Abstract:
Machine-enabled methods of, and system, and processor readable media, embodiments for, tone quantization error diffusion.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is related to US Patent Application, Attorney Docket No. SLA2564, titled “Multi-Level Surround Error Diffusion,” by Ching-Wei Chang, filed Mar. 27, 2009, which is hereby incorporated herein by reference in its entirety for all purposes. 
     
    
       [0002]    A portion of the disclosure of this patent document contains material which is subject to (copyright or mask work) protection. The (copyright or mask work) owner has no objection to the facsimile reproduction by any-one of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all (copyright or mask work) rights whatsoever. 
       FIELD OF ENDEAVOR 
       [0003]    The present invention, in its several embodiments, relates to methods, systems and processor readable media for tone quantization error diffusion. 
       BACKGROUND 
       [0004]    A conversion of an image format may result in a restriction in the gradation of expressions of grayscale and/or color component intensity.  FIG. 1  is a top-level block diagram of a process  100  where a digital image  110  comprised of pixels having tone levels, {P′}, is provided to a processor  120  configured to execute instructions that quantizes the intensity level of each pixel of the digital image, resulting in the possibility of a tone error, i.e., the difference between the provided pixel tone intensity and the quantized tone intensity, for each quantized pixel. In addition to the tone quantization, the processor may allocate the resulting quantized tone error to the tone level of image pixels not yet quantized. The result is a quantized digital image  130  having tone values, {V}, that are affected by the input tone levels, the quantization levels and logic, and the allocation of tone error. The tone levels of pixels of a digital image may be expressed in a matrix of rows and columns. A scan line may be defined as a row or column of pixels scanned serially for tone quantization. When a horizontal scanning direction is employed, the horizontal scanning direction may be from right-to-left, right-to-left, or alternate the scanning direction between lines.  FIG. 2A  illustrates an example of right-to-left scanning of a digital image.  FIG. 2B  illustrates an example of left-to-right scanning of a digital image.  FIG. 2C  illustrates an example of alternating right-to-left and left-to-right scanning of a digital image. 
         [0005]    Image dithering may be used to distribute the resulting pixel tone quantization error. The results of image dithering may be used to adjust pixels of the quantized image for purposes of image display, e.g., intensity of tone levels for light display and density of pigmentation for print display. Methods, such as Floyd-Steinberg dithering, achieve image dithering by diffusing the quantization error of a pixel to the yet-unscanned neighboring pixels according to a weighted apportionment. The Floyd-Steinberg method typically quantizes the pixels of an image by scanning the image from left-to-right, top-to-bottom.  FIG. 3  shows a portion of an image matrix  300 , a three-by-three set of cells or pixels, and an example of a left-to-right scan  310  where the tone value of a pixel, P, is being quantized, and portions  321 - 324  of the resulting tone quantization error are distributed to the yet-unscanned, i.e., yet-to-be-quantized, nearest neighbor pixels  331 - 334  of the pixel, P. That is, each quantization cycle of a pixel in a left-to-right scan includes pushing portions of the quantization error to the neighboring pixel on the right and the three nearest neighbor pixels in the next scan line. 
         [0006]      FIG. 4  shows a process where a pixel tone value may be defined by its row and column locations respectively as P i,j , and conceptually may be comprised of a quantized tone value, V i,j , and a tone error, E i,j , where the tone error of this example is the difference between the original tone level and the quantized tone level. So conceptually, P i,j =V i,j +E i,j . Based on a determined tone quantization threshold, V i,j  can be established for P i,j , as its representation in the quantized tone image. In turn, E i,j  is established, i.e., E i,j  is assigned the difference between P i,j  and V i,j , or E i,j ←(P i,j −V i,j ), and error diffusion (E.D.) may be effected by the value of E i,j  being apportioned according to a weighting scheme to the yet-to-be-quantized nearest neighbors of P i,j . Accordingly, the tone error diffusion of P i,j  may be propagated as follows: (a) P i,j ←(P i,j+1 −w 1 *E i,j ); (b) P i+1,j−1 ←(P i+1,j−1 −w 2 *E i,j ); (c) P i+1j ←(P i+1,j −w 3 *E i,j ); and (d) P i+1,j+1 ←(P i+1,j+1 −w 4 *E i,j ). The Floyd-Steinberg method typically has the values of the weights normalized according to: w 1 = 7/16, w 2 = 3/16, w 3 = 5/16, and w 4 = 1/16. 
