JPS63109681A - Picture processor - Google Patents

Abstract

PURPOSE:To satisfactorily quantize all sample values over the entire sample value existing area, by dividing the entire sample value existing area into at least two areas of a concentrated, area and exceptional area where sample values are not concentrated, and setting a quantizing level at each area. CONSTITUTION:A sample value existing area is divided into two areas of a concentrated area where sample values are concentrated and an exceptional area where the sample value producing probability is low and, it sample values exist in the concentrated area, data codes in the code sequence belonging to the concentrated area are outputted and quantizing and encoding works of the sample values are terminated. When no sample value exists in the concentrated area, flag codes in the code sequence belonging to the concentrated area are outputted and counterplans to quantizing and encoding are transferred to the exceptional area. Therefore, if any output code obtained when sample values are quantized and encoded is the code of code sequence belonging to the exceptional area, the flag code must exists immediately before the code. Because of the flag code, codes of the exceptional area can be distinguished from those of the concentrated area at the time of decoding. Consequently, the quantizing error of the sample values in the exceptional area can be made sufficiently smaller.

Description

DETAILED DESCRIPTION OF THE INVENTION According to the present invention, sample values with a low probability of occurrence can be quantized well, and the average storage capacity of an output code string after encoding can be made to be similar to that of the conventional method.

The present invention relates to an image processing device configured as described above.

The process of dividing the existence range of sample values into several sections and replacing all sample values within the section with a representative value within the section is called "quantization." Further, the level representing the boundary of the section is called the "judgment level j," the representative value within the section is called the "output level J," and these are collectively called the "quantization level."

Usually, the sample value after quantization is encoded using a code word such as a binary code or a Huffman code, and is stored in a predetermined storage means.

Now, in order to set a predetermined number of quantization levels more efficiently, it is preferable to know the probability of occurrence of sample values in advance, and in this case, applying optimal quantization theory,
It is said that it is best to set the level so that the mean square quantization error is minimized.

However, optimal quantization is designed to more finely quantize the range in which the sample value has a high probability of occurring (called the concentrated region), and the range in which the sample value has a very low probability of occurrence (called the exceptional region). ) has the disadvantage that the output level is not set.

Therefore, a normal distribution with a very wide range of exceptions or χ
2 distribution, etc., when applying the optimal quantization method,
The quantization error of sample values in the exceptional region (exceptional sample values) becomes extremely large.

Figure 7 shows that when standard normal distribution is quantized at 8 levels,
Optimal quantization (optimal quantization in normal distribution, especially Max
This shows the setting position of the quantization level when using the method (referred to as quantization). 20 to Z are determination levels (boundaries of sections), and q0 to q7 are output levels (representative values within the sections).

In this case, the concentration region is a very narrow range of around ±3σ, while the exceptional region B has an infinite extent 9
Since there is no output level in the exceptional region B, the sample value a, for example, is quantized to the output level qo in the concentrated region A, and the quantization error becomes enormous.

The quantization error in the sample values of such exceptional region B is
Although the probability of occurrence is small, the margin of error is extremely large, making it a serious problem.

For example, in a data compression technology for gradation images called block transform coding, each component is optimally quantized (Max quantization) by utilizing the property that the distribution of components other than DC components in the frequency domain is a normal distribution. It is quantized using a method.

However, it has been pointed out that in image data compression using block transform encoding, there is a problem in that block boundaries are noticeable. As a result of repeated studies on the causes of block boundaries, the inventors found that the conventional method
It was found that one of the causes was a large quantization error of components existing in the exceptional region because of the use of quantization.

3.3 [Purpose of H] The purpose of the present invention is to quantize and encode a sample group obtained by decomposing image data into frequency components, regardless of the magnitude of the probability of occurrence of the sample group. A quantization code that can satisfactorily quantize all sample values over the entire range in which it exists, and that the average storage capacity of output code data obtained by encoding is almost the same as when using conventional methods. An object of the present invention is to provide an image processing device capable of implementing a method for converting images into images.

3.4 [Day +] For this purpose, the present invention provides an image processing device that decomposes image data into frequency components to obtain sample values, and quantizes and encodes a sample group consisting of these sample values. The present invention has means for dividing the existing range into at least two regions, a concentrated region where the sample values are concentrated and an exceptional region where the sample values are not concentrated, and means for setting the quantization level for each region.

