Continuous image estimation method

A continuous image estimation method of a binary image wherein only one scanning aperture satisfying a predetermined condition for each picture element of a continuous image to be estimated from a plurality of scanning apertures for each kind in a dither image formed of a dither matrix, and the continuous image is estimated on the basis of the number of white or black picture elements in the scanning aperture selected. The predetermined condition is that a gradation expression is conducted in a lower spatial frequency range by using larger scanning apertures and in a higher spatial frequency range by using smaller scanning apertures, and that for the coincidence between patterns of a dither image in the scanning aperture and a binary image, which is made binary with the dither matrix from a continuous image formed on the bases of the number of the white or black picture elements in the scanning aperture, the patterns being obtained by comparing the dither image and the binary image for each aperture.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a continuous image estimation method and, 
more particularly, to a continuous binary or dither image estimation 
method for estimating an original continuous image excellently a binary or 
dither image displayed in pseudo-halftone. 
2. Description of the Prior Art 
Most output units practised at present such as displays or printers cannot 
display images other than in binary values, i.e., in white and black 
colors. 
As the method of falsely expressing a halftone by the use of such output 
unit, there is known a density pattern method (or a luminance pattern 
method) or a dither method. 
Both the density pattern method and the dither method are a kind of areal 
gradation method and express a continuous image by changing the number of 
dots to be recorded in a constant area (i.e., matrix). 
The density pattern method is one for recording a portion of an original 
corresponding to one picture element with a plurality of dots by using a 
threshold matrix, as shown in FIG. 25(B), and the dither method is one for 
recording the portion of the original corresponding to one picture element 
with one dot, as shown in FIG. 25(A) so that binary output data are 
obtained, respectively, as shown. These output data express a continuous 
image falsely in binary white and black values. 
Now, if the continuous image (corresponding to the input data of FIG. 25) 
of an original could be estimated from the pseudo-continuous image thus 
made binary, a binary image having an excellent quality could 
advantageously be formed by a binary treatment using that 
pseudo-continuous tone image. 
In the case of the density pattern image, the continuous image can be 
instantly restored if the arrangement of a pattern level is known. 
However, a resolution is low for the quantity of information. 
On the contrary, the dither image has a higher resolution for the quantity 
of information than that of the density pattern image but is difficult to 
be returned to the original continuous image. 
In case the continuous image is to be thus estimated, on the other hand, it 
is estimated without special consideration into the human visual 
characteristics and the kind of the image. As a result, the features of 
the image are not utilized so that the image quality cannot be sufficed. 
If the visual characteristics are also considered, the original continuous 
image can be copied better. 
In case a picture element to be estimated has its density changing 
drastically as at an edge, on the other hand, the scanning aperture used 
is single to raise a defect that the edge cannot be restored to a 
satisfactory extent, even if the level of the continuous image is to be 
estimated by using one of sixteen kinds of scanning apertures. Since the 
human vision has a high power to discriminate the edge of an image, as is 
well known in the art, it recognizes the entirety of the reproduced image 
in the worse quality if the reproducibility of the edge is the more 
degraded. 
SUMMARY OF THE INVENTION 
An object of the present invention is to solve those problems of the prior 
art and to provide a binary continuous image estimation method for 
estimating an original continuous image excellently from a binary image 
(e.g., a binary dither image). 
In order to solve the aforementioned problems, according to the present 
invention, there is provided a binary pseudo-continuous tone image 
estimation method comprising the steps of: setting a plurality kinds of 
and a plurality of scanning apertures for each kind in a binary image 
formed of a dither matrix; selecting only one scanning aperture satisfying 
a predetermined condition for each picture element of a continuous image 
to be estimated; and estimating said continuous image on the basis of the 
number of white or black picture elements in the scanning aperture 
selected. 
If the image treatment is conducted with the condition that a gradation 
expression is made using a larger scanning aperture in a lower spatial 
frequency region and using a smaller scanning aperture in a higher spatial 
frequency region, it is possible to estimate a continuous image meeting 
the human visual characteristics. 
Moreover, a continuous image including an edge can be estimated in view of 
coincidence of two binary images which are obtained by comparing for each 
aperture a binary image in a scanning aperture and an image made binary 
with a dither matrix from a continuous image formed on the basis of the 
number of white or black picture elements in the scanning aperture. This 
makes the restoration excellent at the edge. 
