Abstract:
Error diffusion is performed using a Floyd-Steinberg-like approach. A integer-representation of a running error is compressed by storing only its most significant bits and returning any remainder to the error diffusion processor. The running error is shifted to the right until only the desired number of significant bits remain, and this compressed error is stored. Any portion of the original running error that is lost due to the shifting is treated as a remainder and is returned to the error diffusion processor for use in calculating an adjusted current pixel value. The amount of the shift is retained in compressed form to keep track of the number of shifts needed to form a truncated running error from the compressed running error.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
       [0001]    None. 
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    None. 
       REFERENCE TO SEQUENTIAL LISTING, ETC. 
       [0003]    None. 
       BACKGROUND 
       [0004]    1. Field of the Invention 
         [0005]    The present invention is directed to systems and methods for implementing error diffusion when processing an image, such as for printing. 
         [0006]    2. Description of the Related Art 
         [0007]    When printing an image using an output device which places discreet units of colorants (ink drops, toner, etc.) on media, it is necessary to reduce the range of the image pixels to match the reproduction capabilities of the printing device. This typically means a reduction in the bit resolution of the image. 
         [0008]    Most often, the reduction in bit resolution is accomplished by halftone transformation. Halftone transformation results, on a pixel-by-pixel basis for all image pixels, in the replacement of an original non-binary, or “gray-level” value of, e.g., 8 bits, with a binary value after comparison with some threshold. The threshold itself may vary dynamically depending on the non-binary pixel value, and other factors. The original 8-bit value at each pixel is thus substituted by either a “0” (representing an 8-bit value of 0) or a “1” (representing an 8-bit value of 255). The consequence of such a transformation at a pixel is that the overall “brightness” of the image is changed. To mitigate this, the change, or “error”, may be diffused to nearby, as yet untransformed pixels through a technique known as error diffusion. Error diffusion works by spreading the inaccuracy, or error, of the halftone decision at one pixel in the output image among nearby pixels, creating a visually superior transformation. Each original pixel value is adjusted based on the error contributed by adjacent and nearby pixels, and these contributions are taken into account in calculating the correct transformed value for the pixel. 
         [0009]    There are a number of error diffusion techniques, each of which uses a different combination of thresholding approaches, collection of nearby pixels to which the error is spread, error weightings to each of these nearby pixels, and other factors. The Floyd-Steinberg algorithm, developed in 1975 and known to those skilled in the art, is one of the more well-known implementations of error diffusion. This algorithm generates a series of error values for each image element as an image line is transformed. These error values are calculated by taking a fraction of nearby pixel error values and adding them together to represent a pixel location. 
         [0010]    In the Floyd-Steinberg algorithm, the error at a transformed pixel  420  is spread to a collection of four specific nearby pixels in the fashion shown in  FIG. 4A . The error from a just-transformed pixel  420  is spread to pixels  422 ,  424 ,  426  and  428  using error spread weights 7/16, 1/16, 5/16 and 3/16, respectively, the error spread weights representing the proportion of error at transformed pixel  420  that is spread to each adjacent untransformed, error-receiving pixel. Thus, from the perspective of a just-transformed pixel  420 , its total error is spread to “Next Back” pixel  428  (with “send backward coefficient” 3/16), “Next Below” pixel  426  (with “send below coefficient” 5/16), “Next Forward” pixel  424  (with “send forward coefficient” 1/16), and “Current Right” pixel  422  (with “send right coefficient” 7/16). In the foregoing nomenclature, the prefix “Next” refers to the next line to which the corresponding errors are spread. 
         [0011]      FIG. 4B  shows receipt of partial errors from the perspective of a pixel  450  that is about to be transformed using Floyd-Steinberg error diffusion. Soon-to-be transformed pixel  450  receives a portion of the error from each of four nearby, previously transformed pixels  452 ,  454 ,  456  and  458 , using error spread weights of 7/16, 1/16, 5/16 and 3/16, respectively. Of these, pixels  454 ,  456  and  458  are on the previous line (“above”), while recently-transformed pixel  452  is immediately to the left of untransformed pixel  450 , on the current line. From the perspective of untransformed pixel  450 , error is received from “Previous Back” pixel  454  (with “receive backward coefficient” 1/16), “Previous Above” pixel  456  (with “receive above coefficient” 5/16), “Previous Forward” pixel  458  (with “receive forward coefficient” 3/16), and “Current Left” pixel  452  (with “receive left coefficient” 7/16). In the foregoing nomenclature, the prefix “Previous” refers to the previous line from which the corresponding errors are received. 