Examples of the present invention will be described below, but prior to that, the principle thereof will be explained.

3.5.1 - IL The quantization encoding method of the present invention takes the following measures.

(2) Consider dividing the existence range of sample values into a concentrated area where sample values are concentrated and an exceptional area where sample values have a low probability of occurrence, each of which independently owns a quantization level sequence and a code sequence.

■ Introducing the concept of flags to code sequences in concentrated areas; In the conventional method, the codes that make up the code sequence were all codes assigned to output levels (these are called data codes); In the invention, within the code sequence of the concentrated area,
One flag code is provided to be used as a flag, and this flag is used as a flag indicating that the sample value is not in the concentrated area.

③ When performing it childization and encoding, first the concentrated area is the target of quantization encoding, and if the sample value does not exist within the concentrated area, the sample value is within one concentrated area with the exception area as the target. If it exists, the data code in the code sequence belonging to the concentrated area is output, and the quantization and encoding work of the sample value is completed. If no sample value exists within the concentrated area, the flag code in the code sequence belonging to the concentrated area is output, and the quantization encoding target is moved to the exception area (see FIG. 1).

Therefore, if the output code obtained by quantizing and encoding sample values is a code of a code sequence belonging to an exceptional region, a flag code always exists immediately before that code.

This flag code allows the code of the exception area to be distinguished from the code of the intensive area at the time of decoding.

3.5.2 (Method of setting the quantization level) The method of setting the quantization level in the present invention will be explained below, taking as an example the case where the probability density function of the sample value can be regarded as a standard normal distribution. Needless to say, it is also applicable to non-normalized normal distributions, 12 distributions, and the like. In this example, the number of output levels in the concentrated area is set to 1.

3.5.2.1 (Assemblies and High Level Establishment)
First, Kl output levels (q) (k=1.
2.3, ..., Kl) Max quantization judgment level (Zm) (k-1, 2, 3, ..., K1+1
), the range of sample values (assumed to be -ω to ■) is divided into one interval. Here, the relationship between Zk and qm is Zk<qk<Zk*1. In Max quantization, 2. =-ω, Z□,.

=+(3), so by the following means, Zl,
Replace the values of Zkl and with finite values.

Define the output level section width Wk as Wk=Zk◆1-2k, set an appropriate boundary value X (>0) that satisfies Zkl+W, x<Zkl+4Wkl, and set Zr=-
Let X-Zrl+I=X. Then, with (Z I-X: 5Z: 5X) as the concentration area, the judgment level (zh) obtained in this way
, let the output level (qm) be the quantization level in the concentrated region.

In addition, the judgment level (2
, ) and the output level (qv).For example, they may be newly determined using the optimal quantization method or the uniform quantization method.

Next, the output code sequence (Ck) in the concentrated region (k=
o, 1.2, . Assignment, C0 (=0) is used as a flag code.

Note that this example is an example of a fixed-length encoding method that uses a binary code as the output code, but a variable-length code that uses a Huffman code or the like to assign codes starting with the code with the shortest code length in order of the output level with the highest probability of occurrence. It is also possible to adopt the

3.5.2.2 (Example: evening area and t of the level
First, let (Zl-■<z<-x, x<z<■) be an exception area. In addition, the quantization levels in this exceptional region are designed to be able to cope with any thick absolute value of the sample value, so it is necessary to prepare a sufficient number of quantization levels or to arrange an infinite number of quantization levels. The upper and lower limits of the judgment level and output level are set when the sample population to be quantized is determined.

Assuming that the number of output levels in the exception area is 2, the judgment level and output level are respectively tz' (k=o, 1.2,..., K2+1)
)(q'h) (k=0.1.2,...,K2
-1), in this example, the sequence of (Z・6) is 0
The above integer X is defined as follows.

k-2x+1 (if Z' h ≧0) k=2x
(if Z' * <QIZ″k l<lZ
'mya21 Therefore, the judgment level interval is Z' ,,,, < Z ≦Z' 2X (
tf Z<0)Z' zx+1≦Z <z' 2X
*3 (if Z2:0), and the output level (q') for any sample value in each interval is Z'2X#2<q' 2X5 Z'tX<
00≦Z'2+1≦q' 2x*l <Z' 2X
+ff is defined. However, a sample value of 1al=X is defined here as belonging to a concentrated region.

