EP2997662A1 - Method for encoding, compressed images in particular, in particular by "range coder" or arithmetic compression - Google Patents

Abstract

Method for encoding a string of symbols using several models of the arithmetic or range coder type and comprising steps where: - each model is associated with a belonging criterion symbol, - the string is traversed so as to determine, for each symbol, the encoding model to which it belongs as a function of the criteria; then, - a probability of occurrence of each symbol in the corresponding model is determined; then, - the string is traversed while encoding each symbol successively; and, - a file is constructed on the basis of the code thus obtained.

Description

 METHOD FOR ENCODING, IN PARTICULAR COMPRESSED IMAGES, IN PARTICULAR "RANGE CODER" OR ARITHMETIC COMPRESSION

The present invention relates mainly to the field of entropic binary coding, more particularly coding using encoding models of the "range encoder" type, that is to say using intervals, or arithmetic.

Encoders of the range encoder or arithmetic type allow lossless encoding of a sequence of symbols. These symbols can be of any type, including alphanumeric characters or punctuation characters. In the case of compression methods of an image, the symbols are numbers resulting from the prior compression of said image, for example by differential compression or wavelet compression, generally preceded by a colorimetric transformation.

An entropic binary coding makes it possible to reduce the number of bits necessary to encode a signal, here represented by the sequence of symbols to be encoded, without loss of the content thereof. The level of reduction depends on the probability of occurrence of the symbols in the signal. In particular, the so-called "arithmetic" and "range encoder" encodings use probability models in which each symbol is associated with a probability. The theoretical number of bits needed to encode the symbol is, in the context of a "Range Coder" encoder or arithmetic encoding, --log2 (P), where P is the probability of occurrence of this symbol in the signal.

An encoder of the range encoder or arithmetic encoder type shall always have, when encoding or decoding a symbol, a probability model comprising one or more symbols and their probability of occurrence, including at least the current symbol. . The probability of the symbol is used to encode. To encode the same signal, several probability models are possible. The most suitable is the model for which the signal is the most compressed, that is, for which the code resulting from the encoding has the lowest weight.

For a binary coding to be efficient, it is necessary that:

 - The decoded data is identical to the input data;

 - The weight of the compressed data is as low as possible;

 - The encoding time is as short as possible;

 - The decoding time is as short as possible.

This depends on two main factors:

 - The coding itself, which must, for a given probability P code the symbol on a number of bits as close as possible to -log2 (P), while restoring the same symbol decoding if it provides the same model ;

 - The calculation of the models, which must make it possible to provide the most suitable model for each of the symbols, while being as fast as possible;

One can thus use a model for all the signal. This results in a compression level close to Shannon 's entropy. On the other hand, some encoders use fully adaptive models, such as the PPMd method, of "Prediction by Partial Matching, escape method D". In this case, the models are established as and when the encoding. These encoders allow to obtain multiple models, adapted for each symbol, but the processing times are much longer.

The object of the invention is to propose an encoding method which makes it possible to obtain a code whose weight is lower than that generally obtained using a single model, and whose processing times are shorter than those generally obtained with multiple models.

In the context of multimedia compression, it can be seen that after signal transformation, for example by so-called wavelet methods, the low values are generally close to one another, just as the highest values are closer to each other. each other.

According to the invention, such an entropic binary coding method for a series of symbols using at least two models, each model being associated with a membership criterion, comprising steps in which:

 said sequence is scanned to determine; for each symbol, the encoding model to which it belongs, according to said membership criteria; then,

 for each model and for each symbol, a probability of occurrence of the symbol in the model is determined; then,

said sequence is scanned again by encoding each symbol successively according to the model to which it belongs; and, ^'

- Stores the models or information to reconstruct them, and the resulting binary code.

 Advantageously, the series is scanned beforehand to determine the membership criteria for each of the models.

Preferably, the membership of a current symbol in a model is determined according to a membership function calculated from one or several symbols preceding said current symbol in the following. Since each symbol may be a number, preferably a base number, the membership function may be the average of absolute values of a given number of reference symbols, preferably four reference symbols, immediately preceding said current symbol in the following.

For the calculation of the membership function, the list is advantageously preceded by a sufficient number of arbitrary symbols, the value of each being preferably zero.

