) is the image value at the pixel ( ), 
     C y ( ) is sum of entries from row zero to y in column ( ), and 
     C y−1 ( ) is sum of entries from row zero to y−1 in column ( ), 
     That is, the summed-area value at the pixel (x,y) of a type  1  triangular region having an upward hypotenuse is the sum of: 1) the image value at the pixel (x,y), 2) the sum of entries from row zero to y−1 in column x, 3) the sum of entries from row zero to y−1 in column x+1, and 4) the summed-area value of a type  1  triangular region at the pixel (x+2,y−1). Similarly, the summed-area value at the pixel (x,y) of a type  2  triangular region having a downward hypotenuse is the sum of: 1) the image value at the pixel (x,y), 2) the sum of entries from row zero to y−1 in column x, 3) the sum of entries from row zero to y−1 in column x−1, and 4) the summed-area value of a type  2  triangular region at the pixel (x−2,y−1). The sum of entries from row zero to y in column x is the sum of entries from row zero to y−1 in column x and the image value at the pixel (x,y). 
     FIG. 4 shows how the area of half a hexagonal region can be determined using triangular areas to find the sum of values in the hexagonal region. The half hexagonal region“abcd” can be formed from the area of the triangular region “amp” minus the area of the triangular region “bmn” minus the area of the triangular region “cnq” and plus the area of the triangular region “dpq.” The left half of the hexagonal region shown in FIG. 4 can be found similarly by just reflecting the diagram left-to-right. The triangular regions represent the values in the summed-area tables. 
     FIG. 5 shows the dimensions and locations of an exemplary hexagonal region. The sum of values within this hexagonal region will be given by: 
     
       
           H=S   1 ( x,y )− S   1 ( x+ 2 w,y−w )− S   2 ( x− 1+2 w,y−w−h )+ S   2 ( x− 1,  y− 2 w−h )+ S   2 ( x− 1 ,y )− S   2 ( x− 1−2 w, y−w )− S   1 ( x− 2 w, y−w−h )+ S   1 ( x, y− 2 w−h )  (9) 
       
     
     where: 
     w is one fourth of the width of the hexagonal region, as shown in FIG. 5, 
     h is the length of an edge of the hexagonal region, as shown in FIG. 5, 
     H is the sum of values within the hexagonal region, 
     S 1 ( ) is the summed-area value for a triangular region at the pixel ( ) having an upward hypotenuse, and 
     S 2 ( ) is the summed-area value for a triangular region at the pixel ( ) having a downward hypotenuse. 
     Thus, summed area H of the hexagonal region is the sum of two half hexagonal regions, determined using the technique discussed above. That is, the summed hexagonal area H of the hexagonal region is the sum of the area of half hexagonal regions [S 1 (x,y)−S 1 (x+2w, y−w)−S 2 (x−1+2w, y−w−h)+S 2 (x−1, y−2w−h)] and the area of the half hexagonal regions [S 2 (x−1,y)−S 2 (x−1−2w,y−w)−S 1 (x−2w,y−w−h)+S 1 (x,y−2w−h)]. As shown in FIG. 5, the number of pixels within the region is 4w(w+h). 
     In order to determine the sum of values for an octagonal region, a summed-area table for a rectangular region and two triangular-region summed-area tables are used. For the octagon, triangular regions having a slope of 1 may be used. The table entries for the type  1  triangular region, the type  2  triangular region and the rectangular region would then be defined respectively as:                  S1        (     x   ,   y     )       =       ∑     j   =   0     y                       ∑     i   =   x       x   +   y   -   j                       I        (     i   ,   j     )             ;           (   10   )                   S2        (     x   ,   y     )       =       ∑     j   =   0     y                       ∑     i   =     x   -   y   +   j       x                     I        (     i   ,   j     )             ;              and           (   11   )                   S3        (     x   ,   y     )       =       ∑     j   =   0     y                       ∑     i   =   0     x                     I        (     i   ,   j     )             ;           (   12   )                                
     where: 
     S 1 (x,y) is the summed-area value at the pixel (x,y) of a type  1  triangular region, 
     S 2 (x,y) is the summed-area value at the pixel (x,y) of a type  2  triangular region, 
     S 3 (x,y) is the summed-area value at the pixel (x,y) of a rectangular region, and 
     I(i,j) is the image value at the pixel (i,j). 
     The table can be incrementally constructed according to: 
     