Also, considering the origin symmetry of the sample normal distribution, for the judgment level (z' h ), Z' zx−+= Z' zx −(a
It is preferable to provide the condition O). If the interval width of the judgment level at this time is defined as W'6, then W' w
=lZ' *-z I IZ'kIW'mouth.l"
W' tN. Furthermore, considering the monotonically increasing property in the region of Z 0 of the sample normal distribution and the property of monotonically decreasing in the region Z≧0, W□≦W'k≦W' k+, ・−(a −
It is more preferable to provide the condition 1).

The output level (q'',) for the judgment level (Z'u) under such conditions is q'tx++''-Q' zx ... (
a -2) 1q"ml-lq'□21≦lq' M
It is assumed that l-1q' b is defined.

The output code sequence in the exceptional region is (C・6)(k=0
．． 1.2,...,K2-1), then (C'*)
can be defined as follows using binary codes, for example.

Since there is no flag code in the exception region in C' k=,
The code O is also assigned to the output level as a data code. That is, for k≧0, let k be the output sign for the output level (q'). Note that a variable length encoding method may also be adopted for the output code (C' u ) in the exceptional region.

The above is an example in which the output code sequence for the exceptional area is one sequence, but two or more output code sequences may be prepared for the exceptional area. In this case, it is necessary to set a flag code within the code sequence to indicate which code sequence was used during encoding.

Now, since the sample population to be quantized (here, the probability density function of the j sample values can be approximated to the standard normal distribution) is a finite population, the maximum value of the sample values (Z, 1,) Although there is a minimum value (Z□7), the value varies depending on the sample group. In this example, Z as mentioned above. ,
, (Z, 1fi), it is desirable to quantize them well and to adopt a quantization method that prevents large quantization errors from occurring in the exceptional region.

3.5.2.2.1 (Example of setting quantization level for exceptional area - Part 1) If a non-uniform quantization method is used for the exceptional area, generally the output level and judgment level should be memorized. The need arises.

Here, an example will be explained in which −-like quantization is adopted.

In uniform quantization, the value of the maximum quantization error is constant regardless of the probability of occurrence of the sample value, so no matter how large the absolute value of the sample value is, the maximum quantization error is guaranteed. This can be said to be a preferable quantization method in this sense.

Uniformly quantizing the exceptional region means that the second (right side) inequality in (a-1) 2 is equal, and the interval width for -1 quantization is newly defined as W゛. Then, W□≦w', =w', +□=w'.

The output level (q' *) and judgment level (Z' d) in uniform quantization are as follows: q' b = (Z' h + Z' k+2 ) /
Since there are two relationships, the output level Q'm for any sample value a can be determined by the following equation.

+□) ・w' +x)...(b-0) However, F(a)=-1(if ago)=+1(i
fa≧0) int(a): A function that cuts off the decimal part of a.

In addition, a patent characterized by 2 brigadiers in the output code C' for the sample value a, where G(a) = O(if a<Q) = 1
(if a ≧0).

At this time, in order to decode the output level q'1 from the output code C', -+ = 1 (if C' is an odd number) =
-1 (when C' is an even number).

When quantizing a sample population, Z I in the sample population is
Check IIIX and Z a in (Z,, x and Z rn
This does not apply if in is known or can be predicted. ), thereby determining the upper and lower limits of the output level in the exceptional region.

Figure 1 is a conceptual diagram of applying uniform quantization to the exceptional region when concentrated regions are quantized at the 2'-IJ level and exceptional regions are quantized at the 2S level.
This is an output code string of sample values a,−,aZ,a, in the figure.

3.5.2.2.2 (11M4- (7) n4rL to child fin Part 2) When the uniform quantification interval width W in the exceptional region is considerably larger than the K1th interval width WX1 in the concentrated region , the exceptional region is divided into a non-uniform quantization range and a subsequent uniform quantization range by an appropriate value Y (>0”), and the non-uniform quantization range: (Zl-y<z<-X,
X<Z<Y) Uniform quantization range: (Zl-oo<Z≦-Y, Y≦Z
〈+ω) (a-0), (
It is desirable to use a quantization level that satisfies equations a-1) and (a-2). − Interval width W・brim of quantized output level that is not similar, second (right side) in equation (a −1)
It is defined when the equality sign of the inequality sign does not hold, and W KI SW'U<W'A-z(〈w' )
becomes.