         [0012]    From the foregoing description, it can be seen that in the Floyd-Steinberg algorithm the error created from transforming a pixel is spread to four adjacent pixels. Furthermore, prior to transformation, each pixel receives a portion of the error from each of the four adjacent pixels that have previously been transformed. 
         [0013]    The Floyd-Steinberg algorithm typically operates in row order (sometimes called “line order”). That is, an entire row, or line, of an image is transformed before the next row or line is transformed. Transformation of a row results in the storage of a large number of error values. For instance, if an image has a resolution of 600 pixels per inch (PPI), and each row of the image is 9 inches wide, then 5400 pixels worth of error data, each error datum comprising anywhere from 1 color (for a black &amp; white printer) to 3 or more colors (for a color printer), may need to be stored. 
         [0014]    Originally, the Floyd-Steinberg algorithm was implemented in software with data being read from, and written to a main memory having ample space. More recently, however, high-speed ASIC-based hardware implementations using integer arithmetic have been realized. For cost reasons, it is best to minimize the amount of memory used in such implementations. 
       SUMMARY OF THE INVENTION 
       [0015]    The target platform for a system in accordance with the present invention is a device, such as a printer, that is configured to perform error diffusion on image data pixels, each image data pixel comprising a non-binary pixel value. 
         [0016]    In one aspect, the present invention is directed to an error diffusion system configured to perform halftoning of image pixel data. The system comprises an error diffusion processor configured to receive a current pixel from a current image line and output an error diffused current pixel in response thereto; a first decompressor connected to the error diffusion processor and configured to decompress a compressed previous running error of a pixel belonging to a previous line of the image for use in calculating an adjusted pixel value of said current pixel; and a first compressor connected to the error diffusion processor and configured to compress a current running error of said current pixel to thereby form a compressed current running error for the current pixel. 
         [0017]    In another aspect, the present invention is also directed to a method for handling running error values during a halftoning process of an image. The method entails decompressing a compressed previous running error of a pixel belonging to a previous line of said image to form a truncated previous running error for use in calculating an adjusted pixel value of a current pixel in a current line of an image; and compressing a current running error of that same current pixel to thereby form a compressed running error for that pixel. 
         [0018]    In still another aspect, the present invention is directed to an error diffusion system for halftoning image data pixels one image line at a time, the system configured to calculate an adjusted pixel value for a current pixel in a current image line, the adjusted pixel value including partial errors from pixels on a previous image line, wherein the partial errors from the pixels on the previous image line are calculated only after halftoning of entire previous line has been completed. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0019]    The invention is now described with reference to the attached drawings in which: 
           [0020]      FIG. 1  shows an error diffusion system in accordance with the present application; 
           [0021]      FIG. 2A  shows a first embodiment of an error spread coefficient subsystem in accordance with the present application; 
           [0022]      FIG. 2B  shows a second embodiment of an error spread coefficient subsystem in accordance with the present application; 
           [0023]      FIG. 2C  shows a third embodiment of an error spread coefficient subsystem in accordance with the present application; 
           [0024]      FIG. 2D  shows a first embodiment of an error spread coefficient subsystem in accordance with the present application; 
           [0025]      FIG. 3  shows a block diagram of an error diffusion processor implementation in accordance with an embodiment of the present application; 
           [0026]      FIG. 4A  illustrates the prior art principle of error spread weights applied to the error of a transformed pixel; and 
           [0027]      FIG. 4B  illustrates the prior art principle of error spread weights received by a pixel to be transformed. 
       
    
    
     DETAILED DESCRIPTION  
       [0028]      FIG. 1  shows a block diagram of an error diffusion system  100  in accordance with an embodiment of the present invention. The system  100  can belong to a printer that receives an image with multi-bit data pixels and outputs halftone images while using an error diffusion algorithm. The system can be part of a stand-alone printer of the sort capable of printing photographs directly from a digital camera without first having to download the photographs to a personal computer. 
