Patent Publication Number: US-6985634-B2

Title: Image processing system for compressing image data including binary image data and continuous tone image data by a sub-band transform method with a high-compression rate

Description:
This application is a divisional of U.S. Ser. No. 10/423,911, filed on Apr. 28, 2003 now U.S. Pat. No. 6,714,685, which is divisional of U.S. Ser. No. 10/175,838, filed on Jun. 21, 2002 now abandoned which is divisional of U.S. Ser. No. 09/630,600, filed on Aug. 1, 2000, now U.S. Pat. No. 6,577,812, which is divisional of U.S. Ser. No. 09/073,873, filed on May 7, 1998, now U.S. Pat No. 6,459,816 and under 35 USC §119 from Japanese Patent Application Nos. 9-118207, filed May 8, 1997, 9-156006, filed May 29, 1997 and 9-156007 filed May 29, 1997, the entire contents of which are incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention generally relates to an image data compressing technique and, more particularly, to an image processing system which compresses and expands image data by using a sub-band encoding method. 
   The image processing system related to the present invention may be used in a digital copy machine, a facsimile machine, a digital printer, a digital camera or a digital video camera, and also may be used in an image recording system such as a CD-ROM drive or a floppy disc drive. 
   2. Description of the Related Art 
   A sub-band encoding method such as the discrete cosine transform (DCT) or the Harr Wavelet transform is considered a method for effectively compressing a continuous tone image. Additionally, Japanese Laid-Open Patent Application No. 2-305272 discloses another method for encoding image data by separating an image area into a character area and a halftone area so as to encode these areas by an encoding method appropriate for each of the areas. 
   Such a method for compressing image data using the sub-band transform such as the DCT or the Harr Wavelet transform can effectively compress a continuous tone image. However, there is a problem in that a compression rate is low when a complete binary image is compressed. 
   Additionally, in a digital copy machine, even if an original image is a complete binary image, image data obtained by scanning such a complete binary image may become incomplete binary image data due to fluctuation in a scanning operation. Thus, there may be a problem in compressing such incomplete binary data by an entropy-encoding method due to fluctuation in a scanned image. 
   As a method for rotating or sorting images in a copy machine, a block truncation encoding (BTC) which is one of fixed length encoding methods is popular. However, there is a problem in that a compression rate for an entropy encoding is low as compared to that of a sub-band transform method, and a calculation is complex. 
   In an image forming apparatus such as a copy machine or a printer, image data obtained by a scanner is subjected to gamma correction or a filtering process so as to adjust image quality. The thus-processed image data is stored in a memory, and then the image data is sent to a printing unit. 
   Generally, such image data is subjected to a data compression in order to reduce a capacity of the memory that stores the processed image data. Generally, in a data compressing method, image data is transformed into frequency components by using an orthogonal transformation such as the discrete cosine transform (DCT), and the quantized image data is subjected to an entropy encoding. Dispersion of a high-frequency factor in the frequency transformation factors varies in response to a magnitude of change in intensity of the image. Thus, the image quality is improved when a quantizing method is changed in response to a type of an area to be processed. 
   Japanese Laid-Open Patent Application No. 7-74959 discloses a technique in which a quantization table is changed based on a transform factor obtained by an orthogonal transformation of an original image by each individual block so that the image quality matches the contents of the image data and a compression rate is improved. 
   When an image is printed by a copy machine, a character image and a line image can be well recognized by rendering the intensity slope of a contour of the characters or the lines to be steep. On the other hand, when an image having a gentle intensity slope such as a photograph is printed, a random change in the intensity having a small amplitude is sensed as a noise. Thus, it is preferred for such a photographic image to reduce the intensity slope of an output image. Particularly, in a mesh point photographic image, a better image quality can be obtained by reducing the intensity slope even for an area having a steep intensity slope. 
   Accordingly, an edge area corresponding to a character image or a line image is separated from a mesh point image and a gentle slope area of a photographic image so that the edge area is subjected to a differential filtering process whereas the photographic image is subjected to a smoothing filtering process. Additionally, when an image data compression is performed, another separation of image areas is performed in response to degrees of the intensity slope in edge areas. 
   As mentioned above, in the conventional technique, two separation processes are performed on the same image data and the filtering process is performed separately from the quantizing process. Thus, there is a problem in that a process time is increased and a hardware cost is increased. Additionally, there is a disadvantage in the technique disclosed in the above-mentioned patent document in that a compression rate is not minimized since a result of the area separation must be also stored as the compressed data. 
   An image data compression technique is generally used in the image data processing field so as to reduce a capacity of a memory for storing image data or reduce a time for transmitting image data. There are various image data compressing methods depending on the processing modes of image data. When image data is printed, a rotation of the image may be requested. In order to rotate the image at a high speed, a fixed length compression is used. 
   Additionally, when image data is exchanged between systems having different resolutions or gradation characteristics, a compressing method using a layered data structure is desired so as to select transmission data corresponding to an image quality of an image outputting system. Especially, when image data is transmitted to a display apparatus, a progressive transmission method is required. In the progressive transmission method, image data of an object such as an icon can be transmitted prior to sending the image data. Thus, data compression is performed in response to the level of layers. 
   Additionally, when a trial printing is performed for checking a layout while reducing toner consumption in an image printing apparatus, a data compressing method is required by which a feature of the image is maintained but image quality is not reduced. 
   Japanese Laid-Open Patent Application No. 1-135265 discloses a data compressing method in which an original image is divided into a plurality of blocks, and each block is divided into image data which is orthogonal-transformed and other data so that a representative image of the image file can be effectively regenerated. 
   Generally, an image comprises an image area and an edge area. In the image area, a gradation of the image gradually changes, such as in a photograph or a graphic image. In the edge area, a gradation sharply changes in an area of an edge of the image and an area adjacent to the edge, such as in a character image or a line image. When the visual sense of human beings is considered, gradation is important in the image area whereas resolution is important in the edge area. 
   In the conventional technique disclosed in the above-mentioned patent document, a sampling is performed on the original image, and the sampled image data is subjected to the discrete cosine transform (DCT). The same transform factor which is obtained from a quantization table is used for all areas. In such a case, a length of data is fixed since a single quantization table is used. However, there is a drawback in that the quantized image data does not accurately represent the feature of the image while a large amount of data is used since a single quantization is used. Additionally, there is a disadvantage in that only two levels of image data can be selected. 
   SUMMARY OF THE INVENTION 
   It is a general object of the present invention to provide an improved and useful image processing system in which the above-mentioned problems are eliminated. 
   A more specific object of the present invention is to provide an image processing system which compresses an image including both a binary image and a natural image by a sub-band transform method with a high compression rate. 
   Another object of the present invention is to provide an image processing system which facilitates processing and editing of image data by using a sub-band transform method or a fixed length encoding method at a low cost. 
   A further object of the present invention is to provide an image processing system which can represent a feature of an image while a reduced amount of data is used, and which can produce image data including a plurality of levels of image quality. 
   In order to achieve the above-mentioned objects, there is provided according to one aspect of the present invention an image processing system comprising: 
   a buffer unit extracting n×m pixel matrix block data from image data, where n and m are integers; 
   a sub-band transform unit transforming the n×m pixel matrix block data by a sub-band transform method so as to obtain a transform factor having a plurality of frequency components; and 
   a quantizing unit quantizing the transform factor by a fixed-length quantizing method by deleting a predetermined number of lower order bits of each of the frequency components. 
   According to the above-mentioned invention, since the high-frequency component of the sub-band transform factor is quantized by deleting the lower order bits in the fixed-length quantizing method, various subsequent processes such as editing of the image or a rotation of the image can be easily performed with a reduced amount of compressed data. 
   Additionally, there is provided according to another aspect of the present invention an image processing system comprising: 
   a buffer unit extracting n×m pixel matrix block data from image data, where n and m are integers; 
   a sub-band transform-unit transforming the n×m pixel matrix block data by a sub-band transform method so as to obtain a transform factor having a plurality of frequency components including a low-frequency component and a high-frequency component; 
   an area discriminating unit discriminating a type of an image area corresponding to the n×m pixel matrix block data being processed so that the image area is determined as one of an edge area and a non-edge area, a discrimination being made based on whether or not an absolute value of each of the components of the transform factor exceeds a threshold value; and 
   a quantizing unit quantizing the transform factor by a fixed-length quantizing method by deleting a predetermined number of lower order bits of each of the frequency components, the number of deleted lower order bits of each of the frequency components of the transform factor being changed in accordance with a type of image area being processed so that image data including the transform factor and flag information indicating a type of image area has a predetermined fixed length. 
   According to this invention, a number of the lower order bits of each of the frequency components of the transform factor is deleted in response to a type of the image, and the transform factor is quantized by a fixed-length quantizing method together with the flag information. Thus, the image data can be efficiently compressed with a high quality irrespective of whether the image data corresponds to an edge area or a non-edge area. Additionally, the original image data can be easily restored on a decoder side based on the flag information. 
   In the above-mentioned invention, the quantizing unit may delete lower order bits of each of the low-frequency component and the high-frequency component so that a number of deleted lower order bits for the edge area is greater than a number of deleted lower order bits for the non-edge area. Accordingly, data corresponding to both the edge area in which a gradation is important and the non edge area in which recognition of an edge is important can be efficiently compressed while a high image quality is maintained. Additionally, the original image data can be easily restored on a decoder side based on the flag information. 
   Additionally, the quantizing unit may quantize the high-frequency component by a vector quantizing method. Further, the quantizing unit may embed the flag information into the transform factor. 
   Additionally, the quantizing unit may change bit data representing the transform factor so that the flag information is represented by a part of the data bits representing the transform factor. The quantizing unit may change the transform factor so that correlation between the transform factors of different types is increased. The quantizing unit may change a bit arrangement of the transform factor so that correlation between the transform factor corresponding to the edge area and the transform factor corresponding to the non-edge area is increased. 