Furthermore, regarding the −-like quantization range, the above-mentioned (b−O),
Modifications of equations (b-1) and (b-2) can be applied.

FIG. 3 is a conceptual diagram of a table in which the above-described quantization level setting method is applied when concentrated areas are quantized at the '2'-IJ level and exceptional areas are quantized at 25 levels. however,
Only the range Z≧O is shown.

Here, the number of output levels in the concentrated region is defined as 1 for the transfer variable e which can take a value of 2 or more, K1=e, and an example of the quantization level designed for an arbitrary e is shown. To indicate that the number of output levels in the concentrated area is e, a subscript (e) is added to the upper right of the symbol.

(Example) Z Wu 2K (*) ■, Boundary value X (・) for different number of levels and concentration area level setting; Boundary value X (6) of concentration area for different e is 1,
X(all≦X<a2> (if s+<5z) W, -1≦W, 2° is preferably set.Also, as mentioned above, the concentrated region is where most of the sample values are Since it is a concentrated area, it is desirable to apply a highly accurate quantization method such as optimal quantization, but it is also possible to apply -spectralization because it has the advantage of keeping the maximum quantization error width constant. .

An example of setting the boundary value X(1)1 for different e is shown in Figure 5 (
Shown in a) to (d).

FIG. 5 Ta) is the X(11) curve when the Max quantization level is taken into consideration as described above. The vertical axis of the figure is the standard deviation σ, and the horizontal axis is the number of output levels.

FIG. 5(b) is an example in which the X(11) curve is set to be a straight line. The straight line may or may not be an approximation of the X(0) curve in FIG. 5(a).

Figures 5 (C) and (d) are Tal in the same figure, and X in (b).
This is an example where the value of (11) is constant above a certain level. This is a method of setting x('II) that limits the expansion of the concentration area as the number of levels increases, and P in the figure is preferably set to about 3σ to 5σ.

When uniform quantization is used in the exceptional region, -like quantization width W (
111', W+"" ≧ W(a!+' (if ,,<
. 2) It is desirable to establish the following conditions.

3.5.3 (Example of case corresponding to block coding) A specific example of the case where the present invention is applied to block transform coding will be shown. Pullok size mb Xmb (m,
: a power of 2), the image size to be encoded is MbxMb' (Mb, Mb': an integer multiple of mb). In this example, it is assumed that the original image size is MbXMb, and n bits/pixel (n: integer).

Each block image is subjected to mb x mb discrete two-dimensional orthogonal transformation, and (Mb/mb)" transformation coefficient matrices [α] are obtained. The transformation coefficient matrix [α] is mbXmb (frequency components) α ( i, j) (i=o, 1.2,..., mb
-1i j = 0% 1.2,..., m.

-1°) and are the same component (Mb
/m, )" conversion coefficients collectively form a sample group. Therefore, sample value=conversion coefficient.

Since quantization is performed independently on sample groups of mbxmb pairs having (M b / mb ) sample values, a map (bit allocation) indicating at what level each sample group is quantized is used. map) is used.

The shape of the distribution of sample values for each sample population is the DC component α(0,0
) can be considered to be normally distributed, except for the sample population of
By normalizing this and regarding it as a standard normal distribution, it is possible to apply the standard normal distribution quantization encoding method, which is an example of the present invention.

In the conventional method, quantization was performed using Max quantization, so it was sufficient to prepare one bit allocation map, but when using the standard normal distribution quantization encoding method, which is an example of the present invention, In principle, the bit allocation map in the concentrated area (first bit allocation map) [β] and the bit allocation map in the exceptional area (second bit allocation map)
Prepare two pieces of [γ].

The first bit allocation map [β] is a map showing how many bits to quantize a concentrated region for each component when using the standard normal distribution quantization encoding method, which is an example of the present invention. It is. If the original image is composed of n bits/pixel, each element β (1% j) of the first bit allocation map usually satisfies 0≦β. +j) ≦n (Lj)≠(Q,
Since it can take any integer such as 0), each β(
in j)1 ≦ β (5+j) ≦ n
For (Lj) ≠ (0,0), the judgment level and output level (Zm) of the concentrated region are respectively (k=0.1.2, ..., 2ρ(it
j＞ )(qm) (1c=0, 1, 2
, ..., 21 (...-)-1) is set.

