Image communication method and apparatus with selection of binarization method for transmission

According to this invention, when n-value image data is transmitted, data associated with its compression method is transmitted to a reception-side apparatus, so that the reception-side apparatus can perform proper image processing. More specifically, there is disclosed an image transmission method having the following advantages. That is, when a reception-side apparatus can select one of a plurality of image processing methods, it selects a processing method matching with an n-value compression method, and properly reproduces an m-value image. Even when the reception-side apparatus does not have an image processing method matching the n-value compression method of a transmission-side apparatus, that fact can be communicated to the transmission-side apparatus or to an operator of the reception-side apparatus, so that operators of the transmission- and reception-side apparatuses can recognize that a color difference will occur between the transmission- and reception-side apparatuses, and an effective countermeasure can be taken.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an image communication method and 
apparatus for transmitting image information, and the like. 
2. Related Background Art 
Conventionally, various color facsimile apparatuses for communicating color 
images have been proposed. In a color image, since color data of each of 
the color components, red (R), green (G), and blue (B), has 256 gradation 
levels between 0 to 255, the data volume is very large, and the 
communication time is prolonged, as compared to those of a black-and-white 
image. For this reason, it is very difficult to put such an apparatus for 
directly transmitting multi-value data into practical application. 
As a method of compressing the data volume of a color image, each of R, G, 
and B data is binarized from 256 gradation levels between 0 to 255 to 2 
gradation levels of 0 and 1, and binary data is coded by a conventional 
coding method in a facsimile apparatus such as MMR, MR, or the like. 
However, when a received color binary image is color-processed, and is 
printed out, colors vary depending on the type used in binarizing method 
of binarizing the original multi-value image, and an image in colors 
different from those of the color image which was to be transmitted is 
undesirably printed out the receiver side. 
Colors of an image to be transmitted are different from those of an image 
printed out by a receiver like in a case wherein image data which is 
binarized by a Fatning type dithering method is transmitted to a receiver 
which is adjusted to reproduce appropriate colors of an image which is 
binarized by a Bayer type dithering method. 
There is also proposed a method of presuming multi-value data from a binary 
pattern of a rectangular region in a binary image by utilizing a neural 
network. 
The method utilizing a neural network can realize good multi-value 
restoration by learning. 
However, multi-value restoration by a neural network depends on the 
binarizing method of the binary data used in learning. Therefore, since 
various binarizing methods exist, even when a neural network which learns 
an image binarized by an error diffusion method is used in restoration of 
an image binarized by a dithering method, good multi-value data cannot 
always be obtained. 
SUMMARY OF THE INVENTION 
It is, therefore, an object of the present invention to provide an image 
communication method or apparatus capable of solving the above-mentioned 
problems individually or entirely. 
It is another object of the present invention to provide an image reception 
method or apparatus capable of dealing with various compression methods. 
It is still another object of the present invention to provide an image 
transmission method or apparatus which allows a reception side to 
appropriately deal with transmission data. 
According to a preferred embodiment of the present invention, when n-value 
image data is transmitted, data associated with its compression method is 
transmitted to a reception-side apparatus, so that the reception-side 
apparatus can perform proper image processing. More specifically, there is 
disclosed an image transmission method having the following advantages. 
That is, when a reception-side apparatus can select one of a plurality of 
image processing methods, it selects a processing method matching with an 
n-value compression method, and properly reproduces an m-value image. Even 
when the reception-side apparatus does not have an image processing method 
matching with the n-value compression method of a transmission-side 
apparatus, that fact can be communicated to the transmission-side 
apparatus or to an operator of the reception side apparatus, so that 
operators of the transmission- and reception-side apparatuses can 
recognize that a color difference will occur between the transmission- and 
reception-side apparatuses, and an effective countermeasure can be taken. 
It is still another object of the present invention to provide an image 
communication method which can satisfactorily perform a printing operation 
even when a color image which is compressed to n-value data, is 
transmitted and is printed out. 
It is still another object of the present invention to provide an image 
communication method which allows a reception side to satisfactorily 
perform image processing without sending data associated with an n-value 
method from a transmission side. 