       
           S   1 ( x,y )= I ( x,y )+ C   y−1 ( x )+ S   1 ( x+ 1,  y− 1), 
       
     
     
       
           S   2 ( x,y )= I ( x,y )+ C   y−1 ( x )+ S   2 ( x− 1,  y− 1), and 
       
     
     
       
           S   3 ( x,y )= I ( x,y )+ C   y−1 ( x )+ S   3 ( x− 1,  y );  (14) 
       
     
     where: 
     S 1 ( ) is the summed-area value at the pixel ( ) of a type  1  triangular region, 
     S 2 ( ) is the summed-area value at the pixel ( ) of a type  2  triangular region, 
     S 3 ( ) is the summed-area value at the pixel ( ) of a rectangular region, 
     I( ) is the image value at the pixel ( ), 
     C y ( ) is sum of entries from row zero to y in column ( ), and 
     C y−1 ( ) is sum of entries from row zero to y−1 in column ( ). 
     That is, the summed-area value at the pixel (x,y) of a type  1  triangular region having an upward hypotenuse is the sum of: b  1 ) the image value at the pixel (x,y), 2) the sum of entries from row zero to y−1 in column x, and 3) the summed-area value of a type  1  triangular region at (x+1,y−1). Similarly, the summed-are value at the pixel (x,y) of a type  2  triangular region having a downward hypotenuse is the sum of: 1) the image value at the pixel (x,y), 2) the sum of entries from row zero to y−1 in column x, and 3) the summed-are value of a type  2  triangular region at the pixel (x−1,y−1). The summed-area value at the pixel (x,y) of a rectangular region is the sum of: 1) the image value at the pixel (x,y), 2) the sum of entries from row zero to y−1 in column x, and 3) the summed-area value of a rectangle at (x−1, y). 
     As in the hexagonal case, the sum of entries is determined as: 
     
       
           C   y ( x )= C   y −1( x )+ I ( x,y )  (15) 
       
     
     As shown in FIG. 6, the octagon can be divided into two half-hexogonal regions separated by a rectangular region. The half-hexagonal regions can be determined from the two triangle summed-area tables, as was done above for the hexagonal region. The rectangular region can be determined using the conventional rectangular-region summed-area table as discussed above. 
     The sum of the values in the octagonal region shown in FIG. 6 is determined to be: 
     
       
           R=S   1 ( x,y )− S   1 ( x+d, y−d )− S   2 ( x− 1 +d, y−d−h )+ 
       
     
     
       
           S   2 ( x− 1,  y− 2 d−h )+ 
       
     
     
       
           S   2 ( x− 1− w,y )− S   1 ( x− 1 −w−d, y−d )− 
       
     
     
       
           S   1 ( x−w−d,y−d−h )+ 
       
     
     
       
           S   1 ( x−w,y− 2 d−h )+ S   3 ( x− 1, y )− 
       
     
     
       
           S   3 ( x− 1 −w,y )− 
       
     
     
       
           S   3 ( x− 1 , y− 2 d−h )+ S   3 ( x− 1 −w,y− 2 d−h )  (16) 
       