   Additionally, there is provided according to another aspect of the present invention an image processing system comprising: 
   a buffer unit extracting n×m pixel matrix block data from image data, where n and m are integers; 
   a binarizing unit transforming the n×m pixel matrix block data into binary data represented by a maximum value and a minimum value; 
   a differential data calculating unit calculating differential data which is a difference between a value of each pixel in the n×m pixel matrix block data and one of the maximum value and the minimum value of the binary data; 
   a sub-band transform unit transforming the differential data by a sub-band transform method so as to obtain a transform factor having a plurality of frequency components; and 
   an encoding unit encoding the binary data and the sub-band transform factor so as to obtain a code representing the image data. 
   According to the above-mentioned invention, a continuous tone image data can be efficiently compressed by a sub-band transform since the original image data is represented by using the binary data and the sub-band transform factor which are encoded by a sub-band transform. Accordingly, an image including a binary image and a continuous tone image can be processed by a single method irrespective of types of the image. 
   In the above-mentioned invention, the encoding unit may delete lower order bits of the sub-band transform factor so that the code has a predetermined fixed length. Accordingly, the image data including the binary image data and the continuous tone image data can be compressed with a high compression rate while a high image quality is maintained. The compression rate is higher than that of the block truncation encoding method. 
   Additionally, the encoding unit may delete a greater number of lower order bits from the high-frequency component than the low-frequency component when both the maximum value and the minimum value exist in the binary data of the same block data. Accordingly, a change in an average intensity in a block having a sharp gradation change can be prevented, resulting in a prevention of deterioration of the image quality. 
   Further, the encoding unit may quantize the high-frequency component of the sub-band transform factor by a vector quantizing method. 
   Additionally, there is provided according to another aspect of the present invention an image processing system comprising: 
   a dividing unit dividing image data into a plurality of n×m pixel matrix block data, where n and m are integers; 
   a transform unit transforming each pixel in the n×m pixel matrix block data by a frequency transform method so as to produce a transform factor including a high-frequency component and a low-frequency component; 
   an image area discriminating unit for determining whether the block being processed corresponds to an edge area or a non-edge area based on the transform factor output from the transform unit; 
   a quantizing unit quantizing the transform factor for the edge area and the transform factor for the non-edge area by different methods; and 
   an encoding unit encoding an output of the quantizing unit by an entropy encoding method, 
   wherein a total of a number of bits of the high-frequency component and a number of bits of the low-frequency is the same regardless of types of the edge area or the non-edge area, and a number of bits of the high-frequency component for the edge area is the same as a number of bits of the low-frequency component of the non-edge area. 
   According to the above-mentioned embodiment, image data representing a feature of the original image can be produced while an amount of data is reduced. Additionally, image data corresponding to a plurality of image quality levels can be produced. 
   In the above-mentioned invention, the encoding unit may also encode error data generated by the quantizing unit. Accordingly, the restored image data can almost completely match the original data. 
   Additionally, an encoding of the image for the edge area may be performed by using only the high-frequency component, and an encoding of the image for the non-edge area is performed by using only the low-frequency component. According to this invention, the image quality of the restored image may be low, but a feature of the original image can be sufficiently maintained. 
   Further, in the above-mentioned invention, every other block data may be used for restoring an original image. According to this invention, the image quality of the restored image may be low, but a feature of the original image can be sufficiently maintained while an amount of data is reduced. Thus, a reduced-size image can be easily obtained. 
   Other objects, features and advantages of the present invention will become more apparent from the following detailed descriptions when read in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram of an image processing system according to a first embodiment of the present invention; 
       FIG. 2  is an illustration for explaining a sub-band transformation unit shown in  FIG. 1 ; 
       FIG. 3  is an illustration for explaining a compressing and expanding operation performed by the image processing system shown in  FIG. 1 ; 
       FIG. 4A  is an illustration for explaining a compressing operation performed by the image processing system shown in  FIG. 1  when a complete binary image fluctuates;  FIG. 4B  is an illustration for explaining an expanding operation for data obtained by the compressing operation of  FIG. 4A ; 
       FIG. 5  is an illustration for explaining an operation performed by the image processing system shown in  FIG. 1  for deleting lower order bits; 
       FIG. 6  is an illustration for explaining an operation performed by the image processing system shown in  FIG. 1  for deleting lower order bits; 
       FIG. 7  is an illustration of a quantization table; 
       FIG. 8  is a block diagram of an image processing system according to a second embodiment of the present invention; 
       FIG. 9  is an illustration for explaining a transformation of image data performed by the image processing system shown in  FIG. 8   
       FIG. 10  is a block diagram of an image processing system according to a third embodiment of the present invention; 
       FIG. 11  is an illustration for explaining a compressing and expanding operation performed by the image processing system shown in  FIG. 10 ; 
       FIG. 12  is a block diagram of an image processing system according to a fourth embodiment of the present invention; 
       FIG. 13  is an illustration for explaining an operation of the image processing system shown in  FIG. 12 ; 
       FIG. 14A  is an illustration for explaining a compressing and expanding operation for a non-edge area performed by the image processing system shown in  FIG. 12 ; 
       FIG. 14B  is an illustration for explaining a compressing and expanding operation for an edge area performed by the image processing system shown in  FIG. 12 ; 
       FIG. 15  is a block diagram of an image processing system according to a fifth embodiment of the present invention; 
       FIG. 16  is an illustration for explaining an operation of the image processing system shown in  FIG. 15 ; 
       FIG. 17A  is an illustration for explaining a bit assignment for an edge area in the fifth embodiment; 
       FIG. 17B  is an illustration for explaining a bit assignment for a non-edge area in the fifth embodiment; 
       FIG. 18A  is an illustration for explaining a compressing and expanding operation for a non-edge area performed by the image processing system according to the fifth embodiment of the present invention: 
       FIG. 18B  is an illustration for explaining a compressing and expanding operation for an edge area performed by the image processing system according to the fifth embodiment of the present invention; 
       FIG. 19  is a block diagram of an image processing system according to a sixth embodiment of the present invention; 
       FIG. 20  is an illustration for explaining a compressing and expanding operation performed by the image processing system shown in  FIG. 19 ; 
       FIG. 21  is an illustration for explaining an operation performed by an image processing system according to a seventh embodiment of the present invention; 
       FIG. 22A  is an illustration for explaining a bit assignment for a non-edge area of the seventh embodiment; 
       FIG. 22B  is an illustration for explaining a bit assignment for an edge area of the seventh embodiment; 
       FIG. 22C  is an illustration for explaining discrimination of the non-edge area and the edge-area; 
       FIG. 22D  is an illustration of a vector quantization table used in the seventh embodiment; 
       FIG. 23A  is an illustration for explaining a compressing operation performed in the seventh embodiment; 
       FIG. 23B  is an illustration for explaining an enlarging operation performed in the seventh embodiment; and 
       FIG. 24A  is an illustration for explaining a bit assignment for,an edge area of-the seventh embodiment; 
       FIG. 24B  is an illustration for explaining a bit assignment for a non-edge of the seventh embodiment; 
       FIG. 24C  is an illustration for explaining a bit assignment for an edge area of an eighth embodiment; 
       FIG. 24D  is an illustration for explaining a bit assignment for a non-edge of the eighth embodiment. 
       FIG. 25  is a block diagram of an image processing system according to a ninth embodiment of the present invention; 
       FIG. 26  is a circuit diagram of a wavelet transform unit shown in  FIG. 25 ; 
       FIG. 27  is an illustration for explaining a pixel block and a frequency transform factor; 
       FIG. 28  is a graph showing a quantization characteristic; 
       FIG. 29A  is an illustration for explaining quantization representative values and ranges defined by threshold values when a gain of a quantizing unit is 2.0; 
       FIG. 29B  is an illustration for explaining quantization representative values and ranges defined by threshold values when a gain of a quantizing unit is 1.0; 
       FIG. 29C  is an illustration for explaining quantization representative values and ranges defined by threshold values when a gain of a quantizing unit is 0.5; 
       FIG. 30A  is an illustration of high-frequency components for an edge area;  FIG. 30B  is an illustration of high-frequency components for a non-edge area;  FIG. 30C  is an illustration of high-frequency components for an edge area in which two high-frequency components have large values; 
       FIG. 31  is a block diagram of an image processing system according to a tenth embodiment of the present invention; 
       FIGS. 32A  is an illustration showing an example of a two-dimensional vector quantization using 7 quantization values;  FIGS. 32B  is an illustration showing an example of a two-dimensional vector quantization using 15 quantization values; 
       FIG. 33  is an illustration for explaining an example of a bit arrangement for each area; and 
       FIG. 34  is an illustration of a part of an original image. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   A description will now be given, with reference to  FIGS. 1 through 6 , of a first embodiment of the present invention.  FIG. 1  is a block diagram of an image processing system according to the first embodiment of the present invention.  FIG. 2  is an illustration for explaining a sub-band transformation unit shown in FIG.  1 .  FIG. 3  is an illustration for explaining a compressing and expanding operation performed by the image processing system shown in FIG.  1 .  FIGS. 4A and 4B  are illustrations for explaining a compressing and expanding operation performed by the image processing system shown in  FIG. 1  when a complete binary image fluctuates.  FIGS. 5 and 6  are illustrations for explaining an operation performed by the image processing system shown in  FIG. 1  for deleting lower order bits. 
   The image processing system according to the first embodiment is applied to a printer using 8-bit data (256 gradation levels) for representing image data. The image processing system shown in  FIG. 1  comprises a buffer unit  201 , a binary image differential data producing unit  202 , a sub-band transformation unit  203 , entropy-encoding units  204   a  and  204   b  and a memory  205 . 
   The buffer unit  201  extracts 2×2 matrix pixels from image data, and stores the 2×2 matrix pixel data therein. The 2×2 matrix pixel data stored in the buffer unit  201  is transformed into binary image data and differential data by the binary image differential data producing unit  202 . The binary data in the present embodiment is obtained by transforming the image data having intensity values from “0” through “255” into,one of binary values “255” and “0”. That is, the image data having an intensity value equal to or greater than “128” is transformed into the value “255” and the image data having an intensity value smaller than “128” is transformed into the value “0”. It should be noted that the binary values “255” and “0” are represented by values “1” and “0”, respectively. 
   The differential data represents an absolute value of a difference between the original image data and one of the binary values “255” and “0”. The data having an intensity value equal to or greater than “128” is calculated by the following equation.
 
