Patent Application: US-65104296-A

Abstract:
an enhanced error diffusion for color and / or black - and - white halftone reproduction of gray scale , color and / or black - and - white images , features enhancements in obtaining the thresholds that are used in error diffusion halftoning as well as enhancements in how to distribute error . thresholds according to the invention are derived by applying a standard error - diffusion technique , using a fixed threshold value of 0 . 5 , to a constant gray level image patch which has a gray level value corresponding to an irrational number . thresholds so - derived are well dispersed in a threshold mask and have only a limited number of threshold values ; use of such thresholds in error diffusion has been found to reduce significantly the presence of structural artifacts in halftone images . as for how to distribute error , the invention provides a different error distribution matrix for each gray level value and selects one such matrix for error distribution based on the gray level value of the target pixel in the original image . particularly in a case where the error distribution matrix is in the form : ## equ1 ## for highlight / shadow regions , distributing error according to the invention has been found to reduce significantly the presence of worm - like chains in such highlight and shadow regions .

Description:
fig5 is a view showing the outward appearance of representative computing equipment which incorporates enhanced error diffusion according to the invention . shown in fig5 is computing equipment 20 such as an ibm pc or pc - compatible computer having a windowing operating system such as a microsoft windows operating system . computing equipment 20 is provided with a display monitor 23 having a display screen 22 on which computing equipment 20 displays images to the user . computing equipment 20 is further provided with a floppy disk drive 24 with which removable floppy disk media may be read or written , fixed disk drive 25 for storing data files and application program files , a keyboard 26 for permitting input of text data and manipulation of objects displayed on display screen 22 , and a pointing device 27 such as a mouse or the like which is also provided to permit manipulation of objects on display screen 22 . a conventional color printer 30 , such as a color bubble jet printer , is also provided . also provided are connections to a network 31 or to an ordinary voice telephone line 32 , both for sending and receiving color image data as well as other files such as files which include program instruction sequences by which computing equipment 20 is operated . while a bubble jet printer is presently preferred , any color printer which forms full color images by mixing colorants in amounts set by corresponding color component values , such as a color laser beam printer or color thermal wax printer or the like , is suitable in the practice of the invention . in accordance with operator instructions , and under control of the windowing operating system , stored application programs such as graphics application programs , drawing application programs , desktop publishing application programs and the like , are selectively activated to process and to manipulate data . also in accordance with operator instructions , and based on those stored application programs , commands are issued to display images on monitor 23 and to print images appearing on monitor 23 , and those images are then printed on printer 30 as described more fully hereinbelow . fig6 is a detailed block diagram showing the internal construction of computing equipment 20 . as shown in fig6 computing equipment 20 includes a central processing unit ( cpu ) 40 such as programmable microprocessor interfaced to a computer bus 41 . also interfaced to computer bus 41 is display interface 44 , network interface 45 for interfacing to network 31 , fax / modem / telephone interface 46 for interfacing to telephone 32 , printer interface 47 , and floppy disk drive interface 49 . main memory 51 such as random access memory ( ram ) interfaces to computer bus 41 so as to provide cpu 40 with access to memory storage . in particular , when executing stored application program instruction sequences such as those associated with application programs stored on disk 25 , cpu 40 loads those instruction sequences from disk 25 ( or other storage media such as media accessed via network 31 or floppy disk drive 24 ) into main memory 51 and executes those stored program