         [0007]    If halftones are used to express the tone quantized image, the quantized tones for any pixel may be expressed via cells of a matrix, e.g., a two-by-two matrix, each cell having at least a monotone pigment level. The pigmentation of a cell is achieved via the application of a dot of pigment which may bleed into the adjacent cells or may be insufficient to fully pigment a designated cell. By measuring dot intensity of various levels of pixel quantization, a gamma correction vector, may be used to adjust the tone density of half-toned images. 
       SUMMARY 
       [0008]    The present invention included method, system, and processor readable media, embodiments for tone quantization error diffusion. For example, a machine-enabled method of tone error diffusion in a pixel array may comprise steps of: (a) receiving a pixel array comprising a second line of pixels interposed between a first line of pixels and a third line of pixels; (b) a first stage process by a computing device comprising: (1) determining a tone error for a first pixel of the first line of pixels of the pixel array based on an input value of the first pixel of the first line of pixels and at least one threshold value, the first pixel having only one lineally adjacent pixel; (2) determining a tone error for a second pixel lineally adjacent to the first pixel of the first line of pixels based on: an input value of the second pixel of the first line of pixels, a portion of the tone error of the first pixel of the first line of pixels, and the at least one threshold value; (3) determining a tone error for a first pixel of the third line of pixels of the pixel array based on an input value of the first pixel of the third line of pixels and at least one threshold value, the first pixel of the third line of pixels having only one lineally adjacent pixel; and (4) determining a tone error for a second pixel lineally adjacent to the first pixel of the third line of pixels based on: an input value of the second pixel of the third line of pixels, a portion of the tone error of the first pixel of the third line of pixels, and the at least one threshold value; and (b) a second stage process by the computing device, or a second computing device in communication with the first computing device, comprising: (1) determining a tone error for a first pixel of the second line of pixels of the pixel array based on: an input value for the first pixel of the third line of pixels, a portion of the tone error of each adjacent pixel of the first line of pixels, a portion of the tone error of each adjacent pixel of the third line of pixels, and the at least one threshold value, the first pixel of the second line of pixels having only one lineally adjacent pixel; and (2) determining a tone error for a second pixel lineally adjacent to the first pixel of the second line of pixels based on: an input value for the second pixel of the third line of pixels, a portion of the tone error of the first pixel of the second line of pixels, a portion of the tone error of each adjacent pixel of the first line of pixels and a portion of the tone error of each adjacent pixel of the third line of pixels, and at least one threshold value. 
         [0009]    The method may start on any line as a first line and continue with subsequent lines of the input pixels array. The method may be structured within a configured computing device, e.g., a processor having addressable memory and responsive to machine-readable instructions, to be performed iteratively until a stopping rule, such as the end of the input pixel array, is achieved. Accordingly, the first stage process of the method of tone error diffusion may further comprise: (a) iteratively determining a tone error for each successive pixel lineally adjacent to the second pixel of the first line of pixels based on an input value of the successive pixel of the first line of pixels, a portion of the determined tone error of the lineally adjacent pixel of the first line of pixels, and the at least one threshold value; and (b) iteratively determining a tone error for each successive pixel lineally adjacent to the second pixel of the third line of pixels based on an input value of the successive pixel of the third line of pixels, a portion of the determined tone error of the lineally adjacent pixel of the third line of pixels, and the at least one threshold value. Likewise, the second stage process may further comprise iteratively determining a tone error for each successive pixel lineally adjacent to the second pixel of the second line of pixels based on: an input value of the successive pixel of the second line of pixels, a portion of the determined tone error of the lineally adjacent pixel of the second line of pixels, a portion of the tone error of each adjacent pixel of the first line of pixels and a portion of the tone error of each adjacent pixel of the third line of pixels, and at least one threshold value. 