     
     where: 
     w is the length of the horizontal edge of the octagonal region, as shown in FIG. 6, 
     h is the length of the vertical edge of the octagonal region, as shown in FIG. 6, 
     d is the distance between the vertical edge and the rectangular region in the octagonal region, as shown in FIG. 6, 
     R is the sum of values within the octagonal region, 
     S 1 ( ) is the summed-area value for a type  1  triangular region at ( ) having an upward hypotenuse, 
     S 2 ( ) is the summed-area value for a type  2  triangular region at ( ) having a downward hypotenuse, and 
     S 3 ( ) is the summed-area value for a rectangular region at ( ). 
     Thus, the octagonal region R is the sum of two half-hexagonal regions and a rectangular region, determined using the technique discussed above. That is, the octagonal region R is the sum of the half-hexagon region [S 1 (x,y)−S 1 (x+d, y−d)−S 2 (x−1+d, y−d—h)+S 2 (x−1, y−2d−h)], the half-hexagonal region [S 2 (x−1−w,y)−S 2 (x−1−w,y−d)−S 1 (x−w−d,y−d−h)+S 1 (x−w,y−2d−h)], and the rectangular region [S 3 (x−1, y)−S 3 (x−1−w, y)−S 3 (x−1, y−2d−h)+S 3 (x−1−w, y−2d−h)]. As shown in FIG. 6, number of pixels in the octagonal region is determined to be wh+2d(d+w+h). 
     Though exemplary embodiments of a hexagonal region and an octagonal region are shown above, it should be appreciated that, as discussed above, any summed-area tables that enable regions having more than four sides may be used. It should be appreciated that the techniques described above are readily extendible to polygonal regions having any number, even or odd, of sides. As shown in FIGS. 7-8, the polygonal regions may include a region having an odd number of sides, such as a pentagonal region, or a region having an even number of sides, such as a decagonal region. As with the hexagonal and octagonal regions, triangular regions may be used to determine the sum of values in these polygonal regions. As with the hexagonal and octagonal regions, the triangular regions represent the values in the summed-area tables. 
     As shown in FIG. 7, the half pentagonal region“abcd” can be formed from the area of the rectangular region “abnp” plus the area of the triangular region “bmn” minus the area of the triangular regions “cmo” and “coq” plus the area of the triangular region “dpq”. The left half of the pentagonal region shown in FIG. 7 can be found similarly by reflecting the diagram left-to-right. 
     In particular, it should be appreciated that the triangular regions “bmn” and “cmo” have hypotenuses having different slopes than the hypotenuses of the triangular regions “coq” and “dpq”. In general, the hexagonal and octagonal regions require only one set of type  1  and type  2  triangular regions, because there is only one angle that the sides of each such region make relative to a vertical, or horizontal, axis of the image. In contrast, any other non-rectangular polygon will have sides that make at least two angles relative to the vertical, or horizontal, axis of the image. For example, the sides “bc” and “ef” make a first angle with the vertical axis in FIG. 7, while the sides “cd” and “de” make a second angle with the vertical axis. Accordingly, to generate pentagonal regions, two sets of type  1  and type  2  triangular regions, each set having hypotenuses that correspond to one of the first and second angles, are required. In general, to form a polygonal region having an arbitrary number of sides, as many sets of the type  1  and type  2  triangular regions will be required as there are angles made by the sides of the polygonal region with a vertical, or horizontal, axis of the image. 
     It should also be appreciated that the type  1  and type  2  triangular regions include trapezoidal portions that result because the triangular regions may extend beyond the boundaries of the image. 
     As shown in FIG. 8, the decagonal regions “abcdefghij” can be formed by adding to the rectangular region “aefj” the triangular regions “apn”, “blk”, “dlm”, and “enq”, and then subtracting the triangular regions “blp”, “cko”, “cmo” and “dlq”. That is, the region “abde” is formed by subtracting the triangular regions “blp” and “del” from the triangular region “apn” and adding back triangular region “enq”. The region “bcd” is then formed by subtracting the triangular regions “cmo” and “cko” from triangular region “blk”, and adding back triangular region “dlm”. 
     As in the pentagonal region shown in FIG. 7, the sides of the decagonal region shown in FIG. 8 make two distinct angles with the vertical, or horizontal, axis of the image. Thus, two sets of the type  1  and type  2  triangular regions are required to form the decagonal region shown in FIG.  8 . 
     Alternatively, the decagonal region “abcdefghij” can be formed from the area of a octagonal region “abdefgij” plus the area of the triangular regions “bcd” and “igh”. The area of the octagonal region “abdefgij” can be determined using the determination discussed above for octagonal regions except that the angles made by the octagonal region “abdefgij” are different than the angles made by the octagonal region shown in FIG.  6 . The triangular region “bcd” can be formed as discussed above. The areas of the pentagonal region “fghij” or the triangular region “igh” can be found similarly by just reflecting the diagram left-to-right. 
     As shown above, summed-area tables that enable polygonal regions having any number, even or odd, of sides may be used in the methods and systems of this invention. Using summed area tables for triangular regions, the sum of values in these polygonal regions can be determined. 
