Abstract:
An error diffusion halftoning system and a method of managing halftoning errors utilize a quantization technique to reduce the required size of a primary error buffer that is needed to diffuse the halftoning errors. By implementing the quantization technique, the primary error buffer can be reduced from an 8-bits-per-bin error buffer to a 2-bits-per-bin error buffer for 256 grayscale. The reduction in bin size decreases the cost of the primary error buffer and, consequently, the cost of an error diffusion halftoning (EDH) device of the system that generates halftone values from grayscale values of a digital image. The quantization technique is executed on cumulated half-toning errors, derived from apportioned halftoning errors associated with previously processed pixels. In addition, the system and method utilize an error diffusion procedure to diffuse quantization errors that are produced from the execution of the quantization technique. In one embodiment, entire quantization errors are sequentially transmitted to a supplemental error diffuser, so that each quantization error can be introduced to the grayscale value of the next pixel to be processed. In another embodiment, the quantization errors are apportioned using predefined multiplicative parameters and eventually diffused to two or more unprocessed pixels that are adjacent to the pixel currently being processed.

Description:
TECHNICAL FIELD 
     The invention relates generally to halftoning techniques and more particularly to an error diffusion halftoning technique. 
     BACKGROUND ART 
     Digital images provide a convenient format for transmission, modification, and/or reproduction of images. When an image is captured digitally, grayscale information for each pixel of an image is extracted. Typically, 256 grayscale levels are utilized to extract the grayscale information. However, the majority of printers that are currently in use are binary with respect to their printing methods. That is, the printers operate to reproduce the original image either by depositing or by refraining to deposit a small amount of ink or toner for each pixel of the captured image. The binary nature of these printers allows only two levels of grayscale to be printed for each pixel. Thus, digitally captured images having more than two levels of grayscale cannot be reproduced by the binary printers, unless a special printing technique, such as halftoning, is utilized. 
     A halftoning technique is a process for printing different shades of grayscale by varying the density of “dark” pixels that have been deposited with ink or toner. A lower density of dark pixels equates to a lighter shade of grayscale, while a higher density of dark pixels equates to a darker shade of grayscale. Since the density of dark pixels can vary in numerous degrees, the number of grayscales that can be produced using the halftoning technique is far greater than two levels. As long as the pixels are sufficiently small, the individual dark pixels will not be apparent to a viewer. Instead, the viewer will see smooth areas having different shades of grayscale, which are directly related to the density of dark pixels. 
     A common type of halftoning technique is known as “an error diffusion halftoning technique.” In error diffusion halftoning, a halftoning error associated with a generated halftone signal for each pixel of a digital image is distributed among neighboring pixels in order to determine which pixel should be deposited with ink or toner. The halftone signal is derived by comparing a given value, which is a combined value of a grayscale value of a pixel and a cumulative error from previously processed pixels, with a predefined threshold value. The difference between the given value and the halftone value is the halftoning error. By distributing the halftoning errors, the density of dark pixels will be determined by the grayscale values from a number of surrounding pixels. Consequently, regions of the digital image having lighter shades of grayscale will yield lower densities of dark pixels, while regions having darker shades of grayscale will yield higher densities of dark pixels. In this fashion, digital images having more than two shades of grayscale can be printed using a binary printer. 
     In FIG. 1, a conventional system  10  that executes error diffusion halftoning is shown. The system includes an input device  12 , an error diffusion halftoning (EDH) device  14 , and a binary output device  16 . The input device provides a digital image that is to be printed by the binary output device. The input device may be a scanner that can capture the digital image from a photograph, a digital camera that can capture the digital image from an actual scene, or a storage device that can receive the digital image from an external source. The error diffusion device includes a summing unit  18 , a thresholding module  20 , a subtraction unit  22 , an error diffuser  24 , and an error buffer module  26 . 