That is, the quantization level for 1 bit (Z(l) □), (
q(1), ), the quantization level for n bits (Z"'
A total of n sets of quantization levels up to k) and (q (n) k) are set in advance.

Therefore, when using the second bit allocation map described below, the ◆ quantization level in the exceptional area is also changed to the quantization level for 1 bit (Z(
1) °, ) , (q (+1', ) to quantization level for n bits (z(n)', ), (q (n)'
, ) to set a total of n sets of quantization levels.

3.5.3.2 (Second bit allocation map) The second bit allocation map [γ] is an example of the present invention in which the exceptional region is This is a map that shows how many bits to quantize for each component, and O≦γ(in j)≦
L (if β(in J) ≠OAHD(i
, j)≠(0,0) ) r (i city, = 0 (if β mountain j) =
00R(inj) = (0,0) ).

Here, L is a constant determined by the sample value with the maximum absolute value. The quantization level in the exceptional region in the present invention is set to quantize well no matter how large the absolute value is, and an integer is the upper limit of the quantization level in the exceptional region. This is a parameter that determines the lower limit.

Furthermore, the number of quantization levels in the exceptional region may be determined for each transform coefficient matrix. In this case, the number of bits with the maximum number of quantization bits is determined among the exceptional sample values in each transform coefficient matrix, and all the exceptional sample values of that transform coefficient matrix are quantized using this number of bits. At this time, the number of exceptional region quantization bits is encoded and stored for each transform coefficient matrix.

3.5.3.3 (Block Diagram Tax B) FIG. 6 shows a block diagram of block transform encoding when the standard normal distribution quantization encoding method, which is an example of the present invention, is applied. This will be explained below.

01 Block image: Divide original image AI (MbxMb) into block images (A1) of mbXm, .

(2) Perform discrete two-dimensional orthogonal transformation on each diblock image; Through this process, a transformation coefficient matrix [α] is determined for each block image [At]. Types of discrete two-dimensional orthogonal transform used in this process include Hadamard transform, Fourier transform, slant transform, and cosine transform, any of which may be used.

(2) Calculate the statistics of the transformation coefficient matrix; The statistics are calculated for each component α (in jl (each sample group) of the transformation coefficient matrix [α], and are output as a statistics map of mbXmb. The statistics are calculated by dividing the standard deviation (assuming the mean value is zero) and the absolute value of the sample value (conversion coefficient) with the maximum absolute value by the standard deviation of the same component (this is calculated by dividing this by the standard deviation width). ), and each standard deviation map [σ,
] and form a deviation width map (S).

However, since the standard deviation map takes very similar values between different images, a predetermined standard deviation map may be used instead of calculating the standard deviation map for each image.

(2) Calculation of first bit allocation map; Calculate the first bit allocation map [β] using the standard deviation map [σ].

However, if a predetermined standard deviation map is used, a predetermined first bit allocation map is also used, so there is no need to perform calculations for each image.

Each element β(i
n j ) is determined by the following formula.

β mountain j> =tnt (lOgg('<=-j,
/ d) ) (if (i, D ≠ (0, 0) ) thousand C (if (i, j) = (Q, Q) ) where d
is a variable that controls the value of β mountain j).

Increasing this d increases the compression ratio, while decreasing d brings the quality of the reproduced image closer to that of the original image.

Further, C indicates the number of bits allocated to the DC component, and when the original image is composed of n bits/pixel, it is usually Can.

(2) Calculation of second bit allocation map: Calculate the second bit allocation map [γ] using the deviation width map (S). Each element S (inj) of (S)
Each element γ(in j) of [β] for is obtained from the following equation.

However, when using a predetermined standard deviation map, the method of determining the number of quantization bits in the exception area for each transform coefficient matrix described above is used instead of determining the second bit allocation map. . In this case, the value obtained by dividing the absolute value of each conversion coefficient in each conversion coefficient matrix by the standard deviation of the same component is regarded as the deviation width map (S), and γ (i, j) obtained by the following formula Among the values of each component of , the maximum value is the number of exceptional area quantization vias of the transform coefficient matrix. In this case, it is necessary to store this number of bits for each transform coefficient matrix.

Int'(x) = x + 1 (If the decimal point of x is not O) =x (If the decimal point of x is O) However, h is the number of output levels of the non-uniform quantization range in the exceptional region. be.