instruction sequences out of main memory 51 . rom ( read only memory ) 52 is provided for storing invariant instruction sequences such as start - up instruction sequences or basic input / output operating system ( bios ) sequences for operation of keyboard 26 . as shown in fig6 and as previously mentioned , fixed disk 25 stores program instruction sequences for the windowing operating system and for various application programs such as a graphics application program , a drawing application program , a desktop publishing application program , and the like . in addition , stored on fixed disk 25 are color image files such as are displayed on monitor 23 or printed on printer 30 under control of a designated application program . fixed disk 25 also stores a monitor driver 33 which controls how rgb color primary values are provided to display interface 44 , and color management system 34 which is a printer driver for controlling how cmyk color component values are provided to printer interface 47 for printout by printer 30 . enhanced error diffusion according to the invention , in this embodiment of the invention , resides in color management system 34 . other device drivers are also stored on fixed disk 25 , for providing appropriate signals to the various devices ( such as the network ) connected in computing equipment 20 . ordinarily , application programs and drivers stored on disk 25 need first to be installed by the user onto disk 25 from other computer readable media on which those programs and drivers are initially stored . for example , it is customary for a user to purchase a floppy disk or other computer readable media on which a copy of color management system 34 is stored . the user would then install color management system 34 onto disk 25 by inserting the purchased floppy disk into floppy disk drive 24 and by commanding cpu 40 to copy color management system 34 from the floppy disk onto disk 25 . it is also possible for the user , via telephone 32 and modem interface 46 , or via network 31 and network interface 45 , to download color management system 34 from a computerized bulletin board to which the drivers had previously been uploaded . fig7 is a functional block diagram showing how computer 20 interacts with monitor 23 and printer 30 . shown in fig7 are computer 20 with monitor driver 33 , color management system 34 , cpu 40 , ram 51 and rom 52 , all arranged functionally rather than structurally , as in fig6 . as mentioned above , using keyboard 26 , an operator can cause cpu 40 to execute stored program instructions which cause color images to be displayed on monitor 23 and which cause corresponding color images to be printed on color printer 30 . specifically , and in cooperation with the stored program instructions in the application program stored on disk 25 , cpu 40 derives a color image for display on monitor 23 . cpu provides the color image to monitor driver 33 which in turn derives gray - level rgb values for each pixel in the monitor 23 . the rgb values are provided via display interface 44 to monitor 23 where those values are displayed . since monitor 23 is a continuous tone analog device , the color image displayed on monitor 23 from the derived rgb values is a continuous tone image based on the gray - levels of each of the r . g and b values . upon request , cpu 40 also feeds a color image to color management system 34 for printing by color printer 30 . color management system 34 derives binary cmyk values for each pixel of the color image based on the gray - level rgb color values provided from cpu 40 . the color management system 34 allows selection , ordinarily by the user but in some cases automatically by cpu 40 , of one of plural rendering modes , here , a perceptual rendering mode , a colorimetric rendering mode , and a business graphics rendering mode . enhanced error diffusion according to the invention , in this embodiment of the invention , operates during the perceptual rendering mode , but it is possible to incorporate gray component replacement according to the invention in any or all of the rendering modes . whichever one of the plural modes is selected , however , the ultimate purpose of color management system 34 is to halftone - process the gray - level rgb values provided from cpu 40 so as to obtain binary cmyk values , and to provide the binary cmyk values to printer 30 for printing . more particularly , for each pixel of an image on monitor 23 , color management system 34 converts the gray - level rgb value of