(differential data)=(binary data “255”)−(intensity value)
 
The data having an intensity value smaller than “128” is calculated by the following equation.
 
(differential data)=(intensity value)−(binary data “0”)
 
When a reverse transformation is performed, the data having an intensity value equal to or greater than “128” is calculated by the following equation.
 
(reverse transform value)=(binary data “255”)−(differential value)
 
The data having an,intensity value smaller than “128” is calculated by the following equation.
 
(reverse transform value)=(differential value)−(binary data “0”)
 
   The binary data “255” and “0” are then encoded by using an entropy encoding by the entropy-encoding unit  104   a . The encoded data is stored in the memory  205 . On the other hand, the differential data is transformed by using a sub-band transform method such as the Harr Wavelet transform method by the sub-band transform unit  203 . Then, the transformed data is encoded by using the entropy-encoding by the entropy encoding unit  204   b . The encoded differential data is also stored in the memory  205 . 
   In this embodiment, the sub-band transform unit  203  transforms the differential data of pixels a through d shown in  FIG. 2  by using the Harr Wavelet transform method so as to obtain a low frequency component LL and high-frequency components HL, LH and HH as shown in FIG.  2 . At this time, decimals are omitted.
 
 LL ={( a+b )/2+( c+d )/2}/2
 
  HL ={( a−b )+( c−d )}/2
 
 LH ={( a+b )−( c+d )}/2
 
 HH =( a−b )−( c−d )  (1)
 
   The differential data between the original image data and one of the binary data “255” and “0”, takes a value from “0”to “127”. The LL component is represented by 7-bit data since it takes a value from “0” to “127”. Each of the HL component and the LH component is represented by 8-bit data since it takes a value from “−127” to “127”. The HH component is represented by 9-bit data since it takes a value from “−255” to “255”. When the reverse sub-band transform is performed, the original image data of the pixels a through d are restored by using the LL, HL, LH, HH components and the above equations (1). 
   A description will now be given, with reference to  FIG. 3 , of an example of a process performed by the image processing system shown in FIG.  1 . It is assumed that original image data  301  including the pixels a through d is input to the image processing system, and the pixels a through d have the following intensity values.
 
a=175
 
b=0
 
 c=175
 
d=20
 
   In this case, the binary data of the pixels a through d are represented as follows.
 
a=255=“1”
 
b=0=“0”
 
c=255=“1”
 
d=0=“0”
 
   Additionally, the differential data  302  of the pixels a through d is represented as follows.
 
 a= 255−175=80
 
 b= 0−0=0
 
 c= 255−175=80
 
 d= 20−0=20
 
   The differential data  302  is transformed by the sub-band transform method, and the following data  303  is obtained.
 
LL=45
 
HL=70
 
 LH=− 10
 
HH=20
 
   The data  303  is temporarily stored in a memory  304 . The data  303  is read to obtain the original differential data  302  by performing a reverse sub-band transform based on the equations (1). Additionally, the differential data  302  can be calculated based on the binary data “0” and “1”.
 
 a= 255−80=175
 
 b= 0−0=0
 
 c= 255−80=175
 
 d= 20−0=20
 
Accordingly, the original data is restored.
 
   When a continuous tone image is compressed, an amount of information of binary data after compression or an amount of information of sub-band transform factors after compression is negligibly small. This is because the binary data of the continuous tone image is a simple binary image, and it can be compressed into very small amount. Additionally, the differential data (sub-band transform factors after compression) is close to “0”. 
   A description will now be given of a case of a digital copy machine in which image data corresponding to a single page is compressed based on a fixed-length compression method, and is stored in a memory (hereinafter referred to as a page memory) for processing and editing (90-degree rotation) the image. With respect to a quantization, as shown in  FIGS. 4A and 4B , the LL component is represented by a multiple of “4”: each of the HL and LH components is represented by a multiple of “16”; and the HH component is represented by a multiple of “64”. That is, when the quantization is performed, the LL component is divided by “4” (two lower order bits are deleted); each of the HL and LH components is divided by “16” (four lower order bits are omitted); and the HH component is divided by “64” (six lower order bits are deleted). According to the above-mentioned quantization, the LL component (0 to 255) can be represented by 6-bit data; each of the HL and LH components (−255 to 255) can be represented by 5-bit data; and the HH component (−510 to 510) can be represented by 4-bit data. The total number of the data bits is 20 bits. 
   When the copy machine scans an original image, complete binary image data cannot be obtained due to fluctuation in an intensity of the image, the complete binary image data comprising only the minimum values “0” and the maximum values “255”.  FIGS. 4A and 4B  shows a process for compressing and expanding original image data  401  which is not the complete binary image data as follows.
 
a=250≠255
 
b=0
 
c=254≠255
 
d=2≠0
 
   Binary data  402  is obtained based on the threshold value “128” as follows.
 
a=255=“1”
 
b=0=“0”
 
c=255=“1”
 
d=0=“0”
 
   Additionally, differential data  403  becomes as follows.
 
 a= 255−250=5
 
 b= 0−0=0
 
 c= 255−254=1
 
 d= 2 − 0 = 2   
 
   The restored data  408  shown in  FIG. 4B  is complete binary image data since the differential data  402  is quantized after being subjected to the sub-band transformation. That is, the quantization is performed so that the LL component of the differential data becomes 6-bit data, each of the HL and LH components of the differential data becomes 5-bit data and the HH component of the differential data becomes 4-bit data. According to such a quantization method, a fixed length encoding can be achieved with a reduced amount of encoded information. Thus, the binary image data can be corrected to complete binary image data by eliminating a fluctuation generated when the original image is scanned. Additionally, when the thus quantized data is encoded by an entropy encoding method, the—quantized data can be compressed at a high compression rate since each of the sub-band transformation factors LL, HL, LH and HH is “0”. Thus, a compression rate, which is almost equal to a compression rate when an image is simply binarized, can be achieved. 
   A description will now be given, with reference to  FIGS. 5 and 6 , of a case in which an image having deterioration is compressed, the deterioration of the image being peculiar to an image having a block in which gradation is sharply changed. For the sake of simplification, it is assumed that a one-dimensional transformation is used so as to transform original data  501  (x 0 , x 1 )=(96, 191) as follows. 
   (1) The original data  501  is binarized based on the threshold value “128”→(0, 255); 
   (2) Differential data  502  between the original image data and one of the binary data “255” and “0” is obtained. →96−0=96, 255−191=64 
   Then, the obtained differential data  502  is transformed by the Harr Wavelet transform method. →L=(96+64)/2=80, H= 64 − 96 =− 32   
   (3) The data L and H are quantized (lower order bits are deleted). 
   Since the low-frequency component L is more important than the high-frequency component H, the high-frequency component H is quantized roughly (more number of lower order bits are deleted) while the low-frequency component L is quantized finely (less number of lower order bits are deleted). If the low-frequency component L is not quantized and the high-frequency component H is quantized by a multiple of “64”, the low-frequency component L and the high-frequency component H become as follows.
 
L=80, H=0
 
   The thus obtained L and H are restored to the differential data  503  by a reverse sub-band transformation. Then, the decoded data  504  is restored from the differential data  503 . That is, as shown in  FIG. 5 , the decoded data  504  is changed from (96, 191) to (80, 175). That is, the intensities of both pixel values in the decoded data  504  are decreased from those of the original pixel values. This phenomenon is generated when a pixel which is rendered to be the value “255” and a pixel which is rendered to be the value “0” are present in the same pixel block. This phenomenon is also generated in a two-dimensional pixel block. Thus, there is a problem in that there is a considerable difference between an original image and a restored image. 
   In order to eliminate the above-mentioned problem, in the present invention, when both a pixel rendered to be the value “255” and a pixel rendered to be the value “0” are present in the same pixel block, the high-frequency components are quantized finely (less number of lower order bits are deleted). Referring to  FIG. 6 , pixel data  601  (96, 191) is transformed into data  602  including binary data and differential data (96, 64). The differential data (96, 64) is transformed by the Harr Wavelet transform method, and factors L=80 and H=−32 are obtained. 
   When the factors are quantized, the high-frequency component H is quantized finely, and the low-frequency component L is quantized coarsely. For example, when the high-frequency component H is quantized by a multiple of 64, and the low-frequency component L is quantized by a multiple of 32, the sub-band factors becomes as follows.
 