     Summed-area tables are used in the image processing of an entire image where determinations are done for each pixel in scanning order. In these applications the point positions just increment from one pixel to the next and their indexing is a simple stepping through the table. 
     FIG. 9 shows one exemplary embodiment of an image processing apparatus  200  incorporating the non-rectangular scanned area generating systems and methods in accordance with this invention. As shown in FIG. 9, an image data source  100  and an input device  120  are connected to the image processing apparatus  200  over the links  110  and  122 , respectively. The image data source  100  can be a digital camera, a scanner, or a locally or remotely located computer, or any other known or later developed device that is capable of generating electronic image data. Similarly, the image data source  100  can be any suitable device that stores and/or transmits electronic image data, such as a client or a server of a network. The image data source  100  can be integrated with the image processing apparatus  200 , a in a digital copier having an integrated scanner. Alternatively, the image data source  100  can be connected to the image processing apparatus  200  over a connection device, such as a modem, a local area network, a wide area network, an intranet, the Internet, any other distributed processing network, or any other known or later developed connection device. 
     It should also be appreciated that, while the electronic image data can be generated at the time of printing an image from an original physical document, the electronic image data could have been generated at any time in the past. Moreover, the electronic image data need not have been generated from the original physical document, but could have been created from scratch electronically. The image data source  100  is thus any known or later developed device which is capable of supplying electronic image data over the link  110  to the image processing apparatus  200 . 
     The image data sink  300  can be any known or later developed device that is capable of receiving image data output by the image processing apparatus  200  over link  310  and either storing, transmitting, and/or displaying that processed image data. Thus, the image data sink  300  can be either or both of a channel device for transmitting the processed image data for display or storage or a storage device for indefinitely storing the processed image data until there arises a need to display or further transmit the processed image data. 
     Further, the image data sink  300  or channel device can be any known structure or apparatus for transmitting the processed image data from the image processing apparatus  200  to a physically remote storage or display device. Thus, the channel device can be a public switched telephone network, a local or wide area network, an intranet, the Internet, a wireless transmission channel, any other distributing network, or the like. Similarly, the storage device can be any known structural apparatus for indefinitely storing the processed image data, such as a RAM, a hard drive and disk, a floppy drive and disk, an optical drive and disk, a flash memory or the like. Finally, the display device can be any known device for displaying or rendering an image. Thus, the display device can be a CRT, an active or passive matrix LCD, an active or passive LED display, a laser printer, an ink jet printer, a digital copier, or the like. 
     Moreover, the image data source  100  and the image data sink  300  can be physically remote from the image processing apparatus  200  and reachable over the channel device described above. Alternatively, the image processing apparatus  200  can be integrated with either or both of the image data source  100  and the image data sink  300 . For example, the image data source  100  can be a scanner of a digital photocopier, while the image data sink  300  is an image output terminal of the digital photocopier. 
     The link  110  can thus be any known or later developed system or device for transmitting the electronic image data from the image data source  100  to the image processing apparatus  200 . The link  110  may include, but are not limited to, wired or wireless communication links such as conventional telephone lines, fiber optic lines, coaxial cable lines, satellite or cellular communication links, and the like. Similarly, the link  310  can be any known or later developed system or device for transmitting the electronic image data from the image processing apparatus  200  to the image data sink  300 . 
     The input device  120  can be any known or later developed device for providing control information from a user to the image processing apparatus  200 . Thus, the input device  120  can be a control panel of the image processing apparatus  200 , or could be a control program executing on a locally or remotely located general purpose computer, or the like. As with the links  110  and  310  described above, the link  122  can be any known or later developed device for transmitting control signals and data input using the input device  120  from the input device  120  to the image processing apparatus  200 . 