the pixel into a binary halftone value for each of the cmyk color components printed by printer 30 . for example , if each pixel of the image on monitor 23 is represented by a 24 - bit rgb value ( i . e ., eight bits for r , eight bits for g , and eight bits for b ), color management system 34 obtains a digital halftone value in which each of the cmyk color components is represented by a single bit indicating whether a dot of the respective color component is to be printed at a corresponding pixel position by printer 30 . thereafter , color management system 34 feeds the cmyk values via printer interface 46 to printer 30 where they are stored in bitmap memory 37 within printer 30 . bitmap memory 37 may store a full bitmap image of the printed image , or it may store only a band or partial bitmap image . when sufficient color data , namely binary halftoned cmyk data , is stored in bitmap memory 37 , a color print head 36 reciprocates across a platen adjacent a sheet of paper . in a preferred embodiment , print head 36 includes 32 ink jet nozzles arranged in a four column by eight row pattern . the nozzles in the first column all eject droplets of cyan ink ; the nozzles in the second column all eject droplets of magenta ink ; the nozzles in the third column all eject droplets of yellow ink ; and the nozzles in the fourth column all eject droplets of black ink . the nozzles are controlled independently in accordance with the color data in bitmap memory 37 such that in one reciprocation of print head 36 across the platen , eight rows of pixels are printed . fig8 is a view showing the functional arrangement of color management system 34 . the color management system shown in fig5 includes plural different rendering modes , in which at least one rendering mode such as the perceptual rendering mode incorporates enhanced error diffusion according to the invention . as shown in fig8 color management system 34 includes a rendering mode selector 60 which allows selection between one of the plural rendering modes of the color management system . preferably , rendering mode selector 60 is a user manipulable graphical user interface which allows a user , after commanding an image to be printed , to select one of the plural rendering modes by which color management system 34 is able to render the image . alternatively , it is also possible for rendering mode selector 60 to be actuatable automatically under control of cpu 40 , in which case cpu 40 would make automatic selection of the proper rendering mode . such automatic selection may , for example , be made based on the type of application software which is generating the image , based on data or image type , based on data structure , based on a histogram or other analysis of color distribution in the image , or the like . for example , all bmp type data might have perceptual rendering automatically selected , while vector graphics might have business graphics rendering automatically selected , and so on . based on the mode selected by rendering mode selector 60 , gray - level values for each of the rgb input colors from cpu 40 are fed for appropriate processing to the selected one of the plural rendering modes , so as to generate printer binary cmyk colorant values . fig9 is a flow diagram used for explaining operation of color management system 34 shown in fig8 . in step s901 , a user issues a command to print . flow then advances to step s902 in which a rendering mode is selected . specifically , as mentioned above in connection with fig8 step s902 utilizes rendering mode selector 60 so as to select one of the plural different rendering modes included in color management system 34 . selection can be manual by the user or automatic by computer , although automatic selection with manual override is preferred . if a perceptual rendering mode is selected in step s902 , then flow advances to step s903 in which perceptual rendering is performed in accordance with perceptual rendering process steps 61 . perceptual rendering in accordance with step s903 , which includes enhanced error diffusion according to the invention , is described in further detail in connection with fig1 through 17 ( b ). thereafter , binary cmyk values derived in perceptual rendering step s903 are provided to printer 30 for printing ( step s906 ). if in step s902 colorimetric rendering is selected , then flow advances to step s904 in which colorimetric rendering is performed in accordance with colorimetric rendering process steps 62 . any suitable colorimetric