         [0010]    The second stage process of the method of tone error diffusion embodiments of claim  1  may further have the step of determining a tone error for the second pixel lineally adjacent to the first pixel of the second line of pixels of the second stage process being based on: (a) an input value for the second pixel of the second line of pixels, (b) a portion of the tone error of the first pixel of the second line of pixels, (c) a portion of the tone error of each pixel of the first line of pixels within two pixel spaces from a pixel of the first line immediately adjacent to the second pixel of the second line, and a portion of the tone error of each pixel of the third line of pixels within two pixel spaces from a pixel of the third line immediately adjacent to the second pixel of the second line; and (d) at least one threshold value. 
         [0011]    In addition, machine-enabled method embodiments of the present invention of diffusing tone quantization error of a digital image may comprise: (a) receiving, by a digital processor, a digital image having input pixel tone levels according to i rows and j columns; (b) for alternate rows of pixels of the digital image, the processor: (1) quantizing an assigned pixel tone level of each pixel, or S i,j , in series j, wherein the assigned tone level, or S i,j , comprises an input tone value, or P i,j , and, if present, a partial tone quantization error, or N i,j−1 , from the last quantized pixel; and (2) determining a total quantization error, or D i,j  comprising a partial tone quantization error, or N i,j , and a remainder tone quantization error, or E i,j , and (3) storing the remainder tone quantization error, or E i,j ; and (c) for rows of pixels interposed between the alternate rows of pixels of the digital image, the processor, or one or more additional processors in communication with the processor: (1) quantizing an assigned pixel tone level of each pixel, or S i,j , in series j, of row i, where the assigned tone level, or S i,j , comprises: (A) an input tone value, or P i,j ; (B) a partial tone quantization error, or N i,j−1 , from the last quantized pixel in row i, if present; and (C) a sum of a weighted remainder tone quantization errors of two or more of the nearest neighbor pixels of the alternate rows comprising the sum: w 2 *E i−1,j +w 5 *E i+1,j +w 6 *E i+1,j+1 ) and, at least one of: (i) the sum: w 1 *E i−1,j−1 +w 4 *E i+1,j−1  and (ii) the sum: w 3 *E i−1,j+1 +w 6 *E i+1,j−1  and (2) determining a total quantization error, or D i,j  comprising a partial tone quantization error, N i,j . The steps of quantizing the assigned pixel tone level of each pixel, or S i,j , in series j for the method of diffusing tone quantization error of a digital image may based on a threshold value. For rows of pixels interposed between the alternate rows of pixels of the digital image, the quantizing step of the method of diffusing tone quantization error of a digital image may comprise quantizing an assigned pixel tone level of each pixel, or S i,j , in series j, or row i, wherein the assigned tone level, or S i,j , comprises: (A) an input tone value, or P i,j ; (B) a partial tone quantization error, or N i,j−1 , from the last quantized pixel in row i, if present; and (C) if remainder tone quantization errors E i−1,j−1 . E i+1,j−1 , E i−1,j+1 , and E i+1,j+1  are present, a sum of weighted remainder tone quantization errors of the nearest neighbor pixels of the alternate rows comprising: the sum: w 1 *E i−1,j−1 +w 2 *E i−1,j +w 3 *E i−1,j+1 +w 4 *E i+1,j−1 +w 5 *E i+1,j +w 6 *E i+1,j+1 . The weights of the method of diffusing tone quantization error of a digital image may sum to unity and may provide additional weight to the pixels immediately above and immediately below the pixel being quantized, i.e., sharing a common column, j. For example, the weights for the remainder tone error values may be assigned as follows: w 1 =⅛; w 2 = 2/8; w 3 =⅛; w 4 =⅛; w 5 = 2/8; and w 6 =⅛. 
         [0012]    Embodiments of the present invention may include devices and systems. For example, a system for producing image output comprising: a image tone quantization module may be configured to: (a) input a digital image having input pixel tone levels according to i rows and j columns; and (b) for alternate rows of pixels of the input digital image: (1) quantize an assigned pixel tone level of each pixel, or S i,j , in series j, wherein the assigned tone level, or S i,j , comprises an input tone value, or P i,j , and, if present, a partial tone quantization error, or N i,j−1 , from a last quantized pixel; (2) determine a total quantization error, or D i,j  comprising a partial tone quantization error, or N i,j , and remainder tone quantization error, or E i,j , and (3) store the remainder tone quantization error, or E i,j ; and (c) for rows of pixels interposed between the alternate rows of pixels of the input digital image: (1) quantize an assigned pixel tone level of each pixel, or S i,j , in series j, of row i, wherein the assigned