JP2012060210A - Method, apparatus and program for adaptive quantization - Google Patents

Abstract

PROBLEM TO BE SOLVED: To achieve adaptive quantization minimizing an approximation error under the constraint of a given coding amount, without depending on an input signal distribution.SOLUTION: When approximating a histogram of input signals with the number of classes given separately, an RD cost calculator 17 stores into a memory a quantization value to minimize a weighted sum of the approximation error and the coding amount relative to the entire candidates of a class boundary, and a minimum value of the weighted sum. When selecting the class boundary for the next class, the RD cost calculator 17 reads out the stored minimum value from the memory, so as to use for the calculation of the minimum value of the weighted sum in the class boundary selection at the time point concerned. A section top end optimum value tracer 20 selects the class boundary minimizing the weighted sum of the approximation error and the coding amount to the entire class boundary candidates from the calculated result by the RD cost calculator 17.

Description

  The present invention relates to a high-efficiency image signal encoding technique, and more particularly to an adaptive quantization technique for improving encoding efficiency.

  In lossy coding, quantization is an indispensable component. In a general encoding method, quantization controls the accuracy of expression of encoded data, and encoding distortion occurs in this control process. The design of the basic quantizer is reduced to a minimization problem for obtaining a codeword (quantization index) for minimizing the evaluation measure for a given distortion amount evaluation measure. The sum of squares or the sum of absolute values is used as a measure for evaluating the amount of distortion.

  In general quantizer design, a constraint on the amount of code is imposed. In this case, the design of the quantizer calculates the codeword (quantization index) for minimizing the evaluation measure for a given evaluation measure of distortion amount under certain constraints on the code amount. This results in a constrained minimization problem. If the probability density function of the signal to be encoded can be expressed parametrically, there may be a case where an analytical optimization method can be obtained. For example, this is the case when the probability density function follows a uniform distribution, Gaussian distribution, or Laplace distribution. However, in general, such parametric expression does not hold for data to be encoded.

  Therefore, an optimization technique (operational optimization) based on discrete numerical computation on a computer is used. A representative method is the Lloyd-Max quantization method (see Non-Patent Document 1). This is a process of repeating the calculation of the quantized representative value and the calculation of the quantized bin boundary up to a certain convergence condition.

S. P. Lloyd, “Least Squares Quantization in PCM”, IEEE Trans. On Information Theory, Vol. IT-28, No.2, pp.129-136, Mar. 1982

  However, it has been pointed out that the Lloyd-Max quantization method is not necessarily guaranteed to obtain an optimal solution. This is due to the fact that the Lloyd-Max quantization method is a method designed in consideration of only the necessary conditions for optimal quantization. For this reason, there is a possibility of falling into a local solution depending on the initial data used in the iterative processing.

  The present invention has been made in view of such circumstances, and an object of the present invention is to establish a quantization method for minimizing an approximation error caused by quantization when a certain constraint on the amount of code is imposed. .

  In order to solve the above-described problem, the adaptive quantization method of the present invention separates all of the class boundary candidates when approximating the histogram with a given number of classes separately from the histogram of the input signal. The quantized value that minimizes the weighted sum of the approximation error and the code amount, and the minimum value of the weighted sum at that time are stored in the memory, and when the class boundary in the next class is selected, the stored minimum value Is used to calculate the weighted sum in the class boundary selection at that time, thereby selecting a class boundary that minimizes the weighted sum for all candidate class boundaries. This is characterized in that a quantized representative value and a class boundary (quantized boundary) that minimize an approximation error caused by quantization are obtained under a certain constraint on the code amount.

  As described above, it is possible to minimize the approximation error caused by the quantization when a certain constraint on the code amount is imposed.

  Also, the adaptive quantization method of the present invention weights all candidate class boundaries based on visual sensitivity when approximating the histogram with a given number of classes separately from the histogram of the input signal. The quantization value that minimizes the weighted sum of the approximated error (visual approximation error) and the code amount, and the minimum value of the weighted sum at that time are stored in memory, and the class boundary in the next class is selected In this case, the class boundary that minimizes the weighted sum is selected for all the class boundary candidates by calling the stored minimum value from the memory and using it for the calculation of the weighted sum in the class boundary selection at that time. This is characterized in that a quantized representative value and a class boundary (quantized boundary) that minimize a visual approximation error caused by quantization are obtained under a certain constraint on the code amount.

  As described above, the visual approximation error generated by the quantization can be minimized when a certain constraint on the code amount is imposed.

  In addition, the adaptive quantization method of the present invention separately provides a class number candidate when each of the class number candidate values is approximated to the histogram of the input signal in a state where the class number candidates are given. Using an approximation error and a weighting factor for the amount of information set appropriately, the quantized representative value / class boundary is obtained by the above-described method, and the approximate error when the quantized representative value / class boundary is used is calculated. It is characterized in that the minimum value is obtained from the approximation error when each candidate value of the number of classes is used, and the quantized representative value / class boundary that realizes the minimum value and the number of classes at that time are identified.

  As described above, when a certain constraint on the amount of code is imposed, it is possible to select the optimum number of classes and minimize the approximation error generated by quantization.

  Further, in the optimization of the number of classes M, the number of classes M to be optimized is determined from the upper limit value and the lower limit value of the generated code amount when the number of classes is M and the weighting coefficient of the approximation error and the code amount is changed. By calculating the upper limit value and the lower limit value and limiting the range between the upper limit value and the lower limit value of the number of classes M, and obtaining the quantized representative value and class boundary for the candidate number of classes, the amount of computation Can be reduced.

  Further, in the process of obtaining the quantization representative value and the class boundary for each candidate value of the class number, the result of obtaining the quantization representative value and the class boundary is stored as the class number M−1, and the quantization representative of the class number M is stored. By using the value and the class boundary for the processing, the calculation amount can be reduced by omitting the overlapping calculation between the class number M-1 and the class number M.

  According to the present invention, it is possible to minimize the approximation error under a given code amount constraint without depending on the distribution of the input signal, and in the lossy coding with quantization, the coding efficiency can be reduced. Can be improved. In addition, since it is possible to minimize a conversion error that occurs when tone conversion of an image signal is performed, it is possible to improve encoding efficiency in an image encoder using bit depth conversion.

It is a figure which shows the apparatus structural example which concerns on one Embodiment of this invention. It is a flowchart of the adaptive quantization process which concerns on one Embodiment of this invention. It is a flowchart of the adaptive quantization process which concerns on one Embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[Configuration example of adaptive quantizer]
FIG. 1 is a diagram illustrating an apparatus configuration example according to an embodiment of the present invention.

