Image treatment method and apparatus with error dispersion and controllable quantization

An image treatment apparatus comprising: an input device for inputting image data; a setting circuit serving as a reference when the image data is quantized in accordance with the image data input by the input device; a quantizing circuit for quantizing the image data; and a device for outputting an image in accordance with the result of treatment performed by the quantizing circuit, wherein the quantizing circuit performs the quantization by correcting the error between the image data input by the input device and the image output by the outputting device.

BACKGROUND OF THE INVENTION 
1. Field of the invention 
The present invention relates to an image treatment method and apparatus 
for treating images by digital signals. More particularly, the present 
invention relates to an image treatment method and apparatus for 
expressing half-tone images in a pseudo-manner by performing a 
quantization treatment of input data. 
2. Related Background Art 
Hitherto, apparatuses of the type described above such as laser beam 
printers (LBP) and ink jet type of printers employing a binary recording 
method in which recording dots are treated to be "whether printed or not" 
have been known. When a copying treatment of images of half-tone density 
such as photographs or half-tone dot original documents is performed with 
a copying machine which employs the above-described binary recording 
method, a method is employed in which a treatment for expressing a 
half-tone in a pseudo-manner is used, the read-out half-tone image data 
being treated using an image treatment circuit thereof is performed. 
As an example of the method of treatment of the above-described type of 
pseudo-half-tone treatment, there is, at present, a so-called "dither 
method" which is the method widely used. 
This dither method has an advantage that the above described type of 
pseudo-half-tone processing can be performed with a low cost since the 
structure of the hardware thereof is simple. However, this method raises 
the following problems: 
1 In a case where the original document is a dot image such as a print, the 
quality of the image deteriorates due to generation of periodical fringes 
(moire) in the copied image. 
2 In a case where the original document contains line drawings and/or 
characters, sufficient reproductivity of the lines cannot be obtained, and 
thereby the quality of the image deteriorates. 
There is a method of overcoming problem 1 by performing a smoothing 
treatment (spatial filtering treatment) upon the read-out half-tone image 
data. Furthermore, there is a method of overcoming problem 2 by performing 
an edge exaggerating treatment. However, with the above-described methods, 
it is difficult to obtain images exhibiting a sufficient productivity upon 
all of various images such as photographs, dot images, line drawings, and 
characters. Furthermore, the size of the circuit for performing the 
above-described treatment is larger. Therefore, the original advantages of 
the dither method can deteriorate. 
To improve on this, as an example of a pseudo-half-tone treatment, there is 
a so-called "error diffusion method" which has recently attracted public 
attention. 
This error diffusion method is a method in which the error in the density, 
which is generated when the input image data is binarized, between that of 
the input (not yet binarized) image data and that of the output 
(binarized) image data is diffused to the peripheral picture elements 
whereby the density can be secured. This method was published in "An 
Adaptive Algorithm for Spatial Grey Scale "SID. 75 Digest" literature by 
R. W. Floyd and L. Steinberg. 
This error diffusion method exhibits a rather improved gradating 
performance and resolution with respect to the above-described dither 
method. On the other hand, this method raises problems that a specific 
fringe pattern can be generated in a portion where the density of the 
image is uniform, and/or granular noise can appear due to generation of 
dots in a diffused manner in highlight portions of the image. 
In order to overcome these problems, a variety of methods have been 
disclosed in U.S. Pat. Nos. 4,876,610, 4,878,125 and 5,008,95, and U.S. 
patent application Ser. No. 192,601. 
Furthermore, a method is disclosed in U.S. Pat. No. 4,958,236, wherein 
generation of lines at the boundary portions of the images is prevented 
when the image is divided into a plurality of regions and the thus-divided 
regions are each quantization-treated in the error diffusion method. 
On the other hand, when an original image is read and it is binarized by 
the error diffusion method so as to be output by a printer, there is a 
problem that there is a blank area in which no dot is printed as shown in 
FIG. 15 if the density of the original image is in a low level. 
Furthermore, in the region next to such blank region, dots are, as shown 
in FIG. 15, printed successively. As described above, the reproduced image 
output after treatment using the error diffusion method raises the problem 
that excessive deterioration in the quality of image is generated in the 
highlight portion in which the density of the image is in a low level. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide an image treatment method 
and apparatus capable of overcoming the problems experienced with the 
conventional methods and apparatuses and further capable of reproducing 
the image exhibiting high grade and excellent accuracy. 
A further object of the present invention is to provide an image treatment 
method and apparatus capable of reproducing the highlight portion of the 
image well when the input data is treated using an error diffusion method. 
Another object of the present invention is to provide an image treatment 
method and apparatus capable of reproducing an image exhibiting an 
excellent quality with a simple structure. 
A still further object of the present invention is to provide an image 
treatment method and apparatus in which a reference value is determined at 
the time of quantizing image data and the image data is quantized using an 
error diffusion method depending upon the thus-determined referential 
value. 
The other object of the present invention is to provide an image treatment 
method and apparatus wherein whether there is a dot printed in the region 
in which treatment has been performed in the periphery of the subject 
picture element or not is determined, and this subject picture element is 
quantized using an error diffusion method in accordance with the result of 
the determination.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
First, the cause for deterioration in image quality in the highlight 
portion of the image described in the prior art will be described prior to 
the description of embodiments of the present invention. 