         [0029]    The system  100  includes a general purpose microprocessor  110  that is connected to a main memory  104 . Main memory  104  typically stores the input pixel data  106  of an image whose pixels are to be transformed from a non-binary format to a binary format, using error diffusion. The microprocessor  110  is part of an Application Specific Integrated Circuit (ASIC)  102  (represented by the dashed) configured to implement error diffusion. The dotted arrows represent connections between the microprocessor  110  and the other components of the ASIC, through data buses, control buses and other structures known to those skilled in the art of integrated circuit design. While in this embodiment, the error diffusion is performed using hardware on the ASIC, it can instead be performed entirely in software by the microprocessor  110 . It is further understood that in some embodiments, the main memory  104  can also be part of the ASIC  102 , or the input pixel data can be stored in a local memory on-board the ASIC. 
         [0030]    In addition to the microprocessor  110 , the ASIC  102  includes an error diffusion processor  120 , and error spread coefficient subsystem  130 , threshold generation circuitry  140 , and a running error compression/decompression subsystem, shown generally at  190 . 
         [0031]    The error diffusion processor  120  receives pixel data  106  from the main memory  104 , error spread coefficients  132  from the error spread coefficient system  130 , and threshold information  142  from threshold generation circuitry  140 . The error diffusion processor  120  uses this information, along with the truncated previous line running error information  124  provided by the error compression/decompression subsystem  190 , to transform the pixel data  106  into error diffused pixel data  126  which is stored in the main memory or in another memory location. Control signals  121  are sent from the error diffusion processor  120  to the error spread coefficient system  130  for requesting coefficients and performing other functions. 
         [0032]    The error spread coefficient system  130  receives input  112  from the microprocessor  110  and pixel data  106  in the case of data-driven determinations of the error spread coefficients. The error spread coefficient system  130  provides the error diffusion processor  120  with the error spread coefficients  132  to be used in allocating the error from a transformed pixel. As discussed further below, the error spread coefficient system  130  may be implemented in a number of different ways. 
         [0033]    The threshold generation circuitry  140  creates a threshold  142  that is used to compare with each adjusted non-binary (e.g., 8 bit) gray level pixel datum to determine whether the corresponding pixel is to be set to “0” or “1”. The threshold generation circuitry  140  is under the control of the microprocessor  110  and can include pseudo-random circuitry or the like to form a dynamic threshold, in a known manner. 
         [0034]    As is known to those skilled in the art, the error diffusion processor  120  typically processes image pixel data in line order—each pixel belonging to one line of an image is error diffused, before pixels of the next line are processed. The running error compression/decompression subsystem  190 , described in further detail below, is used to efficiently store the total error at each transformed pixel in an immediately preceding row of image data for use in adjusting a current pixel value of a pixel in a current row of image data. 
         [0035]      FIG. 3  illustrates the operation of the error diffusion processor  120  of  FIG. 1 , which performs most operations using 16-bit integer math for increased precision. 
         [0036]    The first step  301  is to receive the 8-bit value of a current pixel, from main memory  104 . The next step  302  is to shift this pixel value left by four bits, which is equivalent to multiplying by 16. At this point, the original 8-bit pixel has been transformed into having 12 significant bits. The transformed pixel is then input into a summer  304  along with five other inputs designated  306 A,  306 B,  306 C,  306 D and  340 , to form a 16-bit adjusted pixel value  308 . 
         [0037]    Input error  306 A is the partial error received by the current pixel from the transformed pixel in the preceding row and to the left (“previous back”). Input error  306 A is the product of an 8 to 10 bit representation of the truncated running error from transformed “previous back” pixel and a 4-bit representation of the “receive backward coefficient”  350 A, both of which are input to a first integer multiplier  352 A. 
         [0038]    Input error  306 B is the partial error received by the current pixel from the transformed pixel in the preceding row and directly above (“previous above”). Input error  306 B is the product of an 8 to 10 bit representation of the truncated running error from transformed “previous above” pixel and a 4-bit representation of the “receive above coefficient”  350 B, both of which are input to a second integer multiplier  352 B. 