     In operation, the system  10  processes the digital image by sequentially operating on the image pixels of the digital image in a raster scan order, which is a left-to-right, top-to-bottom sequence. For each pixel of the image, a grayscale value g i,j  of that pixel is transmitted from the input device  12  to the summing unit  18  of the EDH device  14 , where g i,j  ε[0,255] for 256 grayscale. The values i and j identify the row and column, respectively, of the current pixel being processed. The summing unit  18  combines the grayscale value g i,j  with a final error e i,j  and outputs a summed value s i,j . The final error e i,j  is derived from halftoning errors associated with the previous pixels that were processed by the EDH device. The summed value s i,j  is then transmitted to the thresholding module  20  and the subtraction unit  22 . The thresholding module compares the summed value s i,j  to a threshold value, e.g., 127 for 256 grayscale. The comparison produces an output halftone value h i,j , which is one of two values, e.g., 0 or 255. If the summed value s i,j  is less than the threshold value, the output halftone value h i,j  equates to a first value, e.g., 0, that directs the output device  16  to refrain from depositing ink or toner. However, if the summed value s i,j  is equal to or greater than the threshold value, the output halftone value h i,j  equates to a second value, e.g., 255, that directs the output device to deposit the ink or toner. 
     The output halftone value h i,j  is also transmitted to the subtraction unit  22  to derive a halftoning error that results from converting the summed value s i,j  into one of two halftone values. The subtraction unit subtracts the halftone value h i,j  from the summed value s i,j . The result of this operation is a halftoning error n i,j , which is transmitted to the error diffuser  24 . The error diffuser then divides the halftoning error n i,j  using a known distribution process, such as the Floyd-Steinberg error diffusing process. The divided halftoning errors are transmitted to the error buffer module  26 . The error buffer module processes the divided halftoning errors, such that each divided halftoning error can be diffused into a neighboring pixel of the current pixel. These divided halftoning errors are combined with other divided halftoning errors from previously processed pixels to form final errors that are to be diffused into subsequently processed pixels. The final errors are temporarily stored in an error buffer (not shown) within the error buffer module. The error buffer has a capacity to store the final errors for an entire row of image pixels. For 256 grayscale, each bin of the primary error buffer is an 8-bit bin. When the grayscale value g i,j+1  of the next pixel is processed, a final error e i,j+1  stored in the bin of the error buffer associated with that pixel is transmitted to the summing unit  18 . This final error is combined with the grayscale value g i,j+1  and the above-described process is repeated. In this fashion, the halftoning errors from the pixels of the digital image are distributed to reproduce the digital image as a halftone image using the binary output device  16 . 
     Although conventional error diffusion halftoning systems, such as the system  10 , operate well for their intended purpose, what is needed is a cost-efficient error diffusion system and a method of managing errors in such a system. 
     SUMMARY OF THE INVENTION 
     An error diffusion halftoning system and a method of managing halftoning errors utilize a quantization technique to reduce the required size of a primary error buffer that is needed to diffuse the halftoning errors. By implementing the quantization technique, the primary error buffer can be reduced from an 8-bits-per-bin error buffer to a 2-bits-per-bin error buffer for 256 grayscale. The reduction in bin size decreases the cost of the primary error buffer and, consequently, the cost of an error diffusion halftoning (EDH) device of the system that generates halftone signals from grayscale values of a digital image. 
     The error diffusion halftoning system includes an input device, the EDH device, and a binary output device. The input device may be a digital scanner, a digital camera, or a storage device that can acquire digital images. The binary output device may be a conventional inkjet or laser printer. The EDH device is operatively connected to the input device and the binary output device to process grayscale pixel values of a given digital image from the input device, generating halftone signals, and to transmit the generated halftone signals to the binary output device. The halftone signals are used by the binary output device to decide whether to deposit or to refrain from depositing ink or toner in order to print a halftone image in accordance with the given digital image. In addition, the EDH device operates to manage the halftoning errors that are produced from the generation of the halftone signals. 
     The EDH device includes a summing unit, a thresholding module, a subtraction unit, an error diffuser, and a quantization-error diffusion (QED) module. The summing unit is positioned to receive a grayscale value from the input device and a corresponding final error from the QED module for each pixel being processed by the EDH device. The final error contains halftoning errors and quantization errors from previously processed grayscale values. The halftoning errors are the resulting products of a thresholding operation executed by the thresholding module, while the quantization errors are the resulting products of a quantization operation executed by the QED module. The summing unit combines the received grayscale value and the received final error to produce a summed value, which is transmitted to the thresholding module and the subtraction unit. 