The criterion for belonging to one of the models may be a lower limit for a range covered by the model and the comparison of the average of the preceding symbols with said limit. Since the limits of each of the models are arranged in increasing order, the difference between two successive limits advantageously increases when the value of said limits increases. To determine the limit of each model one can:

 - calculate the average of the values of the symbols of the suite; then,

 calculating the value of the difference between the maximum value and the mean on the one hand and the average and the minimum value on the other hand among the symbol values of the sequence, and deducting a distance equal to the maximum of these two; then,

 calculate a deviation equal to the average of the absolute values of the differences between each element of the signal and the average of the sequence; then,

 - calculate a spacing according to the formula:

then,

- calculate the limit between the moving averages for each of the successive models according to the following formula: The invention also relates to a method for compressing a media of the image, video or sound type, characterized in that it uses an encoding method according to the invention. A method of compressing an image preferentially applies to compressed symbols of the image, each corresponding to a box of a matrix, the sequence being formed by placing said symbols on line. For putting symbols online, for each line one can go through a line in a first direction and then the next line, if necessary, in the opposite direction of the first one.

According to another object of the invention, an entropy binary decoding method for a series of symbols using at least two models and encoded using a method according to the invention is characterized in that:

 - we extract each of the models used to the encoding,

 - the criteria for belonging to each of these models are extracted or recalculated, and

 - we use the same membership criteria as the encoding to decode each symbol using the template used in the encoding.

Several embodiments of the invention will be described below, by way of non-limiting examples, with reference to the appended drawings in which:

 FIG. 1 illustrates a layer of an image to which a method according to the invention is applied;

- Figure 2 illustrates a submatrix, said LH ^3rd level, coefficients, in base 10, resulting from transformation of the image of Figure 1 wavelet, followed by quantization and a rounded ;

FIG. 3 illustrates the on-line method of the coefficients of the matrix of FIG. 2, so as to form a sequence of symbols to be processed by the method according to the invention; FIG. 4 illustrates a table giving for each model used the value of a corresponding lower limit;

 FIG. 5 is a graphical representation of the table of FIG. 4;

FIG. 6 is a table representing the set of base values corresponding to the symbols of the sequence and for each value its number of occurrences in the sequence, and hence its probability in the context of a single model;

 FIG. 7 is a graphical representation of the table of FIG. 6; and,

 FIG. 8 is a table representing, for each value, its number of occurrences in each of the models.

To illustrate an exemplary method according to the invention, an original image is used whose pixels are arranged in 320 columns and 240 lines and coded with three components R (red), G (green) and B (blue). This image then underwent a colorimetric transformation of the type Y, Cb, Cr. FIG. 1 illustrates, in the form of an image, the luminance Y component resulting from this colorimetric transformation.

A wavelet transform CDF 5/3 in two dimensions using fixed-point numbers is first applied to the image 1. Figure 2 illustrates a LHQ matrix corresponding to a said subarray LH ^3rd level resulting from this wavelet transformation, which was then quantized by a coefficient of 3.53, then rounded to the nearest integer. This wavelet transformation is performed for each level in two dimensions: a vertical pass, then a horizontal pass. The vertical wavelet transformation generates a so-called matrix of details, or matrix H, and a matrix called approximation, or matrix L. The application of a horizontal wavelet pass to the matrix L generates a matrix of details LH and an approximation matrix LL. The application of a vertical wavelet transition to matrix H generates two matrices of details HL and HH. Recursively, new wavelet levels are then applied to the successive LL approximation matrices. Thus, the third level is the LH LH matrix type matrix obtained at the ^3rd level wavelet. Once the LH matrix is obtained, it is. quantifies by a factor of 3.53 and then rounds its values to obtain the LHQ matrix.

The LHQ matrix has 40 columns and 30 rows, ie 1200 values each corresponding to a symbol to be encoded. In order to apply the treatment according to the invention, the 1200 values are put in line, that is to say that a sequence S of the 1200 values is constituted. In the illustrated example, the setting in line is as illustrated in FIG. 3, the first line of the matrix LHQ being traversed from left to right, then the second from right to left, so that in the following S the last value of the first row of the LHQ matrix precedes the last value of the second row. More generally, a line being traveled in one direction, the next line is traveled in the opposite direction. Thus, a signal formed by the sequence of N symbols Sn, n integer ranging from 1 to N, is obtained with N = 1200, each Sn symbol having a value denoted V (n).

In the example illustrated, in order to determine the models to be applied to the signal S, an analysis of this signal is first carried out.

An arithmetic mean M of all the values of the signal is first calculated according to the formula:

 The minimum value Min [V (n)] and the maximum value Max [V (n)] are then determined; in the illustrated example,

 Min [V (n)] = -42

Max [V (n)] = 35 A distance D is deduced, where D is equal to a maximum of the value of the difference between the mean M and minimum value of the signal Min [V (n)] on the one hand and the value of the difference between the maximum value the signal Max [V (n)] and the average M on the other hand; in the illustrated example,

Then a DV deviation, ie an average dispersion, of the values around the mean M is calculated. This dispersion is calculated as the average of the absolute values of the differences between the values V (n) of each symbol Sn of signal and the average M; in the illustrated example,

An E spacing between the models is then calculated. In the example shown, this spacing is calculated according to the formula:

 Advantageously, the larger the signal to be coded, the greater the number of models. This is an input parameter that can depend on the amount of information in the signal. In the illustrated example, we chose to use 5 models.