 L= 64,  H=− 32
 
   These factors are subjected to a reverse sub-band transformation so as to obtain differential data  603 . Then, pixel data  604  is obtained from the thus-obtained differential data  603 . As shown in  FIG. 6 , the pixel data  604  is changed from the original data (96, 191) to (80, 207), but the sum of the two pixel values is not changed. Accordingly, a relative intensity of the pixels is not changed. 
   Generally, in a pixel block having two binary values, an intensity of an entire pixel block does not change whereas the intensity is changed when the high-frequency components are deteriorated. Accordingly, a change in color over an entire image can be prevented by finely quantizing the high-frequency components H. 
   A description will now be given of a second embodiment of the present invention. In the second embodiment, the high-frequency components are not sampled on each individual component basis but a sampling operation is performed on a combination of the high-frequency components so as to achieve an efficient sampling operation. An image block having the HL component representing a vertical edge and the LH component representing a horizontal edge being a large value rarely appears in an image. If an image block has one of the HL and the LH components being a large value and the other one of the HL and LH components being a small value and also the HH component being a small value, such an image block corresponds to either a vertical line or horizontal line in the image. Thus, such an image block frequently appears in an image. Additionally, if an image block has the high-frequency components HL, LH and HH all of which are small values, such an image block corresponds to an image area having a uniform intensity or an image area having a gentle change in intensity. Thus, such a block frequently, appears in an image. Accordingly, the image data can be efficiently quantized by appropriately assigning codes to a combination of the high-frequency components. This quantization is referred to as a vector quantization. 
     FIG. 7  is a table showing a code assignment to various combinations of the high-frequency components HL, LH and HH which frequently appear in an image. Codes “0”through “15” are assigned to the combinations of the high-frequency components HL, LH and HH. According to this method, each of the high-frequency components HL and LH can be compressed into 4-bit data. In the quantizing method, a difference P between the transformation factor and each value of the vector quantization is obtained for each individual component, and a quantization code which minimizes the difference P is used.
   P=|HL−HLqi|+|LH−LHqi|+|HH−HHqi|   
   Where HLqi, LHqi and HHqi are quantization values corresponding to a code value i in the quantization table shown in FIG.  7 . 
     FIG. 8  is a block diagram of an image processing system according to the second embodiment of the present invention.  FIG. 9  is an illustration for explaining a transformation of image data performed by the image processing system shown in  FIG. 8   
   As shown in  FIG. 8 , the image processing system according to the second embodiment of the present invention has the same structure as the image processing system according to the first embodiment except for a low-frequency component quantizing unit  206  and a high-frequency component quantizing unit  207  being added between the sub-band transform unit  203  and the entropy encoding units  204   b  and  204   c.    
   The 2×2 matrix pixel data extracted and stored in the buffer unit  201  is transformed into binary image data and differential data by the binary image differential data producing unit  202 . Then, the binary data is encoded by the entropy encoding unit  204   a  by using the entropy encoding method. The encoded data is stored in the memory  205 . The differential data is transformed by the sub-band transform unit  203  by using the Harr Wavelet transformation method. The low-frequency component LL of the transformed data is quantized by the low-frequency component quantizing unit  206 , and then the quantized data is encoded by the entropy encoding unit  204   b . The encoded data is stored in the memory  205 . The high-frequency components HL, LH and HH of the transformed data are quantized by the high-frequency component quantizing unit  207 , and then the quantized data is encoded by the entropy encoding unit  204   c . The encoded data is stored in the memory  205 . 
   In  FIG. 9 , image data  901  which is the same as that shown in  FIG. 3  is compressed and enlarged.
 
a=175
 
b=0
 
c=175
 
d=20
 
The binary data  902  is obtained based on the threshold value “128” as follows.
 
a=255=“1”
 
b=0=“0”
 
c=255=“1”
 
d=0=“0”
 
The differential data  902  becomes as follows.
 
 a= 255−175=80
 
 b= 0−0=0
 
 c= 255 − 175 = 70   
 
 d= 20−0=0
 
The differential data  902  is subjected to a sub-band transform using the equation (1), and the following data  903  is obtained as a result.
 
LL=45
 
HL=70
 
 LH=− 10
 
HH=20
 
   The LL component is subjected to a linear quantization using quantization representing values which are multiples of “4”, and the following result is obtained.
 
LL=44
 
As for the high frequency components HL, LH and HH, the following combination which is closest to the combination (HL, LH, HH)=(70, −10, 20) is selected from the quantizaiton table shown in FIG.  7 .
 
( HL, LH, HH )=(64, 0, 0)
 
The corresponding code  5  in the quantization table is set to the vector quantization value H (H=5).
 
   When an encoding operation is performed, differential data  908  restored based on factors  907  which are (LL, HL, LH, HH)=(44, 64, 0, 0) becomes as follows.
 
a=76
 
b=12
 
c=76
 
 d=12
 
Finally, image data  909  is obtained from the differential data  908  based on the binary data a=255, b=0, c=255 and d=12 as follows.
 
 a= 255 − 76 = 179   
 
 b= 12−0=12
 
 c= 155 − 76 = 179   
 
 d= 12 − 0 = 12   
 
   As mentioned above, according to the second embodiment of the present invention, the high-frequency components can be represented by 4-bit data in total since the high-frequency components are quantized by the vector quantizing method. Additionally, the LL component becomes 5-bit data by quantizing the original 7-bit data using a multiple of 4. Further, the binary image data can be represented by 4-bit data. Thus, the entire factor corresponding to the 2×2 pixel block can be represented by 13-bit data. Thus, a fixed length encoding method, which is more efficient than a method which does not use the vector quantization, can be achieved. 
   A description will now be given, with reference to  FIGS. 10 and 11 , of a third embodiment of the present invention.  FIG. 10  is a block diagram of an image processing system according to the third embodiment of the present invention.  FIG. 11  is an illustration for explaining a compressing and expanding operation performed by the image processing system shown in FIG.  10 . In  FIG. 10 , a sub-band transform unit  1202  transforms the image data corresponding to the pixels a through d received from a 2×2 buffer unit  1201  by using the Harr Wavelet transform method so as to obtain the low-frequency component LL and the high-frequency components HL, LH and HH. At his time, decimals are omitted. When a reverse sub-band transform is performed, the original image data corresponding to the pixels a through d is restored based on the components LL, HL, LH and HH and the equations (1). 
   The LL component takes a value from “0” to “255”, and is represented by 8-bit data. Each of the HL and LH components takes a value from “−255” to “255”, and is represented by 9-bit data. The HH component takes a value from “−510”to “510”, and is represented by 10-bit data. Thus, the total number of bits is 36. The importance of each of the sub-band transformation factors LL, HL, LH and HH is different, and a large part of lower order bits of the high-frequency components HL, LH and HH can be deleted. 
   Accordingly, in this embodiment, a LL component quantizing unit  1203  quantizes the LL component into a multiple of 4. An HL component quantizing unit  1204  quantizes the HL component into a multiple of 16. An LH component quantizing unit  1205  quantizes the LH component into a multiple of 16. The HH component is rendered to be “0” that is the HH component is discarded. Specifically, the LL component is transformed from 8-bit data to 6-bit data by being divided by 4. Each of the HL and LH components is transformed from 9-bit data to 5-bit data by being divided by 16. The HH component is transformed from 10-bit data to 0 by being discarded. Accordingly, the total number of bits of the factors of the 2×2 pixel block is reduced from 36 to 16. The quantized values obtained by the quantizing units are stored in a page memory  1206 . 
   A description will now be given, with reference to  FIG. 11 , of a specific operation of the image processing system shown in FIG.  10 . 
   It is assumed that the following image data  1301  corresponding to the pixels a through d shown in  FIG. 2  is input to the sub-band transform unit  1202 .
 
a=200
 
b=202
 
c=204
 
 d=208
 
The image data is transformed by the Harr Wavelet transform method and the following factors  1302  are obtained.
 
LL=203
 
 HL=− 3
 
 LH=− 5
 
HH=2
 
Lower order bits of the factors  1302  are deleted, and the following quantization data  1303  is obtained.
 
LL=50
 
HL=0
 
LH=0
 
HH=0
 
The following quantization data  1303  is stored in the page memory  1206 , and then two 0-bits are added so as to obtain the following factors  1304 .
 