         [0039]    Input error  306 C is the partial error received by the current pixel from the transformed pixel in the preceding row and to the right (“previous forward”). Input error  306 C is the product of an 8 to 10 bit representation of the truncated running error from transformed “previous forward” pixel and a 4-bit representation of the “receive forward coefficient”  350 C, both of which are input to a third integer multiplier  352 C. 
         [0040]    Input error  306 D is the partial error received by the current pixel from the just-transformed pixel immediately to the left in the current row (“current left”). Input error  306 D is delayed by delay  334  and is the delayed product of an 8 to 10 bit representation of the truncated running error from the immediately preceding (i.e., just-transformed pixel) and a 4-bit representation of the “receive left coefficient”  350 D, both of which are input to a fourth integer multiplier  352 D. 
         [0041]    In the foregoing discussion of the input errors  306 A,  306 B,  306 C,  306 D, the term ‘truncated running error’ refers to the fact that the least significant bits of the various running errors have been set to zero by retaining only the most significant bits and/or shifting to the right, as discussed further below. 
         [0042]    Finally, input error  340  is delayed by delay  336  and is the delayed version of a 4 to 6 bit current remainder  352  ( 152 B in  FIG. 1 ) comprising the least significant bits that have been stripped off the current running error by the error compression/decompression subsystem  190  during the compression process. 
         [0043]    Once the 16-bit adjusted current pixel value  308  has been formed by the summer  304 , a decision  312  is made to determine whether it exceeds a threshold. If the 16-bit adjusted current pixel value  308  exceeds the threshold  142 , then, in block  314 , the current pixel is set to “1” and the current running error  322  is calculated. If, on the other hand, the 16-bit adjusted current pixel value  308  does not exceed the threshold  142 , then, in block  318 , the current pixel is set to “0” and the 16-bit adjusted pixel value is used as the current running error  322 . Thus, the current running error  322  is the outcome of the halftoning decision represented by decision block  312  and blocks  314 ,  318 . 
         [0044]    In either case, the current running error  322  is tapped, as shown by line  315 , and input to a shifter  326  where it undergoes a right shift (i.e., a divide by 16). The output of the shifter  326  is then input to the aforementioned fourth multiplier  352 D to help form the ‘current left’ error  306 D which is delayed by delay  334  and which is to be provided to the pixel immediately to the right on the same line for use in the next iteration. 
         [0045]    One consequence of the design shown in  FIG. 3  is that the partial errors  306 A,  306 B,  306 C, contributed by the three pixels on a previous image line are calculated only after halftoning of the entire previous line has been completed. For a current pixel on a current image line, the partial errors from pixels on the previous line are calculated only after halftoning of the immediately preceding pixel (the pixel to the left) on the current image line has been completed. Moreover, these partial errors from the pixels on the previous image line are calculated only after decompressing compressed running errors corresponding to those pixels. 
         [0046]    The current running error  322  is also input to the error compression/decompression block  320 , representing the error compression/decompression subsystem  190  of  FIG. 1 . The output of the error compression/decompression block  320  comprises the aforementioned current running error remainder  352 , ( 152 B in  FIG. 1 ) and the truncated previous line running error  324 , ( 124  in  FIG. 1 ). The previous line truncated running error  324  comprise the total error at each transformed pixel on the previous line, and three of these are needed at any given time, the three corresponding to the “previous back”, previous above” and “previous forward” total errors. It is understood that pipelined systems, buffers and other hardware in the ASIC accommodates this. 
         [0047]    Returning to  FIG. 1 , the error compression/decompression subsystem  190  includes a first error compressor  150  for compressing each current running error value  122 . As it comes in, each current running error  122  is an N=16 bit value, and so the current running error has bit positions in the range [15:0], with 0 denoting the least significant bit. While it is possible to store all N=16 bits, this would mean that one would have to store on the order of 5400 (assuming 600 ppi and 9 inches) pixel&#39;s worth of data, or roughly 86,400 bits per line. The first error compressor  150  helps reduce this total. In particular, the first error compressor  150  stores a maximum of m most significant bits (MSB) of each 16-bit current running error value 122. M is selected to be equal to 8 bits (m=8), although it can be some other number. 
         [0048]    During operation, the first error compressor  150  checks to see the position of the most significant bit in the current running error  122 . 