It is still another object of the present invention to provide an image 
communication method and apparatus which can satisfactorily transmit a 
color image signal using an ISDN. 
It is still another object of the present invention to provide an image 
communication method which can process image data which is compressed to 
n-value data using a neural network. 
The above and other objects and features of the present invention will be 
apparent from the following embodiments, and the accompanying drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 is a block diagram showing an arrangement according to an embodiment 
of the present invention. 
An image communication apparatus of this embodiment comprises a scanner 
unit 1 for reading a color image on an original, a binarizing unit 2 for 
binarizing color image data input from the scanner unit 1, a coding unit 3 
for coding the binary data by MMR, MR, or the like to compress the data 
volume, a transmission control unit 4 for performing a communication with 
another image communication apparatus through a telephone line or an ISDN 
network to exchange coded data, a decoding unit 5 for decoding received 
coded data, an image processing unit 6 for processing image data in 
correspondence with characteristics of a printer unit 7, and the printer 
unit 7 for printing out image data. Note that the binarizing unit 2 
outputs input multi-value image data as multi-value image data without 
binarizing it. 
FIG. 2 is a block diagram showing an arrangement of the binarizing unit 2. 
The binarizing unit 2 of this embodiment comprises four binarizing means 21 
to 24 for respectively binarizing data by a Bayer type dithering method, a 
Fatning type dithering method, an error diffusion method, and a simple 
binarizing method. The unit 2 selects one of these four binarizing units 
21 to 24 to binarize image data, and can also supply image data to the 
coding unit 3 without binarizing it. 
FIG. 3 is a block diagram showing an arrangement of the image processing 
unit 6. 
The image processing unit 6 of this embodiment comprises four image 
processing means 61 to 64 corresponding to the four binarizing methods, 
i.e., the Bayer type dithering method, the Fatning type dithering method, 
the error diffusion method, and the simple binarizing method, and also 
comprises an image processing means 65 for a non-binarized 256-gradation 
image. 
The image processing unit 6 selects one of these image processing means 61 
to 64 to perform image processing of coded image data, and supplies the 
processed data to the printer unit 7. 
FIG. 4 is a schematic flow chart showing a transmission operation, and FIG. 
5 is a schematic flow chart showing a reception operation. 
In a transmission mode, the scanner unit 1 reads a color image, and 
supplies R, G, and B 256-gradation data (0 to 255) corresponding to dots 
at, e.g., 400 dpi to the binarizing unit 2 (S1). The binarizing unit 2 
binarizes the R, G, and B 256-gradation data of the color image data, and 
sends them to the coding unit 3 (S2). In this manner, the scanner unit 1 
requires 8 bits for each of R, G, and B data in units of dots, i.e., a 
total of 24 bits. However, when these data are binarized, each of R, G, 
and B data requires one bit, i.e., these data require a total of only 3 
bits. Thus, these data are compressed to 1/8. 
The coding unit 3 encodes input data by a coding method such as MMR, MR, or 
the like, and sends the coded image data to the transmission control unit 
4 (S3). The transmission control unit 4 exchanges procedure signals with a 
receiver, and then transmits data associated with a binarizing method and 
image data to the receiver (S4). 
In FIG. 5, when the transmission control unit 4 receives the data 
associated with the binarizing method and the image data (S11), the 
received image data is sent to and decoded by the decoding unit 5, and the 
decoded data is supplied to the image processing unit 6 (S12). The image 
processing unit 6 performs image processing in accordance with the data 
associated with the binarizing method received from the transmission 
control unit 4 (S13), and supplies the processed data to the printer unit 
7 to print it out (S14). 
Conventionally, many methods have been proposed as multi-value image 
binarizing methods. However, these methods have both merits and demerits, 
and no optimal binarizing method in all cases and in all respects is 
proposed. 
As typical binarizing methods, (1) the Bayer type dithering method, (2) the 
Fatning type dithering method, (3) the error diffusion method, and (4) the 
simple binarizing method are available. In the Bayer and Fatning type 
dithering methods, an image and a threshold value matrix are compared with 
each other, and if image data is larger than a corresponding threshold 
value, "1" is set; otherwise, "0" is set. 