LL=200
 
HL=0
 
LH=0
 
HH=0
 
Thereafter, the factors  1304  are transformed by the reverse Harr Wavelet transform method so as to restore the following image data  1305 .
 
a=200
 
 b=200
 
c=200
 
d=200
 
   Accordingly, despite of the number of bits being greatly reduced, the restored image data  1305  is almost equal to the original image data  1301 . Additionally, the fixed length encoding using the sub-band transform can be performed by simple calculations such as addition and subtraction in the equations (1) and a bit shift. Additionally, a good image quality can be obtained by the fixed-length encoding according to the present embodiment. 
   A description will now be given, with reference to  FIGS. 12  to  14 , of a fourth embodiment of the present invention.  FIG. 12  is a block diagram of an image processing system according to the present invention. The image processing system according to the fourth embodiment of the present invention comprises the 2×2 buffer unit  1201 , the sub-band transform unit  1202  and the page memory  1206 . The image processing unit shown in  FIG. 12  further comprises an area discriminating unit  1403  and a sub-band transform factor quantizing and encoding unit  1404 . The area discriminating unit  1403  classifies areas of the image into one of an edge area having a sharp gradation change and a non-edge area other than the edge area based on the factors HL and LH which are transformed by the sub-band transform unit  1202 . Specifically, the area discriminating unit  1403  determines that an area to be processed is an edge area if an absolute value of one of the HL and LH components is equal to or greater than a threshold value “64”. The area discriminating unit  1403  determines that the area to be processed is the non-edge area if an absolute value of one of the HL and LH components is less than the threshold value “64”. If the area to be processed is determined to be the edge area, the area discriminating unit  1403  supplies a value “1” as a flag value to the sub-band transform factor quantizing and encoding unit  1404  and the page memory  1206 . If the area to be processed is determined to be the non-edge area, the area discriminating unit  1403  supplies a value “0” as a flag value to the sub-band transform factor quantizing and encoding unit  1404  and the page memory  1206 . 
   The sub-band transform factor quantizing and encoding unit  1404  quantizes the LL component of the edge area by a multiple of 4 (divide by 4) so as to change the LL component from 8-bit data to 6-bit data. Additionally, the sub-band transform factor quantizing and encoding unit  1404  quantizes each of the HL and LH components by a multiple of 64 (divide by 64) so as to change each of the HL and LH components from 9-bit data to 3-bit data. With respect to the non-edge area, the sub-band transform factor quantizing and encoding unit  1404  quantizes the LL component by a multiple of 4 (divide by 4) so as to change the LL component from 8-bit data to 6-bit data. Additionally, the sub-band transform factor quantizing and encoding unit  1404  quantizes each of the HL and LH components by rendering an absolute value of each of the HL and LH components to become one of values 0, 16, 32 and 48 so as to change the HL and LH components from 9-bit data to 3-bit data. Additionally, the HH component of either the edge area or the non-edge area is discarded so as to change the HH component from 10-bit data to 0. 
   A description will now be given, with reference to  FIGS. 14A and 14B , of a specific example of an operation of the image processing system shown in FIG.  12 .  FIG. 14A  shows a case in which the following image data  1501  which is extracted from a non-edge area is processed.
 
a=200
 
b=202
 
c=204
 
 d=208
 
The image data  1501  is subjected to the Harr Wavelet transform, and the following factors  1502  are obtained.
 
LL=203
 
 HL=− 3
 
 LH=− 5
 
HH=2
 
Since absolute values of both the HL and LH components are less than the threshold value “64”, the pixel block is determined as the non-edge area. Accordingly, the LL component is quantized by a multiple of 4 and the HL and LH components are divided by 16 and the HH component is discarded, which results as follows
 
LL=50 (6 bits).
 
HL=0 (3 bits)
 
LH=0 (3 bits).
 
HH=0 (0 bit)
 
Flag=0 (1 bit)
 
Total=13 bits
 
The quantized data  1503  is stored in the page memory  1206 , and then 0-bits are added to obtain the following factors  1504 . The number of added 0-bits corresponds to the number of the previously deleted bits.
 
LL=200
 
HL=0
 
 LH=0
 
HH=0
 
Thereafter, the factors  1504  are subjected to the reverse Harr Wavelet transform so as to obtain decoded image data  1505  as follows.
 
a=200
 
b=200
 
c=200
 
d=200
 
It should be appreciated that the decoded image data is roughly equal to the original image data  1501 .
 
     FIG. 14B  shows a case in which the following image data  1511  that is extracted from an edge area is processed.
 a=20 b=30 c=120 d=150 
The image data  1511  is subjected to the Harr Wavelet transform, and the following factors  1512  are obtained.
 LL=80    HL=− 20   LH=− 110 HH=20 
Since the absolute value of the LH component is not less than the threshold value “64”, the pixel block is determined as the edge area. Accordingly, the LL component is quantized by a multiple of 4 and the HL and LH components are quantized by a multiple of 64 and the HH component is discarded, which produces results as follows.
 LL=20 (6 bits) HL=0 (3 bits)   LH=− 1 (3 bits) HH=0 (0 bit) Flag=1 (1 bit) Total=13 bits 
The quantized data  1513  is stored in the page memory  1206 , and then 0-bits are added to obtain the following factors  1514 . The number of the added 0-bits corresponds to the number of the previously deleted bits.
 LL=80 HL=0   LH=− 64 HH=0 
Thereafter, the factors  1514  are subjected to the Harr Wavelet transform so as to obtain decoded image data  1515  as follows.
 a=24 b=24 
 c=112
 d=112 
It should be appreciated that the decoded image data  1515  still represents an edge area despite of, a large number of bits being deleted.
 
   In the third embodiment, the HL and LH components are quantized by a multiple of 16 irrespective of whether the pixel block to be processed corresponds to the edge area or the non-edge area. However, in the fourth embodiment, the HL and LH components are quantized by a multiple of 64 when the absolute values of the HL and LH components are equal to or greater than the threshold value “64”. Thus, the quantization representative values such as “96” or “106” are eliminated. Thus, the number of bits of the quantized data in the fourth embodiment is less than that of the third embodiment. However, in the edge area in which a gradation change is sharp, recognizable deterioration in the image is rarely generated when the values of the high-frequency components are coarsely sampled. Thus, the information regarding the high-frequency components can be deleted while the image quality is maintained at a certain level. Thus, the fixed-length encoding can be achieved by the above-mentioned separation of an image area. 
   A description will now be given, with reference to  FIGS. 15  to  18 , of a fifth embodiment of the present invention. The fifth embodiment has the same structure as that of the fourth embodiment except for the area discriminating unit  1403  and the sub-band transform factor quantization an encoding unit  1404  being replaced by an area discriminating unit  1403   a  and a sub-band transform factor quantizing and encoding unit  1404   a . The area discriminating area  1403   a  classifies areas of the image into one of an edge area having a sharp gradation change and a non-edge area other than the edge area based on the factors HL and LH which are transformed by the sub-band transform unit  1202 . Specifically, the area discriminating unit  1403   a  determines that an area to be processed is an edge area if an absolute value of one of the HL and LH components is equal to or greater than a threshold value “16”. Otherwise, the area discriminating unit  1403   a  determines that the area to be processed is the non-edge area if an absolute value of one of the HL and LH components is less than the threshold value “16”. If the area to be processed is determined to be the edge area, the area discriminating unit  1403   a  supplies a value “1” as a flag value to the sub-band transform factor quantizing and encoding unit  1404   a  and the page memory  1206 . If the area to be processed is determined to be the non-edge area, the area discriminating unit  1403   a  supplies a value “0” as a flag value to the sub-band transform factor quantizing and encoding unit  1404  and the page memory  1206 . 
   The sub-band transform factor quantizing and encoding unit  1404   a  changes a bit assign ratio used by a fixed-length encoding method in response to the determination as to whether the image area to be processed is the edge area or the non-edge area. For example, for the non-edge area, 6 bits are assigned to the LL component since a gradation is important for visual sense, whereas 3 bits are assigned to each of the HL and LH components. On the other hand, for the edge-area, 4 bits are assigned to the LL component since recognition of an edge is important for visual sense, and 4 bits are assigned to each of the HL and LH components. 
   That is, for the edge-area, the sub-band transform factor quantizing and encoding unit  1404   a  quantizes the LL component of the edge area by a multiple of 16 (divide by 16) so as to change the LL component from 8-bit data to 4-bit data. Additionally, the sub-band transform factor quantizing and encoding unit  1404   a  quantizes each of the HL and LH components by a multiple of 32 (divide by 32) so as to change each of the HL and LH components from 9-bit data to 4-bit data. With respect to the non-edge area, the sub-band transform factor quantizing and encoding unit  1404   a  quantizes the LL component by a multiple of 4 (divide by 4) so as to change the LL component from 8-bit data to 6-bit data. Additionally, the sub-band transform factor quantizing and encoding unit  1404   a  quantizes each of the HL and LH components by a multiple of 4 (divide by 4) so as to change the HL and LH components from 9-bit data to 3-bit data. Additionally, the HH component of either the edge area or the non-edge area is discarded so as to change the HH component from 10-bit data to 0. 
   A description will now be given, with reference to  FIGS. 18A and 18B , of a specific example of an operation of the image processing system according to the present embodiment.  FIG. 18A  shows a case in which the following image data  1801  which is extracted from a non-edge area is processed.
 
a=200
 
b=202
 
c=204
 
d=208
 
The image data  1801  is subjected to the Harr Wavelet transform, and the following factors  1802  are obtained.
 
LL=203
 
 HL=− 3
 
 LH=− 5
 
HH=2
 
Since absolute values of both the HL and LH components are less than the threshold value “16”, the pixel block is determined as the non-edge area. Accordingly, the LL component is quantized by a multiple of 4, the HL and LH components are quantized by a multiple of 4 and the HH component is discarded, which produces results as follows.
 
LL=50 (6 bits)
 
HL=0 (3 bits)
 
LH=0 (3 bits)
 
HH=0 (0 bit)
 
Flag=0 (1 bit)
 
Total=13 bits
 
The quantized data  1803  is stored in the page memory  1206 , and then 0-bits are added to obtain the following factors  1804 . The number of added 0-bits corresponds to the number of the previously deleted bits.
 