Another object of the present invention is to provide a continuous image 
estimation method of a dither image for restoring the edge of a binary 
image excellently to a continuous image. 
According to the present invention, moreover, there is provided a 
continuous image estimation method of a dither image formed of a dither 
matrix, comprising the steps of: setting a plurality of scanning apertures 
having an equal area; selecting only one scanning aperture satisfying a 
predetermined condition for each picture element of a continuous image to 
be estimated; and estimating said continuous image on the basis of the 
number of white or black picture elements in the scanning aperture 
selected. 
The predetermined condition is that the patterns of two binary images 
obtained by comparing for each aperture a dither image in the scanning 
aperture and an image made binary with the dither matrix from the 
continuous image formed on the basis of the number of white or black 
picture elements in the scanning aperture. 
In order to restore even the binary image including the edge excellently to 
the continuous image, it is sufficient that the scanning aperture 
including the estimated picture elements should not overlap that edge. 
For this purpose, a plurality of scanning apertures having their estimated 
picture element positions defined are prepared, and such one of the 
scanning apertures not overlapping the edge that as many as estimated 
picture elements as possible are positioned at the center. This selecting 
condition is called the predetermined condition. 
The aperture selection is conducted for each picture element of the dither 
image, and this dither image is formed on the basis of the estimated 
continuous image thus obtained. Then, the image can be restored without 
damaging the edge. The scanning aperture described above means a region is 
determined when the continuous level is calculated and can be scanned. 
Other objects and features of the present invention will become apparent 
from the following description to be made with reference to the 
accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The present invention will be described in detail in the following in 
connection with the embodiments thereof with reference to the accompanying 
drawings. 
Here, one of ordered binary dither method will first be described in case 
the Bayer type matrix of 4.times.4 is used as the threshold matrix. 
FIGS. 1(A) to 1(C) are diagrams showing an example of a binary either image 
for explaining the present invention. FIG. 1(A) shows an original 
continuous image converted into digital data; FIG. 1(B) shows a binary 
dither threshold matrix of Bayer type of 4.times.4; and FIG. 1(C) is a 
binary dither image of the original image converted into a monochromatic 
binary image (i.e., a binary dither image) by the threshold matrix. 
Incidentally, the binary dither image shown in FIG. 1(C) shows the white 
levels in blanks. 
The Bayer type binary threshold matrix takes the dither pattern in which 
the threshold values 0 to 15 scatter, as shown in FIG. 1(B). 
FIGS. 2(A) to (D) show one example of a plurality of kinds of scanning 
apertures (i.e., unit areas) having different aperture areas to be used in 
the present invention. FIGS. 2(A), 2(B), 2(0) and 2(D) show apertures 
having sizes of 2 rows .times.2 columns, 2 rows .times.4 columns, 4 rows 
.times.2 columns, and 4 rows .times.4 columns, respectively. 
Moreover, these apertures to be prepared are in the numbers corresponding 
to the sizes of those matrices. As shown in FIGS. 3 to 6, therefore, there 
are prepared four scanning apertures A, eight apertures B and C, and 
sixteen apertures D, all of which have an equal area. 
Furthermore, symbols X appearing in the apertures represent picture 
elements of the continuous images to be estimated. For example, an 
aperture A11 is used in such a superposed manner that a picture element to 
be estimated never fails to be located in a predetermined picture region 
(1, 1) indicated at the symbol X. As a result, in the case of an aperture 
A12, an estimated picture element is positioned in a predetermined picture 
region (1, 2). 
The estimated continuousimages, as shown in FIGS. 7 to 10, are obtained by 
sequentially moving the individual predetermined picture regions shown in 
FIGS. 3 to 6 in a fixed state at unit of one picture element on the dither 
image of FIG. 1(C), by totaling the multiple-valued picture element levels 
contained in the apertures at the individual picture element positions, 
and by using the multiplication of that total value by a gain as the 
estimated value of the continuous image. 
FIG. 7 shows the estimated continuous image when the aperture A of FIG. 3 
is used. A continuous image A11' of FIG. 7 is obtained in case it is 
estimated using the aperture A11. Likewise, continuousimages A12' to D44' 
shown in FIGS. 7 to 11 are obtained in case they are estimated using the 
apertures A12 to D44. 