         [0049]    If it is determined that the position of the most significant bit in the current running error  122  is between bit positions J=0 and J=11, then the current running error  122  is shifted to the right by k=4. The thus-shifted version of the current running error  122  is considered to be the compressed current running error  152 A (since the most significant bit, after shifting, is now between bit positions 0-7), and the lowest four bits of current running error  122  (originally in bit positions 0-3) are simply returned  152 B ( 352  in  FIG. 3 ) to the error diffusion processor  120  as a remainder. 
         [0050]    If, however, it is determined that the position of the most significant bit in the current running error  122  is between bit positions J=12 and J=14 then the current running error  122  is shifted to the right by an amount necessary to cause the m=8 most significant bits to occupy bit positions 0-7 to thereby create the compressed current running error  152 A. 
         [0051]    For example, given that the most significant bit is in bit position J=12, the first error compressor  150  shifts the entire current running error value to the right an appropriate amount (in this example, k=5 shifts to the right) until the most significant bit falls into the bit position 7. This way, only m=8 bits need to be stored as the compressed current running error  152 A, along with the shift data value  154 . 
         [0052]    Continuing with this example, the k=5 least significant bits (LSBs) are packed into an 8-bit word and returned  152 B ( 352  in  FIG. 3 ) to the error diffusion processor  120  as a remainder for use in summing errors for the next pixel, as discussed above. Therefore, in the system of  FIG. 1 , the error compressor  150  outputs an error shift value  154  in addition to the m-bit compressed running error  152 A. 
         [0053]    In a sense, one can consider the m=8 MSBs of the compressed running error to be a mantissa and the error shift value k=5 to be an exponent. The m=8 bit mantissa can then be shifted to the left by the k=5 error shift value to form a truncated previous line running error  124  which has a magnitude on the order of the its original running error  122 , and differs from its original running error  122  by just the k=5 least significant bits which, in any event, have been recycled as remainder  152 B ( 352  in  FIG. 3 ). 
         [0054]    As stated above, N is a 16 bit value, and so the current running error has bit positions in the range [15:0], with 0 denoting the least significant bit. It is understood in the foregoing example that if the most significant bit were in bit position J=11, instead of bit position J=12 in the N=16 bit current running error  122  ( 322  in  FIG. 3 ), the mantissa would still be m=8 bits, but there would only be a shift of k=4. Because the amount of required shift can vary among the running errors, we refer to this process of keeping a constant number of most significant bits while varying the amount of the shift as “dynamic shifting”. Furthermore, while in the above example m=8, it is understood that m may take on another value, such as m=5 in which case the coarseness of the truncated running error would increase as well due to the lower resolution in the compressed error. 
         [0055]    From the foregoing, it can be seen that shifting effectively compresses the original 16-bit current running error value  122  from the original N=16 bits down to m=8 bits. The resulting shifted value is output as an m=8 bit “compressed current running error”  152 A and sent to the compressed running error buffer  180  where it is stored. 
         [0056]    The error shift value  154  (which in this example is k=5) is passed on to shift data compressor  160 . The error shift values  154  (the “exponents”) corresponding to the compressed current running errors  152 A for a number of successive 16-bit current running error values  122  are often the same, or vary by 1, at most. Therefore, run length encoding (RLE) of the error shift values can be performed by the shift data compressor  160 . The shift data compressor  160  outputs RLE compressed shift data  162 , in a form such as a packets, for storage in the compressed shift data buffer  182 . These RLE shift data packets  162  can be of variable length, or alternatively, of fixed length, depending on the RLE implementation chosen. 
         [0057]    The compressed running error buffer  180  is a FIFO buffer. Current error compressor  150  compresses a current line running error  122  for a pixel in a current line of an image to thereby form the compressed current running error  152 A which is stored in buffer  180 . 
         [0058]    The calculation of the current line running error  122  itself depends, in part, on the partial errors  306 A,  306 B,  306 C contributed by pixels in the previous line, as discussed above with reference to  FIG. 3 . Therefore, before the current error compressor  150  compresses the current running error  122 , a compressed previous running error  156  is retrieved from the buffer  180  and is decompressed by the previous error decompressor  158 . To reconstitute the previous running error (or more precisely, a truncated version of it), the compressed previous running error  156  and its associated shift value are needed. The stored compressed previous running error  156  must first be retrieved from the compressed running error buffer  180  and then decompressed by previous error decompressor  158 . It should be noted that the decompression of the compressed previous running error  156  can be implicit. Since the decompressed previous running error is to be multiplied by a coefficient  350 , it is possible to apply the shift to the coefficient rather than apply it to the compressed previous running error. Likewise, the coefficient could be stored in a preshifted form eliminating the need for a shift at all. 