LL=200 
 
HL=0
 
 LH=− 4
 
 HH=0
 
Thereafter, the factors  1804  are subjected to the reverse Harr Wavelet transform so as to obtain decoded image data  1805  as follows.
 
a=198
 
b=198
 
c=202
 
d=202
 
     FIG. 18B  shows a case in which the following image data  1811  which is extracted from an edge area is processed.
 a=20 b=30 c=120 d=150 
The image data  1811  is subjected to the Harr Wavelet transform, and the following factors  1812  are obtained.
 LL=80   HL=− 20   LH=− 110 HH=20 
Since the absolute value of the LH component is not less than the threshold value “16”, the pixel block is determined as the edge area. Accordingly, the LL component is quantized by a multiple of 4, the HL and LH components are quantized by a multiple of 32 and the HH component is discarded, which results as follows
 LL=5 (4 bits) HL=0 (4 bits)   LH=− 3 (4 bits) HH=0 (0 bit) Flag=1 (1 bit) Total=13 bits 
The quantized data  1813  is stored in the page memory  1206 , and then 0-bits are added to obtain the following factors  1814 . The number of the added 0-bits corresponds to the number of the previously deleted bits.
 LL=80 HL=0   LH=− 96 HH=0 
Thereafter, the factors  1514  are subjected to the reverse Harr Wavelet transform so as to obtain decoded image data  1515  as follows.
 a=32 b=32 c=128 d=128 
   In the third embodiment, the HL and LH components are quantized by a multiple of 16 irrespective of whether the pixel block to be processed corresponds to the edge area or the non-edge area. However, in the fifth embodiment, the factors are encoded by using different numbers of assigned bits in response to the determination as to whether the image area corresponds to the edge area or the non-edge area. That is, the LL component of the non-edge area in which gradation is important is finely sampled, whereas the HL and LH components of the edge area in which a change in intensity is important are finely sampled. Thus, the fixed-length encoding can be achieved while the feature of an image is maintained. 
   A description will now be given, with reference to  FIGS. 19 and 20 , of a sixth embodiment of the present invention.  FIG. 19  is a block diagram of an image processing system according to the sixth embodiment of the present invention.  FIG. 20  is an illustration for explaining a compressing and expanding operation performed by the image processing system shown in FIG.  19 . 
   In the present embodiment, pixel values a through d are subjected to the Harr Wavelet transform by the sub-band transform unit  1202  as shown in FIG.  12 . Then, the low-frequency component LL is quantized by the low-frequency quantizing unit  206  shown in  FIG. 8 , and the high-frequency components HL, LH and HH are vector-quantized by the vector quantizing unit  207  based on the quantization table shown in FIG.  7 . 
   Referring to  FIG. 20 , the following original image data  1101  is input to the sub-band transform unit  1202 .
 
a=20
 
b=30
 
c=120
 
d=150
 
The original image data  1101  is subjected to the Harr Wavelet transform, and the following factors  1102  are obtained.
 
LL=80 (8 bits)
 
 HL=− 20 (9 bits)
 
 LH=− 110 (9 bits)
 
HH=20 (10 bits)
 
Total 36 bits
 
The LL component is represented by 6-bit data as follows.
 
LL=20 (6 bits)
 
The HL, LH and HH components (−20, −110, 20) are selected from the quantization table shown in FIG.  7 . That is, the following values which are closest to the combination of the values (−20, −110, 20) is selected.
 
 ( HL, LH, HH )=(0, −128, 0)
 
Then, the corresponding code “12” (4 bits) which represents the quantization representative vector is set as the quantization value. Thus, the original image data  1101  is compressed to the data  1103  having 10 bits as the total number of bits.
 
   In a decoding process, two 0-bits are added to the LL component (LL=20 (6 bits)). Then, the quantized data  1103  is decoded to the data  1104  based on the vector quantization value “12” as follows.
 
( LL, HL, LH, HH )=(80, 0, −128, 0)
 
Thereafter, the data  1104  is subject to the reverse Harr Wavelet transform, and the following image data  1105  is obtained.
 
a=16
 
b=16
 
c=144
 
d=144
 
   A description will now be given, with reference to  FIGS. 21  to  23 , of a seventh embodiment of the present invention. In the seventh embodiment, the bit assignment of the fifth embodiment and the vector quantization of the high-frequency components are combined. 
   In the present embodiment, similar to the fifth embodiment, it is determined that an area to be processed is an edge area if an absolute value of one of the HL and LH components is equal to or greater than a threshold value “16”. On the other hand, it is determined that the area to be processed is the non-edge area if an absolute value of one of the HL and LH components is less than the threshold value “16”. If the area to be processed is determined to be the edge area, four higher order bits are assigned to the low-frequency component LL, and four lower order bits are assigned to the high frequency components HL, LH and HH as shown in FIG.  22 A. On the other hand, if the area to be processed is the non-edge area, six higher order bits are assigned to the low-frequency component LL and two lower order bits are assigned to the high-frequency components HL, LH and HH as shown in FIG.  22 B. Additionally, the two lower order bits are used to indicate flag information as shown in FIG.  22 C. That is, the two lower order bits are set to “00”for the non-edge area, and “00”is not set to the two lower order bits for the edge area. 
   With respect to quantization, as shown in  FIG. 22D , the LL component of the edge area is divided by  16  so as to obtain 4-bit data, and the high-frequency components are vector-quantized to be represented by 4-bit data. It should be noted that values 0=0000, 4=0100, 8=1000 and 12=1100 are not used since these values have the two lower order bits “00”which is reserved for the flag information. Additionally, the LL component of the non-edge area is divided by 4 so as to obtain 6-bit data, and only “00”is used for the high-frequency components. 
     FIG. 23A  is an illustration for explaining a compressing operation performed in the seventh embodiment, and  FIG. 23B  is an illustration for explaining an enlarging operation performed in the seventh embodiment. 
   It is assumed that the following image data  1301  which is extracted from the edge area is input.
 
a=20
 
b=30
 
c=120
 
d=150
 
   The image data  1301  is subjected to the Harr Wavelet transform, and the following factors  1302  are obtained
 
LL=80
 
 HL=− 20
 
 LH=− 110
 
HH=20
 
Since absolute values of both the HL and LH components are greater than the threshold value “16”, the block being processed is determined as the non-edge area. Thus, the LL component is divided by 16 and the result is as follows.
 
LL= 20 = 1010  (4 bits)
 
With respect to the high-frequency components, the following combination which is closest to the HL, LH and HH components (−20, −110, 20) is selected.
 
( HL, LH, HH )=(0, −128, 0)
 
Additionally, the code “13=0111 (4 bits)” representing the quantization representative vector is set to the quantization value  1303 . Thus, the quantized data  1304  having a total number of bits being  8  bits is obtained. The quantized data  1304  is stored in the page memory  1206  as data  1305 .
 
   When encoding is performed, the data  1305  being processes is read from the page memory  1206  as data  1306 . The data  1306  is determined as the non-edge area since the two lower order bits are not “00”. Thus, the following factors  1308  are obtained.
 
LL=80
 
HL=0
 
 LH=− 128
 
HH=0
 
Thereafter, the factors  1308  are subject to the reverse Harr Wavelet transform, and the following decoded image data  1309  is obtained.
 
a=16
 
b=16
 
c=144
 
d=144
 
As mentioned above, according to the seventh embodiment, since there is no need to assign bits for indicating the flag information, the image data can be efficiently encoded when the number of bits used by the fixed length encoding method is limited.
 