The causes for the printing of extraneous dots in a region in which the 
density of the image is low can be considered to be as follows: 
The error diffusion method is a method of performing a successive 
quantization of input images by diffusing the error between the density of 
the input image and the same of the output image to the as yet non-treated 
picture elements. However, when the portion in which the density of the 
image is in a low level is binarized in the error diffusion method, the 
positive error gathered in the subject picture element can be made in a 
low level since the position error is diffused, at the time of 
binarization, to the periphery portion is in the low level. As a result of 
this, it is difficult to make the density of the subject picture element 
exceed the threshold value (when the input image is 8 bits=256 level, the 
threshold value is usually 127) in the binarization. As a result of this, 
a portion in which no dot is printed can be generated, as shown in FIG. 
15. 
Furthermore, the cause of generation of the successive dots can be 
considered as follows. The errors generated in the blank areas shown in 
FIG. 15 and generated at the time of binarization become positive values 
since the density of the input image is low. Furthermore, since these 
positive errors are diffused to the region next to the blank area, dense 
generation of the dots occurs in this area. 
Then, an embodiment of the present invention capable of preventing the dot 
blank phenomenon in the highlight portions of the image due to the 
above-described cause or the phenomenon in which dots are successively 
generated will be described. 
First embodiment 
A first embodiment of the present invention will now be described with 
reference to the accompanying drawings. 
FIG. 1 is a block diagram of circuitry used in an image treatment apparatus 
according to a first embodiment of the present invention. 
Image data read out by an input device 1 comprising a phototransducing 
element such as a CCD and a driving system for scanning the same are 
successively supplied to an A/D converter 2. In this A/D converter 2, data 
upon each of the picture elements are converted to, for example, digital 
data of 8 bits. As a result of this, the image data is quantized to 
256-gradations data. Next, a correction such as shading correction for 
correcting for nonuniform sensitivity of the sensor for nonuniform 
illuminance due to the power source for illumination is performed in a 
correction circuit 3 in a digital calculation treatment. Then, a signal 
100 which has been subjected to the above-described correction is input to 
a binarization circuit 5 and a judgment circuit 6. In a threshold value 
setting circuit 4, the threshold for realizing the binarization is set in 
response to a judgment signal 400 output from the judgment circuit 6 so 
that a threshold signal 200 is output. In the binarization circuit 5, the 
corrected signal 100 output from the correction circuit 3 is binarized by 
the threshold value signal 200 output from the threshold value setting 
circuit 4 so that a binary signal 300 is output therefrom. In the judgment 
circuit 6, by using the binary signal 300 output from the binarization 
circuit 5 and the corrected signal 100 output from the correction circuit 
3, the binarized regions in the periphery of the subject picture element 
to be binarized are made reference for the purpose of performing a 
determination whether there is a dot which has been turned on or not. As a 
result of this, a judgment signal 400 is output. An output device 7 
comprises a laser beam printer or ink jet printer and performs an image 
formation of the binary signal 300 output from the binarization circuit 5 
by way of turning on/off of the dots. 
FIG. 2 is a block diagram illustrating in detail the threshold value 
setting circuit 4. 
The judgment signal 400 output from the judgment circuit 6 is input to a 
selector 8. The selector 8, in response to the judgment signal 400, 
selects a threshold value T1=300 when the judgement signal 400 is "1", 
while the same selects a threshold value of T2=127 when the judgment 
signal 400 is "0" so that the threshold signal 200 is output. 
When the judgement signal 400 is "1", the threshold T1=300 is selected 
since it is a highlight portion of the image and furthermore a dot is 
present in the peripheral portion of the subject picture element so that 
the successive printing of the dots is prevented. 
Although T1=300 in this case, the level of the value T1 only needs to 
exceed the maximum value of the corrected signal 100. Furthermore, while 
T2=127 in this case, it can be set to another value. 
FIG. 3 is a block diagram illustrating in detail the binarization circuit 
5. The corrected signal 100 (the density of the subject picture element) 
output from the correction circuit 3 is added to the error E.sub.ij (the 
total sum of the errors distributed from the peripheral picture elements 
to the subject picture element) stored in an error buffer memory 10 by an 
adder 9. As a result of this, an error corrected signal 210 is output. 
The error corrected signal 210 is input to a comparator 11 wherein it is 
compared with the threshold signal 200. If the error corrected signal 210 
is greater than the threshold signal 200, "1" is output, while, the same 
is smaller than the threshold signal 200, "0", output as the binary signal 
300. 
On the other hand, in a converter 12, if the thus-input binary signal 300 
is "0", the value as it is, is output, while if the same is "1", the value 
converted to "Dmax" is output as a signal 220. The value 210 and the value 
220 are input to a calculator 13. In this calculator 13, the difference 
between these two signals is calculated and its result is output as a 
signal 230 (.DELTA.E.sub.ij). This signal 230 is input to an weighting 
circuit 14, wherein an weighting (.alpha..sub.k1) is performed. Next, it 
is added to an error upon the picture element at a predetermined position 
in the error buffer. FIG. 4 illustrates an example of weighting 
coefficients (.alpha..sub.k1), wherein symbol * corresponds to the 
position of the subject picture element (I, J). By repeating the 
above-described operation, the binarization with the error diffusion 
method is performed. In this embodiment, since the corrected signal 100 is 
treated in an 8 bits manner: 
EQU Dmax=255 
However, if the corrected signal 100 is treated in an m bits manner: 
EQU Dmax=2.sup.m-1 +2.sup.m-2 +2+. . . +2.sup.0 
FIG. 5 illustrates in detail a block diagram for use as the judgment 
circuit 6. 