         [0059]    To perform this decompression, the shift data decompressor  168  first retrieves the appropriate compressed shift data  166  from the compressed shift data buffer  182 , then decompresses this to reconstitute the error shift value for each needed pixel&#39;s compressed running error in the previous line, and lastly supplies the corresponding reconstituted error shift value  170  to the previous error decompressor  158 . The previous error decompressor  158  then uses this reconstituted error shift value  170  to shift the compressed previous running error  156  by the appropriate amount to form the truncated previous line running error  124  that is supplied to error diffusion processor  120 . 
         [0060]    In the present context, “truncation” refers to the fact that while the order of magnitude of the truncated running error is comparable to that of the original current running error, its least significant bits are not contained in that value. 
         [0061]    In summary, then, it can be seen that the compression/decompression subsystem  190  includes a first compressor  150  connected to the error diffusion processor  120  and configured to retain, at most, only the m most significant bits of each of a plurality of current running errors to thereby form a corresponding plurality of compressed current running errors  152 A. The compression/decompression subsystem  190  also includes a second compressor  160  configured to compress information sufficient to create a truncated previous line running error  124  corresponding to its original current running error  122 , from the compressed previous running error  156 . 
         [0062]    As mentioned above, error diffusion is performed in line order, and so all the pixels belonging to a single line are processed one after the other. Then, in the general case, one may consider the i th  pixel in a line of image data to have an N-bit current running error with the most significant bit in bit position J i , N&gt;J i . If J i &lt;12, the current running error is shifted to the right by k i =4 bits, the m=8 bits in bit positions [7:0] are stored in the compressed error buffer, and the shift value k i  itself is sent to the second compressor  160 . If J i ≧12, the current running error is shifted to the right by a number of bits k i  such that its most significant bit ends up in bit position  7 , the m=8 bits in bit positions [7:0] are again stored in the compressed error buffer, and the shift value k i  itself is again sent to the second compressor  160 . Finally, the various corresponding k i  shift values are compressed. 
         [0063]    Since the compressed running error buffer  180  is a FIFO buffer, as the first compressor  150  accepts a new running error  122 , the previous error decompressor  158  outputs a truncated previous line running error  124 , the appropriate location in the compressed running error buffer  180  being overwritten in the process. It is further understood from  FIG. 3  that since three such truncated error values (“receive back total”, “receive above total”, and “receive forward total”) are needed at one time by the summer  304 , the diffusion processor  120  must include appropriate registers, circuitry, buffers and the like, all well within the knowledge of one skilled in the art, to accommodate this requirement. 
         [0064]    Considerable savings in buffer memory from using the two compressors  150 ,  160  with the dynamic shifting can be realized. Assuming that m=8 MSBs are stored in the compressed running error buffer  180 , and further assuming that RLE compression of the error shift values  154  requires 1 bit for every 10 pixels, a line of 5400 pixels requires that roughly 5400×8+540=43,740 bits of data be stored by compressed running error buffer  180  and compressed shift data buffer  182 . This is a savings of about 42,660 bits, or roughly 49% fewer bits than would be required if all 5400×16=86,400 bits of the current running error  122  were stored. If, instead, only m=4 MSBs were stored (in which case the remainder  122  ( 352  in  FIG. 3 ) returned to the error diffusion processor would be 8 or 9 bits), then only 5400×8+540=22140 bits of data would have to be stored, for a savings of about 74% over storing all 86,400 bits. 
         [0065]      FIGS. 2A-2D  present four different embodiments for the error spread coefficient subsystem circuitry  130  seen in  FIG. 1 . 