rendering process steps may be used , as will be apparent to those skilled in the art . thereafter , cmyk values derived in colorimetric rendering step s904 are provided to printer 30 for printing ( step s906 ). if in step s902 business graphics rendering is selected , then flow advances to step s905 in which business graphics rendering is performed in accordance with business graphics rendering process steps 63 . any suitable business graphics rendering may be used , as will be apparent to those skilled in the art . thereafter , cmyk values derived in business graphics rendering step s905 are provided to printer 30 for printing ( step s906 ). fig1 is a simplified block diagram of an apparatus for carrying out enhanced error diffusion according to the invention . the apparatus shown in fig1 might be implemented as a physical apparatus , but more preferably the apparatus of fig1 is implemented as software steps in connection with perceptual rendering process steps 61 ( step s903 ). as shown in fig1 , enhanced error distribution according to the invention includes an input gray scale image storage section 110 for storing gray - level values for each of the rgb color components of an output image . comparator 120 operates on each pixel of the gray level values stored in gray level image storage second 110 , and for each pixel compares the gray level value with a threshold obtained from threshold mask storage section 140 . based on the comparison , comparator 120 outputs a binary 1 for the pixel if a white output is desired , or a binary 0 for the pixel if a colored ( or black ) output is desired . the output is stored in halftone image storage section 150 . error between the binary output stored in halftone image storage section 150 and the gray level value in the gray - level image storage section 110 is output to error distribution unit 130 . error distribution 23 unit 130 calculates how the error is to be distributed to adjacent pixels , based on an error distribution coefficient table 135 . error distribution table 135 stores a table of 3 × 3 error distribution matrices , with one of the error distribution matrices being selected based on the gray level value stored in gray scale image storage section 110 . error distribution unit 130 selects the appropriate error distribution matrix based on the gray level value , and distributes error from comparator 120 to adjacent pixels in gray - scale image storage section 110 . the process is thereupon repeated for each x - y pixel address 105 , as generated by path generator 100 which is used to generate the scanning path through image data in storage section 110 , such as a serpentine scanning path , a scan - line scanning path , a blue - noise - modified scanning path , and the like . fig1 is a flow diagram showing operation of the fig1 arrangement . in step s1101 , and based on an x , y address generated by path generator 100 , a gray - level value v in is obtained from gray - scale image storage section 110 at address ( x , y ). a threshold t is obtained from threshold mask storage section 140 , also at position ( x , y ). in this regard , it should be understood that threshold mask storage section 140 stores a threshold mask which contains a large number of threshold values arranged in a generalized u × v matrix arrangement which preferably is square and which preferably is large ( u , v ≧ 256 ). in step s1103 , comparator 120 compares v in to t . if v in is smaller than t , meaning that the gray level value v in is darker than threshold t , comparator 120 sets the output pixel v out to 0 ( i . e ., to a black , or colored , pixel printed output ). on the other hand , if v in is not less than t , then comparator 120 sets output v out equal to 1 ( i . e ., no colorant , or a white pixel ). in either event , flow then advances to step s1106 in which comparator 120 calculates an error e between v out and v in , and sends the error e to error distribution unit 130 . based on the gray level value v in for the pixel under consideration , an error distribution matrix m ed is selected from error distribution coefficient table 135 . using the selected error distribution matrix m ed , error distribution unit 130 distributes error e to adjacent pixels ( step s1108 ). the distributed error is added back into appropriate gray level values for adjacent pixels , as currently stored in gray - scale image storage section 110 . in step s1109 , if path generator 100 determines that more pixels still need to be processed , then