The binary signal 300 output from the binarization circuit 5 is latched 
immediately when the same is input to a line buffer 17. The signal read 
out from the line buffer 17 is also latched immediately when the same is 
input to a line buffer 16. That is, assuming that the position of the 
subject picture element to be now treated is (I,J), the binarized data 
picture elements at 12 peripheral positions are latched, the 12 positions 
being (I-2, J-2), (I-1, J-2), (I, J-2), (I+1, J-2), (I+2, J-2), (I-2, 
J-1), (I-1, J-1), (i, J-1), (I+1, J-1), (I+2, J-1), (I-2, J), and (I-1, 
J). The thus-latched data for the 12 picture elements are input to the OR 
circuit 18, wherein the `OR` of the data for the 12 picture elements are 
calculated, and the results are output as a signal 520. 
The corrected signal 100 is input to the comparator 15 wherein it is 
compared with the threshold D=20, wherein if the signal 100 is greater 
than the threshold D, "1" is, while the same is smaller than the threshold 
D, "0", is output as a signal 510. 
As a result of this, the density of the image can be determined. 
A selector 19, in accordance with the value of the signal 510, outputs a 
signal 520 if the signal 510 is "0", while the same outputs a signal 530 
if the signal 510 is "1" as a signal 400. However, the value of the signal 
530 is "0". 
That is, in a case where the picture element whose density of the image is 
in a low level, the binarized data in the periphery portion of the subject 
picture element is examined, and if there is a signal for making the dot 
turn on, the signal 520 becomes "1". As a result of this, the signal 400 
supplied to the threshold setting circuit 4 becomes "1". Furthermore, 
since the threshold T1=300 is selected in the threshold setting circuit, 
the dot of the subject picture element necessarily is turned off. In this 
state, if there is no signal which makes the dot turn on in the periphery 
portion of the subject picture element, the signal 520 becomes "0". 
Therefore, the threshold T2=127 is selected in the threshold value setting 
circuit 4 so that the binarization treatment is performed. 
In a case where the picture element whose density of image is high, since 
the signal 530 is selected by the selector 19, the threshold T2=127 is 
selected in the threshold setting circuit 4 so that the binarization 
treatment is performed. 
As a result of the examination of the binarized data in the peripheral 
portion of the subject picture element with the structure described above, 
if there is a dot in the periphery in a portion whose density of image is 
low, the dot is forcedly turned off. Consequently, a phenomenon that dots 
are printed in closely positioned manner can be prevented. 
FIG. 6 is a block diagram illustrating a case where the judgment circuit 6 
described in the aforesaid embodiment is changed. 
The binarization signal 300 is latched immediately when the same is input 
to a line buffer 20. The signal read out from the line buffer 20 is also 
immediately latched when the same is input to a line buffer 21. That is, 
assuming that the position of the subject picture element to be now 
treated is (I,J), the binarized data picture elements at 12 peripheral 
positions are latched, the 12 positions being (I-2, J-2), (I-1, J-2), (I, 
J-2), (I+1, J-2), (I+2, J-2), (I-2, J-1), I-1, J-1), (I, J-1), (I+1, J-1), 
(I+2, J-1), (I-2, J), and (I-1, J). 
In an OR circuit 22, the `OR` of the binarized data for 4 picture elements 
at the positions of the picture elements (I-1, J-1), (i, J-1), (I+1, J-1), 
and (I-1,J) are calculated, and as a result of this, a signal 630 is 
output. 
In an OR circuit 23, the `OR` of the binarized data for picture elements at 
the positions of the picture elements (I-2, J-2), (I-1, J-2), (I, J-2), 
(I+I, J-2), (I+2, J-2), (I-2, J-1), (I+2, J-1), and (I-2, J) are 
calculated, and as a result of this, a signal 620 is output. 
In an LUT 24, a switch signal 610 set in three levels corresponding to the 
input corrected signal 100 is output. The switch signal 610 is set to "1" 
when the corrected signal 100 is 20 or less, is set to "2" when the same 
is 21 or more and 50 or less, and is set to "1" when the same is 51 or 
more. 
A selective OR circuit 25 outputs, in response to a selection signal 610 
output from the LUT 24, "0" as a judgment signal 400 when the selection 
signal 610 is "0", outputs the `OR` of the signal 620 and the signal 630 
when the same is "1", and outputs the signal 630 when the same is "2". For 
example, the corrected signal 100 is 18, the switch signal 610 becomes 
"1", and in this state if the signal 620 is "1" and the signal 630 is "0", 
the judgment signal 400 becomes "1". 