FIG. 6 shows a threshold value matrix of the Bayer type dithering method, 
and FIG. 7 shows a threshold value matrix of the Fatning type dithering 
method. 
One feature of the Bayer type dithering method is that dots tend to be 
scattered upon binarizing of this method. Contrary to this, it is a 
feature of the Fatning type dithering method is that dots tend to be 
concentrated. 
FIGS. 8 and 9 show image data obtained by binarizing a flat image having a 
luminance of 160 by the above-mentioned methods. Portions having "0" data, 
i.e., dark portions are scattered when an image is binarized by the Bayer 
type dithering method, while they are concentrated by the Fatning type 
dithering method. 
When these two binarized images are printed by, e.g., an ink-jet printer, 
considerably different images are obtained due to the influence of a 
blurred ink. More specifically, in an image binarized by the Bayer type 
dithering method, since dark portions, i.e., dots formed by an ink are 
scattered, an ink is considerably blurred. Contrary to this, in an image 
binarized by the Fatning dithering method, since dots are concentrated, an 
ink is not so blurred. As a result, the image binarized by the Bayer type 
dithering method becomes a darker image than that by the Fatning type 
dithering method. 
In this manner, if images binarized by the different binarizing methods are 
subjected to the same image processing, different colors are undesirably 
obtained. In order to obtain an optimal color image, image processing 
matching with a binarizing method used must be performed. 
In this embodiment, as the binarizing methods, the Bayer type dithering 
method, the Fatning type dithering method, the error diffusion method, and 
the simple binarizing method are available. In general, when a resolution 
is low, the Bayer type dithering method can provide a good image; 
otherwise, the Fatning type dithering method can provide a good image. The 
dithering methods are suitable for halftone images such as photographs, 
but are not suitable for images having clear contrast such as character 
images. Furthermore, the error diffusion method suffers from a large data 
volume after coding although a good image can be obtained. The simple 
binarizing method is not suitable for halftone images. 
Therefore, in this embodiment, a binarizing method is selected by an 
operator, or by automatic discrimination based on a resolution or a text 
or photograph mode, or by communicating with a receiver in step S2 in FIG. 
4. More specifically, in this embodiment, the binarizing method can be 
selected manually or automatically in step S2. 
In this embodiment, binarizing methods of transmission data in a 
transmitter, and binarizing methods which are available upon image 
processing of received data in a receiver are expressed by predetermined 
codes, and these codes are exchanged between the two apparatuses as the 
above-mentioned data associated with the binarizing method. Thus, the 
binarizing means 21 to 24 and the image processing means 61 to 65 are 
selected with reference to the code data. 
FIG. 10 shows code data corresponding to the four binarizing methods 
described above. 
In this embodiment, a four-bit code corresponds to each binarizing method. 
As described above, a code is also assigned to a case wherein data is not 
binarized. When the code data is sent to a receiver upon transmission of 
image data, the binarizing method of the image data can be identified. 
FIG. 11 shows code data for informing the binarizing methods of an image 
communication apparatus to a destination apparatus. 
The code data is obtained by logically ORing the codes shown in FIG. 10. 
When this code data is sent to a destination apparatus, the binarizing 
methods of this image communication apparatus can be informed to the 
destination apparatus. 
In this embodiment, code data representing binarizing methods of the image 
processing unit 6 when the image data is received is common to the code 
data shown in FIG. 11. 
Note that the code data shown in FIG. 11 is registered in advance in a 
predetermined memory area of the transmission control unit 4. 
FIGS. 12 and 13 are flow charts showing operations for discriminating, 
using the code representing the binarizing methods, whether or not a 
receiver can deal with a binarizing method of a transmitter. FIG. 12 shows 
an operation of the transmitter, and FIG. 13 shows an operation of the 
receiver. 
The transmission control unit 4 informs the code representing the 
binarizing methods to the receiver by means of a predetermined procedure 
signal (S21). 