flow returns to step s1101 for such processing . otherwise , processing is completed , and binary halftone values stored in image storage section 150 are printed by output device 160 . in the present embodiment , intensities of gray - level images are assumed to be within the range of 0 and 1 , where 0 represents a fully colored component ( i . e ., full red , green or blue ) and 1 represents a completely uncolored value ( i . e ., white ). any linear normalization processes , well known in the art , can be applied to bring intensity values in different ranges into that assumed by the present disclosure , or those in the present disclosure can be transformed into any other range , such as 0 to 255 . furthermore , without loss of generality , it can be said that the disclosed invention is able to manipulate gray - level intensity in the range of v min to v max , where v min and v max designate minimum and maximum gray level intensities . the terms &# 34 ; pixel &# 34 ; and &# 34 ; individual cell &# 34 ; are used equally in the present disclosure in order to designate the smallest addressable entity of the image , which has an intensity attribute the output device 160 is able to interpret the set of pixels of the produced digital halftone image , whose output bi - level values stored in the output bi - level image storage unit 150 are equal to 0 , as being blackened pixels , e . g . pixels , where a physical colored substrate is put on the output support . otherwise , the pixels whose output bi - level values stored in the output bi - level image storage unit 150 are equal to 1 , are not colored : they preserve the color of the output support . the disclosed method is a sequential one . the order of the sequence of coordinates ( x , y ) of the pixels to be processed influences the quality of the produced image . this influence is well known in the art . if p ( i ) is the sequence of coordinates ( x , y ) of the pixels to be processed , the goal of the path generator unit 100 is to generate a sequence of integer pixel coordinates ( x , y ), 0 ≦= x ≦ w out ; 0 ≦= y ≦ h out ; ( w out and h out are the width and the height of the output image ) in such a way that all pixels are processed sequentially . the simplest path generation scheme , the so - called scan - line path , is defined as follows : ## equ4 ## where w out is the width of the output image , the operator &# 34 ; mod &# 34 ; is a modulo - division operator details , the &# 34 ; floor ( x )&# 34 ; function is defined as &# 34 ; the biggest integer smaller or equal to x &# 34 ;, and where successive values of integer i give the sequence of processed pixels . there are several variants of path sequences used in the art : left - ward scan - lines instead of right - ward scan - lines ; alternative left - ward and right - ward scan - lines for respectively odd and even scan - lines ( serpentine or boustrophedon ); upward , downward or alternative upward - downward scan - lines , etc . the disclosed method has been implemented using boustrophedon path . nevertheless , other path generation schemes such as scan - line may be applied . the comparator and error distribution unit , which comprises the comparator 120 , the error distribution unit 130 , the threshold mask storage 140 and the error distribution coefficient tables 135 , operates on a set of intensity values of the input image v in ( x , y ) stored in the input gray - scale image storage until 110 . the set of input intensity values v in ( x , y ) is compared , in the comparator 120 , with the threshold value t ( x , y ). according to the result of this comparison , the output value v out ( x , y ) of the pixel ( x , y ) is set to one of two possible values : ## equ5 ## where ( mod n ) designates modulo - n arithmetic ; and xdim and ydim are horizontal and vertical dimensions of the matrix t ( x , y ). the threshold value t ( x , y ) may be constant ( e . g . t ( x , y )= 0 . 5 ) or may depend on the input intensity level ( threshold function becomes t ( x , y , v in ( x , y )) in this case ) or on coordinates ( x , y )( threshold modulation ). the disclosed method has been implemented using a perturbation well - dispersed threshold mask having a limited number of levels which is stored in the threshold mask storage 140 . the output value v out ( x , y ) is carried out towards the output bi - level image storage until 150 . the difference e between the output value v out ( x , y ) and the intensity value of the input image v in ( x , y ) is re - distributed between several pixels of the weighted sum image which have not yet been processed . this re - distribution is performed by the error distribution unit 130 : e = v . sub . out ( x , y )- v . sub . 