JPH07154607A - Binary picture encoder - Google Patents

Abstract

PURPOSE:To attain efficient degeneration by predicting a value indicating the property of picture elements and integrating two of them whose prediction level is close to each other into one state. CONSTITUTION:A picture element prediction means 14 uses a reference picture element pattern 13 generated by a reference picture element generating means 12 to predict a picture element. A prediction level classification means 16 quantizes a prediction level 15 calculated by the prediction of the picture element prediction means 14 and classifies states whose prediction levels are close to each other into one state. A prediction value/prediction coincidence rate decision means 18 reads a prediction value 20 and a prediction coincidence rate 21 from a prediction value/prediction rate reference table 19 based on the result of classification 17 by the prediction level classification means 16. Thus, conditional entropy of picture data is reduced without remarkable increase in the size of the coding parameter reference table to reduce the code quantity.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a binary image data coding device.

[0002]

2. Description of the Related Art Markov model coding is considered to be effective as a binary image coding method for facsimiles and the like, and a technique using this is disclosed in Japanese Patent Laid-Open No. 2-305225. The conventional Markov model coding will be described below.

Here, if P (x _i ) is the probability of occurrence of the information source symbol x _i in certain information, the entropy (average amount of information) of that information source is defined by equation (1).

[0004]

[Equation 1]

This expression means that the information amount −log ₂ P (x _i ) obtained by knowing that the symbol x _i has occurred is weighted by the occurrence probability of each symbol and the average is taken. In the case of a binary image (x _i = 0 or 1), entropy is expressed by equation (2).

[0006]

[Equation 2]

It is generally known that this value shows a theoretical compression limit that cannot be coded with a code amount less than this value when a code is assigned by focusing on only one pixel to be coded. Therefore, in encoding, it is necessary to perform entropy encoding suitable for the occurrence probability P (x _i ) of each symbol so that the code amount is as close to the entropy H as possible.

In general, the probability of a pixel having a value of 0 or 1 in image data depends on what the values of a plurality of pixels preceding it are. When dependent on the values of the preceding n pixels (hereinafter referred to as reference pixels), the information source is called an n-fold Markov information source. The entropy of the n-fold Markov information source, that is, the entropy (conditional entropy) after knowing the n pixel values (x _i-1 , ..., X _in ) preceding the pixel of interest (x _i ) is It is represented by 3). Here, P (x _i-1 , ..., X _in ) has a reference pixel value of x.
_i−1 , ..., Probability of being x _in (join probability), P (x _i /
x _i-1 , ..., X _in ) has reference pixel values of x _i-1 , ..., X
_The probability (conditional probability) that the pixel value of interest becomes x _{i when} it becomes in is shown.

[0009]

[Equation 3]

In the relation between the conditional entropy H'and H in the equation (2), H'≤H (4) holds, and the equal sign holds when the information source is not a Markov information source.

Here, the 2 ⁿ possible states of the ⁿ reference pixels are called the states of the Markov information source, and each state is represented by S _i . Then, when the formula (3) is transformed, the formula (5) is obtained.
Is obtained.

[0012]

[Equation 4]

This is the entropy h (s _i ) in each state.
= −ΣP (x _i / s _i ) log ₂ P (x _i / s _i ) is weighted by the appearance probability P (s _i ) of each state and averaged. At the time of encoding, if the entropy encoding suitable for the probability P (x _i / s _i ) that the pixel of interest takes 0 or 1 is performed for each state, the code amount in each state is the entropy h (s _i ), And the code amount as a whole can also approach H'in Expression (5). Therefore,
The reference pixel should be selected so that the conditional entropy is reduced. In this way, an encoding method that classifies a pixel of interest according to the state of a reference pixel and performs appropriate entropy encoding for each state is called Markov model encoding.

As an example of the Markov model encoding, Japanese Patent Laid-Open No. Hei 2
-305225 arithmetic code type MELCO
The DE will be described. The block diagram is shown in FIG. 11
Is binary image data to be encoded, 12 is a reference pixel pattern creating means for creating a reference pixel pattern by selecting a reference pixel to be used for classification of Markov state from input pixels before the target pixel, and 18 is Prediction value / prediction match rate determining means for calculating the prediction value of the pixel of interest and the prediction hit rate (prediction match rate) using the reference pixel pattern 13, and 19 stores the prediction value and the prediction match rate for the reference pixel pattern. Predicted value / predicted matching rate reference table, 20 is a predicted value (0 or 1), 21 is a predicted matching rate, 22 is an encoding target symbol indicating matching / mismatch between the predicted value and the target pixel, 2
Reference numeral 3 is an arithmetic encoder that encodes the encoding target symbol according to the predictive matching rate 21, and reference numeral 24 is a code output from the arithmetic encoder.