Here, the method for obtaining the estimated continuous image designated at 
D11' in FIG. 10 will be described in the following. 
Now, the aperture D defined at D11 in FIG. 6 is superposed, as shown in 
FIG. 11, at the initial position (in which the center position is located 
at the right-hand lower intersection of second row and second column, as 
will be expressed at [2, 2]in the following) of the dither image. 
In this case, the picture elements contained in the aperture D11, as shown, 
are desired to be completely contained. In other words, the containment is 
preferred such that a picture element is not partially deficient. 
Next, the numbers of white (or black)picture elements of the portion 
enclosed by that aperture D11 are totaled, and this total value is used as 
the estimated value of the continuous image, i.e., 7 in this case. 
Therefore, the estimated value of the position (1, 1) of first row and 
first column is 7. 
Next, the aperture D11 is moved rightward for one picture element (i.e.. 
one column in this case), and the numbers of white picture elements in the 
aperture D11 at (1, 2) are similarly totaled to 7. These calculations are 
sequentially executed for all the columns of the same row. 
When the first column is finished, moreover, the aperture D11 is moved to a 
next (i.e., second) column, and the continuous density estimations are 
sequentially executed likewise from the position in which the aperture 
center is located at [3, 2]. 
By executing these calculations up to the last column of the last row while 
sequentially moving the aperture, the continuous image estimation value is 
determined to finish the continuous image estimations. The result thus 
calculated is the estimated continuous image D11' shown in FIG. 10. 
Symbols * appearing in FIG. 10 represent the regions where the continuous 
image treatment cannot be conducted because there is no corresponding 
dither image data. 
Next, the method for determining the estimated continuous image using the 
aperture B11 shown in FIG. 4 will be described in the following. 
In case the aperture B11 is selected, its movement starting position is 
taken, as shown in FIG. 12. The total of the numbers of white picture 
elements in this state is 2, the total value in the aperture B11 has to be 
doubled so that the area may conform to that of the aperture of FIG. 2(D). 
As a result, the picture element level in the aperture B11 is 2.times.2=4. 
In this case, the gain of the apertures B (i.e., B11 to B24) is 2. 
If the gains of the individual apertures shown in FIG. 2 are likewise 
determined, the apertures A (i.e., A11 to A22) have a gain 4, and the 
apertures C (i.e., C11 to C24) have a gain 2. 
If this calculation is executed each time the aperture B11 is moved for 
each picture element, the continuous image shown in FIG. 8 is obtained. 
The descriptions of FIGS. 7 and 9 will be omitted because they can be 
similarly thought. 
Even in this state of the fixed aperture, the half-tone image can be 
excellently estimated. 
Of course, according to the method described above, the continuous image of 
FIG. 10, is estimated from the binary dither image (of FIG. 1(C)) having 
less information than the original continuous image shown in FIG. 1(A). 
Therefore, the continuous image of FIG. 10 is not completely coincident 
with that which is formed from the original continuous image shown in FIG. 
1A. 
However, the continuous image obtained fairly resembles the original 
continuous image except the portion of the original continuous image, in 
which the density level abruptly changes. 
Here, the human vision has such characteristics that it has a high picture 
element level gradation discriminating ability in a lower spatial 
frequency region (where the picture element level less changes) but a 
lower picture element level gradation discriminating ability in a higher 
spatial frequency region (where the picture element level more changes). 
Therefore, if a higher gradation expression is conducted with larger 
apertures in the lower spatial frequency region whereas an image of higher 
resolution is reproduced with smaller apertures in the higher spatial 
frequency region, it is possible to conduct a far better estimation than 
the estimated value of the continuous image shown in FIGS. 7 to 10. 
In order to restore even the edge of a binary image excellently to a 
continuous image, moreover, it is sufficient to prevent the scanning 
apertures containing the estimated picture elements from overlapping that 
edge. 
For this purpose, a plurality of scanning apertures having estimated 
picture element positions specified are prepared, and such one of the 
scanning apertures failing to overlap the edge that as many as estimated 
picture elements as possible be positioned at the center. 
If these aperture selections are conducted for the individual picture 
elements of the dither image so that the dither image may be formed on the 
basis of the estimated continuous image thus obtained, the image can be 
restored without damaging the edge. 
In the present invention, therefore, the continuous image is to be 
estimated considering the human picture element level gradation 
discriminating ability and edge discriminating ability. 