In this embodiment, the region to be made a reference with respect to the 
value of the corrected signal 100 is set to three stages (that is, the 
three stages that the periphery of the subject picture element is not 
examined, that the peripheral four picture elements are examined, and that 
the peripheral 12 picture elements are examined). As a result of this, 
since the range of peripheral regions to be examined is enlarged as the 
density of the image becomes lower, the dots can be diffused in accordance 
with the density. As a result of this, closely positioned printing of dots 
performed in the portion whose density is low can be prevented. 
By increase in the number of the line buffers, the latches and the OR 
circuits at need, the regions to be made the reference can be made a 
multistage. An example in which the region is set to four stages will now 
be described. 
It is assumed that the position of the subject picture element to be now 
treated is (I,J) and there are line buffers and latches needed for 
maintaining the binarized data for picture elements at 24 positions, the 
24 positions being: (I-3, J-3), (I-2, J-3), (I-1, J-3), (I, J-3), (I+1, 
J-3), (I+2, J-3), (I+3, J-3), (I-3, J-2), (I-2, J-2), (I-1, J-2), (I, 
J-2), (I+1, J-2), (I+2, J-2), (I+3, J-2), (I-3, J-1), (I-2, J-1), (I-1, 
J-1), (I, J-1), (I+1, J-1), (I+2, J-1), (I+3, J-1), (I-3, J), (I-2, J), 
and (I-1, J). 
Furthermore, it is assumed that three OR circuits (a, b, c) and one 
selective OR circuit (d) are included. In the OR circuit a, the `OR` of 
the binarized data upon four picture elements at the positions (I-1, J-1), 
(i, J-1), (I+1, J-1), and (I-1, J) are calculated. As a result of this, a 
signal e is output. In the OR circuit b, the `OR` of the binarized data 
upon the eight picture elements at the positions (I-2, J-2), (I-1, J-2), 
(I, J-2), (I+1, J-2), (I+2, J-2), (I-2, J-1), (I+2, J-1), and (I-2, J) are 
calculated. As a result of this, a signal f is output. In the OR circuit 
c, the `OR` of the binarized data upon 12 picture elements at the 
positions (I-3, J-3), (I-2, J-3), (I-1, J-3), (I, J-3), (I+1, J-3)r (I+2, 
J-3), (I+3, J-3), (I-3, J-2), (I+3, J-2), (I-3, J-1),(I+3, J-1), and (I-3, 
J). As a result of this, a signal g is output. In the selective OR circuit 
d: if the corrected signal 100 is 10 or less, the result of the `OR`. of 
the signal e, the signal f, and the signal g; if the corrected signal 100 
is 11 or more and simultaneously 20 or less, the result of the `OR` of the 
signal e and the signal f; if the corrected signal 100 is 21 or more and 
50 or less, the result of the `OR` of the signal e; and if the corrected 
signal 100 is 51 or more, "0", may be output as the judgement signal. In 
this embodiment the level of the corrected signal 100 is set to four 
stage; 10 or less, 11 or more and 20 or less, 21 or more and 50 or less, 
and 51 or more. However, this is described only as an example. 
Furthermore, in a case where the color image, it can be realized in such a 
manner that a predetermined number of the circuits described in this 
embodiment may be provided corresponding to the number of the colors. 
FIG. 7 is a block diagram in a case where the embodiment shown in FIG. 1 is 
applied to a ternarization treatment. 
The input sensor 1, the A/D converter 2, and the correction circuit 3 are 
the same as those shown in FIG. 1. The corrected signal 100 is input to a 
ternarization circuit 27 and a judgment circuit 28. 
In a threshold value setting circuit 26, a threshold for ternarization is 
set by judgment signals 750 and 760 output from the judgment circuit 28. 
For example, if the judgment signal 750 is "0", 80 is output, while if the 
same is "1", 160 is output as a threshold signal 710. If the judgment 
signal 760 is "0", 160 is output, while if the same is "1", 300 is output 
as a threshold signal 720. This threshold value setting circuit 26 can be 
realized by two circuits such as that shown in FIG. 2. 
In the ternarization circuit 27, the corrected signal 100 output from the 
correction circuit 3 is ternarized by the threshold signals 710 and 720 
output from the threshold value setting circuit 26 so that signals 730 and 
740 are output. For example, if the signal 100 is smaller than the signal 
710, both signals 730 and 740 are set to "0", if the signal 100 is greater 
than the signal 710 and smaller than the signal 720, the signal 730 is set 
to "1". Furthermore, if the signal 100 is greater than the signal 720, the 
signal 710 is set to "0", and the signal 740 is set to "1". The 
ternarization treatment in this state is performed with an error diffusion 
method in which the difference between the density of the output image and 
that of the input image is diffused to the peripheral picture elements. 
The judgment circuit 28 can be realized by two of the circuits shown in 
FIG. 5 or FIG. 6. In this state, by the signal output from the 
ternarization circuit 27 and the corrected signal 100 output from the 
correction circuit 3, the ternarized region in the periphery of the 
subject picture element to be ternarized is made reference, and whether 
there is a printed dot in this region or not is judged. As a result of 
this, judgment signal 750 and 760 are output. For example, if the signal 
100 is 20 or less, the presence of the dot in the treated region in the 
periphery of the subject picture element is examined in the circuit to 
which the signal 730 is input. The result of this is output as the signal 
750. In this state, the signal 760 becomes "0". If the signal 100 is 128 
or more and 150 or less, the presence of the dot in the treated region in 
the periphery of the subject picture element is examined in the circuit to 
which the signal 740 is input. The result of this is output as the signal 
760. In this state, the signal 750 becomes "0". If the signal 100 is 21 or 
more and less than 128, or the same is 150 or more, both signals 750 and 
760 becomes "0". 