  The adaptive quantization apparatus 10 is an apparatus that inputs an input signal of K levels (also referred to as class numbers), adaptively quantizes the number of levels M (M <K), and outputs a quantization result value. . The adaptive quantization apparatus 10 includes an input signal level number storage unit 11 that stores the level number K of the input signal, a post-quantization level number storage unit 12 that stores a level number M after quantization, and a given undetermined multiplier λ. An undetermined multiplier storage unit 13 is provided.

  The histogram generator 14 stores the frequency of the pixel value k in the input signal as h [k] (k = 0,..., K−1). The approximation error calculator 15 approximates the histogram with the number of levels M (number of classes) stored in the quantized level number storage unit 12 with respect to the histogram h [k] of the input signal. An entire section [0, K] is divided into M sections, and an approximation error when each section is approximated by a centroid (representative value) is calculated for each section candidate with the section width changed. Further, the information amount calculation unit 16 divides the entire section [0, K] of the histogram into M sections, and the information amount (code amount) of the quantization result when each section is approximated by the center of gravity (representative value). Is calculated.

  The RD cost calculation unit 17 calculates an approximation error from the approximation error calculated by the approximation error calculation unit 15, the code amount calculated by the information amount calculation unit 16, and the undetermined multiplier λ stored in the undetermined multiplier storage unit 13. A weighted sum (RD cost) with the code amount is calculated, and a candidate having a minimum RD cost among the candidates from the first section to the i-th section is stored in the RD cost minimum value storage unit 18. To do. At this time, in the calculation of the minimum value of the RD cost of the i-th section, the minimum value of the RD cost of the i-1th section is used. Further, the RD cost calculation unit 17 stores the value of the upper end (class boundary) of the section in which the RD cost is minimum in the section upper end optimum value storage unit 19.

  The section upper end optimum value tracking unit 20 selects a class boundary that minimizes the RD cost for all class boundary candidates from the upper end value of the section stored in the section upper end optimum value storage unit 19. The quantization processing unit 21 quantizes the input signal with the quantization level number M based on the class boundary selected by the section upper end optimum value tracking unit 20 and outputs a quantization value of the quantization result.

[Flow of adaptive quantization processing (basic processing)]
2 and 3 are flowcharts of adaptive quantization processing according to an embodiment of the present invention.

  First, the adaptive quantization apparatus 10 inputs the class number M after quantization, stores it in the quantized level number storage unit 12, and stores the undetermined multiplier λ in the undetermined multiplier storage unit 13. The histogram generation unit 14 calculates a histogram h [k] (k = 0,..., K−1) of the input signal according to the class number K stored in the input signal level number storage unit 11 (step S10). The RD cost calculation unit 17 initializes the minimum value of the weighted sum (RD cost) of the approximation error and the code amount in the RD cost minimum value storage unit 18 to 0 (step S11).

Thereafter, with respect to the level m after quantization, while the value of m is increased by 1 from m = 1 to m = M−1, the approximation error calculation unit 15, the information amount calculation unit 16, and the RD cost calculation unit 17 perform steps. The processing up to S24 is repeated (step S12). In the loop of this process, further to each candidate of the upper end L _m of the section representing the quantization level m, from L _m = m L _m = K-up (M-m), while increasing the L _m by one, The processing up to step S23 is repeated (step S13). Note that L ₀ is initialized to ₀ in advance.

Also, further for each candidate interval length delta _m sections representing the quantization level m, the _{Δ m = 1 Δ m = L} m - to (m-1), while increasing the delta _m by 1, step S20 The processes up to are repeated (step S14).

The approximation error calculation unit 15 calculates a representative value of the histogram section [L _m − (Δ _m −1), L _m ] (step S15), and calculates an approximation error when the histogram section is approximated by the representative value. Calculate (step S16). On the other hand, the information amount calculation unit 16 calculates the amount of code generated when the section of the histogram is approximated with a representative value (step S17).

The RD cost calculation unit 17 calculates the interval of the histogram from the approximation error calculated by the approximation error calculation unit 15, the code amount calculated by the information amount calculation unit 16, and the undetermined multiplier stored in the undetermined multiplier storage unit 13. A weighted sum (RD cost) of an approximation error and a code amount when L _m − (Δ _m −1), L _m ] is approximated by a representative value is calculated (step S18). Subsequently, the RD cost calculation unit 17 determines the minimum value of the RD cost stored in the RD cost minimum value storage unit 18 calculated up to the previous section, and the RD cost of the current section calculated in step S18. Is calculated and stored (step S19). Returning now to step 14, until after the processing of the last of the candidate interval length delta _m, it repeats the processing of steps S14～S20.

Once processed for all the candidate interval length delta _m, in the candidate interval length delta _m, stores a value RD cost to the current interval is minimum RD cost minimum value storage section 18 (step S21) . Further, section information for minimizing the RD cost with respect to the upper end L _m of the section (section width Δ _m , upper end L _m of the section, etc.) is stored in the section upper end optimum value storage unit 19 (step S22).

The above processing is performed for all candidates at the upper end L _m (step S23), and is repeated for all levels m (up to m = M−1) (step S24). When the above processing is completed, the section upper end optimum value tracking unit 20 selects section information (class boundary) that minimizes the overall approximation error from the section upper end optimum value storage unit 19, and selects the selected class boundary information. Is output to the quantization processing unit 21 (step S25).

  The quantization processing unit 21 quantizes the input signal according to the class boundary output by the section upper end optimum value tracking unit 20, thereby obtaining a quantized value that minimizes the weighted sum of the approximation error (conversion error) and the code amount. Can be output.

  In the above processing, an embodiment that minimizes the weighted distortion amount considering the visual sensitivity characteristic is also suitable. When minimizing the weighted distortion amount in consideration of the visual sensitivity characteristics, the approximation error weighted based on the visual sensitivity is calculated in the calculation of the approximation error in step S16. For example, for the pixel value k (k = 0,..., K−1), a weighting factor w [k] based on the visual characteristic for the luminance difference is set, and the weighting factor w is set to the frequency h [k] for the pixel value k. An approximation error (visual approximation error) is calculated using a value obtained by multiplying [k].

Further, in the case of applying a quasi-optimization method that limits the scope of the section width delta _m at step S14, in the case of changing the respective delta _m, within a range of a preset maximum value A, i.e., 1 It is also possible to implement the present invention by calculating the minimum value of the approximation error for each Δ _m within the range of ≦ Δ _m ≦ A.