More specifically, when the receiver is an image communication apparatus 
complying with the G3 facsimile standards, the code representing the 
binarizing method can be transmitted to the receiver using an initial 
identification signal of a non-standard function, e.g., four specific bits 
of an NSF signal. 
When the receiver is an image communication apparatus complying with the G4 
facsimile standards, the code representing the binarizing method can be 
transmitted to the receiver using, e.g., specific four bits of a 
user-to-user signal based on the TTC recommendation, ISDN network 
interface part 3, layer 3 specification 4.5.24. 
On the other hand, the receiver receives the four specific bits of the 
above-mentioned NSF signal or the user-to-user signal (S31), and decodes 
it to identify the binarizing method (S32). 
When the receiver can deal with the binarizing method (S33), it transmits 
the binary code using the NSF signal or the user-to-user signal (S34); 
otherwise, it transmits a binary code other than the received binary code 
using the NSF signal or the user-to-user signal (S35), thereby informing 
the transmitter whether or not the receiver can deal with the identified 
method. 
The transmitter receives the NSF signal or the user-to-user signal from the 
receiver (S22), and discriminates its specific four bits (S23), thereby 
discriminating whether or not the receiver can deal with the binarizing 
method represented by the transmitted binary code (S24, S25). 
Thereafter, if the transmitter discriminates that the receiver can deal 
with the identified method, it transmits image data binarized by the 
binarizing means corresponding to the identified binarizing method (S26). 
When the receiver cannot deal with the informed method, in step S35, it can 
transmit the code (in this embodiment, 1111 shown in FIG. 11) which is 
registered in the transmission control unit 4 and represents binarizing 
methods which are available in the receiver using the NSF signal or the 
user-to-user signal. 
In this case, the transmitter discriminates the specific 4 bits of the NSF 
signal or the user-to-user signal, thereby discriminating binarizing 
methods available in the receiver. Therefore, the transmitter compares the 
binarizing methods available in the receiver, and those available in the 
transmitter, and selects an optimal one. Thus, the transmitter can 
binarize data by a binarizing method available in the receiver, and can 
transmit the binarizing method and image data to the receiver by the 
above-mentioned transmission operation. 
When the transmission control unit 4 of the receiver discriminates the 
binarizing method informed from the transmitter, it supplies the 
discriminated binarizing method to the decoding unit 5 and the image 
processing unit 6. The image processing unit 6 selects the corresponding 
image processing means on the basis of the input binarizing method to 
perform image processing of the received image data, and supplies the 
processed data to the printer unit 7 to print it out. 
Note that the above-mentioned code data may be exchanged in advance with a 
specific image communication apparatus, and binarizing methods of the 
specific image communication apparatus, and corresponding binarizing 
methods may be registered in, e.g., a memory area of the transmission 
control unit 4. Thus, the binarizing means 21 to 24 and the image 
processing means 61 to 65 may be selected based on the registered code 
data. Code data of an image communication apparatus, which data cannot be 
registered in advance, can be exchanged in a communication protocol when 
image data is transmitted/received, as described above. 
FIG. 14 is a block diagram showing another arrangement of the image 
processing unit. 
More specifically, the image processing unit comprises a multi-value 
converting unit 71, a density conversion unit 72, a color masking unit 73, 
a .gamma. correction unit 74, and a binarizing unit 75. 
The multi-value converting unit 71 performs multi-value conversion by 
smoothing processing. Another arrangement of the multi-value converting 
unit 71 will be described later. FIGS. 15 and 16 show arrangements of 
smoothing filters for image data which are binarized by the Bayer type 
dithering method and the Fatning type dithering method, respectively. 
In this manner, when a multi-value conversion method is switched in 
accordance with the type of transmitted binary signal, a high-quality 
image signal can be obtained. For data binarized by the error diffusion 
method, a window for filtering binary data may be continuously moved, 
while for data binarized by a dithering method, the window may be 
intermittently moved without being moved continuously. 
The density conversion unit 72 searches a look-up table to convert image 
data from luminance (RGB) data to density (cmy) data. Different look-up 
tables may be prepared in accordance with binarizing methods, or the same 
table may be used for the different methods. 