tone level, or S i,j , comprises: (A) an input tone value, or P i,j ; (B) a partial tone quantization error, or N i,j−1 , from the last quantized pixel in row i, if present; and (C) a sum of a weighted remainder tone quantization errors of two or more of the nearest neighbor pixels of the alternate rows comprising the sum: w 2 *E i−1,j +w 5 *E i+1,j +w 6 *E i+1,j+1 ) and, at least one of: (i) the sum: w 1 *E i−1,j−1 +w 4 *E i+1,j−1  and (ii) the sum: w 3 *E i−1,j+1 +w 6 *E i+1,j+1 ; and (2) determine a total quantization error, or D i,j  comprising a partial tone quantization error, N i,j . The image tone quantization module of the system for producing image output may be further configured to quantize the assigned pixel tone level of each pixel, or S i,j , in series j based on a threshold value. 
         [0013]    Embodiments of the present invention include machine-readable medium, particularly computer/processor readable medium having processor executable instructions thereon which, when executed by a processor cause the processor to: (a) for alternate rows of pixels of a digital image having input pixel tone levels according to i rows and j columns: (1) quantize an assigned pixel tone level of each pixel, or S i,j , in series j, wherein the assigned tone level, or S i,j , comprises an input tone value, or P i,j , and, if present, a partial tone quantization error, or N i,j−1 , from a last quantized pixel; (2) determine a total quantization error, or D i,j  comprising a partial tone quantization error, or N i,j , and remainder tone quantization error, or E i,j , and (3) store the remainder tone quantization error, or E i,j ; and (b) for rows of pixels interposed between the alternate rows of pixels of the digital image: (1) quantize an assigned pixel tone level of each pixel, or S i,j , in series j, of row i, wherein the assigned tone level, or S i,j , comprises: (A) an input tone value, or P i,j ; (B) a partial tone quantization error, or N i,j−1 , from the last quantized pixel in row i, if present; and (C) a sum of a weighted remainder tone quantization errors of two or more of the nearest neighbor pixels of the alternate rows comprising the sum: w 2 *E i−1,j +w 5 *E i+1,j +w 6 *E i+1,j+1 ) and, at least one of: (i) the sum: w 1 *E i−1,j−1 +w 4 *E i+1,j−1  and (ii) the sum: w 3 *E i−1,j+1 +w 6 *E i+1,j−1 ; and (2) determine a total quantization error, or D i,j  comprising a partial tone quantization error, N i,j . The processor readable medium embodiments having processor executable instructions thereon, when executed by a processor, may additionally cause the processor to quantize the assigned pixel tone level of each pixel, or S i,j , in series j based on a threshold value. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]    Embodiments of the present invention are illustrated by way of example and not limitation in the figures of the accompanying drawings, and in which: 
           [0015]      FIG. 1  is a top-level image tone quantization process functional block diagram; 
           [0016]      FIGS. 2A ,  2 B, and  2 C illustrate exemplary scan patterns; 
           [0017]      FIG. 3  illustrates apportioning tone quantization error to the tone levels of yet-to-be-quantized pixels; 
           [0018]      FIG. 4  illustrates apportioning tone quantization error to the tone levels of yet-to-be-quantized pixels; 
           [0019]      FIG. 5  illustrates, at a top level an exemplary system comprising a plurality of processing devices in communication with a multi-function peripheral (MFP) device; 
           [0020]      FIG. 6A  illustrates a top level functional block diagram of an exemplary MFP device; 
           [0021]      FIG. 6B  illustrates a top level functional block diagram of an exemplary host computer that may host a driver embodiment of the present invention; 
           [0022]      FIG. 7  is a top-level flow chart of a process embodiment of the present invention; 
           [0023]      FIG. 8  illustrates exemplary scan patterns of the first stage and second stage processing of the present invention; 
           [0024]      FIG. 9A  illustrates an example of the apportionment of tone quantization error to the tone levels of yet-to-be quantized pixels during the first stage processing; 
           [0025]      FIG. 9B  illustrates an example of the apportionment of tone quantization error to the tone levels of yet-to-be quantized pixels during the second stage processing; 
           [0026]      FIG. 10  illustrates an example of the apportionment of tone quantization error to the tone levels of yet-to-be quantized pixels during the first stage processing; 
           [0027]      FIG. 11  illustrates an example of the apportionment of tone quantization error to the tone levels of yet-to-be quantized pixels during the second stage processing; and 
           [0028]      FIG. 12  illustrates an example of the thresholding for quantizing and half-toning the tone levels of the pixels. 
       