  In the example of FIG. 1, the number of quantization levels (number of classes) M is determined in advance, but adaptive quantization according to the present invention can also be performed with the number of classes variable. In this case, for each candidate value of the class number given separately, the quantization representative value and the weighting coefficient of the appropriately set approximation error and the information amount are processed by the processing described in FIGS. Find the class boundary, calculate the approximation error when using the quantized representative value and the class boundary, determine the minimum value from the approximation error when using each candidate number of classes, and realize the minimum value Quantization representative value / class boundary to be identified and the number of classes at that time are identified.

  The embodiment of the present invention will be described in more detail.

[Basic solution]
The frequency of the pixel value k is stored as h [k] (k = 0,..., K−1). For example, in the case of an 8-bit luminance signal, the possible range of k is a value from 0 to 255. Consider a case where the signal of K gradation is quantized to M gradation (M <K).

The following two types (Δ _m and L _m ) are introduced as parameters expressing histogram quantization. Δ _m represents the section width of the m-th section of the histogram. Further, L _m is the upper end of the m-th section in the histogram, and is defined by the following equation.

In addition, since each gradation after quantization needs to include at least one gradation before quantization, L _m (0 ≦ m ≦ M−2) is limited to the following range.

m ≦ L _m ≦ K− (M−m)
Hereinafter, the section [L _m − (Δ _m −1), L _m ] of the histogram is referred to as the m-th quantization bin.

In quantization, it is necessary to consider two types of distortion and code. First, as an amount of distortion, as an approximation error when a histogram section [L _m − (Δ _m −1), L _m ] is approximated by a representative value c (L _m − (Δ _m −1), L _m ). , E (L _m − (Δ _m −1), L _m ) expressed by the following equation is used.

c (L _m − (Δ _m −1), L _m ) represents the position of the center of gravity in the histogram section [L _m − (Δ _m −1), L _m ], and is determined by the following equation.

Next, as a code amount, a representative value when the histogram section [L _m − (Δ _m −1), L _m ] is approximated by a representative value c (L _m − (Δ _m −1), L _m ). As the amount of information necessary to express, l (L _m − (Δ _m −1), L _m ) expressed by the following equation is used.

Here, p (L _m , Δ _m ) is the ratio of the frequency in the histogram interval [L _m − (Δ _m −1), L _m ] to the total frequency, and is defined by the following equation.

What is required here is to minimize the amount of distortion under the condition that the amount of code for quantization is below a certain threshold. In other words, the parameters to be obtained (Δ ₀ , ..., Δ _M-1 ) are

  Under the condition that satisfies the above equation, the following equation is minimized.

  Such a constrained minimization problem can be transformed into a constrained minimization problem by introducing an undetermined multiplier λ by Lagrange's undetermined multiplier method. That is, the parameters to be obtained are M parameters that satisfy the following expression.

Here, ψ (L _m − (Δ _m −1), L _m , λ) is an evaluation scale (referred to as RD cost) defined by the following equation.

ψ (L _m − (Δ _m −1), L _m , λ)
_{= E (L m - (Δ} m -1), L m) + λ · l (L m - (Δ m -1), L m) (8)
M number of parameters _{(Δ 0, ..., Δ M} -1) possible combinations of, for increases exponentially with M, optimal combination from among the ^{_{(Δ 0 *, ..., Δ}} M-1 *) It is difficult to search for brute force in terms of computational complexity.

Therefore, paying attention to the RD cost ψ (L _m − (Δ _m −1), L _m , λ) of the m-th quantization bin depends on the upper end L _m of the bin and the section width Δ _m of the bin, The optimal solution is calculated as follows. First, the sum of the RD costs when the histogram section [0, L _m ] is divided into m + 1, Σ _{i = 0} ^m ψ (L _i − (Δ _i −1), L _i , λ)
Is defined as S _m (L _m ). That is, the optimum delta _m, ..., sigma in the case of using the Δ _{0 i = 0} ^m ψ - is the minimum value for the _{(L i (Δ i -1)} , L i, λ).

Here, paying attention to that ψ (L _m − (Δ _m −1), L _m , λ) depends on the upper end L _m of the m-th quantization bin and the section width Δ _m of the bin, S _m (L _m ) is expressed as follows using S _m−1 (L _m −Δ _m ).

Note that m = 0,..., M-1. Further, L _m = m,..., K− (M−m).

Consider possible range of delta _m. Since L _m−1 = L _m −Δ _m , the range of L _m −Δ _m is m−1 ≦ L _m −Δ _m ≦ K− (M−m + 1). For this reason, the range of Δ _m is expressed as follows using the given L _m .

L _m −K + (M−m + 1) ≦ Δ _m ≦ L _m −m + 1 (10)
Further, considering that Δ _m ≧ 1, the following equation is obtained.

1 ≦ Δ _m ≦ L _m −m + 1 (11)
As in the following equation, the maximum value of delta _m by limiting the A, can also take approach to reduce the amount of calculation. However, in this case, the optimality of the solution is not guaranteed.

1 ≦ Δ _m ≦ A (12)
Here, the calculated S _m (L _m ) is stored and used in the calculation of S _{m + 1} (L _{m + 1} ). Furthermore, L _m-1 giving the minimum value of the equation (9) is set as ^ L _m-1 (L _m ) (where ^ is a symbol on L. The same applies to others). This ^ L _m-1 (L _m ) (m ≦ L _m ≦ K− (M−m)) is all stored.

S _m−1 (L _m−1 ) (L _m−1 = m−1,..., K−M + m−1) can be calculated using the same recurrence formula, and the calculated value is S _m Used to calculate (L _m ). By using the recurrence formula (9), the calculation of S _m (L _m ) is reduced to an optimal parameter selection problem from Δ _m = 1,..., L _m −m + 1. Let Δ _m (L _m ) be the value of Δ _m that minimizes the right side of equation (9), and for each L _m (= m,..., K−M + m), L _m−1 (L _m ) = L _m − ^ Δ _m (L _m ) is stored in the memory.

  The minimization problem in Eq. (6) is expressed as

Using L _M-1 = K-1 in Equation (9) and Equation (1), the minimization problem in Equation (6) is (K−M) × (1 + K−M) × (M−1) / This results in an optimization problem for obtaining an optimal solution (Δ ₀ ^* ,..., Δ _M-1 ^* ) from the two candidates. In this way, the method according to the present method makes it possible to find the optimal solution in polynomial time. S _M−2 (L _M−1 −Δ _M−1 ) + ψ (L _M−1 − (Δ _M−1 −1), L _M−1 , λ) of the equation (13)
After obtaining the minimum value of, the optimal solution (Δ ₀ ^* , ..., Δ _M-1 ^* ) can be obtained through the backtracking process. As shown in the following equation, _let the solution of the minimization problem of Equation (13) be Δ _M-1 ^* .