The method of the present invention will be described specifically in the 
following. 
This method is conducted, assuming that digital binary images have already 
been stored in storage means such as a memory, by setting a plurality of 
kinds of scanning apertures for those digital binary images, by subjecting 
the digital binary images to a predetermined arithmetic processing,- by 
selecting the most appropriate one for each picture element from the 
plural kinds of scanning apertures, by totaling the numbers of white or 
black picture elements in the scanning aperture selected, and by using the 
total value as the estimated value of the continuous image. 
As the predetermined arithmetic processing, there is used such an algorithm 
that the larger scanning apertures are selected in the lower spatial 
frequency range (i.e., the range where the picture element level less 
changes) whereas the smaller scanning apertures are selected in the higher 
spatial frequency range (i.e., the range where the picture element level 
more changes). 
In order that the edge of the estimated image may not overlap the end of 
the scanning aperture, moreover, the aperture selected is one whereas the 
estimated picture elements are located at the center of the scanning 
aperture as many as possible. 
Therefore, the fundamental concept of the present invention is to select 
the scanning aperture which is as large as possible and in which the 
estimated picture elements are located near the center, so long as no 
density change is found in the scanning apertures. 
With these in mind, the selecting order of the scanning apertures is 
basically D.fwdarw.C.fwdarw.B.fwdarw.A, as shown in FIG. 13. More 
specifically, the aperture selections are executed in the following order: 
D23.fwdarw.D32.fwdarw.D22.fwdarw.D33.fwdarw.D12 
.fwdarw.D43.fwdarw.D31.fwdarw.D24.fwdarw.D34.fwdarw.D21.fwdarw.D42.fwdarw. 
D13.fwdarw.D41.fwdarw.D14.fwdarw.D44.fwdarw.D11.fwdarw.C21.fwdarw.B23.fwdar 
w.B12.fwdarw.C32.fwdarw.B22.fwdarw.C22.fwdarw.C31 
.fwdarw.B13.fwdarw.C12.fwdarw.B11.fwdarw.B24.fwdarw.C41.fwdarw.B14.fwdarw. 
C42.fwdarw.C11.fwdarw.B21.fwdarw.A21.fwdarw.A12.fwdarw.A22.fwdarw.A11. 
When the estimated picture element is located at (1, 1), it is at the end 
so that the apertures to be used are of four kinds, which specifically 
follow the order, as shown in FIG. 13: 
D11.fwdarw.B11.fwdarw.C11.fwdarw.A11. 
FIGS. 14(A) to 14(D) are explanatory diagrams showing the estimation method 
in case the continuous image level of the picture element (1, 1) is to be 
estimated. 
Step (1): 
At this step, the aperture D11 is first selected as the scanning aperture. 
Then, this scanning aperture D11 is superposed on the initial position (as 
shown in FIG. 11) of FIG. 1(C), as shown in FIG. 14(A). The total number 
of the white picture elements in this aperture D11 is 7. Assuming that the 
total value 7 is at an average picture element level, the individual 
picture elements are compensated by 7, as shown in FIG. 14(B). If the 
average picture element level image shown in FIG. 14(B) is made binary 
with the dither matrix shown in FIG. 14(C), a binary image shown in FIG. 
14(D) is obtained. Here, the binary dither images (A) and (D) are compared 
and found to be not an identical pattern. 
The fact that the binary dither images (A) and (D) do not have an identical 
pattern means that the picture element levels have changed. In this case, 
therefore, the scanning aperture D11 is not appropriate for one to be 
selected. 
Since the scanning aperture D11 is not selected at the step (1), the 
process advances to the following step (2): 
Step (2): 
The scanning aperture to be selected at the step (2) is the aperture C11. 
Then, if the selected aperture C11 is superposed on the initial position of 
FIG. 1(C), it is shown at the step (2) in FIGS. 14(A) to 14(D). The total 
number of the white picture elements in the scanning aperture C11 is 3. 
Assuming that the average picture element takes the level 66 which is 
obtained by multiplying the total value 3 by the gain 2, the individual 
picture elements are compensated with 6, as shown in FIG. 14(B). The 
average picture element level image shown in FIG. 14(B) is made binary 
into that shown in FIG. 14(D) with the dither matrix (i.e., such one of 
the threshold matrices of FIG. 1(B) as is composed of first and second 
columns in the scanning aperture C11) shown in FIG. 14(C). 