    
    
     DETAILED DESCRIPTION 
       [0029]      FIG. 5  illustrates an exemplary system embodiment  500  of the present invention where a printing device or a multi-functional peripheral (MFP) device  510  may be in direct communication  512  with a processing device  520 , such as a computer hosting one or more drivers applicable to the printing device or multi-functional peripheral device  510 . In addition, via a network  530  and a network link  531 - 533 , the printing device or a multi-functional peripheral device  510  may be in communication with one or more processing devices  540 ,  541 , such as a one or more computers that may each host one or more drivers applicable to the printing device or the MFP device  510 . 
         [0030]    The exemplary printing device or MFP device  510  of  FIG. 5  may be illustrated in greater exemplary functional detail in  FIG. 6A . Interface ports  602  may be present to connect a printer cable, a network link, or an external wireless module. The interface ports  602  may be serviced by one or more interface controllers  604  that function to direct communications and/or condition signals between the respective interface port  602  and one or more modules of the MFP device  510  which may be in common communication via a data bus  606 . The MFP device  510  may include one or more processing modules  608  that may draw data from read-only memory (ROM)  610  and exchange data with random access memory (RAM)  612  and may store files having sizes greater than the RAM  612  capacity in one or more mass storage units  614 . The MFP device  510  may maintain a log of its images  616  and have a user display and interface  618 . The image log  616  may be a separate module or distributed, for example, with a portion executed via the processing module  608  that may access parameters, files, and/or indices that may be stored in ROM  610 , RAM  2612 , a mass storage unit  614  or in combination thereof. The MFP device  510  may include as individual or separate modules a scan control module  620 , a facsimile (FAX) control module  622 , and a copy control module  624  where each module may service the scanner  630  to direct communications and/or condition signals between the scanner  630  and one or more modules of the MFP device  510 , for example, via the data bus  606 . The MFP device  510  may include as individual or separate modules the FAX control module  622 , the copy control module  624  and a print control module  626  where each module may service the printer  640  to direct communications and/or condition signals between the printer  640  and the one or more modules of the MFP device  510 , for example, via the data bus  606 . The exemplary MFP device  510  may store a calibration table in ROM  610 , RAM  612 , a mass storage unit  614  or in combination thereof and accordingly, the calibration table may be accessed by the print control module  626  and/or a processing module  608  and made available to devices external to the MFP device  510  via one or more interface ports  602 . The exemplary MFP device  510  may have notice, for example, due to a user input via the user interface  618  or sensed by an output orientation sensor  642  of the printer  640  and may be communicated via the print control module  626  to devices external to the MFP device  510  via one or more interface ports  602 .  FIG. 6B  illustrates a top level functional block diagram of a processing device that is an exemplary host computer  650  that may host a driver embodiment of the present invention that, via an input/output interface  655  may interface  659  with the exemplary MFP of  FIG. 6A  via a wireless or wired network link  656  or a parallel, serial, or universal serial bus (USB) cable  657 . The user interface  670  may include tactile input via keyboard, mouse and/or touch screen and/or audio input via a microphone. The user interface  670  may provide output to the user via a display, e.g. a graphical user interface (GUI), and/or provide audio output to the user via one or more speakers, headphones or ear buds. The host computer  650  may further comprise a central processing unit (CPU)  651 , read only memory (ROM)  652 , random access memory (RAM)  653  and a mass storage unit  654 , such as a hard disk drive (HD). Two or more elements of the host computer  650  may be in communication via a data bus  660 . The general accessing of data, processing of data and communication and display of data may be handled at the CPU level of the host computer  650  by an operating system such as MICROSOFT™ WINDOWS™. 
         [0031]    Viewing  FIGS. 5 ,  6 A, and  6 B together, image tone quantization may be performed by a computer  540 ,  541 ,  520 ,  650 , for display purposes, and, for printing purposes, by a computer  540 ,  541 ,  520 ,  650  in communication  530 ,  656 ,  657  with an MFP  510 , by the MFP  510 , or via a combination of steps distributed between two or more processing units that may include the MFP  5   10 . The resulting images may have a quantized tone level per pixel that may be based on a determined or predetermined threshold setting. For a printing example, two-by-two monotone cells may be used as a halftone cell to express five levels of tone. An image region comprises several cells to achieve a resolution such as 300 dpi or 600 dpi. While the ideal tone intensities of one, two, and three pigmented cells may be expected to be 25%, 50%, and 75% respectively, due to pigmentation mechanics, measured tone intensities may be much different, e.g., 60%, 80%, and 92% respectively. Eight-bit expressions of tone levels may equate these measured exemplary results to “153,” “204,” and “235” respectively, where “255” would be 100%—the highest intensity level. 