     After the summed value is received by the thresholding module, the summed value is thresholded by the thresholding module using a predefined threshold value to generate a halftone signal. The halftone signal is then transmitted to the binary output device to control the depositing operation of the output device. The halftone signal is also transmitted to the subtraction unit, where the summed value from the summing unit is subtracted by the halftone signal to derive a halftoning error. The halftoning error is used by the error diffuser to distribute portions of the halftoning error to different components of the QED module, so that the portions of the halftoning error can be diffused to unprocessed pixels that are adjacent to the current pixel being processed. In the preferred embodiment, the error diffuser is configured to generate four apportioned halftoning errors from the halftoning error using a Floyd-Steinberg scheme. That is, the halftoning error is multiplied using parameters a, b, c and d, where a={fraction (3/16)}, b={fraction (5/16)}, c={fraction (1/16)} and d={fraction ( 7 / 16 )}. However, the error diffuser may be configured to generate the four apportioned halftoning errors using a different set of parameters. In an alternative embodiment, the error diffuser may be configured to generate any number of apportioned halftoning errors using a corresponding number of predefined parameters. 
     The QED module operates to manage the apportioned halftoning errors for each pixel of the digital image being processed. The apportioned halftoning errors from different pixels are combined by the QED module and added to selected pixels when these pixels are processed by the EDH device. 
     The QED module includes the primary error buffer, an intermediate error buffer, a supplemental error buffer, a quantization unit, a de-quantization unit, and three weighting units. The primary error buffer includes a number of bins. Each bin of the primary error buffer has a capacity to store 2-bit information. The number of bins included in the primary error buffer is not critical to the invention. However, the primary error buffer contains a sufficient number of bins to store error information for an entire pixel row of a typical digital image that is to be processed by the system. The intermediate error buffer is a 3-bin buffer that can temporarily store three apportioned halftoning errors from the error diffuser. Similarly, the supplemental error buffer is a single bin buffer that can temporarily store the remaining apportioned halftoning error from the error diffuser. Notice that the number of bins in the intermediate and supplemental error buffers is the number of error terms to which the error is diffused. These numbers are equal to four in the present case, but may be greater or less. The intermediate and supplemental error buffers are of size 8 or more bits per bin. The intermediate error buffer is configured such that when the next pixel is processed, values stored in the bins are shifted to the left. The stored value in the far left bin of the intermediate error buffer, however, is transmitted to the quantization unit of the QED module. This configuration allows apportioned halftoning errors from different pixels to be combined and stored within the bins of the intermediate error buffer. 
     The quantization unit is configured to convert the stored value in the left bin of the supplemental error buffer into a quantized value using a predefined quantization table. The operation of the quantization unit produces a quantization error, which is diffused in a manner similar to the diffusion of the halftoning error. In one embodiment, the quantization error is apportioned by the three weighting units using predefined multiplicative parameters to produce three apportioned quantization errors. One of the apportioned quantization errors is transmitted to the supplemental error buffer, while the two remaining apportioned quantization errors are transmitted to the middle and right bins of the intermediate error buffer. In another embodiment, the entire quantization error is combined with an apportioned halftoning error and transmitted to the supplemental error buffer, so that the quantization error can be introduced to the grayscale value of a pixel that is to be processed next. 
     The de-quantization unit of the QED module is coupled to the primary error buffer. When a grayscale value of a pixel is received by the EDH device, a quantized value that corresponds to that pixel is extracted from a bin of the primary error buffer. The quantized value is then expanded by the de-quantization unit using a predefined de-quantization table. The de-quantized value is combined with a stored value in the supplemental error buffer, resulting in a final error. The final error is then added to the grayscale value of the pixel being processed to derive a summed value that will be used to generate the halftone signal. In this manner, the halftoning errors and the quantization errors of previously processed pixels are diffused to grayscale values of subsequently processed pixels. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic illustration of a prior art error diffusion halftoning system. 
     FIG. 2 is a schematic illustration of an error diffusion halftoning system in accordance with the present invention. 
     FIG. 3 is an example of a quantization table utilized by the error diffusion halftoning system of FIG.  2 . 