The color masking unit 73 performs masking processing for correcting 
muddiness of inks in the printer unit 7. 
The .gamma. correction unit 74 performs .gamma. correction in 
correspondence with characteristics of the printer unit 7, and the 
binarizing unit 75 performs binarization for a printer output. 
Different sets of the masking unit 73, the .gamma. correction unit 74, and 
the binarizing unit 75 may be prepared in accordance with binarizing 
methods, or they may be common to different binarizing methods. 
Alternatively, a common circuit may be employed, and only parameters may 
be changed in such a manner that a color masking parameter varies 
depending on binarizing methods. 
The image processing unit discriminates the binarizing method of a received 
image, and selects the image processing means 61 to 65 or the multi-value 
converting unit 71, the density conversion unit 72, the color masking unit 
73, the .gamma. correction unit 74, and the binarizing unit 75, thus 
performing optimal image processing. 
FIGS. 17 and 18 are flow charts showing other transmission/reception 
operations. FIG. 17 shows an operation of a transmitter, and FIG. 18 shows 
an operation of a receiver. 
In this embodiment, when the transmitter transmits a binary code (S41), and 
the receiver receives the binary code (S51), if the receiver can deal with 
the binarizing method represented by the code (S52), it sends back the 
received binary code (S53); otherwise, it sends back a logical sum code 
(FIG. 11) representing all the binarizing methods which the receiver can 
use (S54). When the transmitter receives the code sent back from the 
receiver (S42), it compares the transmitted binary code and the received 
binary code (S43). If a coincidence is found between the two codes, the 
transmitter binarizes image data by one of the binarizing methods which 
can be dealt with in the receiver (S46); otherwise, the transmitter checks 
if the received binary code includes a usable binarizing method (S44). If 
the binary code includes a usable binarizing method, the transmitter 
selects that binarizing method (S45) to binarize image data, and then 
transmits the binary image data (S46); otherwise, it transmits image data 
without binarizing it. 
As still another embodiment, the image processing unit may comprise a 
correction unit for performing correction in correspondence with 
binarizing methods, and an image processing means common to the binarizing 
methods. For example, correction corresponding to the binarizing methods 
may be performed as follows. That is, a look-up table according to a 
3.times.3 dot pattern having a pixel of interest as the central pixel is 
prepared, and a value is assigned to the pixel of interest. 
Furthermore, the Bayer type dithering method may be further classified into 
various compression methods, such as a 4.times.4 Bayer type dithering 
method, an 8.times.8 Bayer type dithering method, and the like. 
In the above embodiment, a code representing a binarizing method is 
transmitted to a receiver by means of a predetermined procedure signal. 
However, a binary code may be transmitted as the four initial bits of 
image data. 
In the above embodiment, when data associated with an n-value compression 
method is transmitted, it may be transmitted in advance or after image 
data is transmitted. Alternatively, the data may be transmitted during 
transmission of image data. 
In the above embodiment, in order to discriminate whether or not a receiver 
can deal with an n-value compression method of image data upon 
transmission of n-value data, a method based on the G3 or G4 
recommendation may be employed. Alternatively, a code in the 
above-mentioned layer of the ISDN may be used. Such a protocol may be 
variously changed. 
In the above embodiment, a receiver communicates a usable n-value 
compression method to a transmitter, upon communication with the 
transmitter. In this information, for example, a user-to-user signal of 
the layer 3 specification in the TTC recommendation as described above, or 
other signals may be used. 
As the image processing means of the above embodiment, all or some of a 
2.fwdarw.multi-value converting method, .gamma. correction, masking, and 
the like may be used. 
The above-mentioned embodiment has the following effects. Since data 
associated with an n-value compression method is transmitted together with 
n-value image data, a receiver can perform proper image processing. More 
specifically, the receiver can select an image processing means matching 
with the n-value compression method of received image data. Since image 
data is transmitted when a receiver can deal with n-value image data to be 
transmitted, transmission of n-value image data which cannot be dealt with 
by the receiver can be prevented. 