         [0032]      FIG. 7  is a top-level process block diagram  700  of an embodiment of the present invention. The surround error diffusion process  710  is shown comprising a first stage process  711  and a second stage process  712 . Also shown is a testing process  720  by which quantized pixels may be expressed according to halftones. Once the quantization and error diffusion are completed for lines scanned according to the first stage  711 , the quantized pixels may be tested  721  to determine their actual output halftone pattern. Once the quantization and error diffusion are completed for lines scanned according to the second stage  712 , the quantized pixels may be tested  722  to determine their actual output halftone pattern. Before the testing, threshold levels for an exemplary five-level halftone output are determined  730  by measuring dot intensities for the output device, e.g., the MFP, at the three intermediate tone levels. 
         [0033]      FIG. 8  illustrates an exemplary scanning pattern of the present invention. An exemplary horizontal scanning pattern, i.e., the order and direction of serial tone quantization, of the first stage processing may be every other row of pixels of an image, or every other column according to a vertical scanning pattern. The scanning direction may be right-to-left, left-to-right, or alternate between the two directions, as shown in  FIG. 8 . Accordingly, every other row may be skipped, i.e., not quantized, during the first stage processing. An exemplary horizontal pattern of the second stage processing is along the rows interposed between the rows scanned during the first stage of processing. The direction of scanning may be right-to-left, left-to-right, or alternate between the two directions, as shown in  FIG. 8 . For purposes of illustration, the pixels of the matrix of  FIG. 8  are referenced serially, left-to-right, starting with the first pixel  801  that may be referenced also as pixel location no.  1  in this example, and the last pixel  802  that may be referenced also as pixel location no.  56  in this example. A portion of  FIG. 8  is shown in  FIG. 9A  where the top or first row is scanned right-to-left. The pixel tone value of a pixel  901  has been quantized, leaving a quantization tone error, a portion of which, N 3 , may be added to the pixel tone value of the next pixel, P 4 , prior to quantization. The second row of  FIG. 9A  is shown as skipped, for now, and the third row of  FIG. 9A  is shown to be scanned in an opposite direction from the first row, in this example, where the pixel tone value of the quantized pixel  902  results in a quantization tone error, a portion of which, N 21 , may be added to the pixel tone value of the next pixel, P 20 , prior to its tone value quantization. Portions of the tone quantization error of the pixels of the first and third rows, and tone error not already allocated to the pre-quantized adjacent pixel in the row may be saved for allocation to the rows to be scanned during the second stage of processing. For example, the total tone error associated with the first pixel  901  may be N 3 +E 3 . A portion of  FIG. 8  is shown in  FIG. 9B  where the second or middle row (of  FIG. 9B ) is scanned right-to-left. Prior to the tone quantization of the center pixel (of  FIG. 9B ), the tone error, N 45 , of the previously quantized pixel in the middle row and portions of the saved tone quantization error from the nearest neighbors of the pixels scanned during the first stage of processing, i.e., portions of E 37  to E 39  and E 53  to E 55 , are added to the yet unquantized tone value of pixel  910 . 
         [0034]      FIG. 10  illustrates the first stage process in more detail where a pixel having a tone value either not yet quantized or undergoing quantization is shown by the variable P with subscript indicating a row and column location respectively. Accordingly, P i,j    1011  is the tone value of a pixel undergoing quantization in the i th  row and j th  column of the digital image  1010 . To facilitate faster processing by reducing total pixels, the digital image may be a scaled-down version of an original digital image, i.e., the image comprising P i,j  may be a lower resolution of an image comprising more than one pixel, e.g., P′ i,j , in place of P i,j . A portion of the tone error  1020 , N i,j−1 , from the previously quantized pixel in the exemplary left-to-right scan line is added to the pixel tone value, P i,j , to generate a summed value  1030 , S i,j . This summed valued, e.g., an assigned value of: S i,j ←(P i,j +N i,j−1 ), may be compared  1040  with one or more threshold values for tone quantization to generate a quantized tone value  1050 , V i,j . The quantized image  1051 , at its base, then may be comprised of an array of quantized tone values, V i,j . The quantized tone values, V i,j , may provide a basis for a process  1090  of half-toning and expanding the resolution of the quantized image. For example, by being within one of the ranges available for half-toning, a calibrated halftone value will be assigned to the pixel as its quantized tone value, V i,j . The difference between the quantized tone value  1050 , V i,j , value and the assigned or summed value  1030 , S i,j , may be treated as the total tone error  1060 , D i,j , i.e., D i,j ←(S i,j −V i,j ). A portion, e.g., n%, of the total tone error  1060 , D i,j , may be assigned as a tone value addition  1070 , N i,j , for the next pixel in the scan line, i.e., N i,j ←(n%*D i,j ). An exemplary embodiment of the first stage processing may have the value of n=50, and so N i,j ←50%*(S i,j −V i,j )=(S i,j −V i,j )/2. In addition, the remainder of the total error  1080 , E i,j , i.e., the portion not assigned for the next pixel, e.g., (100−n)%, may be saved to a buffer  1081  or memory location corresponding to the presently quantized pixel. For example, E i,j ←((100−n)%*D i,j ) or E i,j ←(D i,j −N i,j ). Reference is made the Appendix section below providing exemplary pseudocode of an embodiment of the present invention. 