An outputting device 29 comprises a laser beam printer or an ink jet 
printer, wherein an image formation is performed by the signal 730 and 740 
output from the ternarization circuit 27. 
Although the ternarization circuit is described in this embodiment, if 
(N-1) of the threshold value setting circuit shown in FIG. 2 and the same 
number of the judgement circuit shown in FIG. 6 are used, the present 
invention can be applied to an N-value treatment. 
A color image can be realized by providing the circuits shown in the 
above-described embodiments in numbers corresponding to the predetermined 
number of colors. 
As described above, according to this embodiment, the presence of the dot 
in the periphery of the subject picture element is determined at the time 
of performing N-value treatment so that the binarization (N-value) 
treatment is performed. As a result of this, the problem experienced with 
the error diffusion method, that the close positioned printing of dots, 
can be prevented. 
Furthermore, by changing the binarized regions to be made the reference in 
accordance with the density of the lo images, dots can be printed in 
accordance with the density of the image so that the quality of the image 
can be improved. 
Furthermore, according to the present invention, the white noise generated 
due to the fact that no dot is in the region in which the density of the 
image is high, can be prevented. In this case, the structure may be 
constituted in such a manner that a dot is arranged to be printed in the 
subject picture element if a dot is not printed in the referential region, 
while if dots are completely printed, it is binarized at the usual 
threshold. 
As described above, according to the present invention, the presence of the 
dot printed in the treated region in the periphery of the subject picture 
element is determined and the subject picture element is quantized in 
accordance with the result of the judgment. Therefore, a phenomenon of 
close positioned printing of dots in the region in which the image density 
is low can be prevented. Consequently the quality of the image can be 
improved. 
Next, as a second embodiment, an embodiment capable of, in addition to the 
effect obtained in the first embodiment, preventing blanking in which no 
dot is printed in the portions in which the image density is low will be 
described. 
Second embodiment 
According to the accompanying drawings, a second embodiment of the present 
invention will now be described. 
FIG. 8 is a block diagram for use in an image treatment device according to 
this embodiment. 
Image data read out by an input device 101 comprising a photo-transducing 
element such as CCD and a driving system for scanning the same are 
successively supplied to an A/D converter 102. In this A/D converter 102, 
data upon each of the picture elements are converted to, for example, 6 
digital data of 8 bits. As a result of this, the image data is quantized 
to 256 gradations data. Next, a correction such as shading correction for 
correcting for nonuniform sensitivity of the sensor or for nonuniform 
illuminance due to the power source for illumination is performed in a 
correction circuit 3 in a digital calculation treatment. Then, a signal 
1100 which has been subjected to the above-described correction is input 
to a threshold value setting circuit 104, a binarization circuit 105 and a 
judgment circuit 106. In a threshold value setting circuit 104, the 
threshold for realizing the binarization is set in response to a judgment 
signal 1400 output from the judgment circuit 106 and the corrected signal 
1100 output from the correction circuit 103 so that a threshold signal 
1200 is output. In the binarization circuit 105, the corrected signal 1100 
output from the correction circuit 103 is binarized by a threshold value 
signal 1200 output from the threshold value setting circuit 104 so that a 
binary signal 1300 is output therefrom. In the judgment circuit 106, by 
using the binary signal 1300 output from the binarization circuit 105 and 
the corrected signal 1100 output from the correction circuit 103, the 
binarized regions in the periphery of the subject picture element to be 
binarized are made reference for the purpose of performing a determination 
whether there is a dot which has been turned on or not is made. As a 
result of this, a judgment signal 1400 is output. An output device 107 
comprises a laser beam printer or ink jet printer and performing an image 
formation of the binary signal 1300 output from the binarization circuit 
105 by way of turning on/off of the dots. 
FIGS. 9A is a block diagram illustrating in detail the threshold value 
setting circuit 104. 
The judgment signal 1400 output from the judgement circuit 106 and the 
corrected signal 1100 output from the correction circuit 103 are input to 
a ROM 108. The ROM 108 outputs as a signal 1100: "0" when the judgment 
signal 1400 is "0" and the signal 110 is 1 or more and less than 5; "1" 
when the judgment signal 1400 is "0" and the signal 1100 is 5 or more and 
less than 15; "2" when the judgment signal 1400 is "0" and the signal 1100 
is 15 or more and less than 30; "3" when the signal 1400 is "0" and the 
signal 1100 is 30 or more; and "4" regardless of the value of the signal 
1100 when the judgment signal 1400 is "1". 
FIG. 9B illustrates a ROM table stored in the ROM 108, wherein the 
above-described signal 1100 is accessed in accordance with the signal 1110 
and the signal 1400. 