     FIG. 4 is an example of a de-quantization table utilized by the error diffusion halftoning system of FIG.  2 . 
     FIG. 5 illustrates the distribution of halftoning and quantization errors from a pixel currently being processed by the system of FIG. 2 to its neighboring unprocessed pixels. 
     FIG. 6 is a flow diagram of a method of managing halftoning errors for error diffusion halftoning in accordance with the invention. 
    
    
     DETAILED DESCRIPTION 
     With reference to FIG. 2, an error diffusion halftoning system  30  in accordance with the invention is shown. The system includes a number of conventional devices. Therefore, the same reference numerals of FIG. 1 will be used to identify these conventional devices. The system  30  includes the input device  12 , an error diffusion halftoning (EDH) device  32 , and the binary output device  16 . The input device may be a digital scanner, a digital camera, or a storage device that can acquire digital images. The binary output device may be a typical inkjet or laser printer. The EDH device is operatively connected to the input device and the binary output device to process gray-scale pixel values of a given digital image from the input device, thereby generating halftone signals, and to transmit the generated halftone signals to the binary output device. The halftone signals are used by the binary output device to decide whether to deposit or to refrain from depositing ink or toner. In addition, the EDH device operates to manage the halftoning errors that result from the generation of the halftone signals. 
     The EDH device  32  includes the summing unit  18 , the thresholding module  20 , the subtraction unit  22 , the error diffuser  24 , and a quantized-error diffusion (QED) module  34 . Similar to the error buffer module  26  of system  10 , the QED module operates to manage the diffused halftoning errors that are associated with each pixel of a given digital image. However, the operational design of the QED module allows a primary error buffer  36  having 2-bit bins to be used, instead of a standard 8-bit bin error buffer, for 256 grayscale. Consequently, the cost of manufacturing the EDH device  32  is significantly reduced. 
     The QED module  34  includes the primary error buffer  36 , an intermediate error buffer  38 , and a supplemental error buffer  40 . The primary error buffer includes a number of bins. Each bin of the primary error buffer has a capacity to store 2-bit information. The number of bins included in the primary error buffer is not critical to the invention. However, the primary error buffer contains a sufficient number of bins to store error information for an entire pixel row of a digital image that is to be processed by the system  30 . The intermediate error buffer is a 3-bin buffer that operates to temporarily store apportioned halftoning errors from the error diffuser  24 . The error diffuser is preferably configured to distribute an input value, i.e., a halftoning error, using the Floyd-Steinberg scheme in which the input value is divided into four values, {fraction (1/16)}th, {fraction (3/16)}th, {fraction (5/16)}th, and {fraction (7/16)}th of the original input value. However, other distribution schemes may be utilized by the error diffuser to generate four different divided values of the halftoning error. In an alternative embodiment, the error diffuser may be configured to generate three or less apportioned halftoning errors using a corresponding number of predefined parameters, in which case the intermediate buffer will include the number of error terms minus one. In the preferred embodiment, the intermediate error buffer includes three bins  41 ,  42  and  43 . These bins of the intermediate error buffer are of size  8  or more bits per bins. The supplemental buffer is a single bin buffer. The bin of the supplemental buffer is also of size  8  or more bits. 
     The QED module  34  further includes summing units  46 ,  48 ,  50 ,  52 ,  54  and  56 , weighting units  58 ,  60  and  62 , a quantization unit  64 , and a de-quantization unit  66 . The summing unit  46  is coupled to the bin  41  of the intermediate error buffer  38 , while the summing unit  48  is coupled to the bin  42 . Both of these bins are connected to the error diffuser  24  via paths  68  and  70 , respectively. The summing unit  46  operates to add a first error value, received from the error diffuser  24  through the path  68 , to the value stored in the bin  41  of the intermediate error buffer. The first error value is {fraction (3/16)}th value of the original halftoning value that is received by the error diffuser. Similarly, the summing unit  48  adds a second error value, i.e., {fraction (5/16)}th value, from the error diffuser to the value stored in the bin  42  of the intermediate error buffer. However, the bin  43  of the intermediate error buffer is directly coupled to the error diffuser via path  72  to receive a third error value, i.e., {fraction (1/16)}th value, from the error diffuser. 