         [0035]      FIG. 11  illustrates the second stage process in more detail where a pixel having a tone value either not yet quantized or undergoing quantization is shown by the variable P with subscript indicating a row and column location respectively. Accordingly, P i,j    1011  is the tone value of a pixel undergoing quantization in the i th  row and j th  column of the digital image. A portion of the tone error  1020 , N i,j−1 , from the previously quantized pixel in the exemplary left-to-right scan line is added to the pixel tone value, P i,j , and weighted portions  1110  of the error buffer entries from the nearest neighbors of the rows scanned as part of the first stage, are also added to the pixel tone value  1011 , P i,j , to generate an assigned or summed value  1130 , S i,j . Weighting values  1110  may be used to combine remainder of the total error of the row above and row below from the buffer  1081 , and the sum of the six weights, e.g., w 1  to w 6 , may sum to unity. The assigned or summed valued, e.g., S i,j ←(P i,j +N i,j−1 +w 1 *E i−1,j−1 +w 2 *E i−1,j +w 3 *E i−1,j+1 +w 4 *E i+1,j−1 +w 5 *E i+1,j +w 6 *E i+1,j+1 ), may be compared with one or more threshold values for purposes of tone quantization. Exemplary values of the weights may be at least one tone error portion from each of the three closest quantized pixels of the immediately adjacent rows and a doubling of that portion for the quantized pixel immediately above and immediately below the pixel being quantized according to the second stage process. So, examples of the weights may be: w 1 =⅛; w 2 = 2/8; w 3 =⅛; w 4 =⅛; w 5 = 2/8; and w 6 =⅛. By being within one of the ranges available for half-toning, the calibrated halftone value will be assigned to the pixel as its quantized tone value  1050 , V i,j , and the difference between the quantized tone value  1050 , V i,j , and the assigned or summed value, may be treated as the total tone error  1060 , D i,j ,i.e. D i,j ←(S i,j −V i,j ). A portion, e.g., n%, of the total tone error may be assigned as an tone value addition for the next pixel in the scan line, i.e., N i,j ←((n%/100)*D i,j ). 
         [0036]      FIG. 12  illustrates a process  1090  of half-toning and expanding the resolution of the quantized image in an exemplary arrangement of threshold tests for a five-level half-toning. For each pixel, prior to quantization, the assigned or summed value  1030 ,  1130 , S i,j , may be tested against successively decreasing tone level threshold values, e.g., L 1  to L 4 . For example, a summed value, S i,j , may be close to 100% intensity. Its quantized value, V i,j , may be assigned the value corresponding to 100% intensity, e.g., X 1 . The total quantization tone error, for this assignment, D i,j , may then be apportioned according to the surround error diffusion process. A numerical example may be illustrated where 100% intensity may be expressed according to the 8-bit integer scale as 255. If S i,j &gt;(L 1 =248), then the pixel would be quantized to a value of 255, i.e., V i,j ←X 1 =255. If (L 1 =248)&gt;S i,j &gt;(L 2 =236), then the pixel would be quantized to a value of 242, i.e., V i,j ←X 2 =242. If (L 2 =236)&gt;S i,j &gt;(L 3 =150), then the pixel would be quantized to a value of 230, i.e., V i,j ←X 3 =230. If (L 3 =150)&gt;S i,j &gt;(L 4 =56), then the pixel would be quantized to a value of 112, i.e., V i,j &lt;X 4 =112. If S i,j &lt;(L 4 =56), then the pixel would be quantized to a value of 0, i.e., V i,j ←0. The value of n may be assigned accordingly: if n=50%, then 50%, or one-half, of the tone error is apportioned to the next pixel to be quantized then: N i,j ←(S i,j −V i,j )/2 or N i,j ←(D i,j )/2, and then E i,j ←D i,j −N i,j . 
         [0037]    One of ordinary skill in the art will appreciate that the elements, modules, and functions described herein may be further subdivided, combined, and/or varied and yet still be in the spirit of the embodiments of the invention. In addition, while a number of variations of the invention have been shown and described in detail, other modifications, which are within the scope of this invention, will be readily apparent to those of ordinary skill in the art based upon this disclosure, e.g., the exemplary flowcharts or processes described herein may be modified and varied and yet still be in the spirit of the invention. It is also contemplated that various combinations or subcombinations of the specific features and aspects of the embodiments may be made and still fall within the scope of the invention. Accordingly, it should be understood that various features and aspects of the disclosed embodiments may be combined with or substituted for one another in order to form varying modes of the disclosed invention. Thus, it is intended that the scope of the present invention herein disclosed should not be limited by the particular disclosed embodiments described above. 
       APPENDIX 
       [0038]    The following comprises pseudocode of an exemplary embodiment of the present invention, where the text of line, separated by and following the “%” symbol is included as explanatory comment: 
         [0000]    
       