[0015]

[Table 1]

Next, the operation of this encoder is shown in Table 1-2.
The value image will be described as an example. In this example, 31 in FIG. 3 is a target pixel x _i , and 32 is a reference pixel x _i-1 and x _i-2 .
Since the reference pixel is 2 pixels, as shown in Table 1, there are four kinds of states s ₀ to s ₃ , the occurrence probability P (s _i ) of each state, and the probability P (0 / s _i ) that the pixel of interest becomes 0 in each state. Probability of 1
(1 / s _i ) has the values shown in Table 1. In this case, the probability P (0) = 0.47 that the target pixel is 0 and the probability P (1) = 0.53 that the target pixel is 1, so that H = 0.
997 bits are obtained. As described above, this value is a theoretical compression limit when only one pixel to be coded is focused and a code is assigned. Further, the conditional entropy calculated from Expression (5) by classifying the target pixel according to the state s _i of the two pixels of x _i-1 and x _i-2 is H ′ = 0.72 bit. In this way, H ′ = 0.72 bit by classifying into Markov states and performing appropriate encoding for each state.
It is possible to perform coding with a code amount close to.

At the time of coding, first, the reference pixel pattern creating means 12 selects the pixels x _i-1 and x _i-2 from the coded pixels and creates the reference pixel pattern 13. Based on this reference pixel pattern 13, the predicted value 20 and the predicted matching rate 21 are read from the predicted value / predicted matching rate reference table.
If the state of the reference pixel is s ₁ , then from Table 1, the predicted value is 1, and the predicted matching rate is 0.6. Then, the predicted matching rate 21 is input to the arithmetic encoder 23.

If the pixel value to be encoded is 1, the prediction is correct, so the symbol 0 indicating that the prediction is correct is input to the arithmetic encoder 23 as the encoding target symbol 22. To do. If the pixel value to be encoded is 0, the prediction is incorrect, and therefore the symbol 1 indicating that the prediction is incorrect is input to the arithmetic encoder 23 as the encoding target symbol 22. In the arithmetic encoder 23, the encoding target symbol 2 is encoded with an encoding parameter suitable for the predictive matching rate.
By encoding 2, it is possible to perform encoding with almost the same code amount as entropy.

At this time, if k (bit) is required in each state to store the predicted value / predicted matching rate, the size of the reference predicted value / predicted matching rate reference table 19 is determined by the number of reference pixels. Since there are two pixels, k × 2 ² bits are obtained.

[0020]

In the Markov model coding, entropy generally decreases as the number of reference pixels increases and the number of states increases, but a reference table 19 storing predicted values / predicted concordance rates for each state. There is a problem in that it is difficult to increase the number of reference pixels drastically, because the size of the number increases exponentially with the increase of the number of reference pixels.

In Table 1, the pixel of interest is classified into four states according to the values that the reference pixel can take, but it is considered that some of these four states are newly combined into one state. Hereinafter, this process is called degeneracy of Markov state, or simply degeneracy. For example, if the states s ₁ and s ₂ in Table 1 are combined into one state, the states are degenerated into three states s ′ _{0 to} s ′ ₃ shown in Table 2.

[0022]

[Table 2]

When the states are degenerated, the entropy generally rises. However, when the states having similar predicted coincidence rates are degenerated, the entropy rise is slightly suppressed. In the degeneracy from Table 1 to Table 2, degeneracy is achieved without an increase in entropy because the predicted concordance rates of the two degenerate states are equal. An object of the present invention is to realize a Markov model coder that performs such efficient degeneracy.

[0024]

The Markov state degeneracy means according to the present invention predicts a value indicating the property of a pixel of interest,
The Markov state is degenerated by combining states with similar prediction levels into one state.

In the encoder of the present invention, the prediction target is the value of the target pixel or the black pixel appearance probability of the target pixel, and the target pixel is classified (that is, the state is degenerated) based on the value.

In the encoder of the present invention, a plurality of prediction means and prediction level classification means are prepared, and those are adaptively selected in the screen according to the property of the reference pixel to degenerate the Markov state. Is.

[0027]

According to the inventions of claims 1 to 3, a value reflecting the nature of the reference pixel is obtained by the prediction target pixel value, black pixel appearance probability, etc., and a state in which the prediction levels are close is summarized. As a result, the degeneracy of Markov state that suppresses the rise in entropy is performed. In the invention of claim 4, the predicting means and the prediction level classifying means in the prediction for the pixel value of interest, the black pixel appearance probability, etc. in the inventions of claims 1 to 3 are set according to the state of the reference pixel. By switching, the Markov state is degenerated with the increase in entropy suppressed.