   A description will now be given, with reference to  FIGS. 24A ,  24 B,  24 C and  24 D, of an eighth embodiment of the present invention. 
     FIG. 24A  is an illustration of 8-bit data corresponding to the edge area obtained in the above-mentioned seventh embodiment. The 8-bit data comprises four higher order bits which represent the LL component and four lower order bits which represent the vector quantization value of the high-frequency components. Generally, since a pixel block having a large intensity change rarely appears in an image, most of the vector quantization values take small values when the quantization table shown in  FIG. 22D  is used. Accordingly, in many cases, each of the two most significant bits is “0”, and each of the two least significant bits is randomly either “1” or “0”. 
     FIG. 24B  is an illustration of 8-bit data corresponding to the non-edge area obtained in the above-mentioned seventh embodiment. The 8-bit data comprises six higher order bits which represent the LL component and two lower order bits which represent the flag information. Each of the two lower order bits among the six higher order bits is randomly either “1” or “0”, and each of the two lower order bits is always “0”. 
   In the above-mentioned arrangement of bits, the four most significant bits of each of the 8-bit data corresponding to the edge area and the non-edge area represent the four most significant bits of the LL component. These four most significant bits have a good correlation to each other. Each of the fifth and sixth order bits counted from the most significant bit corresponding to the edge area is “0” in most cases. However, each of the fifth and sixth order bits randomly takes either the value “1” or “0”. That is, the good correlation is lost due to low correlation of the non-edge area. Additionally, each of the seventh and eighth order bits counted from the most significant bit has a good correlation in the non-edge area since it is always “0” for the non-edge area. However, the seventh and eighth order bits take randomly either “1” or ton for the edge area and, thus, correlation is lost due to the randomness for the edge area. 
   Accordingly, in the eighth embodiment, the fifth order bit and seventh order bit counted from the most significant bit of the 8-bit data corresponding to the non-edge area are exchanged, and the sixth order bit and eighth order bit counted from the most significant bit of the 8-bit data corresponding to the non-edge area are exchanged. According to this rearrangement of the order of bits, the codes (8-bit data) for the edge area and the non-edge area can be in a good correlation. This is because the first to fourth order bits counted from the most significant bit for the 8-bit data corresponding to both the edge-area and the non-edge area represent the four most significant bits of the LL component; each of the fifth and sixth order bits counted from the most significant bit is “0” in most cases for both the edge area and non-edge area; and each of the seventh and eighth order bits counted from the most significant bit is randomly either “1” or “0” for both the edge area and non-edge area. As a result, when the data in the page memory is stored in another memory for sorting, the data can be efficiently compressed by the entropy encoding method. 
   A description will now be given, with reference to  FIG. 25  to  30 , of a ninth embodiment of the present invention.  FIG. 25  is a block diagram of a printer system which is an image processing system according to the ninth embodiment of the present invention. 
   The printer system shown in  FIG. 25  comprises an image processing unit  2100 , a host unit  2200  such as a personal computer, a hard disc drive unit (HDD)  2300  as a large capacity memory unit and a printer engine  2400 . 
   The image processing unit  2100  comprises an RIP unit  2101 , a frame memory  2102 , a block dividing unit  2103 , a wavelet transform unit  2104 , a quantizing unit  2105 , an encoding unit  2106 , a reverse wavelet transform unit  2107 , an edge degree calculating unit  2108  and a gain changing unit  2109 . 
   A description will now be given of an operation of the above-mentioned components of the printer system shown in FIG.  25 . 
   When image data is input from the host unit  2200  to the RIP unit  2101 , the RIP unit  2101  transforms the image data to bit map data and stores the bit map data in the frame memory  2102 . Then, the bit map data corresponding to a single page is transferred to the block dividing unit  2103 . The block dividing unit  2103  divides the bit map data into a plurality of block data each having a predetermined size. The block data is sequentially transferred to the wavelet transform unit  2104 . The wavelet transform unit  2104  transforms the block data to a transform factor, and sends the transform factor to the quantizing unit  2105  and the edge degree calculating unit  2108 . The edge degree calculating unit  2108  calculates a slope of a rate of change in intensity in the block data based on the data supplied by the wavelet transform unit  2104 . The result of the calculation is output to the gain changing unit  2109 . The gain changing unit  109  changes a gain of the quantizing unit  2105  based on the intensity slope calculated by the edge degree calculating unit  2108 . The quantizing unit  2105  quantizes the data supplied by the wavelet transform unit  2104  by a gain changed by the gain changing unit  2109 . The quantized data is transferred to the encoding unit  2106 . The encoding unit  2106  is provided with a buffer memory having a small capacity. The encoding unit  2106  performs a data compression (encoding) such as the QM-coder by using the buffer memory. The compressed data is sequentially written in the HDD  2300 . The compressed data stored in the HDD  2300  is read upon request, and is supplied to the encoding unit  2106 . Then, the compressed data is expanded by the encoding unit  2106  by using a reverse encoding method. Thereafter, the quantizing unit  2105  restores the expanded data by a reverse quantizing method, and supplies the factor to the reverse wavelet transform unit  2107 . Accordingly, the image data is regenerated by the reverse wavelet transform unit  2107 , and is output as a visible image by,the printer engine  2400 . 
   The image processing system according to the present embodiment uses a sub-band encoding method for two-dimensional image data. Accordingly, as shown in  FIG. 26 , the wavelet transform unit  2104  first separates a horizontal direction signal of the original image into a low-frequency signal and a high-frequency signal by using a low-pass filter (LPF)  2011  and a high-pass filter (HPF)  2012 . Then, a vertical signal of the original image is subjected to the same process by low-pass filters  2013  and  2014  and high-pass filters  2015  and  2016 . Thus, the original image data is separated into four bands, which are, horizontal high-band (HL), vertical high-band (LH), a diagonal high-band (HH) and a low band (LL) as, shown in FIG.  27 . 
   When the band separation is performed, the original image is divided into a plurality of 2×2 pixel matrix blocks as shown in FIG.  27 . That is, each pixel block comprises two, horizontally arranged pixels and two vertically arranged pixels. First, the pixels in the pixel block are subjected to a (2, 2) transformation in the horizontal direction based on the following equation (11). In this operation, an LPF output s(n) and an HPF output d(n) are obtained. Thereafter, each of the outputs is subjected to a (2, 2) transformation in a vertical direction so that the transform factor shown in  FIG. 27  is obtained. The horizontal high-band HL represents a high-frequency component of the original image in the horizontal direction. The vertical high-band LH represents a high-frequency component in a vertical direction. The diagonal high-band HH represents a high-frequency component in a diagonal direction. The low band LL represents a low-frequency component. 
   It should be noted that the original image may be divided into 4×4 matrix pixel blocks. In such a case, each of the components (HL, LH, HH, LL) includes four components. 
   The transform factor is restored to image data by a (2, 2) reverse transform based on the following equation (2) after being subjected to a quantizing process, an entropy encoding process and a reverse quantizing process described later.
 
“(2, 2) transform”
 
 LPF: s ( n )=└{ X (2 n )+ X (2 n+ 1)}/2┘
 
 HPF: d ( n )= X (2 n )− X (2 n+ 1)  (11)
 
“(2, 2) reverse transform”
 
 X (2 n )= s ( n )+└{ d ( n )+1}/2┘
 
 X (2 n+ 1)= s ( n )−└ d ( n )/2┘  (12)
 
   Generally, a probability density function of high-frequency factors is approximated by the Laplacian distribution having a mean value of 0. Thus, the quantizing unit  2105  performs a non-linear quantization with respect to high-frequency factors so as to minimize average quantization noise power. 
     FIG. 28  is a graph showing a quantizing characteristic of the quantizing unit  2105 . Actually, the transform factor takes either a plus value or a minus value. Since the plus and minus values are symmetric, only a plus side is shown in the figure. In the example shown in  FIG. 28 ,  511  values between −255 and 255 are quantized into 9 values, which are, −219, −125, −70, −30, 0, 30, 70, 125, 219. These quantization representative values are compressed by n entropy encoding such as the Huffman encoding. 
   The quantizing unit  2105  determines one of ranges into which an input value falls, the ranges being defined by plurality of threshold values. Then, the quantizing unit  105  outputs one of the quantization representative values corresponding to the one of the ranges into which the input value falls. 
   If the gain of the quantizing unit  2105  is set to 1.0, the quantization representative value lies between the two adjacent;threshold values which defines the range. For example, in an example shown in  FIG. 29B , the quantization representative value  70  is a value between the threshold values  50  and  98 . However, if the gain is not 1.0, this condition is not established. That is, in an example shown in  FIG. 29A  in which the gain is set to 2.0 which is greater than 1.0, the quantization representative value 70 is a value within a range between 25 and 49. On the other hand, in an example shown in  FIG. 29C  in which the gain is set to 0.5 which is smaller than 1.0, the quantization representative value 70 is assigned to a range between 101 and 196. 
   If the gain of the quantizing unit  2105  is greater than 1.0, an output of the quantizing unit  2105  is always greater than an input thereof. On the contrary, if the gain of the quantizing unit  2105  is smaller than 1.0, the output of the quantizing unit  2105  is always smaller than the input thereof. 
   Sharpness of change in gradation of a block is proportional to a magnitude of an absolute value of the high-frequency factor. Thus, if the gain of the quantization  2105  with respect to the high-frequency factor is set to a value grater than 1.0, a slope of change in intensity of the image restored by a reverse transform becomes steeper. On the contrary, if the gain is set to a value less than 1.0, the slope becomes gentler. 
   If the gradation change in the block is sharp, the absolute value of the high-frequency factor is increased. 
   The high-frequency factor of an area having a sharp gradation change, such as a character image area or a line image area, takes a relatively large value as shown in FIG.  30 A. However, the high-frequency factor of an area, in which the gradation change is gentle such as a photograph image, takes a relatively small value. 
   Accordingly, the edge degree calculating unit  2108  calculates a difference d between the largest component and the second largest component among the three components LH, HL and HH of the high-frequency factor. The calculated difference d is determined as an edge degree. 
   If the 4×4 pixel matrix is used, each of the three components of the high-frequency factor includes four components. Thus, one of the four components having the maximum absolute value is selected as a representative of the corresponding one of the three components. Then, a difference d between the largest representative value and the second largest representative value is calculated. 
   As mentioned above, in an area such as a character image area or a line image area, a differential filtering process is performed so as to increase an intensity slope of a contour of the image. On the other hand, in an area such as a photograph image in which an intensity slope is gentle, a smoothing filtering process is performed. 
   Conventionally, the filtering process for adjusting an image quality and a quantizing process are performed in different processes. However, in the present embodiment, the filtering process is performed in the data compressing process. This is achieved by the gain changing unit  2109  changing the gain of the quantizing unit  2105  in response o the edge degree, calculated by the edge degree calculating unit  2108 . Thus, the process time is reduced and a manufacturing cost of the system can be reduced. The gain of the quantizing unit  2105  is changed by changing the threshold values thereof. New threshold values are obtained by dividing the threshold values at the gain of 1.0 by a desired gain. 
   Accordingly, if the desired gain is previously defined by a function of the edge degree, the new threshold values can be obtained sequentially in an order of high-frequency factor→edge degree→gain→new threshold value. Thus, the gain of the quantizing unit  2105  can be changed to the desired gain by the new threshold values. 
   When the gain of the quantizing unit  2105  is changed in response to a type of image area, there is no need to announce the quantization table used when the encoding is performed to the decoding side since the quantization representative value is fixed, that is, not changed. In the conventional technique such as disclosed in the aforementioned patent document, information with respect to the used quantization table must be stored together with the image data in the compressed data. However, in the present embodiment, such information regarding the quantization table is not necessarily stored as compressed data and, thus, the compression rate is increased. 
   If the information is omitted at a part which is not sensitive to a visual sense of human beings, the compression rate can be increased without changing an image quality. For example, a small intensity change adjacent to an area having a sharp intensity slope is hardly recognized. This effect is known as a mask effect. According to the mask effect, when a difference between edge degrees of adjacent blocks exceeds a predetermined value, the intensity change of the block having the smaller edge degree is hardly recognized. 
   Accordingly, when a difference between edge degrees of adjacent blocks exceeds a predetermined value, the edge degree calculating unit  2108  changes the smaller edge degree to a further smaller value. As a result, the gain of the quantizing unit  2105  is changed to a smaller value by the gain changing unit  2109  and, thereby, dispersion of the quantized value is decreased which result in an increase in the compression rate. 
   Additionally, in an area in which mesh point images or line images are randomly and densely populated, there may be no problem in a visual sense even when the smoothing process is performed. In many cases, a plurality of components of the high-frequency factor of such an area may be large values as shown in FIG.  30 C. 
   In such a case, the edge degree calculating unit  2108  does set the largest component to the edge degree but set a difference between the largest component and the second largest component to the edge degree. Thereby, the edge degree is changed to a smaller value. As a result, the gain of the quantizing unit  2105  is changed to a smaller value by the gain changing unit  2109  and, thus, dispersion of the quantized value is decreased which results in an increase in a compression rate. 
   A description will now be given, with reference to  FIG. 31 , of a tenth embodiment of the present invention.  FIG. 31  is a block diagram of a printer system which is an image processing system according to the tenth embodiment of the present invention. In  FIG. 31 , parts that are the same as the parts shown in  FIG. 25  are give the same reference numerals. 
   The printer system shown in  FIG. 31  comprises an image processing unit  3100 , a host unit  2200  such as a personal computer, a hard disc drive unit (HDD)  2300  as a large capacity memory unit and a printer engine  2400 . 
   The image processing unit  3100  comprises an RIP unit  2101 , a frame memory  2102 , a block dividing unit  2103 , a wavelet transform unit  2104 , an image area discriminating unit  3105 , a quantizing unit  3106 , an encoding unit  2106  and a reverse wavelet transform unit  2107 . 
   A description will now be given of an operation of the above-mentioned components of the printer system shown in FIG.  31 . 
   When image data is input from the host unit  2200  to the RIP unit  2101 , the RIP unit  2101  transforms the image data to bit map data and stores the bit map data in the frame memory  2102 . Then, the bit map data corresponding to a single page is transferred to the block dividing unit  2103 . The block dividing unit  2103  divides the bit map data into a plurality of block data each having a predetermined size. The block data is sequentially transferred to the wavelet transform unit  2104 . The wavelet transform unit  2104  transforms the block data to a transform factor, and sends the transform factor to the image area discriminating unit  3105  and the quantizing unit  3106 . The image area discriminating unit  3105  determines whether each block corresponds to an edge area or a non-edge area based on the data from the wavelet transform unit  2104 . The quantizing unit  3106  quantizes the data from the wavelet transform unit  2104  based on a result of a determination of the image area discriminating unit  3105 . The quantized data is transferred to the encoding unit  2106 . The encoding unit  2106  is provided with a buffer memory having a small capacity. The encoding unit  2106  performs a data compression (encoding) such as the QM-coder by using the buffer memory. The compressed data is sequentially written in the HDD  2300 . The compressed data stored in the HDD  2300  is read upon request, and is supplied to the encoding unit  2106 . Then, the compressed data is expanded by the encoding unit  2106  by using a reverse encoding method. Thereafter, the quantizing unit  3106  restores the expanded data by a reverse quantizing method, and supplies the factor to the reverse wavelet transform unit  2107 . Accordingly, the image data is regenerated by the reverse wavelet transform unit  2107 , and is output as a visible image by the printer engine  2400 . 
   The image processing system according to the present embodiment uses a sub-band encoding method for two-dimensional image data. An operation of the sub-band encoding method used in this embodiment is the same as that of the ninth embodiment as shown in  FIG. 26 , and a description thereof will be omitted. 
   When the band separation is performed, the original image is divided into a plurality of 2×2 pixel matrix blocks (refer to FIG.  27 ). That is, each pixel block comprises two horizontally arranged pixels and two vertically arranged pixels. First, the pixels in the pixel block,are subjected to a (2, 6) transformation in the horizontal direction based on the following equations (13). In this operation, an LPF output s(n) and an HPF output d(n) are obtained. Thereafter, each of the outputs is subjected to a (2, 2) transformation in a vertical direction based on the above-mentioned equation (11) so that the transform factor shown in  FIG. 27  is obtained. The horizontal high-band HL represents a high-frequency component of the original image in the horizontal direction. The vertical high-band LH represents a high-frequency component in a vertical direction. The diagonal high-band HH-represents a high-frequency component in a diagonal direction. The low band LL represents a low-frequency component.
 