The signal 1110 output from the ROM 108 is input to a selector 112 wherein, 
in accordance with the value of the signal 1110: when the signal 1110 is 
"1" a signal 1120 from a RAM 109; when the signal 1110 is "1" a signal 
1130 from a RAM 110; when the signals 1110 is "2" a signal 1140 from a RAM 
111; when the signal 1110 is "3" a signal 1150; when the signal 1110 is 
"4" a signal 1160, is selected, and is output as a threshold signal 1200. 
In the RAM 109, a uniform random number column (integer) of 20 or more and 
230 or less is stored, while in the RAM 110, a uniform random number 
column (integer) of 50 or more and 200 or less is stored, and while in the 
RAM 111, a uniform random number column (integer) of 100 or more and 150 
or less is stored. In this state, the signal 1150 is arranged to be 127, 
while the signal 1160 is arranged to be 255. 
The threshold stored in the RAM 109 is selected when the density of the 
signal 1100 is low. That is, since the threshold stored in the RAM 109 
includes a small valued ones, a dot can be output if the density of the 
signal 1100 is low. 
The judgment signal 1400 is a signal representing whether the dot is 
present in the region in the peripheral portion of the binarized subject 
picture element. If this judgment signal 1400 is 1, a dot is present in 
the peripheral portion of the subject picture element. Therefore, the 
signal 1160 ("255") is selected as the threshold so as not to let any dot 
appear in the binarization of the subject picture element. The signal 1160 
is, to be described later, selected only in the highlight portion of the 
image. Therefore, in the highlight portion of the image, successive 
printing of dots can be prevented. 
In this embodiment shown in FIG. 9A, a three staged uniform random number 
column is used as the threshold by using three RAMS. However, the number 
of the RAMs may be increased so as to use the multistaged uniform random 
column. In this case, it is preferable to widen the region in which the 
random number is generated in the portions in which the density of the 
image is low, and the higher the density becomes, the narrower the region 
in which the random number is generated. The signal 1160 only needs to be 
a value above 255. 
In the portion whose density is 0, in order to generation of the dots, the 
stationary threshold (for example "127") is made the threshold signal 1200 
if the density is 0. 
As a result of this, the dot generated, for example, in the background of 
the characters can be prevented. 
By lowering the threshold for binarization in a certain probability in the 
portion whose density is low, the blanking in which no dot is printed and 
generated in the portion whose image density is low can be prevented. 
Furthermore, by controlling the size of the threshold in accordance with 
the image density, the deterioration in the character portion can be 
prevented and the smoothness of the image can be secured. 
Furthermore, since a random number is used as the threshold, the uniforming 
of the portion whose image density is in an allowable level after the 
binarization can be improved. 
FIG. 10 is a block diagram illustrating in detail the binarization circuit 
5. The corrected signal 1100 (the density of the subject picture element) 
output from the correction circuit 3 is added to an error E.sub.ij (the 
total sum of the errors distributed to the subject picture elements) 
stored in an error buffer memory 114 by an adder 113. As a result, an 
error corrected signal 1210 is output. 
Next, the error corrected signal 1210 is input to a comparator 115 wherein 
it is compared with a threshold signal 1200 output from the threshold 
value setting circuit 104. If the error corrected signal 1210 is greater 
than the threshold signal 1200, "1" is output, while if it is smaller than 
the same "0" is output as the binary signal 1300. 
On the other hand, a converter 116 outputs the "0" as it is when the input 
binary signal 1300 is the same, while if it is "1", the value converted to 
"Dmax" is output as the signal 1220. The signal 1210 and the signal 1220 
are input to a calculator 117, wherein the difference between the two 
signals is calculated and is output as a signal 1230 (.DELTA.E.sub.ij). 
This signal 1230 is input to a weighting circuit 118 wherein weighting is 
performed. Next, it is added to the error at the picture element at a 
predetermined position in the error buffer. This weighting coefficient 
(a.sub.k1) is the same as that shown in FIG. 4. By repeating the 
above-described operation, the binarization with the error diffusion 
method is performed. In this embodiment, since the corrected signal 1100 
is treated in an 8-bits manner: 
EQU Dmax=255 
However, it the corrected signal 1100 is treated in an m bits manner: 
EQU Dmax=2.sup.m-1 +2.sup.m-2 +2+. . . +2.sup.0 
FIG. 11 illustrates in detail a block diagram for use as a judgment circuit 
106. 
The binary signal 1300 output from the binarization circuit 5 is latched 
immediately when the same is input to a line buffer 1019. The signal read 
out from a line buffer 119 is also latched immediately when the same is 
input to a line buffer 118. That is, assuming that the position of the 
subject picture element to be now treated is (I,J), the binarized data 
picture elements at 12 peripheral positions are latched, the 12 positions 
being (I-2, J-2), (I-1, J-2), (I, J-2), (I+1, J-2), (I+2, J-2), (I-2, 
J-1), (I-1, J-1), (i, J-1), (I+1, J-1), (I+2, J-1), (I-2, J), and (I-1, 
J). The thus-latched data for the 12 picture elements are input to the OR 
circuit 20, wherein the `OR` of the data for the 112 picture elements are 
calculated, and the results are output as a signal 1320. 
The corrected signal 1100 output from the correction circuit 103 is input 
to a comparator 117 wherein it is compared with the threshold D=20, 
wherein if the signal 1100 is greater than the threshold D, "1" is output, 
while if the same is smaller than the threshold D, "0" is output as a 
signal 1310. 