Image data can be transmitted by selecting a usable n-value compression 
method, and proper reproduction of an m-value image at a receiver can be 
guaranteed. 
In this embodiment, since a receiver informs a usable n-value compression 
method to a transmitter, the transmitter can perform proper n-value 
compression. 
In the above embodiment, data associated with a compression method executed 
by a transmitter is transmitted to a receiver. A method which does not 
perform such transmission will be described below. 
FIG. 19 is a block diagram showing another embodiment of the present 
invention, and corresponds to an arrangement to be replaced with the image 
processing unit 6 shown in FIG. 1. FIG. 20 is a flow chart showing a 
processing sequence of an image processing apparatus of this embodiment. 
In FIG. 20, steps 201 to 207 illustrated on the left side correspond to a 
sequence of processing for presuming a binarizing method of an input 
binary image, and steps 208 to 212 on the right side correspond to a 
multi-value conversion processing sequence. In this embodiment, a 
compression method executed by a transmitter, e.g., a binarizing method is 
presumed from received data, and then, multi-value conversion processing 
is executed. 
The functions of the respective units shown in FIG. 19 will be described 
below while explaining the processing sequence shown in FIG. 20. In FIG. 
19, a line buffer 101 comprises a FIFO, and stores data for four raster 
lines upon reception of input binary data. The buffer 101 is connected to 
a data latch 102 for latching data for four lines from the line buffer 
101, i.e., data for four pixels in units of lines. Therefore, binary image 
data of a 4.times.4 window can be obtained from the data latch 102 (step 
202). 
4.times.4 pixel (16-bit) data is supplied to a ROM type conversion table 
103 as an address. The conversion table 103 is determined by a neural 
network, as will be described later, and outputs data corresponding to one 
of predetermined binarizing methods on the basis of input data as a 
presumed binarizing method (step 203). In this embodiment, the 
predetermined binarizing methods correspond to an error diffusion method, 
a Bayer type dithering method, a Fatning type dithering method, and a 
simple threshold value method, as shown in FIG. 21. A counter 109 
individually counts four types of data corresponding to these four 
binarizing methods. For example, if the table 103 determines that the 
input image is binarized by the error diffusion method, a counter 
corresponding to a portion of "1" is incremented (step 204). In step 205, 
it is checked if steps 202 to 204 described above are ended for the entire 
image. If NO in step 205, the above-mentioned steps are repeated. 
When the above-mentioned processing is ended for the entire image, a select 
unit 110 presumes a binarizing method having a maximum count value in the 
counter 109 as that for the input image, and selects it. The select unit 
110 then sets the selected method in a latch 111. The set data is used as 
a select signal for a selector 108 (to be described later) (step 206). The 
processing for presuming the binarizing method has been described. 
Then, multi-value conversion processing as an object is executed. 
In step 209, 4.times.4 image data is read out again from an image memory 
100. This is the same processing as step 202 described above. 
The read-out image data is input to multi-value conversion tables 104 to 
107 each comprising a ROM. The tables 104 to 107 respectively correspond 
to the above-mentioned four binarizing methods, and are prepared based on 
multi-value processing by a neural network, as will be described later. 
Outputs from the tables 104 to 107 are input to the selector 108. The 
selector 108 selects one of the outputs from the tables 104 to 107 in 
accordance with a select signal from the latch 111, and outputs the 
selected data as final multi-value data (step 210). The selected output is 
an output from the table corresponding to the presumed binarizing method 
selected by the select unit 110. 
Steps 209 to 210 described above are repeated until it is determined in 
step 211 that the processing is ended for the entire image. 
The above-mentioned units are controlled by a CPU (not shown). 
Presumption of a binarizing method using a neural network, and multi-value 
processing using a neural network will be described below. 
A general learning sequence in a back propagation type neural network will 
be described below with reference to FIG. 22A. 
In the neural network shown in FIG. 22A, outputs (i-out) 404 from an input 
layer 401 (the number of neurons ii) are input to a middle layer 402 (the 
number of neurons jj) comprising one layer, outputs (j-out) from the 
middle layer 402 are input to an output layer 403 (the number of neurons 
kk), and outputs (k-out) 406 are output from the output layer 403. Note 
that 407 designates ideal outputs (ideal-out). 