         
               
             
           
               
                   
               
             
             
               
                 % Surround Error Diffusion 
               
               
                 % 
               
               
                 % Copyright 2009 Sharp Labs of America 
               
               
                 % Tone curve adjusted from 95/90/50 to 95/90/37.6 
               
               
                 % Output gray-levels ranging from 0 to 15, where 15 is the highest density 
               
               
                 % for a 4-bit scale, equivalent to the highest density of the 8-bit 
               
               
                 scale, i.e., 255. 
               
               
                 % pp is calibrated actual density: 
               
               
                 % output 1 pixel: pp=112, 2: pp=230, 3: pp=242, 4 pixels: pp=255 
               
               
                 im=imread(filename_in); 
               
               
                 [M,N,P]=size(im); 
               
               
                 % out=zeros(M,N,‘uint16’); 
               
               
                 eout=zeros(M*2,N*2,4,‘uint8’); 
               
               
                 er=zeros(M,N,4,‘int16’);    % error buffer 
               
               
                 ww=[0 0 0 0]; 
               
               
                 xx=[0 0 0 0]; 
               
               
                 yy=[0 0 0 0]; 
               
               
                 zz=[0 0 0 0]; 
               
               
                 cc=0; 
               
               
                 % count row numbers 
               
               
                 if (mod(M,2)&gt;0) 
               
               
                  m2=M/2; 
               
               
                  m1=m2+1; 
               
               
                 else 
               
               
                  m1=M/2; 
               
               
                  m2=m1−1; 
               
               
                  cc=1; 
               
               
                 end 
               
               
                 % first time 
               
               
                 for (i=1:m1) 
               
               
                   kk=i*2−1; 
               
               
                   nn=[0 0 0 0]; 
               
               
                  for (j=1:N) 
               
               
                  cmyk = double(reshape(im(kk,j,:),[1,4])); 
               
               
                  for (k=1:4) 
               
               
                   x=cmyk(k); 
               
               
                    x=x+nn(k); 
               
               
                    if(x&gt;248) 
               
               
                     ww(k)=15; xx(k)=15; yy(k)=15; zz(k)=15; pp=255; %100 
               
               
                    elseif(x&gt;236) 
               
               
                     ww(k)=15; xx(k)=15; yy(k)=15; zz(k)=0; pp=242; %95 
               
               
                    elseif(x&gt;150) 
               
               
                     ww(k)=15; xx(k)=15; yy(k)=0; zz(k)=0; pp=230; %90 
               
               
                    elseif(x&gt;56) 
               
               
                     ww(k)=15; xx(k)=0; yy(k)=0; zz(k)=0; pp=112; %37.6 
               
               
                    else 
               
               
                     ww(k)=0; xx(k)=0; yy(k)=0; zz(k)=0; pp=0; 
               
               
                    end 
               
               
                    nn(k)=(x−pp)/2; 
               
               
                    er(kk,j,k)=nn(k); 
               
               
                  end 
               
               
                  eout(kk*2−1,j*2−1,:)=reshape(ww,[1,1,4]); 
               
               
                  eout(kk*2−1,j*2,:)=reshape(xx,[1,1,4]); 
               
               
                  eout(kk*2,j*2−1,:)=reshape(yy,[1,1,4]); 
               
               
                  eout(kk*2,j*2,:)=reshape(zz,[1,1,4]); 
               
               
                  end 
               
               
                 end 
               
               
                 % second time 
               
               
                 for (i=1:m2) 
               
               
                   kk=i*2; 
               
               
                  cmyk = double(reshape(im(kk,1,:),[1,4])); 
               
               
                  % j=1 //code skipped 
               
               
                  % j=2~N−1 
               
               
                  for (j=2:(N−1)) 
               
               
                  cmyk = double(reshape(im(kk,j,:),[1,4])); 
               
               
                  for (k=1:4) 
               
               
                   x=cmyk(k); 
               
               
                    x=x+er(kk,j−1,k)+double(er(kk−1,j−1,k)+2*er(kk−1,j,k)+ 
               
               
                  er(kk−1,j+1,k)+er(kk+1,j−1,k)+2*er(kk+1,j,k)+er(kk+1,j+1,k))/8; 
               
               
                    if(x&gt;248) 
               
               
                     ww(k)=15; xx(k)=15; yy(k)=15; zz(k)=15; pp=255; %100 
               
               
                    elseif(x&gt;236) 
               
               
                     ww(k)=15; xx(k)=15; yy(k)=15; zz(k)=0; pp=242; %95 
               
               
                    elseif(x&gt;150) 
               
               
                     ww(k)=15; xx(k)=15; yy(k)=0; zz(k)=0; pp=230; %90 
               
               
                    elseif(x&gt;56) 
               
               
                     ww(k)=15; xx(k)=0; yy(k)=0; zz(k)=0; pp=112; %37.6 
               
               
                    else 
               
               
                     ww(k)=0; xx(k)=0; yy(k)=0; zz(k)=0; pp=0; 
               
               
                    end 
               
               
                    mm=(x−pp)/2; 
               
               
                    er(kk,j,k)=mm; 
               
               
                    er(kk+1,j,k)=er(kk+1,j,k)+mm; 
               
               
                  end 
               
               
                  eout(kk*2−1,j*2−1,:)=reshape(ww,[1,1,4]); 
               
               
                  eout(kk*2−1,j*2,:)=reshape(xx,[1,1,4]); 
               
               
                  eout(kk*2,j*2−1,:)=reshape(yy,[1,1,4]); 
               
               
                  eout(kk*2,j*2,:)=reshape(zz,[1,1,4]); 
               
               
                 end 
               
               
                  cmyk = double(reshape(im(kk,N,:),[1,4])); 
               
               
                  % j=N //code skipped 
               
               
                 % last scanline // code skipped