     As shown in FIG. 9, the image processing apparatus  200  includes a controller  210 , an input/output interface  220 , a memory  230 , and an image data manager  240 , each of which is interconnected by a control and/or data bus  250 . The links  110 ,  122  and  310  from the image data source  100 , the input device  120  and the image data sink  300 , respectively, are connected to the input/output interface  220 . The electronic image data from the image data source  100 , and any control and/or data signals from the input device  120 , are input through the input interface  220 , and, under control of the controller  210 , are stored in the memory  230  and/or provided to the controller  210 . 
     The memory  230  preferably has at least an alterable portion and may include a fixed portion. The alterable portion of the memory  230  can be implemented using static or dynamic RAM, a floppy disk and disk drive, a hard disk and disk drive, flash memory, or any other known or later developed alterable volatile or non-volatile memory device. If the memory includes a fixed portion, the fixed portion can be implemented using a ROM, a PROM, an EPROM, and EEPROM, a CD-ROM and disk drive, a DVD-ROM and disk drive, a writable optical disk and disk drive, or any other known or later developed fixed or non-volatile memory device. 
     The image data manager  240  analyzes the electronic data stored in the memory  230  and generates summed-area tables. The image data manager  240  then outputs processed electronic image data to the memory  230 , or directly to the input/output interface  220 , where the processed image data is output over the link  310  to the image data sink  300 . 
     While FIG. 9 shows the image data manager  240  and the image data sink  300  as separate devices, the image data sink  300  could be integrated into the image processing apparatus  200 . In various other exemplary embodiments, the image data manager  240  may be a separate device attachable upstream of a stand-alone image data sink  300 . 
     Furthermore, the image data manager  240  may be implemented as hardware in, or as software executing on, the image processing apparatus  200  and/or the image data sink  300 . Other configurations of the elements shown in FIG. 9 may be used without departing from the spirit and scope of this invention. 
     FIG. 10 shows in greater detail one exemplary embodiment of a functional block diagram of the image data manager  240  of FIG.  9 . As shown in FIG. 10, the image data manager  240  includes a summed-area table generator  242 , an image processing circuit  244  and a post-processing subsystem  246 . The summed-area table generator  242  analyzes and prepares the image prior to processing of the image by generating some or all of the various rectangular region and triangular region summed-area tables discussed above. The image processing circuit  244  processes the image using at least some of the various triangular-region summed-area tables such that the image is processed using non-rectangular regions. After the image has been processed, the post-processing subsystem  246  performs various processes on the processed image to generate an output image. The summed-area table generator  242 , the image processing circuit  244  and the post-processing subsystem  246  are all connected to the data bus  250 . 
     It should be appreciated that it is not necessary that the entire image be stored in memory, or that the summed area tables be completed in order or image processing to take place. It should be appreciated that processing may be conducted provided that sufficient summed-area table data has been generated to cover the image processing of the current pixel of interest. Thus, image can be streamed through the summed-area table generator, image processor, and post-processor while only storing the portions actually needed for the determinations. 
     FIG. 11 shows in greater detail one exemplary embodiment of the organization of the memory  230  of FIG.  9 . As shown in FIG. 11, the memory  230  includes an input image portion  232 , a processed image portion  234 , a holding image portion  236 , and a summed-area table portion  238 . The input image portion  232  temporarily stores image data, prior to processing, that has been input into the image processing system  200 . The processed image portion  234  temporarily stores processed image data that has been processed by the image processing system  200  prior to outputting the processed image. The holding image portion  236  stores image data on a long term basis either before or after processing. The image data stored in the input image portion  232  may be input from the image data source  100  through the input/output interface  220 , or, alternatively, may result from converting an image previously stored in the image processing system  200 , and specifically stored in the holding image portion  236 . The summed-area table portion holds the summed-area table data created by the summed-area table generator  242  and used by the image processing circuit  244 . 
     In operation, an image to be processed, i.e., an “original image” is input into the image processing system  200  or, alternatively, retrieved from the holding image memory  236  of the image processing system  200 . 
     The summed-area table generator  242  generates at least a number of triangular-region summed-area tables. As a result, the image may be easily processed by the image processing circuit  244  in the image data analyzing circuit  240 . It should be appreciated that the summed-area table generator  242  may generate the triangular-region summed-area tables using any of the various methods discussed above. 