         [0066]    In  FIG. 2A , the error spread coefficient subsystem circuitry  130 A uses a static 16-bit error spread vector  210 . The error spread vector  210  comprises error spread information that is used by the error diffusion processor  120  to determine how to weight the total error from each of four previously transformed adjacent pixels in preparation for summer  304 . In one embodiment, this error spread information comprises four 4-bit error spread coefficients  212 . For this, the 16-bit error spread vector  210  can be considered as four 4-bit numbers ranging from 0-15, each number corresponding to the relative weight one of the four error spread weights discussed above. Thus, as seen in  FIG. 2A , the first four bits [15:12] of the 16-bit error spread vector  210  comprises “0001”, which corresponds to a weight of 1 (for the “back” coefficient”  350 A), the next four bits [11:8] comprises “0101”, which corresponds to a weight of 5 (for the “above” coefficient  350 B), next four bits [7:4] comprises “0011”, which corresponds to a weight of 3 (for the “forward” coefficient  350 C), and the last four bits [3:0] comprises “0111”, which corresponds to a weight of 7 (for the “left” coefficient  350 D). 
         [0067]    The error diffusion processor  120  uses each of these 4-bit values as a relative weighting, and so multiplies each of the truncated running errors by an appropriate corresponding 4 bit value to create four partial errors  306 A,  306 B,  306 C and  306 D used in the summer  304  within the error diffusion processor  120 . When the 16-bit error spread vector  210  is provided to the error diffusion processor  120 , the latter understands the meaning of the four groupings of bits and uses them accordingly. 
         [0068]    In  FIG. 2B , the error spread coefficient subsystem  130 B uses a pixel data-driven paradigm to determine the error spread coefficients. The 8-bit gray-level value of the pixel data  106  being transformed is used to select from among a predetermined set of four error spread coefficients, each set comprising a 16-bit error spread vector. In particular, the 8-bit pixel data is input to a 256×16 bit lookup table (LUT)  224 . Each entry in the lookup table  224  comprises a set of four 4-bit error spread coefficients, one for each of the 256 possible 8-bit gray level values (0-255), which are used to index the appropriate entry in the lookup table  224 . 
         [0069]    In the case of error spread coefficient subsystem  130 B, each of the  256  error spread vectors comprises four 4-bit weights dictating how to spread the running error from the current pixel to adjacent untransformed pixels. This contrasts with embodiment  130 A where the fixed error spread vector  210  dictates how to weight the total error from each of the previously transformed pixels in preparation for summer  304 . 
         [0070]    In response to a particular 8-bit pixel value input thereto, the lookup table  224  supplies the appropriate 16-bit error spread vector and splits it in two parts. The first part comprises a 4-bit weight that is sent via output  222 A to the error diffusion processor  120  for use as the “receive left” coefficient  350 D for the next pixel (and also happens to be the “send right” coefficient for the current pixel). The second part is a 12 bit value  228  which comprises the “send back”, “send below” and “send forward”, coefficients for the current pixel. These are stored in a 5400×12-bit spread buffer  226  (12 bits for each pixel in a row) again assuming 600 ppi by 9 inch line length. The error diffusion processor  120  retrieves the appropriate set of previous line “receive” coefficients via output  222 B of the error spread coefficient subsystem  130 B. 
         [0071]      FIG. 2C  shows a third embodiment of an error spread coefficient subsystem  130 C. The error spread coefficient subsystem  130 B of  FIG. 2B  required a 5400×12-bit spread buffer  226 , totaling 64,800 bits of data. The error spread coefficient subsystem  130 C of  FIG. 2C  uses less memory by compressing a plurality of consecutive sets of the 12-bit error spread coefficient data that ultimately will be used in the error diffusion processor  120  as the “receive back”, “receive above” and “receive forward” coefficients  350 A,  350 B,  350 C, respectively. 
         [0072]    The error spread coefficient subsystem  130 C of  FIG. 2C  includes a 256×16 data-driven lookup table  232  which behaves much the same as lookup table  224  in error spread coefficient subsystem  130 B of  FIG. 2B . Thus, an indexed  16 -bit error spread vector is split into two parts, the first part being the same 4-bit weight provided to the error diffusion processor via output  242 A. The second part, which is the 12 bit value  232 A comprising the current set of “send backward”, “send below”, and “send forward” 4-bit error spread coefficients is sent to block compressor  234 . 