In the neural network, input data, and a corresponding ideal output 
(ideal-out) are prepared, and are compared with an output (k-out) 406 to 
determine a coupling intensity W.sub.ji [jj,ii] in the middle layer (408 
in FIG. 22A), and a coupling intensity W.sub.kj [kk,jj] in the output 
layer (409 in FIG. 22A). 
The learning sequence using the above-mentioned neural network will be 
described in detail below with reference to the flow chart shown in FIG. 
22B. 
In step S401, initial values of weightinig factors (coupling intensities) 
W.sub.kj [jj,ii] and W.sub.kj [kk,jj] are provided. In this case, values 
within a range of -0.5 to +0.5 are selected in consideration of 
convergence in a learning process. 
In step S402, learning input data i-out(i) is selected, and in step S403, 
this data i-out(i) is set in the input layer. In step S404, an ideal 
output (ideal-out) corresponding to the input data i-out(i) is prepared. 
In step S405, outputs j-out(j) of the middle layer are calculated. 
The weightinig factor W.sub.kj of the middle layer is multiplied with the 
data i-out(i) from the input layer, and a total sum Sum.sub.Fj of the 
products is calculated as follows: 
##EQU1## 
A sigmoid function is used to calculate an output j-out(j) of a j-th 
middle layer from Sum.sub.Fj as follows: 
##EQU2## 
In step S406, outputs k-out(k) of the output layer are calculated. This 
procedure is the same as that in step S406. 
More specifically, the weightinig factor W.sub.kj of the output layer is 
multiplied with the outputs j-out(j) from the middle layer, and a total 
sum Sum.sub.Fk of the products is calculated as follows: 
##EQU3## 
The sigmoid function is used to calculate an output k-out(k) of a k-th 
output layer from Sum.sub.Fk as follows: 
##EQU4## 
Note that this output value is normalized. 
In step S407, the output k-out(k) obtained in this manner is compared with 
the ideal output ideal-out(k) prepared in step S404, and a teaching signal 
teach-k(k) of the output layer is calculated as follows: 
EQU teach-k(k)={ideal-out(k)-k-out(k)}*k-out(k)*{1-k-out(k)} 
where k-out(k)*{1-k-out(k)} has a significance of differentiation of the 
sigmoid function k-out(k). 
In step S408, a changing width .DELTA.W.sub.kj [kk,jj] of the weightinig 
factor of the output layer is calculated as follows: 
EQU .DELTA.W.sub.kj [kk,jj]=.beta.*j-out(j)*teach-k(k)+.alpha.*.DELTA.W.sub.kj 
[kk,jj] 
where .alpha. is the stabilization constant, and .beta. is a constant 
called a learning constant, which serves to suppress any abrupt change. 
In step S409, the weightinig factor W.sub.kj [kk,jj] is renewed based on 
the changing width as follows: 
EQU W.sub.kj [kk,jj=W.sub.kj [kk,jj]+.DELTA.W.sub.kj [kk,jj] 
That is, learning is performed. 
In step S410, a teaching signal teach-j(j) of the middle layer is 
calculated. For this purpose, contribution from the output layer to the 
respective elements of the middle layer in the reverse direction is 
calculated based on the following equation: 
##EQU5## 
The teaching signal teach-j(j) of the middle layer is calculated based on 
Sum.sub.Bj as follows: 
EQU teach-j(j)=j-out(j)*{1-j-out(j)}*Sum.sub.Bj 
In step S411, a changing width .DELTA.W.sub.ji [jj,ii] of the weightinig 
factor of the middle layer is calculated as follows: 
EQU .DELTA.W.sub.ji [jj,ii]=.beta.*i-out()*teach-j(j)+.alpha.*.DELTA.W.sub.ji 
[jj,ii] 
In step S412, the weightinig factor W.sub.ji [jj,ii] is renewed based on 
the changing width as follows: 
EQU W.sub.ji [jj,ii]=W.sub.ji [jj,ii]+.DELTA.W.sub.ji [jj,ii] 
That is, learning is performed. 