Here, the binary dither images shows in FIGS. 14(A) and 14(D) are compared 
and found to have no identical pattern. 
The fact that the two patterns are different means that the picture element 
levels have changed. In this case, therefore, the scanning aperture C11 is 
also improper for the selected aperture. 
Since the scanning aperture C11 is not selected at the step (2), the 
process advances to the following step (3): 
Step (3): 
The scanning aperture to be selected at the step (3) is the aperture B11. 
Then, if the selected aperture B11 is superposed on the initial position of 
FIG. 1(C), it is shown in FIG. 14(A). The total number of the white 
picture elements in the scanning aperture B11 is 2. Assuming that the 
average picture element takes the level 4 which is obtained by multiplying 
the total value 2 by the gain 2, the individual picture elements are 
compensated with 4, as shown in FIG. 14(B). The average picture element 
level image shown in FIG. 14(B) is made binary into that shown in FIG. 
14(D) with the dither matrix shown in FIG. 14(C). 
Here, the comparison of the binary dither images shown in FIGS. 14(A) and 
14(D) reveals that their two patterns are identical. It is therefore 
estimated that the picture element level does not change in the scanning 
aperture B11. 
Incidentally, if the patterns do not become identical even after those 
steps are sequentially passed, it is assumed that the minimum scanning 
aperture A is selected. 
Thus, the scanning aperture B11 is selected. The total number of the white 
picture elements in the scanning aperture B11 is 2. Since the gain of the 
scanning aperture B11 is 2, the image estimation value to be determined is 
2.times.2=4. In other words, the number of the white picture elements 
shown in FIG. 14 (B) of the step (3) of FIGS. 14(A) to 14(D) is used as it 
is as the continuous image estimation value. 
The scanning apertures to be used in the estimation at the picture element 
(1, 2) and their selected order are as follows: 
D12.fwdarw.D11.fwdarw.B12.fwdarw.C12.fwdarw.B11.fwdarw.C11.fwdarw.A12.fwdar 
w.A11. 
The resultant aperture selected at this time is the aperture B12. 
If the operations described above are conducted for each picture element of 
the binary dither image of FIG. 1(C), it is possible to obtain an 
estimated continuous image shown in FIG. 15(A). Incidentally, what 
scanning aperture is used for estimating each continuous image will be 
described with reference to FIG. 15(B). On first line: the first to 
seventh columns are such that the continuous estimation images (1, 1), (1, 
2), (1, 3), (1, 4), (1, 5), (1, 6) and (1, 7) are B11, B12, B12, B12, B12, 
B12 and D11, respectively. 
Thus, the estimated continuous image shown in FIGS. 15(A) and 15(B) matches 
the human visual characteristics, because it is estimated with the larger 
scanning apertures in the region of less change in the picture element 
level and with the smaller scanning apertures in the region of more change 
in the picture element level. 
As a result, the estimated continuous image remarkably resembles the 
continuous image obtained from the original continuous image shown in FIG. 
1(A). 
Moreover, in case the patterns are incoincident, the one of the scanning 
apertures to be compared, in which the pattern has a smaller number of in 
coincident picture elements, is selected. In case the numbers of the in 
coincident picture elements are equal, the scanning aperture having the 
estimated picture elements closer to the center is selected. There arises 
no possibility that the edge of the image overlaps the end of the scanning 
aperture. 
Incidentally, the description thus far made is directed to the case in 
which the continuous image is estimated from the binary image. Despite 
this fact, however, a new binary image can be obtained by converting the 
gradation of the continuous image estimated, by filtering the continuous 
image or by enlarging or reducing the size of the continuous image. 
FIG. 16 is a flow chart showing the case in which the estimated continuous 
image has its gradation converted (or subjected to the gradation 
treatment). According to this flow chart, as shown, the continuous image 
is subjected to the gradation conversion, and the continuous image thus 
converted is formed into a new binary image by the use of the threshold 
matrix. 
The gradation conversion characteristics conceivable are shown in FIG. 17. 
Gradation conversion characteristic curves f1 and f2 are plotted in terms 
of an output against an input. Numerical values appearing in FIG. 17 
represent the density levels. 