Using this Δ _M-1 ^* , the optimum value of the upper end of the M-2th bin is
L _M−2 ^* = L _M−1 −Δ _M−1 ^* = K−1−Δ _M−1 ^*
It is obtained. Optimal value of the upper end of the M-3 bins, as the optimal solution for ^{_{L M-2 *, ^ L}} M-3 so (L _M-2 ^*) are stored as, with reference to the appropriate value, L _{M -3} ^* = ^ L _M-3 (L _M-2 ^* ). As a result, the section width of the (M−2) -th bin is obtained as Δ _M−2 ^* = L _M−2 ^* −L _M−3 ^* . Hereinafter, the same reference processing is performed as follows: L _M-4 ^* = ^ L _M-4 (L _M-3 ^* ),..., L ₁ ^* = ^ L ₁ (L ₂ ^* )
And using the obtained top value for each bin,
Δ _M-3 ^* = L _M-3 ^* −L _M-4 ^* ,..., Δ ₁ ^* = L ₁ ^* −L ₀ ^* , Δ ₀ ^* = L ₀ ^* + 1
Asking.

[Adaptive quantization algorithm (basic form)]
The basic processing procedure of the above adaptive quantization is as follows.
1. A histogram (number of classes K) of the input signal is generated.
2. Read the number of classes M after quantization.
3. S ₀ (i) ← 0 (i = 0,..., KM).
4). for m = 0,..., M-1 (loop of processing 4 to 12)
5. for L _M = m,..., K− (M−m) (loop of processing 5 to 12)
6). However, when m = M−1, it is limited to L _m = K−1 for Δ _m = 1,..., L _m − (m−1) (loop of processing 7 to 10)
8). However, when m = 0, it is limited to Δ _m = L _m +1. The RD cost is obtained when the histogram section [L _m − (Δ _m −1), L _m ] is approximated by a representative value. The RD cost is obtained by Expression (8), and the RD cost is stored in ψ (L _m − (Δ _m −1), L _m , λ).
10. _{S m-1 (L m -Δ} m) + ψ (L m - (Δ m -1), L m, λ) to calculate the value of.
11. S _m−1 (L _m −Δ _m ) + ψ (L _m − (Δ _m −1), L _m , λ) (Δ _m = 1,..., L _m − (m−1)) Store the value in S _m (L _m ).
12 Δ that minimizes S _m−1 (L _m −Δ _m ) + ψ (L _m − (Δ _m −1), L _m , λ) (Δ _m = 1,..., L _m − (m−1)) _{Using m} , L _m −Δ _m is stored in ^ L _m−1 (L _m ).
13. L _M-1 ^* ← K-1
14 form = M−1,..., 1 (loop of processes 14 to 16)
15. ^ L _m-1 (L _m ^* ) is read and L _m-1 ^* ← ^ L _m-1 (L _m ^* ) is set.
16. Δ _m ^* ← L _m ^* -L _m-1 ^*
17. Δ ₀ ^* ← L ₀ ^* +1
As described above, the section width Δ _m ^* (m = 0,..., M−1) is determined, and the class boundary (quantization boundary) is determined.

[How to set the undetermined multiplier]
A method for setting the undetermined multiplier λ will be described. Two undetermined multipliers λ _l and λ _u are prepared. This undetermined multiplier is set so as to satisfy the following conditions. When the number of quantization bins is M and undetermined multipliers λ _u and λ _l are given, the information sums of parameters generated by the above-described adaptive quantization algorithm are respectively R (Δ _M ^* (λ _u ), λ _{If u} ) and R (Δ _M ^* (λ _l ), λ _l ), the following equation is satisfied.

R (Δ _M ^* (λ _u ), λ _u ) ≦ R ₀ ≦ R (Δ _M ^* (λ _l ), λ _l )
As an undetermined multiplier,
λ = (λ _l + λ _u ) / 2 (15)
And the above [adaptive quantization algorithm (basic form)] is executed using the undetermined multiplier. Therefore, an information amount sum R (Δ _M ^* (λ), λ) of the generated parameters is obtained.

Based on the obtained value of R (Δ _M ^* (λ), λ), the following processing is performed.
(I) When R ₀ −ε ≦ R (Δ _M ^* (λ), λ) ≦ R ₀ :
Set λ as an undetermined multiplier. ε is a sufficiently small positive number. I would like to evaluate R (Δ _M ^* (λ), λ) = R ₀ , but in the case of real values, it is difficult to evaluate an equation from the viewpoint of calculation accuracy, so the evaluation of inequality used here is used.
(Ii) When R (Δ _M ^* (λ), λ)> R ₀ :
Set λ _l ← λ, and repeat the processing from equation (15).

(iii) When R (Δ _M ^* (λ), λ) <R ₀ −ε:
Set λ _u ← λ, and repeat the processing from equation (15).

[Undecided multiplier setting algorithm]
The above algorithm for setting the undetermined multiplier is summarized as follows.
1. The quantization bin number M is read.
2. The upper limit R _{0 of the} information amount is read.
3. The undetermined multipliers λ _l and λ _u satisfying the following expressions are prepared.

R (Δ _M ^* (λ _u ), λ _u ) ≦ R ₀ ≦ R (Δ _M ^* (λ _l ), λ _l )
4). As an undetermined multiplier, λ = (λ ₁ + λ _u ) / 2 is set.
5. [Adaptive quantization algorithm (basic form)] is executed using the undetermined multiplier λ.
6). An information amount sum R (Δ _M ^* (λ), λ) of the parameters generated in the previous process 5 is obtained.
7). If R ₀ −ε ≦ R (Δ _M ^* (λ), λ) ≦ R ₀ :
Set λ as an undetermined multiplier.
8). If R (Δ _M ^* (λ), λ)> R ₀ :
Return to process 4 as λ _l ← λ.
9. If R (Δ _M ^* (λ), λ) <R ₀ −ε:
Return to process 4 as λ _u ← λ.

[Method for setting the number of quantized bins (basic solution)]
In the example of the adaptive quantization, the quantization bin number M is described as being given from the outside. Next, a method for setting the quantization bin number M when the quantization bin number is variable will be described. The value that the number of quantized bins M can take is B _l ≦ M ≦ B _u, and each of the quantized bin numbers M (B _l ≦ M ≦ B _u ) is optimized based on the above-mentioned [undefined multiplier setting algorithm]. Find the undecided multiplier. An undetermined multiplier obtained when the number of quantized bins is M is assumed to be λ _M ^* .

M = B _l, ..., with respect to B _u, the approximation error sum D in the case of using an undetermined multiplier ^{_{λ M * (Δ Bl * (}} λ Bl *), λ Bl *), ..., D (Δ Bu * ( λ _Bu ^* ) and λ _Bu ^* ) are obtained, and the number of quantization bins that minimizes the approximate error sum is determined as the optimum number of quantization bins. That is, M ^* satisfying the following equation is obtained.

