JP2017123614A - Quantization method, quantization device and quantization program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a quantization method, a quantization device and a quantization program which can reduce the amount of computation required for quantization even when minimizing conversion errors occurring in gradation conversion of signals.SOLUTION: A quantization method includes a step of comparing the position of a significant element corresponding to a value obtained by adding the maximum value of consecutive numbers of nonsignificant elements in each section whose lower end is the upper limit of a selectable range with the position of a significant element which can be taken as the upper limit of a class and is closest to the upper limit of the selectable range, and storing, in a memory, a quantization value for minimizing the cumulative value of the approximation error up to a class boundary and a minimum value of the cumulative value of the approximation error, and a step of excluding non-significant elements from calculation of the cumulative values of approximation error, obtaining the stored minimum value from the memory, and using the minimum value for calculation of the approximation error in selection of a class boundary when a class boundary is selected, thereby selecting a class boundary that minimizes the sum of approximation errors for all elements of the class boundary.SELECTED DRAWING: Figure 13

Description

  The present invention relates to a quantization method, a quantization apparatus, and a quantization program.

  In recent years, with the improvement of image quality, expectations for wide dynamic range images are increasing. Expression using a high bit depth for an image signal having a wide dynamic range has been studied. Devices that can acquire a high bit depth signal expanded from the conventional 8 bits to 10 bits or more have appeared.

  The code amount of the image increases as the bit depth of the image signal is increased. For this reason, an efficient encoding method is required. FIG. 18 is a diagram illustrating a first conventional encoding method for a high bit depth signal. In the first conventional high bit depth signal encoding method, the encoding apparatus performs bit depth conversion processing on the image signal of the high bit depth signal, thereby converting the image signal into a low bit depth signal and encoding the image signal. And decryption processing. Further, the encoding device performs inverse bit depth conversion processing on the decoded image to generate a high bit depth image. Finally, the encoding device encodes a differential signal between the high bit depth image and the input signal. The output of the encoding device is an encoded stream of a differential signal and an encoded stream of a low bit depth signal. As described above, the first conventional encoding method of a high bit depth signal is a method corresponding to the bit depth scalable encoding.

  FIG. 19 is a diagram illustrating a second conventional encoding method of a high bit depth signal. In FIG. 19, the encoding apparatus does not output the encoded stream of the difference signal. The encoding device performs a bit depth conversion process on the acquired image signal, thereby converting the image signal into a decoded signal and performing encoding and decoding processes. Thereafter, the encoding apparatus performs inverse bit depth conversion processing on the decoded signal of the low bit depth image, and outputs the decoded signal of the high bit depth image.

  The coding efficiency in the first coding method of the conventional high bit depth signal shown in FIG. 18 largely depends on the bit depth conversion processing. In the first conventional high bit depth signal encoding method, the sum of squares of the difference value between the input signal and the decoded signal after the inverse bit depth conversion process (hereinafter referred to as “bit depth conversion error”) is suppressed. Thus, the code amount of the output signal of the encoder can be suppressed. Non-Patent Document 1 discloses a method using several tone mappings in bit depth conversion processing. In order to improve the coding efficiency, the bit depth conversion needs to be designed so as to minimize the bit depth conversion error.

E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda, "Photographic Tone Reproduction for Digital Images", In SIGGRAPH 2002 Conference Proceeding, ACM SIGGRAPH, Addison Wesley, pp. 267-277, August 2002.

  Focusing on the sparseness of the pixel values in the amplitude direction, some images may not include all values that can be expressed by a given bit depth. For example, in the case of a 10-bit signal, 1024 types of values from 0 to 1023 can be expressed. The sparseness in the amplitude direction refers to the property that there are less than 1024 kinds of values included in an image as pixel values. That is, in such an image, when the frequency of pixel values is expressed as a histogram, there are pixel values that have a zero frequency. The bit depth change process described above can be regarded as a kind of quantization process for the histogram.

  Pixel values whose frequency is zero do not affect the bit depth conversion error. However, the conventional quantization method has a problem that the amount of calculation required for quantization cannot be reduced when the conversion error that occurs when performing gradation conversion of a signal is minimized.

  In view of the above circumstances, the present invention provides a quantization method and a quantization apparatus that can reduce the amount of calculation required for quantization even when the conversion error that occurs when performing gradation conversion of a signal is minimized. And to provide a quantization program.

  According to one aspect of the present invention, a histogram of an input signal representing a value that can take a range expressed by the first number of levels is taken as a range expressed by a second number of levels smaller than the first level. A quantization method in a quantization apparatus that approximates with a histogram of an output signal representing a value to be obtained, wherein a class that is a set of elements of the histogram of the input signal is defined, and a candidate of a class boundary that is a boundary of the class is a significant element The upper limit and the lower limit are defined for the significant element that can be the class boundary, the significant element included in the range from the upper limit to the lower limit is determined as the class boundary candidate, and the class boundary selectable range The position of the significant element corresponding to a value obtained by subtracting the maximum value of the consecutive number of insignificant elements in each section having the upper limit of the selectable range as the lower end with respect to the upper limit; The position of the significant element that is closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class is compared, and the significant element showing a relatively large value is added to the new selectable range of the class boundary. An upper limit, a step of storing in a memory a quantized value for minimizing a cumulative value of approximation errors up to the class boundary and a minimum value of the cumulative value of approximation errors, and selecting the class boundary, Removing the insignificant element from the calculation of the cumulative value of the approximation error, obtaining the stored minimum value from the memory, and using the minimum value in the calculation of the approximation error in the selection of the class boundary, Selecting the class boundary that minimizes the sum of the approximation errors for all elements of the boundary.