For each model numbered from 0 to 4, we define a lower bound from which the symbol can belong to this model. Preferably, the more the model will concern small variations, the more the thresholds will be close to each other. We thus define the following formula to calculate, within the framework of the example, the lower limits of each model:

Where m is the number of a model among the 5, m taking integer values 0 to 4. The lower values thus calculated are listed in the table Tabl, shown in FIG. 4 and illustrated in the graph of FIG.

In order to associate each Sn symbol with a model, it is necessary to define a ^" membership criterion that can be compared with the previously calculated limits Γ (ϊη)." In addition, this criterion must be identical to the encoding and decoding. , so that the same model is applied to the same symbol, so that the value returned from this symbol during the decoding is the same as its initial value.For this purpose, the membership criterion is chosen as a function of symbol values. preceding the current symbol, that is to say, to encode or decode, the encoding and the decoding being carried out without loss, the values preceding the current symbol will be identical to the compression and the decompression. the same criterion of belonging to these same values at the time of encoding and decoding will affect the same model to the current symbol.

In the example shown, the values after wavelet are assumed centered or almost centered on zero; in fact, the average M is substantially equal to zero. As a result, the function determining the membership criterion chosen is an average of the absolute values of the four symbols immediately preceding the current symbol, rounded to four decimal places. The number of preceding symbols used may be different, but sufficient to limit the influence of a too deviant value of the others, which would generate an untimely change of model, and advantageously a power of 2, to facilitate its binary notation. The number of decimals may also be different from 4, but advantageously a power of 2, to facilitate its binary notation.

The criterion of belonging to a model, in the example illustrated, is thus determined by the formula:

 Where, the size of the moving average T being equal to 4, that is to say the number of preceding symbols taken into account for its calculation, n 'varying from 1 to 4.

This makes it possible to select a suitable model for each symbol Sn. The moving average mm (n) is calculated with a precision given in parameter, here four decimal places, which is identical to the encoding and the decoding.

Each symbol Sn of value V (n) belongs to the largest model m whose lower limit l (m) is less than or equal to the moving average of the previous absolute values mm (n): l (m) <mm (n).

The table Tab2, illustrated in FIG. 6, presents the number of occurrences of each value V (n) in the signal S. FIG. 7 is the graphical representation. Note that the null value is over-represented. The use of a single model would therefore be particularly inappropriate.

The table Tab3, illustrated in FIG. 8, presents the number of occurrences of each value V (n) in each model M.

At the end of the selection of a model m for each symbol Sn, an encoder of the "range encoder" or arithmetic type is applied to the values of this model. For that we calculate first the number of occurrences of each symbol Sn in this model m and we deduce a probability of appearance of this symbol in this model m.

For encoding, the signal is scanned in the direction of increasing indices n, as defined above with reference to FIG. 3. For each symbol, the model to which it belongs is determined according to the membership criterion defined above. This model is then used in the chosen encoder by example an encoder type "range encoder" or arithmetic. For each model it is also possible to choose an encoder of a type different from that chosen for another model. -

The first symbols to be encoded being preceded by a number of symbols insufficient to calculate the membership criterion, the signal is preceded by a number of arbitrary values sufficient for this calculation. Thus, in the example illustrated, the signal is preceded by four values, arbitrarily chosen as zero; these values make it possible to calculate the membership criterion of the first four symbols S1-S4 to be encoded.

Advantageously, a file F containing the binary code C obtained by the encoding of the signal S is created. To enable the decoding of the binary code C, all the information necessary for decoding, in particular in the header of the file, is provided in a file header. the illustrated example:

 - the number of models;

 - the average M;

 - the DV deviation

 the number of elements preceding to be used for the calculation of the moving average mm, in the form of a power of two; and,

 - The precision to be used for the calculation of the moving average, in the form of a power of two.

For the decoding, one recovers the limits of the models, by simple reading or recalculation, then one determines the membership of a symbol Sn to decode to a model in the same way as for the encoding, from the symbols previously decoded without loss, then we use the model found to decode the symbol. In the same way as in encoding, the first symbols to be decoded being preceded by a number of symbols insufficient to calculate the membership criterion, the code corresponding to the encoded S signal is preceded by a number of characters. arbitrary values sufficient for this calculation. These values are identical to those used for encoding. Thus, in the illustrated example, the code is preceded by four values, arbitrarily chosen as zero; these values make it possible to calculate the membership criterion of the first four symbols SI -S4 to be decoded.