     The summing unit  50  is coupled to the bin  42  of the intermediate error buffer  38 , while the summing unit  52  is coupled to the bin  43 . Each summing unit  50  and  52  is connected to one of the three weighting units  58 ,  60  and  62 . The summing units  50  and  52  are connected to the weighting units  58  and  60 , respectively. The weighting units  58 ,  60  and  62  are operatively connected to the quantization unit  64 , which is coupled to the bin  41  of the intermediate error buffer  38  and the “j-1” bin of the primary error buffer  36 . The quantization unit operates to quantize the value from the bin  41  of the intermediate error buffer, using a predefined quantization table. An exemplary quantization table is shown in FIG.  3 . Consequently, the quantization introduces a quantization error, which is transmitted to the weighting units  58 ,  60  and  62 . Each of the weighting units multiplies the quantization error by predefined weighting parameters to derive a weighted quantization error. In one embodiment, the weighting parameters that are utilized by the weighting units are as follows: A=0.5; B=0.25; and C=0.25. Using these quantization error weighting parameters is preferable for image quality considerations. However, if computational efficiency is an important factor, the following alternative is a good trade-off between halftone pattern quality and computational complexity. The alternative weighting parameters are as follows: A=1.0; B=0; and C=0. 
     The weighted quantization error from the weighting unit  58  is added to the value stored in the bin  42  of the intermediate error buffer  38  by the summing unit  50 , while the weighted error from the weighting unit  60  is added to the value stored in the bin  43  of the intermediate error buffer by the summing unit  52 . The weighted quantization error from the weighting unit  62  is transmitted to the summing unit  54 , where it is summed with the fourth error value, i.e., {fraction (7/16)}th value of the original halftone value, from the error diffuser  24 . The resulting summed value from the summing unit  54  is then transmitted to the supplemental error buffer  40 . 
     The supplemental error buffer  40  is coupled to the summing unit  56 , as well as the summing unit  54 . The summing unit  56  is positioned to receive information from the de-quantization unit  66 , which is connected to the “j” bin of the primary error buffer  36 . The de-quantization unit operates to de-quantize the value stored in the “j” bin, using a predefined de-quantization table. An exemplary de-quantization table is shown in FIG.  4 . The de-quantized value is then transmitted to the summing unit  56  that combines the de-quantized value with the value from the supplemental error buffer  40 . The resulting summed error value is transmitted out of the QED module  34  as a final error and into the summing unit  18 , where it is summed with a grayscale value of a pixel currently being processed. 
     The mode of operation for the error diffusion halftoning system  30  will now be described with reference to FIG.  5 . FIG. 5 illustrates the distribution of halftoning and quantization errors from a pixel currently being processed by the system to its neighboring unprocessed pixels. Initially, the input device  12  acquires a digital image that will be processed by the system. The input device may capture the digital image from an actual scene or from a photograph, depending on input device. If the input device is a storage device, the digital image may have been received from an external source, such as a database of images. Preferably, the digital image is a 256 gray-scale image, although the system may be modified to accommodate digital images having fewer or more grayscales. 
     In order to print the digital image, grayscale pixel values of the input image are sequentially transmitted to the EDH device  32  in a raster scan order, which is a left-to-right, top-to-bottom sequence. For a pixel currently being processed, a grayscale value g i,j  of that pixel is transmitted from the input device  12  to the summing unit  18 , where g i,j  ε[0,255] for 256 grayscale. The values i and j identify the row and column, respectively, of the current pixel being processed. The current pixel is identified as pixel (i,j) in FIG.  5 . The summing unit  18  adds the grayscale value g i,j  and a final error e i,j  and outputs a summed value s i,j . The final error e i,j  is derived from halftoning and quantization errors associated with selected pixels that were previously processed by the EDH device. The selected pixels are shown in FIG. 5 as pixels (i−1,j−1), (i−1,j), (i−1,j+1), and (i,j−1) that are adjacent to the current pixel (i,j). The summed value s i,j  is then transmitted to the thresholding module  20  and the subtraction unit  22 . The thresholding module compares the summed value s i,j  to a threshold value, e.g.,  127  for 256 grayscale. The comparison produces an output halftone value h i,j , which is one of two values, e.g., 0 or 255. If the summed value s i,j  is less than the threshold value, the output halftone value h i,j  equates to a first value, e.q., 0, that directs the output device  16  to refrain from depositing ink or toner. However, if the summed value s i,j  is equal to or greater than the threshold value, the output halftone value h i,j  equates to a second value, e.g., 255, that directs the output device to deposit the ink or toner. 