As a result of this, the density of the image can be determined. 
A selector 121, in accordance with the value of the signal 1310, outputs a 
signal 1320 if the signal 1310 is "0", while the same outputs a signal 
1330 if the signal 1310 is "1" as a signal 1400. However, the value of the 
signal 1330 is "0". 
That is, in a case where the picture element whose density of the image is 
low, the binarized data in the periphery portion of the subject picture 
element is examined, and if there is a signal for making the dot turn on, 
the signal 1320 becomes "1". As a result of this, the signal 1400 supplied 
to the threshold setting circuit 104 becomes "1". The threshold value 
setting circuit 4 selects as the threshold the signal 1160 (see FIG. 9A). 
As a result of this, the result of the binarization of the subject picture 
element becomes 0, so that the appearance of extraneous dots can be 
prevented. 
Furthermore, in this state, if there is no signal which can turn on the dot 
in the peripheral portion of the subject picture element, the signal 1320 
becomes "0". Therefore, the threshold value setting circuit 104 selects 
any of the threshold signal 1120, 1130, 1140 and 1150 in accordance with 
the density of the subject picture element. 
In a case of a picture element whose image density is in a high level, the 
signal 1330 is selected by the selector 121. Therefore, the threshold 
value setting circuit 104 selects any of the threshold signal 1120, 1130, 
1140 and 1150 in accordance with the density of the subject picture 
element so that the binarization treatment is performed. 
As a result of the above-described structure, no dot is printed in the 
peripheral portion of the area in which a dot is printed in the portion 
whose density is low. 
Therefore, the dot blanking phenomenon in the portion whose picture density 
is in a low level can be prevented. Furthermore, close positioned dot 
printing in the portion whose image density is in a low level can be 
prevented by examing the binarized data in the peripheral portion of the 
subject picture element. 
FIG. 12 is a block diagram in which the threshold value setting circuit 104 
described in the above-described embodiment is changed. 
The signal 1100 output from the correction circuit 103 is input to a ROM 
122. This ROM 122 outputs a signal 1410 in accordance with the following 
equation; 
EQU (signal 1410)=[(L1-L2)*(signal 1100)/255], 
wherein []represent the Gaussian integer function. In this case, it is 
employed that L1=.intg.185" and L2="20". FIG. 13 illustrates the 
relationship between the Signal 1100 and the signal 1410 only as an 
example. It is not limited to this, but need only satisfy the condition 
that when the signal 1100 is small, the signal 1410 is also small. 
As for the L1 and L2 they are not limited to this description but need only 
satisfy the condition that L1&gt;L2. 
The RAM 123 stores a uniform random column which is 0 or more and L3 or 
less, but satisfying the relationship L3+L1&gt;"255". 
In the adder 24, the signal 1410 and the signal 1420 are added and the 
result is output as the signal 1430. 
The selector 125 outputs, in accordance with the judgement signal 1400, a 
signal 1430 if the signal 1400 is "0", while if the signal 1400 is "1", it 
outputs a signal 1440, as a threshold signal 1200. 
In this case, the signal 1440 is set to "255", however, it may be other 
values, and need only exceed "255". 
As a result of the above-described structure, the function of setting the 
threshold is realized similarly to the above-described embodiments, and in 
addition, the size of the hardware can be reduced. 
FIG. 14 is a block diagram for use in a case where the judgment circuit 106 
described in the above-described embodiment is changed. 
The binarization signal 1300 is latched immediately when the same is input 
to a line buffer 126. The signal read out from the line buffer 126 is also 
immediately latched when the same is input to a line buffer 127. That is, 
assuming that the position of the subject picture element to be now 
treated is (I,J), the binarized data picture elements at 12 peripheral 
positions are latched, the 12 positions being (I-2, J-2), (I-1, J-2), (I, 
J-2), (I+1, J-2), (I+2, J-2), (I-2, J-1), (I-1, J-1), (I, J-1), (I+1, 
J-1), (I+2, J-1), (I-2, J), and (I-1, J). 
In an OR circuit 128, the `OR` of the binarized data for 4 picture elements 
at the positions of the picture elements (I-1, J-1), (I, J-1), (I+1, J-1), 
and (I-1,J) are calculated, and as a result of this, a signal 1520 is 
output. 
In an OR circuit 129, the `OR` of the binarized data for 8 picture elements 
at the positions of the picture elements (I-2, J-2), (I-1, J-2), (I, J-2), 
(I+I, J-2), (I+2, I-2), (I-2, J-1), (I+2, J-1) and (I-2, J) are 
calculated, and as a result of this, a signal 1530 is output. 
In a LUT 130, a switch signal 1510 set in three levels corresponding to the 
input corrected signal 1100 is output. The switch signal 1510 is set to 
"1" when the corrected signal 1100 is 20 or less, is set to "2" when the 
same is 21 or more and 50 or less, and is set to "0" when the same is 51 
or more. 