68 ( x , y ) 0 ≦( u , v )& lt ; n . sub . ed ## equ6 ## where n . sub . ed is the size of the square matrix of error - distribution coefficients m . sub . ed ( u , v ) stored in the error distribution coefficient table 135 . the square matrix of error - distribution coefficients m ed ( u , v ) of odd size m ed , stored in the error distribution tables 862 , characterizes the error distribution process . for example , the size n ed of the square matrix of error - distribution coefficients m ed ( u , v ) may be n ed = 3 . there are several matrices of error - distribution coefficients known in the art . for example , the distribution according to the well - known floyd - steinberg distribution scheme uses a 3 × 3 matrix m ed ( u , v ): ## equ7 ## the preferred embodiment performs error distribution using a selected one of plural 3 - dimensional matrix of error - distribution coefficients m ed ( u , v , v in ( x , y )), stored in the error distribution coefficient table 135 . for any input signal intensity gray level g = v in ( x , y ), a 2 - dimensional 3 × 3 square matrix of error - distribution coefficients m ed ( u , v , g ) is defined : ## equ8 ## only four elements of this matrix are non - zero and are effectively used in the error distribution process : the elements m 23 , m 31 , m 32 and m 33 when the scan - line is processed in left - to - right order , and the elements m 21 , m 31 , m 32 and m 33 where the scan - line is processed in right - to - left order . for the sake of simplicity , only the set of elements { m 23 , m 31 , m 32 , m 33 } is considered . for the right - to - left pass , the elements m 23 and m 23 are interchanged , as well as the elements m 33 and m 31 . the disclosed method uses different error - distribution coefficient matrices m ed ( u , v ) for different intensities of the input signal g = v in ( x , y ). in fact , the error distribution coefficient table 135 can be seen as a 3 - dimensional table m ed ( u , v , g ). typically , the input signal is often represented as a set of 8 - bit sampled gray - scale values . in such a case , 256 different matrices m ed ( u , v ) which correspond to 256 gray levels of the input signal are stored in the error - distribution coefficient table 135 . this section describes the process of building the error - distribution coefficient table , as illustrated in fig1 . two particular matrices m ed ( u , v , g ) are defined which have turned out to be particularly effective for error - diffusion in two ranges of values of the input signal : the matrix m 1 ( u , v , g ) in highlights and in shadows ( step s1201 ), and the matrix m 2 ( u , v , g ) in mid - tones ( step s1202 ): ## equ9 ## for highlights and shadows , i . e ., where in the interval g 1 , g 2 ! between dark grays and mid - tones , the following process which is illustrated at step s1203 ensures smooth transition between between error - distribution with the matrix m 1 ( u , v , g ) and error - distribution with the matrix m 2 ( u , v , g ): for every gray - level intensity level g , calculate intermediate coefficients im 23 ( g ), im 31 ( g ), im 32 ( g ), im 33 ( g ) and is ( g ) according to the following formulae . the formulae apply a weighted average to the values of m 1 and m 2 , with the weight depending on gray - level g : ## equ11 ## for every gray - level intensity level g , calculate the greatest common divisor d ( g )= gcd ( im 23 ( g ), im 31 ( g ), im 32 ( g ), im 33 ( g ), is ( g )). for every gray - level intensity level g , calculate all elements of the matrix m ed ( u , v , g ): ## equ12 ## in the interval g 3 , g 4 ! between highlights and mid - tones , an algorithm similar to previously disclosed one can be applied . in the particular case when the highlights , dark grays and mid - tones are defined by numbers g 1 = 8 , g 2 = 32 , g 3 = 223 and g 4 = 247 , this algorithm produces the set of coefficients { m 23 ( g ), m 31 ( g ), m 32 ( g ), m 33 ( g )} shown in the appendix . the disclosed method uses a perturbation well - dispersed threshold mask having a limited number of levels which is stored in the threshold mask storage 140 , in matrix form . this matrix contains set of threshold values t ( x , y ) which may be constant ( e . g . t ( x , y )= 0 . 