[0028]

EXAMPLES Example 1. An embodiment of the present invention will be described below. FIG. 1 shows an arithmetic code type MELCODE using the present invention.
It is a block diagram of. In FIG. 1, 14 is a reference pixel pattern 13 created by the reference pixel pattern creating means 12.
Pixel-of-interest predicting means for predicting a pixel-of-interest value using
Is a prediction level classification unit that quantizes the prediction level 15 calculated by the prediction by the pixel-of-interest prediction unit 14 and classifies states with close prediction levels into one state. 18 is a classification result 17 by the prediction level classification unit 16. The prediction value / prediction coincidence rate reference table 19 reads out the prediction value / prediction coincidence rate in accordance with the above. The only difference from FIG. 2 is the above-mentioned part, and the description of the other parts will be omitted.

Next, the operation will be described using the binary image having the probability distribution shown in Table 1. First, using the reference pixels x _i-1 and x _i-2 of the reference pixel pattern 13, the pixel _-of- interest prediction unit 14 calculates the prediction level y _i 15 from the equation (6). This y _i takes a real value and is called a prediction level to distinguish it from the prediction value 20 (0 or 1). y _i = 0.52x _i-1 + 0.44x _i-2 (6)

This prediction function is designed in advance so that the mean square error between the pixel value of interest and the prediction level is minimized as shown below. When e _i is a prediction error and a _i is a prediction coefficient, the prediction error e _i is expressed by the following equation. e _i = y _i −x _i = a ₁ · x _i−1 + a ₂ · x _i −2 −x _i (7) Here, if E [e _i ² ] is the mean square of the prediction error e _i , , E [e _i ² ] can be obtained by calculating the prediction coefficients a ₁ and a ₂ that satisfy the equation (8). ∂E [e _i ² ] / ∂a ₁ = 0 ∂E [e _i ² ] / ∂a ₂ = 0 (8) Expression (8) can be written as the following expression. This is Yule-Wa
This is called the lker equation.

[0031]

[Equation 5]

The prediction coefficient of the equation (6) is obtained by solving the equation (9) for the binary image of the probability distribution shown in Table 1.

[0033]

[Table 3]

[0034]

[Table 4]

[0035]

[Table 5]

Prediction level 15 thus obtained
Becomes y _i in Table 1. Next, the prediction level classification means 16 sets the prediction level y _i to 2 with a threshold value of 0.4 as shown in Table 3.
By quantizing into levels, states with similar prediction levels are combined into one and the states are degenerated. Due to this degeneracy, the conditional entropy becomes 0.78 bit. This value is higher than the entropy H = 0.72 bit shown in Table 1 due to degeneration. However, Table 4
Alternatively, as shown in Table 5, the reference pixel is set to x _i-1 or x _i-2.
This is lower than the entropy when only one pixel has the same number of states, and the degeneracy effect of the present invention can be confirmed. That is, the predicted value 20 corresponding to each state shown in Table 3,
The predicted matching rate 21 is set to the predicted value / predicted matching rate reference table 19
It is possible to perform coding with a smaller code amount as compared with the case of Table 4 or Table 5 having the same predicted value / predictive coincidence rate reference table 19 by performing arithmetic coding.

Example 2. In the first embodiment, the linear prediction function is used as the pixel-of-interest prediction unit 14, but a hierarchical neural network shown in FIG. 4 may be used as the prediction function, for example. Each layer is called an input layer, an intermediate layer, and an output layer in order from the left of the figure, and each layer is composed of several units 43. Each unit of the input layer sends the input signal 41 to the next layer as it is, and in the intermediate layer and the output layer, each unit takes the weighted sum of the output of each unit of the previous layer and calculates the output value of each unit according to the value. To do. Then, the output of the unit in the output layer becomes the output 42 of the neural network. The input / output characteristics of the neural network are determined by the weighting coefficient when the weighted sum of the outputs of the previous layer is taken, and the weighting coefficient has a different value for each connection. This weighting factor is previously determined by a process called learning.

The operation will be described below. Since the prediction function is the same as that of the first embodiment except that a neural network is used,
Descriptions of other parts are omitted. First, the reference pixel pattern 13 is input to the neural network of FIG. 4, and the prediction level 15 of the pixel value of interest is output from the neural network.
Then, the prediction level 15 is converted to the prediction level classification means 16
The state is determined by classifying with.