Theoretical weight values are calculated with the following assumptions:

• We neglect the weight of models and other header information needed to decode the signal; and

• The binary coder used is a perfect encoder encoding each symbol Sn according to its probability P (Sn) on -log ₂ (P (Sn)) bits, P (Sn) being its probability according to the model provided.

The following notations are used for the theoretical calculation:

 • P (Sn): probability of the symbols, equal to the number of occurrences of this symbol divided by the number of symbols for this model;

• ^' N (Sn) number of occurrences of the Sn symbol

Thus, each symbol encountered will weigh in. -log ₂ (P (Sn)), the set of symbols s in the context of a given model will therefore weigh:

N (Sn) x log ₂ (P (Sn)).

In the case in point, the symbols are between -42 and 35, the theoretical weight of all the symbols in the context of the single model illustrated by the table Tab2 is: With the values above, we obtain a weight of P _{single model} = 1941 bits.

In the framework of the separation into 5 models, we use the same formula, by calculating the probability with respect to the number of symbols of the current model. We then obtain:

 • Model 0: 300 bits;

 • Model 2: 92 bits;

 • Model 3: 505 bits;

 • Model 4: 588 bits;

 • Model 5: 34 bits:

The total weight is therefore the sum of the weights of the symbols coded with each of these models, namely:

P _{5 models} = 300 + 92 + 505 +588 +34 = 1519 bits.

According to these calculation assumptions, we have gained 422 bits compared to the single model. The predictable gain is even greater than the number of symbols to be encoded is greater. In addition, the more different symbols in a signal, the more it may be advantageous to increase the number of models used.

Of course, the invention is not limited to the examples which have just been described.

Claims

claims

An entropy binary coding method for a sequence (S) of symbols (Sn) using at least two models (m), each model being associated with a membership criterion, comprising steps in which:

 said sequence is scanned to determine, for each symbol, the encoding model (m) to which it belongs, according to said membership criteria; then,

 for each model and for each symbol, a probability of occurrence (P) of the symbol in the model is determined; then,

 said sequence is scanned again by encoding each symbol successively according to the model to which it belongs; and,

 - Stores the models or information to reconstruct them, and the resulting binary code.

2. Encoding method according to claim 1, characterized in that the series is scanned beforehand to determine the membership criteria for each of the models.

3. Encoding method according to one of claims 1 or 2, characterized in that the membership of a current symbol (Sn) to a model is determined according to a membership function mm (n) computed from one or more symbols (S _n-4 - S _n-1 ) preceding said current symbol in the following.

4. Encoding method according to one of claims 1 to 3, characterized in that each symbol is a number, preferably a base number 10.

5. Encoding method according to claims 2 and 3, characterized in that the membership function is the average (mm) of absolute values a given number of reference symbols, preferably four reference symbols (S _n-4 - S _n-1 ), immediately preceding said current symbol in the following.

6. Encoding method according to claim 4, characterized in that for calculating the membership function is preceded by the list of a sufficient number of arbitrary symbols, the value of each being preferably zero.

7. A method according to claim 5 or 6, characterized in that the criterion of belonging of a current symbol to one of the models is a lower limit l (m) of the interval covered by the model and the comparison of the average (mm) absolute values of symbols preceding said current symbol.

8. The method of claim 7, characterized in that the limits of each of the models being arranged in an increasing order, the difference between two successive limits increases when the value of said limits increases.

9. Encoding method according to claim 7 or 8, characterized in that for determining the limit l (m):

 the average value of the symbols of the sequence is calculated; then,

the difference between the maximum value and the average is calculated on the one hand and the mean and the minimum value on the other hand among the symbol values of the sequence, and a distance (D) equal to the maximum of these values is deduced therefrom; two; then,

 a deviation (DV) equal to the average of the absolute values of the differences between each element of the signal and the average of the sequence is calculated; then,

a spacing (E) is calculated according to the formula:

 then,

- The limit l (m) between the moving averages for each successive model (m) is calculated according to the following formula:

10. A method of compressing a media of the image, video or sound type, characterized in that it uses an encoding method according to one of claims 4 to 9.

11. A method of compressing an image according to claim 10, characterized in that it applies to compressed symbols of said image, each corresponding to a box of a matrix, the rest being formed by the setting on line said symbols.

12. A method of compression according to claim 1 1, characterized in that for putting online My symbols, for each line we walk the line in a first direction and then the next line, if necessary, in the opposite direction from the first.

An entropy binary decoding method for a symbol sequence using at least two models and encoded by a method according to one of the preceding claims, characterized in that:

 - we extract each of the models used to the encoding,

 - the criteria for belonging to each of these models are extracted or recalculated, and

 - we use the same membership criteria as the encoding to decode each symbol using the template used in the encoding.