5 ) or may depend on the input intensity level ( threshold function becomes t ( x , y , v in ( x , y )) in this case ) or on coordinates ( x , y )( threshold modulation ). the disclosed method has been implemented using a perturbation well - dispersed threshold mask having a limited number of levels which is stored in the threshold mask storage 140 . the output value v out ( x , y ) is carried out towards the output bi - level image storage unit 150 . this section describes the best expected mode for building well - dispersed threshold mask used in the disclosed enhanced error - diffusion method . this particular well - dispersed threshold mask has only three intensity levels . without loss of generality , it can be stated that by employing very similar techniques one can obtain other masks , with limited number of intensity levels : 2 -, 3 -, 4 -, 5 - or , in general , n - level well - dispersed threshold masks , where n is a small number . it has been observed that the floyd - steinberg error - diffusion method has its biggest structure artifacts when the intensity level of the input signal is close to small rational numbers : 1 / 2 , 1 / 3 , 2 / 3 , 1 / 4 , 3 / 4 etc . structure artifact means that a set of perfectly structured patches of arbitrary shape is incorporated between randomly dispersed structures . fig2 illustrates this phenomenon . non - linear behavior of almost all printing devices , and especially strong dot gain of current ink - jet printers accentuate harmful nature of structure artifacts . namely , the areas 15 , 16 and 17 in fig2 appear particularly odd when printed with real ink - jet printers . on the other hand , it has been observed that the same floyd - steinberg error - diffusion method produces much more even and stable results when the intensity level of the input signal is close to irrational numbers such as ## equ13 ## where e is the exponential constant e ( base of natural logarithms ), with numerical value 2 . 71828 . . . ; π is pi , with numerical value 3 . 14159 . . . ; φ is the golden ratio φ =( 1 + sqrt 5 ! )/ 2 , with numerical value 1 . 61803 . . . . the best mode of the disclosed enhanced error - diffusion method employs an original iterative technique for building a well - dispersed multi - level threshold masks which is based on the observation mentioned above . this technique may be subdivided into several steps , which are illustrated in fig1 , as follows : produce a square bi - level halftone patch using any error - diffusion method ( e . g . floyd - steinberg error - distribution scheme or an error - distribution scheme with other distribution coefficients ), which corresponds to an irrational constant input intensity level . the threshold is constant and equals 0 . 5 in this step . fig1 ( a ) illustrates the step b1 . in a preferred implementation , the input intensity level g for this first patch is chosen as g = 1 / φ = 0 . 618034 . invert the values of the square bi - level halftone patch produced in the step b1 . inversion means that the pixels of the patch having the value of 0 receive the value of 1 , and vice versa . produce a square bi - level halftone patch using the same error - diffusion method as that used in step b1 , which corresponds to an irrational constant input intensity level . use the square halftone patch produced in the previous steps as basic threshold mask . fig1 ( a ) illustrates the step b3 . in a preferred implementation , the input intensity level g for this second patch is chosen as g = 1 / φ 3 = 0 . 236068 . invert the value of the square bi - level halftone patch produced in the step b3 and average it together with the mask produced in b2 . one pass of steps b1 - b4 is sufficient for building a 3 - level well - dispersed multi - level threshold mask . when the number of levels in well - dispersed multi - level threshold mask is bigger than 3 , the steps b3 and b4 should be repeated iteratively . the main idea which governs the iterative technique described above is the fact that ( a ) the first - iteration bi - level pattern obtained in step b1 has visually pleasant dispersion structure and ( b ) all successive patterns obtained in steps b3 - b4 are built upon the first - iteration mask . this means that , according to the above - described technique , a pseudo - random distribution obtained during the n - th step contains the distribution obtained during ( n - 1 )- th step , as a subset . consequently , all halftone masks are dependent , and by averaging all masks ( which inherently adds all masks together ), one can obtain a multi - level mask whose levels individually have very similar visual appearance and very similar well - dispersed nature . fig1 ( a ) illustrates this technique of building multi - level well - dispersed mask . the matrix shown in fig1 ( a ) can be rearranged in such a way that all three levels are symmetrically spaced around the intensity g 0 = 0 . 