A selective OR circuit 131 outputs, in response to a selection signal 1510 
output from the LUT 130, "0" as a judgment signal 1400 when the selection 
signal 1510 is "0", and outputs the "OR" of the signal 1520 and the signal 
1530 when the same is "1", and outputs the signal 1520 when the same is 
"2". For example, the the corrected signal 1100 is 18, the switch signal 
1510 becomes "1", and in this state if the signal 1520 is "1" and the 
signal 1530 is "0", the judgment signal 1400 becomes "1". 
In this embodiment, the region to be made reference with respect to the 
value of the corrected signal 1100 is set to three stages (that is, the 
three stages that the periphery portion of the subject picture element is 
not examine, that the peripheral four picture elements are examined, and 
that the peripheral 12 picture elements are examined). As a result of 
this, since the range of periphery regions to be examined is enlarged as 
the lower the density of the image, the dots can be diffused in accordance 
with the density. As a result of this, the quality of the image can be 
improved. 
By increase in the number of the line buffers, the latches and the OR 
circuits at needy, the regions to be made reference can be made a 
multistage. An example in which the region is set to four stages will now 
be described. 
It is assumed that the position of the subject picture element to be now 
treated is (I,J) and there are line buffers and latches needed for 
maintaining the binarized data for picture elements at 24 positions, the 
24 positions being; (I-3, J-3), (I-2, J-3), (I-1, J-3), (I, J-3), (I+1, 
J-3), (I+2, J-3), (I+3, J-3), (I-3, J-2), (I-2, J-2), (I-1, J-2), (I, 
J-2), (I+1, J-2), (I+2, J-2), (I+3, J-2), (I-3, J-1), (I-2, J-1), (I-1, 
J-1), (I, J-1), (I+1, J-1), (I+2, J-1), (I+3, J-1), (I-3, J), (I-2, J), 
and (I-1, J). Furthermore, it is assumed that three OR circuits (a, b, c) 
and one selective OR circuit (d) are included. In the OR circuit a, the 
`OR` of the binarized data upon four picture elements at the positions 
(I-1, J-1), (I, J-1), (I+1, J-1), and (I-1, J) are calculated. As a result 
of this, a signal e is output. In the OR circuit b, the `OR` of the 
binarized data upon the eight picture elements at the positions (I-2, 
J-2), (I-1, J-2), (I, J-2), (I+1, J-2), (I+2, J-2), (I-2, J-1), (I+2, 
J-1), and (I-2, J) are calculated. As a result of this, a signal f is 
output. In the OR circuit c, the `OR` of the binarized data upon 12 
picture elements at the positions (I-3, J-3), (I-2, J-3), (I-1, J-3), (I, 
J-3), (I+1, J-3), (I+2, J-3), (I+3, J-3), (I-3, J-2), (I+3, J-2), (I-3, 
J-1),(I+3, J-1), and (I-3, J). As a result of this, a signal g is output. 
In the selective OR circuit d: if the corrected signal 1100 is 10 or less, 
the result of the `OR` of the signal e, the signal f, and the signal g; if 
the corrected signal 1100 is 11 or more and simultaneously 20 or less, the 
result of the `OR` of the signal e and the signal f; if the corrected 
signal 1100 is 21 or more and 50 or less, the result of the `OR` of the 
signal e; and if the corrected signal 1100 is 51 or more, "0", may be 
output as the judgment signal. In this embodiment the level of the 
corrected signal 1100 is set to four stage; 10 or less, 11 or more and 20 
or less, 21 or more and 50 or less, and 51 or more. However, this is 
described only as an example. 
Furthermore, in a case where the color image, it can be realized in such a 
manner that a predetermined number of the circuits described in this 
embodiment may be provided corresponding to the number of the colors. 
According to this embodiment, as described above, by lowering the threshold 
for binarization in a certain probability in the portion whose density is 
in a low level, the blanking in which any dot is not printed and generated 
in the portion whose image density is in a low level can be prevented from 
generation. Furthermore, by controlling the size of the threshold in 
accordance with the image density, the deterioration in the character 
portion can be prevented and the smoothness of the image can be also 
secured. 
Furthermore, by not only lowering the threshold for binarization, but also 
quantizing the subject picture element in accordance with the result of 
judgment made upon whether there is a dot printed in the treated region in 
the periphery of the subject picture element or not. As a result of this, 
close printing the dots generated in a portion whose image density is in a 
low level can be prevented. 
Furthermore, according to this embodiment, by enlarging the treated region 
to be made the reference as the density becomes lower, the dot can be 
printed in accordance with the image density. As a result of this, the 
quality of images can be improved. 
Although in this embodiment, the structure is employed in which the 
blanking and a phenomenon that dots are closely printed in the portion 
whose density is low can be prevented, white noise generated due to 
nonprinting of dots in the portion whose density is high can be also 
prevented. 
In this case, by changing the threshold (random number) in accordance with 
density and employing an arrangement that a dot is inevitably printed if 
any dot is not printed in the region to be made reference in the periphery 
portion of a subject picture element, the dot may be printed or not in 
accordance with the threshold if all of the dots are printed. 
In the above-described first and second embodiments, the examples are 
described in which input images are binarized and multivalued in the error 
diffusion method. However, the method of quantization according to the 
present invention is not limited to the error diffusion method. It can be 
used in a method of performing quantization by correcting the error 
between the input image and the output image, such as the average error 
minimum method.