^{_{D (Δ M * * (λ}} M * *), λ M * *) <D (Δ M * (λ M *), λ M *)
for all M ≠ M ^*
[Algorithm bin setting algorithm]
The algorithm for setting the number of quantization bins is as follows.
1. The upper limit R _{0 of the} information amount is read.
2. for M = B ₁ ,..., B _u (loop of processes 2-1 to 2-2)
2-1. [Undetermined multiplier setting algorithm] is executed to determine the optimum undetermined multiplier λ _M ^* and the quantization parameter Δ _M ^* (λ _M ^* ) for the undetermined multiplier.
2-2. The approximate error sum D (Δ _M ^* (λ _M ^* ), λ _M ^* ) using the quantization parameter Δ _M ^* (λ _M ^* ) obtained in the previous process 2-1 is represented by ^ D [M]. Store.
3. ^ D [M] (M = B ₁ ,..., B _u ) M ^* that returns the minimum value is obtained, and the quantization parameter Δ _M ^** (λ _{M *} ^* ) for this M ^* is output.

[Quantization bin number setting method (low computational complexity)]
A value that can be taken by the quantization bin number M is B ₁ ≦ M ≦ B _u, and when the quantization bin number M (B ₁ ≦ M ≦ B _u ) is given, a quantum that does not require calculation of an optimum undetermined multiplier. For the number of bins, an approach that omits the calculation process is used.

  Here, the upper limit value and the lower limit value of the generated code amount when λ is changed with the number of quantization bins as M will be considered. When Equation (7) is regarded as a function of λ, the upper limit of the generated code amount is given when λ = 0, that is, when only the distortion amount is used as the cost function. This is the case when the following minimization problem is solved with the number of quantization bins as M.

  On the other hand, the lower limit of the generated code amount is given when λ = + ∞, that is, when only the code amount is used as the cost function. This is the case when the following minimization problem is solved with the number of quantization bins as M.

Let R _u (M) and R _l (M) be the upper and lower limits of the generated code amount obtained by solving the above minimization problem. R _u (M) and R _l (M) are both non-decreasing functions with respect to the quantization bin number M. This is because the amount of generated code increases if a large value is set as the number of quantization bins. Further, since the upper limit and the lower limit are set, R _l (M) ≦ R _u (M).

Here, first, the maximum value of M that satisfies R ₁ (M) ≦ R ₀ is defined as M _upper . Because of the non-decreasing property of R _l (M) with respect to M, in the case of M satisfying M _upper ≦ M, the constraint condition that the generated code amount is R ₀ or less cannot be satisfied. For this reason, the optimization is guaranteed even if the optimization target including the setting of λ is limited to M that satisfies M ≦ M _upper .

Next, let M _{lower be} the maximum value of M that satisfies R _u (M) ≦ R ₀ . Because of the non-decreasing property of the generated code amount with respect to M, the constraint condition is always satisfied when M satisfies M <M _lower . On the other hand, due to the non-increasing property of quantization distortion with respect to M, when M satisfies M <M _lower , encoding distortion cannot be reduced more than when M = M _lower . For this reason, even if the optimization target including the setting of λ is limited to M that satisfies M _lower ≦ M, the optimality is guaranteed. Therefore,
max (B _l , M _lower ) ≦ M ≦ min (B _u , M _upper )
The optimum undetermined multiplier is obtained based on the algorithm for setting the undetermined multiplier described above, while limiting to M that satisfies the above. Here, max () is a function that returns the larger value of the two arguments, and min () is a function that returns the smaller value of the two arguments.

An undetermined multiplier obtained when the number of quantized bins is M is assumed to be λ _M ^* . M = B _l, ..., with respect to B _u, the approximation error sum D in the case of using an undetermined multiplier ^{_{λ M * (Δ Bl * (}} λ Bl *), λ Bl *), ..., D (Δ Bu * ( λ _Bu ^* ) and λ _Bu ^* ) are obtained, and the number of quantization bins that minimizes the approximate error sum is determined as the optimum number of quantization bins. That is, M that satisfies the following equation is obtained.

^{_{D (Δ M * * (λ}} M * *), λ M * *) <D (Δ M * (λ M *), λ M *)
for all M ≠ M ^*
<Computation amount reduction method for setting M _upper and M _lower >
In setting M _upper, the optimal cost value for each number of quantized bins is calculated with the cost function as e (). This corresponds to the case where λ = 0 is set in the RD cost of equation (8). On the other hand, in the setting of M _lower , the cost function is l (), and the optimum cost value for each number of quantized bins is calculated. This corresponds to the case where λ = + ∞ is set as λ in the RD cost of equation (8).

All of the above can be said to be problems for optimization for different numbers of quantized bins when a common λ is used. In this case, the amount of calculation can be reduced by paying attention to the fact that there are overlapping calculation processes with different numbers of quantized bins. Specific processing procedures for M _lower and M _upper are shown below.

[M _lower calculation algorithm]
1. A histogram (number of classes K) of the input signal is generated.
2. M _lower ← B _l
3. The processing of [adaptive quantization algorithm] is performed with λ = 0 and M = B _l , the value of L _m−1 (L _m ) is stored in the lookup table T [m, L _m ], and S The value of _m (L _m ) is stored in another look-up table Φ _Bl [m _, L _m ].
4). If R (Δ _Bl ^* (0), 0) ≧ R ₀ , the process is terminated. Otherwise, go to the next process.
5. for ^ M = B ₁ +1,..., B _u (loop of processing 5 to 9)
6). When M = ^ M, the lookup table T [] and the lookup table Φ ^ _M-1 [] are read and the processing of [adaptive quantization algorithm (M-1 bin quantization result utilization type)] to be described later is performed. To do.
7). A sum R (Δ _M ^* (0), 0) of information amounts of generated parameters is obtained.
8). If R (Δ _M ^* (0), 0) ≧ R ₀ , the processing is terminated as M _lower ← ^ M−1. Otherwise, the process proceeds to the next process 9.
9. The lookup table T [] is updated, and the lookup table Φ ^ _M [] is output.