In this manner, in steps S401 to S412, the weightinig factors W.sub.ji and 
W.sub.kj are learned once on the basis of a set of input data and a 
corresponding ideal output. 
It is checked in step S413 if the weightinig coefficients are sufficiently 
converged by the above-mentioned learning. If NO in step S413, steps S401 
to S412 are repeated. 
The learning procedure of the neural network based on the back propagation 
method has been described. 
The above-mentioned learning is a preparation stage for processing, and in 
actual processing, only the obtained weighting coefficients, that is, only 
a table of processing results for all the possible inputs using these 
weighting coefficients is used. 
A case will be exemplified below wherein the above-mentioned "learning" is 
performed for a neural network for presuming a multi-value image from a 
binary image. 
Input data are values (0 or 1) of pixels in a 4.times.4 window of image 
data binarized by a binarizing method as an object to be learned. 
Therefore, the number of neurons of the input layer is 16, the number of 
neurons of the output layer is one since a multi-value output is for one 
pixel, and the number of neurons of the middle layer is arbitrary but is 
12 in this embodiment. 
On the other hand, an ideal output is assumed to be multi-value image data 
as an original image of input binary data. 
As a method of selecting input data, a learning pixel is randomly selected, 
and a 4.times.4 window including the selected pixel is arranged. 
The weightinig factors are determined by the above-mentioned learning 
sequence using the above-mentioned parameters (therefore, coupling of the 
neural network is determined). 
In this embodiment, the processing of the neural network is prepared as a 
table. For this purpose, outputs corresponding to all the 4.times.4 input 
patterns (2.sup.16 patterns) based on the determined neural network are 
obtained, and are stored in a ROM. 
In this embodiment, the above-mentioned processing operations (learning and 
preparation of ROMs) are independently performed for the respective 
methods in correspondence with the four binarizing methods, thereby 
preparing for the four conversion tables 104 to 107. 
On the other hand, learning for presuming a binarizing method is almost 
similarly performed. 
First, input data are values (0 or 1) of pixels in a 4.times.4 window of 
image data binarized by four binarizing methods as objects to be learned. 
Therefore, the number of neurons of the input layer is 16, the number of 
neurons of the output layer is four since one of the four binarizing 
methods is to be presumed, and the number of neurons of the middle layer 
is arbitrary but is 12 in this embodiment as in the above case. 
On the other hand, an ideal output is assumed to be a logical value 
representing one of the four binarizing methods as that for input data. 
As a method of selecting input data, a learning pixel is randomly selected, 
and a 4.times.4 window including the selected pixel is arranged in the 
same manner as in the above-mentioned case. Furthermore, data binarized by 
one of the four binarizing methods is randomly selected to cause one 
neural network to learn. 
In the above embodiment, the processing of the neural network is performed 
using the conversion tables. Alternatively, a neuro chip having the 
obtained weighting factors may be used. 
The window size is not limited to 4.times.4 but may be 5.times.5, 
3.times.4, and the like. 
Different window sizes may be adopted in presumption of a binarizing 
method, and in presumption of a multi-value image, and may be adopted 
depending on binarizing methods in presumption of a multi-value image. 
As described above, according to this embodiment, a binarizing method of an 
input binary image is presumed, and multi-value conversion is performed in 
accordance with the presumed binarizing method. Therefore, a high-quality 
multi-value image can be obtained. 
In the above embodiment, binarization is performed as n-value compression. 
However, the present invention is not limited to binarization, but may be 
three-value conversion, four-value conversion, and the like. 
In the above embodiment, image data is input from the scanner unit 1. 
However, the present invention is not limited to the scanner. For example, 
image data may be input from a video camera, a still video camera, or an 
image database. 
In the above embodiment, an image is output to the printer unit 7, but may 
be output to a CRT, an image database, or the like. 
In the above embodiment, R, G, and B data are processed as image data. 
Similarly, X, Y, and Z data or L*, a*, b* data representing color data, or 
Y, I, Q data used in a television signal may be used.