FIG. 18(A) shows the continuous image which has its gradation converted 
with the f1 characteristics of FIG. 17 from the image shown in FIG. 15(A); 
FIG. 18(B) shows the continuous image which has its gradation converted 
with the f2 characteristics of FIG. 17. FIG. 18(C) shows the binary image 
which is made binary with the aforementioned Bayer type binary dither 
matrix from the image shown in FIG. 18(A). FIG. 18(D) shows the binary 
image which is made binary from the image shown in FIG. 18(B). It is 
apparently found from FIGS. 18(C) and 18(D) that the binary images are 
made drastically different due to the difference in the gradation 
conversion characteristics. 
FIG. 19 is a flow chart showing the case in which the estimated continuous 
image is to be filtered. According to the flow chart, as shown, the 
continuous image estimated by the present invention is filtered, and the 
continuous image thus filtered is formed into a new binary image by the 
use of the threshold matrix. 
The filter characteristics are exemplified in FIGS. 20(A) and 20(B). FIG. 
20(A) shows a high-pass convolution filter, and FIG. 20(B) shows a 
low-pass convolution filter. 
If the estimated continuous image shown in FIG. 15(A) is filtered with the 
filter having the characteristics shown in FIGS. 20(A) and 20(B), the 
high- and low-pass continuous images are obtained, respectively, as shown 
in FIGS. 21(A) and 21(B). If these continuous images are made binary with 
the dither matrix shown in FIG. 21(C), there are obtained the binary 
dither images, as shown in from FIGS. 21(A) to 21(D) and from 21(B) to 
21(E), respectively. 
FIG. 22 is a flow chart showing the case in which the estimated continuous 
image is to be enlarged or reduced. According to the flow chart, as shown, 
the continuous image estimated by the present invention is enlarged or 
reduced, and a new binary image is obtained from the enlarged or reduced 
continuous image by the use of the threshold matrix. An interpolation, for 
example, is used as the enlarging or reducing method. 
FIG. 23(A) shows the continuous image which is enlarged 1.25 times from the 
continuous image shown in FIG. 15(A) by the simplest Nearest Neighborhood 
method of the interpolations. FIG. 23(B) shows the continuous image which 
is reduced 0.75 times from the same by the same method. 
If these continuous images are made binary with the dither matrix shown in 
FIG. 23(C), there are obtained the enlarged and reduced binary images, 
respectively, as shown in FIGS. 23(D) and 23(E). 
Incidentally, the matrix having the threshold value shown in FIG. 14(B) can 
be used as the dither matrix. If this matrix is used, slightly different 
binary images are obtained even in case the same continuous image level is 
used. 
More specifically, if the dither matrix shown in FIG. 24(B) is used for the 
continuous image of FIG. 24(A), the dither image is obtained, as shown in 
FIG. 24(C). 
Incidentally, in case the continuous image is to be estimated from the 
aforementioned binary image, this binary image is preferably a binary 
dither image or a binary density pattern image and more preferably the 
binary dither image. 
In case the binary dither image is to be used, the binary image according 
to the ordered binary dither method is more preferable than the random 
dither or conditional dither so that each threshold value may enter the 
aperture of the maximum area. Moreover, a dispersion type binary dither 
image is preferable so that the threshold values may evenly enter the 
aperture of the minimum area, and the Bayer type binary dither image 
having its threshold values dispersed completely is more preferable. 
Incidentally, in the description made above, the continuous image is 
obtained by scanning each picture element. Despite of this fact, however, 
the present invention should not be limited to the above but may scan 
every two ore more picture elements. 
In the description made above, moreover, the plural kinds of apertures are 
exemplified by the case of four kinds, but no limitation is given to the 
kinds of apertures. Nor should the sizes of the apertures be limited to 
the exemplified ones but may be arbitrary. 
As has been described hereinbefore, according to the embodiment of the 
present invention, a plurality of kinds of scanning apertures are set, and 
the most appropriate one is selected from those scanning apertures by a 
predetermined arithmetic operation for each picture element. 
In this case, according to the present invention, a higher gradation 
expression is conducted in a lower spatial frequency range by using larger 
scanning apertures, and an image of higher resolution is reproduced in a 
higher spatial frequency range by using smaller scanning apertures. This 
makes it possible to estimate the continuous image at a higher level than 
the continuous image estimation value shown in FIGS. 7 to 10. 