[Calculation algorithm for M _upper ]
1. A histogram (number of classes K) of the input signal is generated.
2. M _upper ← B _u
3. lambda = lambda _{+ max,} as M = B _l, performs processing of the adaptive quantization algorithm, and stores ^ L _m-1 the value of (L _m) look-up table T [m, L _m], and further , S _m (L _m ) are stored in another lookup table Φ _Bl [m, L _m ]. Here, λ _{+ max} is a sufficiently large value.
4). If R (Δ _Bu ^* (λ _{+ max} ), λ _{+ max} ) ≧ R ₀ , the process is terminated. In this case, there is no solution that satisfies the given constraints. Otherwise, the process proceeds to the next process 5.
5. for ^ M = B ₁ +1,..., B _u (loop of processing 5 to 9)
6). When M = ^ M, the lookup table T [] and the lookup table Φ ^ _M-1 [] are read and the processing of [adaptive quantization algorithm (M-1 bin quantization result utilization type)] to be described later is performed. To do.
7). The sum R (Δ _M ^* (λ _{+ max} ), λ _{+ max} ) of the information amount of the generated parameters is obtained.
8). If R (Δ _M ^* (λ _{+ max} ), λ _{+ max} ) ≧ R ₀ , the processing is terminated as M _upper ← ^ M−1. Otherwise, the process proceeds to the next process 9.
9. The lookup table T [] is updated, and the lookup table Φ ^ _M [] is output.

<Calculation method of optimum number of bins>
In setting M _upper, the optimal cost value for each number of quantized bins is calculated with the cost function as e (). This corresponds to the case where λ = 0 is set in the RD cost of equation (8). On the other hand, in the setting of M _lower , the cost function is l (), and the optimum cost value for each number of quantized bins is calculated. This corresponds to the case where λ = + ∞ is set as λ in the RD cost of equation (8).

[Quantization bin number setting algorithm (low complexity type)]
The algorithm for setting the number of low-computation-type quantization bins is shown below.
1. The upper limit R _{0 of the} information amount is read.
2. Request M _lower by the above-described [the algorithm for calculating the M _lower].
3. Request M _upper by the aforementioned [the algorithm for calculating the M _upper].
4). for M = max (B ₁ , M _lower ),..., min (B _u , M _upper )
(Repeat processing 4-1 to 4-2)
4-1. If M> max (B ₁ , M _lower ), enter λ _M-1 ^* as the initial value of the undetermined multiplier, execute the [Undecided multiplier setting algorithm (inherited type)] shown below, and And the quantization parameter Δ _M ^* (λ _M ^* ) for the unknown multiplier λ _M ^* and the unknown multiplier.

In the case of M = max (B ₁ , M _lower ), the [undecided multiplier setting algorithm] is executed, and the optimum undetermined multiplier λ _M ^* and the quantization parameter Δ _M ^* (λ _M ^* ) for the undetermined multiplier are set. Ask.
4-2. The approximate error sum D (Δ _M ^* (λ _M ^* ), λ _M ^* ) when the quantization parameter Δ _M ^* (λ _M ^* ) obtained in the previous process 4-1 is used is represented by ^ D [M]. To store.
5. ^ D [M] (M = B ₁ ,..., B _u ) M that returns the minimum value is obtained, and the quantization parameter Δ _M ^** (λ _{M *} ^* ) for this M is output.

[Undecided multiplier setting algorithm (inherited)]
The procedure of the undetermined multiplier setting algorithm (inherited type) used in the above process 4-1 is as follows.
1. The quantization bin number M is read.
2. The upper limit R _{0 of the} information amount is read.
3. The initial value of the undetermined multiplier λ and its upper limit value λ _u are read.
4). As an undetermined multiplier, λ = (λ ₁ + λ _u ) / 2 is set.
5. [Adaptive quantization algorithm (M-1 bin quantization result utilization type)] to be described later is executed using the undetermined multiplier λ.
6). An information amount sum R (Δ _M ^* (λ), λ) of the parameters generated in the process 5 is obtained.
7). If R ₀ −ε ≦ R (Δ _M ^* (λ), λ) ≦ R ₀ :
Set λ _u as an undetermined multiplier.
8). Using the undetermined multiplier λ _u , a later-described [adaptive quantization algorithm (M-1 bin quantization result use form)] is executed.
9. An information amount sum R (Δ _M ^* (λ _u ), λ _u ) of the parameters generated in the process 8 is obtained.
10. If R ₀ −ε ≦ R (Δ _M ^* (λ _u ), λ _u ) ≦ R ₀ :
Set λ _u as an undetermined multiplier.
11. If R (Δ _M ^* (λ _u ), λ _u )> R ₀ :
as λ ← 2λ _u, returns to the processing 5.
12 If R (Δ _M ^* (λ _u ), λ _u ) <R ₀ −ε:
Return to process 4 as λ _l ← λ.
13. If R ₀ −ε ≦ R (Δ _M ^* (λ _l ), λ _l ) ≦ R ₀ :
Set λ _l as the undetermined multiplier.
14 If R (Δ _M ^* (λ _l ), λ _l )> R ₀ :
Return to process 4 as λ _u ← λ.
15. If R (Δ _M ^* (λ _l ), λ _l ) <R ₀ −ε:
Return to processing 5 as λ ← λ _u / 2.

  The above is the algorithm for setting the undetermined multiplier (inherited type).

  All of the above can be said to be problems for optimization for different numbers of quantized bins when a common λ is used. In this case, the amount of calculation can be reduced by paying attention to the fact that there are overlapping calculation processes with different numbers of quantized bins. The specific processing procedure is shown below.