The weighting coefficient of the neural network at this time is
It is determined in advance by the back propagation learning rule so as to minimize the mean square error between the pixel of interest and the output value.
This is an operation in which an input signal is applied and the weighting coefficient is modified many times so that its output approaches a desired value called an output called a teacher signal. For example,
In the case of the binary image having the probability distribution shown in Table 1, the reference pixel values (x _i-1 , x _i-2 ) in each state and the teacher signal x _{i corresponding} thereto
Are sequentially applied to the neural network, and learning is repeated until the squared error between the output value and the teacher signal converges. That is, the teacher signals in the states S ₀ , S ₁ , S ₂ , and S ₃ are 0,
It becomes 1,1,1.

[0040]

[Table 6]

Table 6 shows the outputs y _{i in} each state of the neural network constituted by the weighting factors thus determined. By inputting this into the prediction level classification means 16 shown in Table 3, it becomes possible to degenerate the Markov state as in the first embodiment.

Example 3. In the first and second embodiments, the target pixel value is used as the prediction target, but the probability that the target pixel is a black pixel (black pixel appearance probability) may be predicted. For example, in the second embodiment for the binary image in Table 1, the target pixel value x _i which is the prediction target is used as the teacher signal when learning the neural network, but instead, the black pixel appearance probability P (1 / S _i )
To use. That is, the teacher signals in the states S ₀ , S ₁ , S ₂ , and S ₃ are 0.2, 0.6, 0.6, and 0.9, respectively.
Becomes

Example 4. In the first to third embodiments, only one type of quantizer is used to classify the prediction function and the prediction level. However, a plurality of quantizers are prepared, and adaptively in the screen according to the reference pixel. You may switch.

[0044]

[Table 7]

[0045]

[Table 8]

The reference pixels are the three pixels x _i−1 , x in FIG.
_i-2 and x _i-3 . The binary image at this time is shown in Table 7.
The probability distribution shown in is taken. The conditional entropy H ′ when classified into the states S _{0 to} S ₇ according to the value that the reference pixel can take is H ′ = 0.77 bit from the equation (4). In the fourth embodiment, first, the prediction level 1 is calculated by the equation (10).
Calculate 5.

[0047]

[Equation 6]

In the case of the images shown in Table 7, the prediction level 15 in each state is y _{i in} Table 7. Next, as shown in Table 8, the prediction level 15 is quantized by different quantizers according to the value of x _i-3 . That is, when x _i-3 = 0, the threshold value 0.4
Then, when x _i−3 = 1 is set, the threshold value is 0.5 and the level is classified into two levels. The difference from the first to third embodiments is that the reference pixel x
_The prediction function and the quantizer are switched according to the value of _i-3 . As a result, the binary image in Table 7 is classified into four states in Table 8, and the conditional entropy H '= 0.80 bit.
Becomes

[0049]

[Table 9]

Table 9 shows the probability distribution and conditional entropy when the state is classified into four states according to the possible values of x _i-1 and x _i-3 . Despite being classified into the same four states as in Table 8, the entropy is higher than in Table 8, and the effect of Example 4 can be confirmed.

[0051]

According to the present invention, the conditional entropy of image data can be reduced without significantly increasing the size of the coding parameter reference table, and the code amount can be reduced.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an arithmetic code type MELCODE using the present invention.

FIG. 2 is a configuration diagram of a conventional arithmetic code type MELCODE.

FIG. 3 is a diagram showing a pixel arrangement of a target pixel and a reference pixel in a conventional example and Examples 1 to 3 of the present invention.

FIG. 4 is a diagram showing a structure of a neural network according to Examples 2 and 3 of the present invention.

FIG. 5 is a diagram showing a pixel arrangement of a target pixel and a reference pixel according to a fourth embodiment of the present invention.

[Explanation of symbols]

 14 Target Pixel Predicting Means 15 Prediction Level 16 Prediction Level Classifying Means 18 Prediction Value / Prediction Matching Rate Determining Means 19 Prediction Value / Prediction Matching Rate Reference Table 31 Target Pixels 32 Reference Pixels

Claims (4)

[Claims] 1. A prediction unit that predicts a value indicating the property of a target pixel by using reference pixels around the target pixel, and target pixels with similar prediction levels output from the prediction unit are collectively set as one Markov state. A binary image coding apparatus by Markov model coding, comprising prediction level classification means for classifying, and performing entropy coding suitable for each classification according to a prediction level classification result. 2. The binary image coding device according to claim 1, wherein the prediction target is a pixel value of interest. 3. The binary image coding apparatus according to claim 1, wherein the prediction target is a probability that the pixel of interest is a black pixel (hereinafter, black pixel appearance probability). 4. The prediction means and the prediction level classification means are provided in plural, and the prediction means and the prediction level classification means are adaptively selected on the screen according to the state of the reference pixel. The first claim, the second claim, and the third claim
Item 2. The binary image coding device according to item.