     The output halftone value h i,j  is also transmitted to the subtraction unit  22  to derive a halftoning error that results from converting the summed value s i,j  into one of the two halftone values. The subtraction unit subtracts the output halftone value h i,j  from the summed value s i,j . The result of this operation is a halftoning error n i,j , which is transmitted to the error diffuser  24 . The error diffuser then divides the halftoning error n i,j  using the Floyd-Steinberg error diffusing scheme, and distributes the divided errors into different components of the QED module, so that these divided errors can be diffused to selected adjacent pixels of the current pixel being processed, as shown by the solid arrows in FIG.  5 . These adjacent pixels are identified in FIG. 5 as pixels (i+1,j−1), (i+1,j), (i+1,j+1), and (i,j+1). However, as previously noted, the error diffuser may be configured to divide the halftoning error n i,j  using a different scheme than the Floyd-Steinberg error diffusing scheme. 
     The first divided value, i.e., the {fraction (3/16)}th value of the halftoning error n i,j  is transmitted to the summing unit  46 , while the second divided value, i.e., the {fraction (5/16)}th value of the error n i,j  is transmitted to the summing unit  48 . The first and second divided values will eventually be diffused to the pixels (i+1,j−1) and (i+1,j), respectively. The summing unit  46  adds the first divided value to the value stored in the bin  41  of the intermediate error buffer  38 . Similarly, the summing unit  48  adds the second divided value to the value stored in the bin  42 . The third divided value, i.e., the {fraction (1/16)}th value of the halftoning error n i,j , is transmitted directly to the bin  43  of the intermediate error buffer. The third divided value will eventually be diffused to the pixel (i+1,j+1). The bin  43  is always empty when a divided value from the error diffuser  24  is received. This is due to the fact that the values stored in the bins of the intermediate error buffer are shifted to the left when a subsequent pixel value is processed by the EDH device  32 . The values stored in the bins  42  and  43  are shifted to the bins  41  and  42 , respectively. The value stored in the bin  41 , however, is transmitted to the quantization unit  64 . 
     The quantization unit  64  quantizes the stored value from the bin  41  of the intermediate error buffer  38 , using the quantization table of FIG.  3 . The quantized value is transmitted to the “j−1” bin of the primary error buffer  36 . The “j−1” bin will be read when the pixel value of the pixel (i+1,j−1) is processed by the EDH device  32 . In addition to generating the quantized value, the quantization unit is configured to generate a quantization error that is distributed to the weighting units  58 ,  60  and  62 . The weighting units  58 ,  60  and  62  distributes portions of the quantization error to the intermediate error buffer  38  and the supplemental error buffer  40 , using the weighting parameters A, B and C. 
     In one embodiment, the weighting parameters A, B and C are predefined such that A=0.5, B=0.25, and C=0.25. In this embodiment, the weighting unit  58  transmits a first portion of the quantization error, i.e., the product derived by multiplying the quantization error with C, to the summing unit  50 , while the weighting unit  60  transmits a second portion, i.e., the product derived by multiplying the quantization error with B, to the summing unit  52 . The summing unit  50  adds the first portion to the value stored in the bin  42  of the intermediate error buffer. Similarly, the summing unit  52  adds the second portion to the value stored in the bin  43 . The third portion of the quantization error, i.e., the product derived by multiplying the quantization error with A, is transmitted to the supplemental error buffer  40  via the summing unit  54 . The first, second and third portions of the quantization error are distributed to the intermediate and supplemental error buffers  38  and  40 , so that these divided errors can be diffused to selected adjacent pixels of the pixel currently being processed, as shown by the dotted arrows in FIG.  5 . These adjacent pixels are identified in FIG. 5 as pixels (i+1,j), (i+1,j+1), and (i,j+1). 