[Adaptive quantization algorithm (M-1 bin quantization result use form)]
The following adaptive quantization algorithm is an example in the case of calculating M bin quantization using the result of M-1 bin quantization. In order to simplify the description here, 3 ≦ M is targeted.
1. Reads the histogram (number of classes K) of the input signal.
2. Read the number of classes M after quantization.
3. for m = 0,..., M-3 (loop of processing 3 to 6)
4). for L _m = m,..., K− (M−m) (loop of processing 4 to 6)
5. Φ _M [m, L _m ] ← Φ _M-1 [m, L _m ]
6). L _m −Δ _m is stored in L _m−1 (L _m ).
7). for m = M−2, M−1 (loop of processing 7 to 16)
8). for L _m = m,..., K− (M + 1−m) (Processing 8 to 16 loops)
9. However, when m = M−1, it is limited to L _m = K−110. for Δ _m = 1,..., L _m − (m−1) (loop of processes 10 to 16)
11. The RD cost is obtained when the histogram section [L _m − (Δ _m −1), L _m ] is approximated by a representative value. The RD cost is obtained by equation (8), and the RD cost is stored in ψ (L _m − (Δ _m −1), L _m , λ).
12 _{Φ m-1 (L m -Δ} m) + ψ - to calculate the value of _{(L m (Δ m -1)} , L m, λ).
13. Φ _m−1 (L _m −Δ _m ) + ψ (L _m − (Δ _m −1), L _m , λ) (Δ _m = 1,..., L _m − (m−1)) Store the value in S _m (L _m ).
14 Φ _{M + 1} [m, L _m ] ← Φ _m (L _m ) (omitted when m = M−1)
15. Δ that minimizes Φ _m−1 (L _m −Δ _m ) + ψ (L _m − (Δ _m −1), L _m , λ) (Δ _m = 1,..., L _m − (m−1)) _{Using m} , L _m −Δ _m is stored in ^ L _m−1 (L _m ).
16. T [m, L _m ] ← ^ L _m−1 (L _m )
17. L _M ^* ← K-1
18. form = M−1,..., 1 (loop of processes 18 to 21)
19. ^ L _m-1 (L _m ^* ) is read and L _m-1 ^* ← ^ L _m-1 (L _m ^* ) is set.
20. Δ _m ^* ← L _m ^* -L _m-1 ^*
21. Δ ₀ ^* ← L ₀ ^* +1
[Calculation method using lookup table]
In the above processing, depending on the combination of L _m and Δ _m , the RD cost ψ (L _m − (Δ _m −1), L _m , λ) is required in different quantization bins (meaning that the value of m is different). It becomes. It is not a good idea from the viewpoint of calculation cost to calculate the RD cost ψ (L _m − (Δ _m −1), L _m , λ) each time. The calculation amount can be reduced by storing the calculation result and calling the storage result as necessary. Therefore, values that can be taken as ψ (L _m − (Δ _m −1), L _m , λ) are stored in a lookup table ((K−1) × K elements). The storage process is as follows.
1. for m = 0,..., K-2 (loop of processing 1 to 3)
2. for k = 1,..., K-m-1 (loop of processing 2 to 3)
3. E [m, m + k] ← ψ (m, m + k, λ)
In the above [Quantization bin number setting method (basic solution)] and [Quantization bin number setting method (low complexity solution)], when this lookup table is used, all quantization bin numbers ([ In the case of [Quantization bin number setting method (basic solution)], B ₁ ≦ M ≦ B _u , and in the case of [Quantization bin number setting method (low computational complexity method)], M _lower ≦ M ≦ M _upper ) On the other hand, it can be shared by all the number of quantized bins. For this reason, even if the number of target quantization bins increases, the processing for obtaining the lookup table does not increase.

[Computation amount reduction method using recurrence relation of RD cost calculation]
There is an overlapping calculation in the calculation process of the RD cost ψ (L _m −Δ _m , L _m−1 , λ) stored in the lookup table ((K−1) × K elements) E [m, m + k]. Since it exists, the amount of calculation is reduced by omitting such overlapping parts.

  First, the following values are defined.

Using these, the centroid position c (L _m − (Δ _m −1), L _m ) and the quantization error e (L _m − (Δ _m −1), L _m ) are redefined as follows. Become.

From this, it can be seen that c (L _m − (Δ _m −1), L _m ) and e (L _m − (Δ _m −1), L _m ) have the following recurrence relationship.

Furthermore, it can be seen that the information amount l (L _m − (Δ _m −1), L _m ) has the following recurrence relationship.

Here, T is the sum of frequencies.

T = Σ _{k = 0} ^K-1 h [k]
Based on the above relationship, e (L _m − (Δ _m −1), L _m ), l (L _m − (Δ _m −1), L _m ) is calculated, and the RD cost that is the weighted sum of the two is looked up. Store in the up table ((K-1) × K elements). The storage process is as described in [RD cost calculation algorithm (reduction method)] described below.

In the above [Quantization bin number setting method (basic solution)] and [Quantization bin number setting method (low complexity solution)], when this lookup table is used, all quantization bin numbers ([ In the case of [Quantization bin number setting method (basic solution)], B ₁ ≦ M ≦ B _u , and in the case of [Quantization bin number setting method (low computational complexity method)], M _lower ≦ M ≦ M _upper ) On the other hand, it can be shared by all the number of quantized bins. For this reason, even if the number of target quantization bins increases, the processing for obtaining the lookup table does not increase.

[RD cost calculation algorithm (reduction method)]
1. for k = 0,..., K-1 (loop of processes 1 to 4)
2. q ₁ [0, k] ← 0
3. q ₂ [0, k] ← 0
4). q ₃ [0, k] ← 0
5. T ← Σ _{k = 0} ^K-1 h [k]
6). for m = 0,..., K-2 (loop of processing 6 to 14)
7). for k = 0,..., K-m-1 (loop of processing 7 to 14)
8). q ₁ [m, m + k + 1] ← q ₁ (m, m + k) + h [m + k + 1]
9. q ₂ [m, m + k + 1] ← q ₂ (m, m + k) + (m + k + 1) h [m + k + 1]
10. q ₃ [m, m + k + 1] ← q ₃ (m, m + k) + (m + k + 1) ² h [m + k + 1]
11. c [m, m + k + 1] ← q ₂ (m, m + k + 1) / q ₁ (m, m + k + 1)
12 e [m, m + k + 1] ← q ₃ (m, m + k + 1) −2c (m, m + k + 1) q ₂ (m, m + k + 1) + c (m, m + k + 1) ² q ₁ (m, m + k + 1)
13. l (L _m − (Δ _m −1), L _m ) ← − {q ₁ (L _m −Δ _m −1), L _m ) / T} {log ₂ q ₁ (L _m − (Δ _m −1) ), L _m ) −log ₂ T}
14 E [m, m + k + 1] ← e [m, m + k + 1] + λ · l (L _m − (Δ _m −1), L _m )
Based on the above, the low-computation type adaptive quantization algorithm in the case of the method of referring to the lookup table is as follows.

[Adaptive quantization algorithm (low complexity)]
1. A histogram (number of classes K) of the input signal is generated.
2. Read the number of classes M after quantization.
3. RD cost calculation based on [RD cost calculation algorithm (reduction method)] and storage in a lookup table.
4). In the [adaptive quantization algorithm (basic form)], the calculation processing of the object to be stored in ψ (L _m − (Δ _m −1), L _m , λ) is referred to as the lookup table E [L _m (Δ _m −1), L Replaced with the process of reading from [ _m , λ], and implemented the process after process 3 of the same algorithm.

[Minimization of weighted distortion considering visual sensitivity characteristics]
The visual system is less sensitive to changes in high luminance pixel values than changes in low luminance pixel values. Therefore, when quantization is performed in consideration of such visual characteristics, it is performed as follows. First, w [k] is set as a weighting factor for the pixel value k (k = 0,..., K−1). This weighting factor shall be given from the outside. For example, if the weight of high luminance (large k) is set to a value smaller than the weight of low luminance (small k), it is possible to incorporate the visual characteristic for the luminance difference into the quantization process. Using this weighting factor, the frequency h [k] for the pixel value k is corrected as ~ h [k] = w [k] × h [k] (where ~ is a symbol on h), The above-described quantization processing is performed on the corrected histogram to h [k].