“(2, 6) transform”
 
 LPF: s ( n )=└{ X (2 n )+ X (2 n+ 1)}/2┘
 
 HPF: d ( n )= X (2 n )− X (2 n+ 1)+└{− S ( n− 1)+ s ( n+ 1)+ 2 }/4┘  (13)
 
 “(2, 6) reverse transform
 
 X (2 n )= s ( n )+┐{ d ( n )−└[− S ( n− 1)+ s ( n+ 1)+2]/4┘}/2┘
 
 X (2 n+ 1)= s ( n )−└{ d ( n )−└[− S ( n− 1)+ s ( n+ 1)+2]/4┘}/2┘  (14)
 
   The image area discriminating unit  3105  determines whether each block corresponds to an edge area or a non-edge area based on the spatial gradation change in the block. If the gradation change is sharp, an absolute value of the high-frequency component is large. That is, if the absolute value of the high-frequency component is greater than a predetermined value, is can be determined as an edge area. Otherwise, it can be determined as a non-edge area. For example, blocks satisfying the following relationship (15) are determined as edge area blocks, and blocks other than the edge area blocks are determined as non-edge area blocks.
 
31&lt;|HL| or 31&lt;|LH| or 31&lt;|HH|  (15)
 
   Generally, a probability density function of high-frequency factors is approximated by the Laplacian distribution having a mean value of 0. Thus, the quantizing unit  3106  performs a non-linear quantization with respect to high-frequency factors so as to minimize average quantization noise power. 
     FIG. 32A  shows an example of a two-dimensional vector quantization using the components HL and LH, the vector quantization being represented by 7 values (3 bits).  FIG. 32B  shows an example of a two-dimensional vector quantization using the components HL and LH, the vector quantization being represented by 15 values (4 bits). 
   Since the high-frequency component HH has less importance in a visual sense, the high-frequency component is discarded in the present embodiment. Additionally, the probability density function of the low-frequency component LL fluctuates for images, and there is no correlation. Thus, the probability density function of the low-frequency component LL is regarded as a uniform distribution, and is subjected to a linear quantization. If the component LL is 8 bits and a 3-bit quantization is performed, five least significant bits are deleted. If a 4-bit quantization is performed, four least significant bits are deleted. 
   The quantizing unit  3106  changes a ratio of numbers of bits assigned to the high-frequency component and the low-frequency component while the number of bits assigned to a single block is maintained to be the same. That is, a greater number of bits are deleted from the high-frequency component of the edge area, whereas a smaller number of bits are deleted from the high-frequency component of the edge area. However, the number of bits of the high-frequency component of the edge area is equal to the number of bits of the low-frequency component of the non-edge area. 
     FIG. 33  is an illustration for explaining an example of a bit arrangement for each area. In the example shown in  FIG. 33 , 8 bits are always assigned to a single block. For the edge area, 4 bits are assigned to the high-frequency component, 3 bits to the low-frequency component, and 1 bit to area information. For the non-edge area, 3 bits are assigned to the high-frequency component, 4 bits to the low-frequency component, and 1 bit to area information. 
   As mentioned above, the encoding unit  2106  produces data for compensating errors so as to produce an image having higher image by complementing the data represented by a quantization factor having a fixed length for a single block. For example, a difference between the original image and the restored image is previously obtained, the restored image being obtained from the quantizing factor having a fixed length by being subjected to a reverse transform using the equations (12) and (14). Then, the quantization factor and data (error data) corresponding to the above-mentioned difference are encoded by an entropy encoding method. 
   The above-mentioned quantization factor and the error data are compressed (encoded) by a variable length reverse encoding method such as the QM-coder. When an image is rotated by a printer, data structure is preferably a fixed length. Thus, in such a case, a rotation of the image is performed prior to the entropy encoding. 
   As mentioned above, the compressed data read from the HDD  2300  is reverse encoded (decoded) by the encoding unit  2106 , and is reverse quantized by the quantizing unit  3106  so as to return to the transform factor. The transform factor is subjected to a reverse transform by the reverse wavelet transform unit  2107  so as to restore the image data. At this time, both the quantization factor and the error data are decoded so as to restore the transform factor. Then, the transform factor is subjected to reverse transform and, thereby, the original image can be almost completely restored. Additionally, an image having an image quality at a certain level can be restored by reverse transforming the quantized factor having a fixed length, that is, both the high-frequency component and the low-frequency component. 
   Additionally, when only the high-frequency component of the quantized factors with a fixed length is reverse transformed for the edge area, and when only the low-frequency component of the quantized factor with a fixed length is reverse transformed for the non-edge area, image quality is considerably deteriorated, but a feature of the original image can be still maintained. Such a restored image can be used for a trial printing. 
   Further, if the decoding process of the image is not performed for all blocks but for every other block as shown in  FIG. 34 , image quality and resolution may be deteriorated, but the restored image can still provide a certain feature of the original image. Such a restored image can be used as an icon on a display unit. 
   The present invention is not limited to the specifically disclosed embodiments, and variations and modifications may be made without departing from the scope of the present invention. 
   The present application is based on Japanese priority applications No. 9-118207 filed on May 8, 1997, No. 9-156006 filed on May 29, 1997 and No. 9-156007 file on May 29, 1998, the entire contents of which are hereby incorporated by reference.