According to the present invention, moreover, the scanning aperture 
allowing the estimated picture element to come to the center of the 
scanning aperture is selected to improve the restoration of the edge so 
that a continuous image of excellent quality can be estimated by the 
aforementioned effect. 
Image treatments such as the gradation conversion or the size enlargement 
or reduction can be conducted on the basis of such continuous image, if 
obtained. 
FIG. 26 is a flow chart showing an image treatment for implementing the 
continuous image estimation method of a dither image according to another 
embodiment of the present invention. 
First of all, a dither image (i.e., an original dither image) is formed (at 
a step 1) from an original continuous image. For forming this original 
dither image, the dither matrix having predetermined size and threshold 
level is used, as shown in FIG. 1(B), and the threshold level of that 
dither matrix and the level (as shown in FIG. 1(A)) of the original 
continuous image are compared for each picture element so that the 
original continuous image is converted into the binary image (i.e., the 
dither image) having values "1" and "0" (as shown in FIG. 1(C)). 
On the basis of the original dither image thus formed, the estimated dither 
image is formed (at a step 2) by using a plurality of scanning apertures. 
In this case, the original dither image is so compensated (at a step I of 
FIGS. 29(A) and 29(B) and 30(A) to 30(D) into the binary image that its 
picture elements to be estimated become coincident With the estimated 
picture elements (of sixteen kinds, as shown in FIG. 6) defined by those 
scanning apertures. 
If the binary image thus obtained is called the "estimated dither image", 
the numbers of the white or black picture elements in this estimated 
dither image are counted. In the present embodiment, the numbers of the 
white picture elements in the scanning aperture are counted, and the 
counted value is estimated (at a step II of FIGS. 29(A) and 29(B) and 
30(A) to 30(D)) as the continuous image level of all the picture elements 
in the scanning aperture. 
Next, the levels of the individual picture elements of that estimated 
continuous image are compared (at a step III of FIGS. 29(A) and 29(B) and 
30(A) to 30(D) with the threshold values of the dither matrix and again 
made binary (at a step IV of the same Figures). 
The pattern comparisons of this binary image and the estimated dither image 
are executed at a subsequent step 3. These pattern comparisons are 
accomplished at the scanning apertures of sixteen kinds, respectively. 
In the case of coincidence of the patterns, the continuous image at this 
time is used (at a step 4) as the estimated continuous image for the 
picture element because the pattern of the estimated dither pattern is 
correct. 
In the case of incoincidence of the patterns, the numbers of the 
incoincident picture elements are counted (at a step 6), and the estimated 
dither image having the minimum number of the in coincident picture 
elements is detected (at a step 7). Next, the numbers of tho white (or 
black) picture elements of the estimated dither image thus detected are 
counted, and this counted value is estimated (at a step 5) as the level of 
the continuous image of that estimated picture element. 
Incidentally, by the use of the continuous image thus estimated for each 
picture element, the final dither image is obtained by making that 
continuous image binary by the use of the dither matrix having an 
appropriate threshold level. 
In this embodiment, a plurality of scanning apertures including estimated 
image regions are prepared in advance, and such one of the scanning 
apertures apart from the edge that the estimated picture element is as 
near as possible the center of the dither image is selected. 
The selecting order of the scanning apertures is determined such that the 
scanning apertures in positions gradually apart from the center of the 
picture element of the dither image are sequentially selected. One example 
of the apertures is described in the following: 
D23.fwdarw.D32.fwdarw.D22.fwdarw.D33.fwdarw.D12.fwdarw.D43.fwdarw.D31.fwdar 
w.D24 
.fwdarw.D34.fwdarw.D21.fwdarw.D42.fwdarw.D13.fwdarw.D41.fwdarw.D14.fwdarw. 
D44.fwdarw.D11. 
These selections are conducted for each of the estimated picture elements. 
One example of the aperture selections will be described with reference to 
FIGS. 27 and so on. First of all, the picture element level of the dither 
image on coordinates (1, 1) will be estimated. 
Since the picture element (1, 1) is present in the scanning aperture D11 
only, this aperture D11 automatically becomes the aperture to be selected 
so that the numbers of the white picture elements in this aperture are 
counted. The number of the white picture elements in this case is 7, which 
value becomes the estimated continuous level (as shown in FIG. 15(A)). 