  The above adaptive quantization processing can be realized by a computer and a software program, and the program can be recorded on a computer-readable recording medium or provided through a network.

DESCRIPTION OF SYMBOLS 10 Adaptive quantization apparatus 11 Input signal level number memory | storage part 12 Quantized level number memory | storage part 13 Undetermined multiplier memory | storage part 14 Histogram generation part 15 Approximate error calculation part 16 Information amount calculation part 17 RD cost calculation part 18 RD cost minimum value memory | storage Section 19 Upper section optimum value storage section 20 Section upper section optimum value tracking section 21 Quantization processing section

Claims (9)

An adaptive quantization method for quantizing an input signal of class number K into M class numbers smaller than K,
Generating a class number K histogram for the input signal;
When approximating the histogram with a given number of classes M, an approximation error and code amount generated by quantization are calculated in order from the first class boundary candidate for all class boundary candidates, and the approximation error is calculated. When calculating the class boundary information corresponding to the quantized value that minimizes the weighted sum of the code amount and the minimum value of the weighted sum at that time, storing it in the memory, and selecting the class boundary in the next class The stored minimum value is read from the memory, and used to calculate the minimum value of the weighted sum in the selection of the class boundary at that time, and the class boundary that minimizes the approximation error from the first class to the class is obtained. Steps,
Selecting a class boundary that minimizes a weighted sum of approximation error and code amount for all candidate class boundaries based on the class boundary information stored in the memory and the minimum value of the weighted sum;
And a step of quantizing the input signal using the finally selected class boundary. The adaptive quantization method according to claim 1, wherein:
As the approximation error, the absolute value sum or square sum of errors between the representative value of each class of class number M and the value of the input signal in each class, or the representative value of each class of class number M and each class. An adaptive quantization method, characterized in that an absolute value sum or a square sum of errors between a value of an input signal and a weighted value based on visual sensitivity is calculated. In the adaptive quantization method according to claim 1 or 2,
A value that can be taken as a weighted sum of the approximation error and the code amount is calculated in advance and stored in a lookup table, and the weighted sum for the class boundary candidates is obtained by referring to the lookup table. Adaptive quantization method. An adaptive quantization method for separately quantizing an input signal having a class number of K into a class number selected from a given class number candidate,
The adaptive quantization method according to claim 1, claim 2, or claim 3, for each given value of the given number of classes, using the set approximation error and the weighting coefficient of the code amount, Find quantized representative values and class boundaries,
And, by changing the weighting factor and repeating the adaptive quantization method, optimizing the weighting factor,
Approximation error when using the quantized representative value and class boundary obtained by the adaptive quantization method under the optimized weighting coefficient is calculated, and from among the approximation errors when using each candidate value of class number Find the minimum value,
An adaptive quantization method characterized by identifying the quantization representative value and class boundary that realize the minimum value, and the number of classes at that time. The adaptive quantization method according to claim 4, wherein
The upper limit value and lower limit value of the class number M to be optimized are calculated from the upper limit value and lower limit value of the generated code quantity when the number of classes is M and the weighting coefficient of the approximation error and code quantity is changed. An adaptive quantization method characterized in that processing for obtaining the quantization representative value and class boundary for the candidate number of classes is limited to a range between an upper limit value and a lower limit value of the class number M. In the adaptive quantization method according to claim 4 or 5,
In the process of obtaining the quantized representative value and class boundary for each candidate value of the class number, the result of obtaining the quantized representative value and the class boundary is stored as the class number M−1, and the quantized representative value of the class number M is stored. And an adaptive quantization method characterized by omitting an overlapping operation between the class number M-1 and the class number M by being used for processing for obtaining a class boundary. An adaptive quantization apparatus that quantizes an input signal having a class number of K into an M class number smaller than K,
Histogram generating means for generating a histogram of K classes for the input signal;
An approximation error calculating means for calculating an approximation error generated by quantization for each class boundary candidate when approximating the histogram with a given number of classes M;
Information amount calculating means for calculating the amount of code generated by quantization for each candidate of the class boundary;
Weighted sum calculating means for calculating a weighted sum of the approximation error and the code amount;
Storage means for storing class boundary information that minimizes the calculated weighted sum among the class boundary candidates and a minimum value of the weighted sum;
Optimal value tracking means for selecting a class boundary that minimizes the weighted sum for all candidate class boundaries based on the class boundary information and the minimum value of the weighted sum stored in the storage means;
Quantization processing means for quantizing an input signal using the class boundary selected by the optimum value tracking means,
The weighted sum calculation means reads the minimum value of the weighted sum stored in the storage means when selecting a class boundary in the next class among the class boundary candidates, and selects the class boundary at that time. An adaptive quantizer characterized by obtaining a class boundary that minimizes the weighted sum from the first class to the class by using it to calculate the minimum value of the weighted sum. An adaptive quantizer that quantizes an input signal having a class number of K separately into a class number selected from given class number candidates,
Histogram generating means for generating a histogram of K classes for the input signal;
When the histogram is approximated for each candidate value M of the given number of classes using the set approximation error and the weighting coefficient of the code amount, each candidate of the class boundary is quantized. An approximation error calculating means for calculating an approximation error to be generated;
Information amount calculating means for calculating the amount of code generated by quantization for each candidate of the class boundary;
Weighted sum calculating means for calculating a weighted sum of the approximation error and the code amount;
Storage means for storing class boundary information that minimizes the calculated weighted sum among the class boundary candidates and a minimum value of the weighted sum;
Optimal value tracking means for selecting a class boundary that minimizes the weighted sum for all candidate class boundaries based on the class boundary information and the minimum value of the weighted sum stored in the storage means;
Quantization processing means for quantizing an input signal using the class boundary selected by the optimum value tracking means,
The weighted sum calculation means reads the minimum value of the weighted sum stored in the storage means when selecting a class boundary in the next class among the class boundary candidates, and selects the class boundary at that time. The class boundary that minimizes the weighted sum from the first class to the class is obtained by calculating the minimum value of the weighted sum.
For each candidate value M of the given number of classes, optimization of the weighting coefficient used for the weighted sum of the approximation error and the code amount is performed, and a quantized representative value and Calculate the approximation error when using class boundaries, determine the minimum value from the approximation errors when using each candidate value for the number of classes, quantize representative values and class boundaries that realize the minimum value, and An adaptive quantizer characterized by identifying the number of classes at that time.   An adaptive quantization program for causing a computer to execute the adaptive quantization method according to any one of claims 1 to 6.

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