         [0073]    Block compressor accepts a plurality of consecutive sets of 12-bit error spread coefficients, and outputs compressed error spread data  234 A corresponding to these consecutive 12-bit error spread coefficients. These compressed error spread data can be in the form of multi-bit, such as 64-bit, compressed data blocks  234 A. These blocks  234 A of compressed 12-bit error spread coefficients are then stored in compressed spread buffer  236 . Thus, in this third embodiment  130 C, the compressor  234  is configured to compress a plurality of sets of at least three of said four error spread coefficients to thereby form compressed error spread data  234 A. 
         [0074]    When the error diffusion processor  120  needs to retrieve a set of previous line “receive” coefficients, the decompressor  238  selectively retrieves the appropriate compressed error spread coefficient block  236 A from the compressed spread buffer  236 , decompresses it, and provides the required information to the error diffusion processor  120  via output  242 B. 
         [0075]    Compression of consecutive 12-bit sets is possible because of their redundancy. This redundancy is due to a combination of two factors: (1) although the lookup table  232  stores one error spread vector for each gray level value, these vectors are not unique—as few as only 16 or so different vectors may need to be stored—thus, two gray level values that are close to each other typically will index entries comprising identical error spread vectors; and (2) in a line of an image, due to the relatively low spatial frequencies, it is not uncommon for runs of adjacent pixels&#39; gray level values to be identical or very close to one another, and so these map onto the same error spread vector. The degree of compression depends on such factors as the spatial frequencies present in image, the number of different error spread vectors in the lookup table  232 , the correlation between neighboring gray level values and the error spread vectors onto which they map, and the like. 
         [0076]      FIG. 2D  shows a fourth embodiment of an error spread coefficient subsystem  130 D. The error spread coefficient subsystem  130 D includes a 16×4 bit left pixel coefficient array  264 , and a 16×12 error spread coefficient array which stores 16 predetermined sets of three 4-bit coefficients which ultimately will be used in the error diffusion processor  120  as the “receive back”, “receive above” and “receive forward” coefficients  350 A,  350 B,  350 C, respectively. 
         [0077]    In this embodiment, incoming 8-bit pixel data  106  first indexes 256×4 bit pointer lookup table  252 . In response to a pixel value, the pointer lookup table  252  outputs a 4-bit error spread pointer  252 A to left pixel coefficient array  264  and to pointer compressor  254 . 
         [0078]    The 4-bit pointer  252 A selects one from among 16 possible (2 4 ) entries in the 16×4 bit left pixel coefficient array  264 . In response to the 4-bit error spread pointer  252 A, left pixel coefficient array  264  provides the error diffusion processor  120 , via output  262 A, the “receive left” coefficient  350 D for use by the next pixel that is processed. 
         [0079]    The 4-bit error spread pointer  252 A is also supplied to a pointer compressor  254  which compresses a plurality of consecutive pointers to thereby from compressed error spread pointer information  254 A. In one embodiment this compressed error spread pointer information  254 A is formed as 64-bit compressed pointer blocks  254 A which are then stored in a compressed pointer buffer  256 . 
         [0080]    When the error diffusion processor  130  needs the “receive back”, “receive above” and “receive forward” coefficients  350 A,  350 B,  350 C, respectively, it sends appropriate control signals  121 D to the pointer decompressor  258  within the error spread coefficient subsystem  130 D. 
         [0081]    Decompressor  258  then obtains the correct compressed pointer block(s)  256 A from the compressed pointer buffer  256 , decompresses the compressed error spread pointer information and thereby forms at least one decompressed 4-bit error spread pointer. The appropriate decompressed 4-bit error spread pointer(s) are then used to retrieve the needed coefficients. In this regard, it should be noted that in embodiments where the coefficient array  266  comprises the triplet of “send backward”, “send below” and “send forward” 4-bit error spread coefficients, more than one such 12-bit triplet may need to be retrieved, since the “receive backward”, “received above” and “receive forward” coefficients  350 A,  350 B,  350 C, respectively, may belong to as many as 3 different entries within the 16 entry coefficient array  266 . 
         [0082]    The present invention has been described with respect to specific embodiments. However, it will be appreciated that modifications and variations of the present invention are covered by the above teachings and within the purview of the appended claims without departing from the spirit and intended scope of the invention.