In the case of the picture element (1, 2), the apertures D11 and D12 are 
used. Since, in this case, the estimated picture element in the aperture 
D12 is nearer the center, the estimation is executed from the aperture 
D12, and the relationship between the dither image and the aperture D12 is 
shown in FIG. 28(A). 
As a result, the number of the white picture elements in the scanning 
aperture in this case is 7, which value is first estimated (at I and II of 
FIG. 29(A)) as the level of the estimated continuous image, and the matrix 
compensated with this estimated continuous image value is compared (at III 
of the same Figure) for each picture element with the dither matrix. As a 
result, the estimated dither image is obtained, as shown at IV of the same 
Figure. 
This estimated dither image and the original dither image have their 
patterns compared. In the case of pattern incoincidence, the number of the 
in coincident picture elements is counted. The counted number is 4 in 
FIGS. 29(A) and 29(B). 
A Similar comparison is executed for the scanning aperture D11. This 
comparing step is shown in FIG. 29(B). As is apparent from this Figure, 
the patterns are not coincident. The number of the in coincident picture 
elements is 4. 
Thus, the patterns of the original dither image and the estimated dither 
image are not coincident in either case of the apertures D11 or D12. 
In this case, the image having a smaller number of incoincident picture 
elements is preceded. lf the numbers of the incoincident picture elements 
are equal, the scanning aperture having the estimated picture elements 
nearer the center of the dither image is selected. 
In the case of FIGS. 28(A) and 28(B), therefore, the scanning aperture D12 
is selected, and the estimated continuous image at this time has a level 
7. 
Subsequently, the level of the continuous image at the picture element (1, 
3) is estimated with reference to FIGS. 30(A) to 30(D), as follows. In 
this case, as shown in FIGS. 30(A) to 30(0), the four apertures D11 to D14 
are selected, and what is selected first of all is the aperture located 
nearest the center. 
In the aperture D12, as shown in FIG. 30(A), the estimated continuous image 
has a level 4, and the pattern of the estimated continuous image resulting 
from the comparison with the dither matrix is as shown at IV of FIG. 30(A) 
so that it does not coincide with the pattern of the original dither 
image. The number of the incoincident picture elements at this time is 4. 
Similar comparisons and estimations are sequentially executed for each 
scanning aperture, and the levels of the estimated continuous images and 
the patterns of the estimated dither images are shown in FIGS. 30(B) to 
30(D). The pattern comparisons and the counts of the incoincident picture 
elements executed are also shown. 
Here, the numbers of the in coincident picture elements of the scanning 
apertures D12 to D14 are 4, but the estimated continuous image level at 
this time is 7. Therefore, the selected aperture of the picture element 
(1, 3) is D12, and the estimated continuous image level selected is 7. 
Thus, the aperture selections and the estimations of the continuous image 
levels are executed for the individual picture elements. One example of 
the estimated continuous image levels thus determined is shown in FIG. 
15(A). Moreover, what aperture is selected for each picture element is 
shown in FIG. 15(B). 
Incidentally, what scanning aperture is selected for each continuous image 
estimation will be described by taking up the first row as an example. 
That is to say, the apertures D11, D12, D12 and D12 are selected for (1, 
1), (1, 2), (1, 3) and (1, 4) of the continuous estimation image. 
Thus, the estimated continuous image shown in FIG. 15(A) is estimated from 
the continuous image by sequentially selecting for each picture element 
that one of the scanning apertures failing to overlap the edge, which has 
its estimated picture element as near the center as possible. The 
continuous image does not have its level deviated seriously from that of 
the original continuous image. 
As a result, the estimated continuous image excessively resembles the 
original continuous image shown in FIG. 1(A). 
As has been described hereinbefore, according to the embodiment of the 
present invention, in the dither image formed with the dither matrix, the 
continuous image is estimated such that the scanning aperture including 
the estimated image does not overlap the edge of the image where the 
density changes drastically. The edge of the image can be restored 
excellently to a continuous image. 
As a result, according to the present invention, it is possible to conduct 
an image treatment matching the human visual characteristics. 
Since, moreover, a continuous image near the original continuous image can 
be obtained relatively simply, a variety of image treatments such as the 
gradation conversions, or the size enlargements or reductions can be 
advantageously conducted by making use of such continuous image.