     After the summed-area table generator  242  generates the various triangular-region, and possibly rectangular-region, summed-area tables, the image is processed using these summed-area tables. This process is performed by the image processing circuit  244 . The image processing circuit  244  processes the image using any of a variety of known or later developed image processing methods. 
     Once the image is processed, the processed image is input to the post-processing subsystem  246  and further processed to generate an output image. This processed output image may be directly output to the image data sink  300 . Alternatively, the image may be stored in the holding image portion  236  of the memory  230 . 
     In accordance with this illustrative example using the image processing system  200 , the process according to the invention is performed using a computer. However, it should be recognized that the systems and methods of the invention are not limited to application using a computer. Rather, the systems and methods according to the invention may be implemented using any suitable arrangement of electronic and imaging components, expert knowledge, or alternatively, a mixture of electronic and imaging components in conjunction with expert knowledge. 
     The image processing according to the invention may be applied to a variety of applications and environments. Further, it should be recognized that numerous variations of the systems and methods in accordance with the invention may be performed using the general process described in conjunction with FIGS. 9-11. Illustratively, further embodiments of the image processing process according to the systems and methods of the invention are described below. Each of these illustrative embodiments is performed by the image processing system  200 . However, any suitable computer system or arrangement of imaging components may be used in the implementation of further embodiments. 
     FIG. 12 is a flowchart outlining one exemplary embodiment of an image processing method according to this invention. As shown in FIG. 12, beginning in step S 100 , control continues to step S 200 , where an electronic image is input. Then, in step S 300 , a number of triangular-region and possibly rectangular-region, summed-area tables are generated. Next, in step S 400 , the image data is processed using the triangular-region, and possibly rectangular-region, summed-area tables. Control continues to step S 500 . 
     In step S 500 , the processed image is output to some suitable storage device or over a network, for example. Then, in step S 600 , the image processing method ends. 
     FIG. 13 is a flowchart outlining in greater detail one exemplary embodiment of a method for generating summed-area tables of step S 300 . As shown in FIG. 13, beginning in step S 300 , control continues to step S 310 , where the desired non-rectangular image processing regions are determined. That is, polygonal regions such as the pentagonal regions, the hexagonal regions, the octagonal regions or the decagonal regions discussed above are determined. Then, in step S 320 , for each of the non-rectangular regions, at least one set of the type  1  and type  2  triangular summed-area tables are set up. Next, in step S 330 , the non-rectangular regions are analyzed to determine whether any rectangular summed-area tables are required. If so, control continues to step S 340 . Else, control jumps to step S 350 . 
     In step S 340 , the rectangular region summed-area table is set up. Then, in step S 350 , the data for the set-up summed-area tables is generated. That is, the data for summed-area tables for the triangular regions, and possibly rectangular regions, is generated. Next, in step S 360 , the control returns to step S 400 . 
     The image processing system  200  shown in FIGS. 9-11 is preferably implemented on a programmed general purpose computer. However, the image processing system  200  shown in FIGS. 9-11 can also be implemented on a special purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit elements, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmable logic device such as a PLD, PLA, FPGA or PAL, or the like. In general, any device, capable of implementing a finite state machine that is in turn capable of implementing the flowchart shown in FIGS. 12-13, can be used to implement the image processing system  200 . 
     In particular, it should be understood that each of the circuits shown in FIGS. 9-11 can be implemented as portions of a suitably programmed general purpose computer. Alternatively, each of the circuits shown in FIGS. 9-11 can be implemented as physically distinct hardware circuits within an ASIC, or using a FPGA, a PDL, a PLA or a PAL, or using discrete logic elements or discrete circuit elements. The particular form each of the circuits shown in FIGS. 9-11 will take is a design choice and will be obvious and predicable to those skilled in the art. 
     The memory  230  is preferably implemented using static or dynamic RAM. However, the memory  230  can also be implemented using a floppy disk and disk drive, a writable optical disk and disk drive, a hard drive, flash memory or any other known or later developed alterable volatile or non-volatile memory device or system. 
     While this invention has been described in conjunction with specific embodiments outlined above, it is evident that many alternative modifications and variations may be apparent to those skilled in the art. Accordingly, the exemplary embodiments of the invention as set forth herein are intended to be illustrative, not limiting. Various changes may be made without departing from the spirit and scope of the invention.