5 , as shown in fig1 ( a ). the distance d between g 0 and two other intensity levels influences the force of the effect of scattering the structure effect . by increasing d , one reinforces the randomness of the halftoned output image , when the 3 - level dispersed mask is used as basic threshold matrix . on the contrary , by diminishing d , one makes the halftoned output image closer to the result obtained with conventional error - diffusion , with no threshold modulation . it is emphasized that several changes may be applied on the above - described system without departing from the teaching of the invention . it is intended that all the mater contained in the present disclosure , or shown in the accompanying drawings , shall be interpreted as illustrative rather than limiting . the invented method was conceived in order to cope with several drawbacks and imperfections of different halftoning methods known in the art , which are described in the section description of the related art . the disclosed method improves the following aspects of the floyd - steinberg popular error - diffusion scheme : ( 1 ) it suppress wormy structures in highlights and dark grays , proper to floyd - steinberg error - diffusion ; ( 2 ) it have smoother tone reproduction curve , with respect to floyd - steinberg &# 39 ; s one ; and ( 3 ) it diminishes considerably structure artifacts of the floyd - steinberg error - diffusion scheme . the disclosed method is simple , highly understandable , and may be implemented in the printer driver in very efficient way . the invention has been described with respect to a particular illustrative embodiment . it is to be understood that the invention is not limited to the above described embodiment and that various changes and modifications may be made by those of ordinary skill in the art without departing from the spirit and scope of the invention . appendix______________________________________g m . sub . 23 ( g ) m . sub . 31 ( g ) m . sub . 32 ( g ) m . sub . 33 ( g ) s ( g ) ______________________________________ 0 2 0 1 0 3 1 2 0 1 0 3 2 2 0 1 0 3 3 2 0 1 0 3 4 2 0 1 0 3 5 2 0 1 0 3 6 2 0 1 0 3 7 2 0 1 0 3 8 2 0 1 0 3 9 377 6 190 3 576 10 185 6 94 3 288 11 121 6 62 3 192 12 89 6 46 3 144 13 349 30 182 15 576 14 19 2 10 1 32 15 335 42 178 21 576 16 41 6 22 3 72 17 107 18 58 9 192 18 157 30 86 15 288 19 307 66 170 33 576 20 25 6 14 3 48 21 293 78 166 39 576 22 143 42 82 21 288 23 31 10 18 5 64 24 17 6 10 3 36 25 265 102 158 51 576 26 251 114 154 57 576 27 251 114 154 57 576 28 61 30 38 15 144 29 79 42 50 21 192 30 115 66 74 33 288 31 223 138 146 69 576 32 3 2 2 1 8 33 3 2 2 1 8 34 3 2 2 1 8 35 3 2 2 1 8 36 3 2 2 1 8 37 3 2 2 1 8 38 3 2 2 1 8 39 3 2 2 1 8 40 3 2 2 1 8 41 3 2 2 1 8 42 3 2 2 1 8 43 3 2 2 1 8 44 3 2 2 1 8 45 3 2 2 1 8 46 3 2 2 1 8 47 3 2 2 1 8 48 3 2 2 1 8 49 3 2 2 1 8 50 3 2 2 1 8 51 3 2 2 1 8 52 3 2 2 1 8 53 3 2 2 1 8 54 3 2 2 1 8 55 3 2 2 1 8 56 3 2 2 1 8 57 3 2 2 1 8 58 3 2 2 1 8 59 3 2 2 1 8 60 3 2 2 1 8 61 3 2 2 1 8 62 3 2 2 1 8 63 3 2 2 1 8 64 3 2 2 1 8 65 3 2 2 1 8 66 3 2 2 1 8 67 3 2 2 1 8 68 3 2 2 1 8 69 3 2 2 1 8 70 3 2 2 1 8 71 3 2 2 1 8 72 3 2 2 1 8 73 3 2 2 1 8 74 3 2 2 1 8 75 3 2 2 1 8 76 3 2 2 1 8 77 3 2 2 1 8 78 3 2 2 1 8 79 3 2 2 1 8 80 3 2 2 1 8 81 3 2 2 1 8 82 3 2 2 1 8 83 3 2 2 1 8 84 3 2 2 1 8 85 3 2 2 1 8 86 3 2 2 1 8 87 3 2 2 1 8 88 3 2 2 1 8 89 3 2 2 1 8 90 3 2 2 1 8 91 3 2 2 1 8 92 3 2 2 1 8 93 3 2 2 1 8 94 3 2 2 1 8 95 3 2 2 1 8 96 3 2 2 1 8 97 3 2 2 1 8 98 3 2 2 1 8 99 3 2 2 1 8100 3 2 2 1 8101 3 2 2 1 8102 3 2 2 1 8103 3 2 2 1 8104 3 2 2 1 8105 3 2 2 1 8106 3 2 2 1 8107 3 2 2 1 8108 3 2 2 1 8109 3 2 2 1 8110 3 2 2 1 8111 3 2 2 1 8112 3 2 2 1 8113 3 2 2 1 8114 3 2 2 1 8115 3 2 2 1 8116 3 2 2 1 8117 3 2 2 1 8118 3 2 2 1 8119 3 2 2 1 8120 3 2 2 1 8121 3 2 2 1 8122 3 2 2 1 8123 3 2 2 1 8124 3 2 2 1 8125 3 2 2 1 8126 3 2 2 1 8127 3 2 2 1 8128 3 2 2 1 8129 3 2 2 1 8130 3 2 2 1 8131 3 2 2 1 8132 3 2 2 1 8133 3 2 2 1 8134 3 2 2 1 8135 3 2 2 1 8136 3 2 2 1 8137 3 2 2 1 8138 3 2 2 1 8139 3 2 2 1 8140 3 2 2 1 8141 3 2 2 1 8142 3 2 2 1 8143 3 2 2 1 8144 3 2 2 1 8145 3 2 2 1 8146 3 2 2 1 8147 3 2 2 1 8148 3 2 2 1 8149 3 2 2 1 8150 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