■, Normalize each sample population; If each component of the transformation coefficient after normalization is expressed as (α (i + j) ), and the element of the standard deviation map [σ] is σ (i + j), the normalization is as follows. It is defined by the formula.

σ + i + j) ■, It childization and encoding; Each component of the transform coefficient after normalization (α (Lj) ) (
(i, j)≠(0,0)) is quantized and encoded using the standard normal distribution quantization encoding method, which is an example of the quantization encoding method of the present invention, using the algorithm shown in Figure 1. do.

In general, the shape of the distribution of the transformation coefficients of the DC component α (. It is not possible to apply the standard normal distribution quantization coding method.The shape of the distribution of the DC component transform coefficient is unique to the original image and the shape of the distribution is not determined. It is preferable to carry out

For example, if the input image is 8 bits, it is preferable to uniformly quantize the DC component using 12 bits or more.

(2) Creation of overhead: Information necessary for restoring (decoding) the original image is efficiently encoded and used as overhead.

(2) Combining overhead; The encoded data obtained by quantizing and encoding the transform coefficients is combined with the overhead to obtain final compressed data F.

Support i''j 已junkuma 9 I) From the above, the present invention has the following effects.

(2) Since an output level can be set in an exceptional region where no output level has conventionally been set, it is possible to sufficiently reduce the quantization error of exceptional sample values, which is a problem with the conventional method.

(2)0 By using the quantization encoding method of the present invention, it is possible to minimize the increase in the average storage capacity of the output code caused by quantizing and encoding the sample values in the exceptional region.

For example, in Figure 2, if the value of the boundary value The output code average storage capacity iB when 2 brigadiers are used in the quantization encoding method of the present invention is: B≦0.99x3 +0.01x(3+5)=3.05
(bit). This is hardly different from the output code average storage capacity (3 bits) when two brigadiers are used in the conventional system as shown in FIG.

This effect can be obtained because the quantization encoding method of the present invention has the following three characteristics.

(1) Area division is performed so that the probability of occurrence of a sample value in the 0 exception area is much smaller than that in the concentrated area.

(2) By providing the code sequence in the 0-exception area separately from the code sequence in the concentrated area, only when the sample value exists in the exception area, the code sequence used during encoding is changed from the sequence in the concentrated area to the code sequence in the exception area. It was possible to switch to the series.

(3) By using flag codes, it is possible to switch code sequences as in (2).

■When the Keiko encoding method of the present invention is applied to block transform encoding, the compression rate will not be lowered (exceptional transform coefficients with large absolute values) As the size increases, the number of occurrences also increases; for example, in an image with 2048 x 2048 pixels,
Conversion coefficients with absolute values that are 20 to 50 times the standard deviation of each frequency component may occur. ) can be well quantized and encoded.

In block transform encoding, if a large quantization error occurs in an exceptional transform coefficient, block boundaries become noticeable in the restored image, but by using the quantization encoding method of the present invention, Block boundaries caused by quantization errors can be made less visible, allowing higher quality data compression.

[Brief explanation of the drawing]

Figure 1 is a flowchart of the quantization encoding of the present invention for an arbitrary sample value, and Figure 2' shows the probability density function of the sample value (
Standard) An explanatory diagram of quantization in the case of normal distribution. Figure 3 is also the same explanatory diagram. Figure 4 is the sample values aI, ax, a in Figure 2.
: A diagram showing an example of a specific output code for I, Figure 5 (
aJ~(dl is a diagram showing an example of the X(11) curve, FIG. 6 is a block diagram of block transform encoding when using the quantization encoding method of the present invention, and FIG. Fig. 1 is an explanatory diagram of quantization of step Max. Agent: Patent Attorney Tsuneaki Nagao Fig. 1 1-bit data code

Claims (3)

[Claims] (1) In an image processing device that decomposes image data into frequency components as sample values, and quantizes and encodes a sample group consisting of the sample values, the range in which the sample values exist is defined as a concentration of the sample values. An image processing apparatus comprising means for dividing an image into at least two regions, a region and an exceptional region, and means for setting a quantization level for each region. (2) The image processing apparatus according to claim 1, wherein each region has its own code sequence. (3) A flag code is provided in the code sequence in the concentrated area.
The image processing device described in Section 1.