     In another embodiment, the weighting parameters A, B and C are predefined such that A=1.0, B=0, and C=0. In this embodiment, the entire quantization error is transmitted to the supplemental error buffer  40 , so that the quantization error can be diffused into the pixel (i,j+1), which is the next pixel to be processed by the EDH device  32 . 
     In both embodiments, the summing unit  54  combines the value from the weighting unit  62  with the fourth divided value, i.e., {fraction (7/16)}th of the halftoning error n i,j , from the error diffuser  24 . The resulting summed value from the summing unit  54  is transmitted to the supplemental buffer  40 . This summed value will then be used to derive the final error value that is to be added to the grayscale value of the pixel (i,j+1). 
     The final error value e i,j  that was added to the pixel value g i,j  by the summing unit  18  is derived in the following manner. The stored value in the “j” bin of the primary error buffer  36  of the QED module  34  is extracted and transmitted to the de-quantization unit  66 . Using the de-quantization table of FIG. 4, the de-quantization unit expands the value from the “j” bin. The expanded value is transmitted to the summing unit  56 , where the expanded value is summed with the value from the supplemental error buffer  40 , resulting in the final error value e i,j . The value from the supplemental error buffer includes a portion of a halftoning error, as well as a portion of a quantization error or the entire quantization error, that are associated with the previously processed pixel value. When the next pixel value g i,j+1 is processed by the system  30 , the value stored in the “j+1” bin of the primary error buffer  36  is processed to derive the final error e i,j+1 . In this fashion, each pixel value of the digital image is processed by the system. 
     A method of managing halftoning errors for error diffusion halftoning, using the EDH device  32  of the system  30 , will be described with references to FIGS. 2 and 6. At step  74 , an 8-bit halftoning error associated with the current pixel of a digital image being processed by the system is received by the error diffuser  24  of the EDH device. The halftoning error is a result of a thresholding procedure to convert the grayscale value of the current pixel, including errors from other pixels that are introduced to the gray-scale value, to a halftone value. Next, at step  76 , portions of the halftoning error are distributed to the intermediate and supplemental error buffers  38  and  40  of the QED module  34  by the error diffuser. These portions of the halftoning error will eventually be diffused to the unprocessed neighboring pixels of the current pixel. At step  78 , an 8-bit intermediate error extracted from the intermediate error buffer is quantized by the quantization unit  64  into a 2-bit value. Assuming that the Floyd-Steinberg scheme is utilized to distribute the halftoning error, the intermediate error includes a portion of the halftoning error. This 2-bit quantized value is then stored in a designated bin of the primary error buffer  36 , at step  80 . In one embodiment, a resulting quantization error is distributed to the bins  42  and  43  of the primary error buffer and the bin of the supplemental error buffer, so that the quantization error can also be diffused to some of the unprocessed neighboring pixels. In another embodiment, the entire quantization error is distributed to the supplemental error buffer, so that the quantization error can be added to the grayscale value of the next pixel to be processed. In both embodiments, the value stored in the supplemental error buffer includes a portion of the halftoning error, as well as either a portion of the quantization error or the entire quantization error. 
     At step  82 , the stored quantized value is extracted from the primary error buffer  36 , when a grayscale value of a subsequent pixel is being processed. The subsequent pixel is one of the unprocessed neighboring pixels of the current pixel. Next, at step  84 , the quantized value is de-quantized by the de-quantization unit  66  of the QED module  34 . At step  86 , the value stored in the supplemental error buffer  40  is combined with the de-quantized value to produce a final error. The value stored in the supplementary error buffer includes a portion of the halftoning error and a portion of the quantization error or the entire quantization error from the preceding pixel. The final error is combined with the grayscale value of the subsequent pixel to generate a halftone signal. In this manner, the halftoning and quantization errors that are associated with each pixel of the input image are processed by the EDH device  32 . 
     Although the system and method in accordance with the present invention have been described with respect to grayscale printing, the system and method can be readily applied to color printing. For color printing application, the thresholding and error accumulation may be executed separately for each color plane, or in another appropriate manner which might be more suitable for color printing.