  According to one aspect of the present invention, a histogram of an input signal representing a value that can take a range expressed by the first number of levels is taken as a range expressed by a second number of levels smaller than the first level. A quantization method in a quantization apparatus that approximates with a histogram of an output signal representing a value to be obtained, wherein a class that is a set of elements of the histogram of the input signal is defined, and a candidate of a class boundary that is a boundary of the class is a significant element The upper limit and the lower limit are defined for the significant element that can be the class boundary, the significant element included in the range from the upper limit to the lower limit is determined as the class boundary candidate, and the class boundary selectable range The position of the significant element corresponding to a value obtained by adding the maximum value of the continuous number of non-significant elements in each section having the lower limit of the selectable range as the upper end relative to the lower limit The position of the significant element closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class boundary is compared, and the significant element showing a relatively small value is added to the new selectable range of the class boundary. A lower limit, a step of storing in a memory a quantized value for minimizing a cumulative value of approximation error up to the class boundary and a minimum value of the cumulative value of approximation error, and selecting the class boundary, Removing the insignificant element from the calculation of the cumulative value of the approximation error, obtaining the stored minimum value from the memory, and using the minimum value in the calculation of the approximation error in the selection of the class boundary, Selecting the class boundary that minimizes the sum of the approximation errors for all elements of the boundary.

  According to one aspect of the present invention, a histogram of an input signal representing a value that can take a range expressed by the first number of levels is taken as a range expressed by a second number of levels smaller than the first level. A quantization device for approximating with a histogram of an output signal representing a value to be obtained, defining a class that is a set of elements of the histogram of the input signal, limiting class boundary candidates that are boundaries of the class to significant elements, An upper limit and a lower limit are set for the significant element that can be the class boundary, the significant element included in the range from the upper limit to the lower limit is determined as a candidate for the class boundary, and the upper limit of the selectable range of the class boundary is determined The position of the significant element corresponding to the value obtained by subtracting the maximum number of consecutive non-significant elements in each section having the upper limit of the selectable range as the lower end, and the upper limit of the class. Comparing the position of the significant element that is closest to the upper limit of the selectable range among the significant elements that can be determined, the significant element showing a relatively large value as a new upper limit of the selectable range of the class boundary, When selecting the class boundary, an approximate error minimum value determining unit that stores a quantized value that minimizes the cumulative value of the approximate error up to the class boundary and a minimum value of the cumulative value of the approximate error in a memory; Removing the insignificant element from the calculation of the cumulative value of the approximation error, obtaining the stored minimum value from the memory, and using the minimum value in the calculation of the approximation error in the selection of the class boundary, An upper end tracking unit that selects the class boundary that minimizes the sum of the approximation errors for all elements of the boundary.

  According to one aspect of the present invention, a histogram of an input signal representing a value that can take a range expressed by the first number of levels is taken as a range expressed by a second number of levels smaller than the first level. A class of a set of elements of the histogram of the input signal is defined in a computer of a quantizer that approximates with a histogram of an output signal representing a value to be obtained, class boundary candidates that are boundaries of the class are limited to significant elements, An upper limit and a lower limit are set for the significant element that can be the class boundary, the significant element included in the range from the upper limit to the lower limit is determined as a candidate for the class boundary, and the upper limit of the selectable range of the class boundary is determined , The position of the significant element corresponding to the value obtained by subtracting the maximum value of the consecutive number of insignificant elements in each section having the upper limit of the selectable range as the lower end, and the upper limit of the class The significant element that is closest to the upper limit of the selectable range among the significant elements that can be taken, and the significant element showing a relatively large value is a new upper limit of the selectable range of the class boundary And a procedure for storing a quantized value for minimizing a cumulative value of approximation error up to the class boundary and a minimum value of the cumulative value of approximation error in a memory, and when selecting the class boundary, the non-significant Removing the element from the calculation of the cumulative value of the approximation error, obtaining the stored minimum value from the memory, and using the minimum value for the calculation of the approximation error in the selection of the class boundary. And a procedure for selecting the class boundary that minimizes the sum of the approximation errors for all elements.

  According to the present invention, it is possible to reduce the amount of calculation required for quantization even when the conversion error generated when performing gradation conversion of a signal is minimized.

It is a figure which shows the example of the process which produces | generates reference table (rho) _u [m] in embodiment. It is a figure which shows the example of the process which produces | generates reference table (rho) _l [m] in embodiment. It is a figure which shows the example of the process stored in the lookup table in embodiment. It is a flowchart which shows the example of the adaptive quantization process in embodiment. It is a figure which shows the example of the process which produces | generates the reference table which stored the correspondence of an element index and a significant element index in embodiment. It is a figure which shows the example of the process which produces | generates the reference table which stored the number of insignificant elements in embodiment. It is a flowchart which shows the example of the calculation amount reduction type | mold adaptive quantization process in embodiment. It is a flowchart which shows the example of the process (step S205) which produces | generates an approximation error reference table in embodiment. It is a flowchart which shows the example of the process which produces | generates the upper reference table in step S104-2 and step S204-2 in embodiment. It is a flowchart which shows the example of the process which produces | generates the reference table for lower bounds by step S104-2 and step S204-2 in embodiment. It is a flowchart which shows the example of the process which produces | generates the reference table in step S401 in embodiment. It is a flowchart which shows the example of the process which produces | generates the reference table in step S501 in embodiment. It is a figure which shows the 1st example of a structure of the quantization apparatus in embodiment. It is a figure which shows the 2nd example of a structure of the quantization apparatus in embodiment. It is a figure which shows the example of the basic process of an adaptive quantization process in embodiment. It is a figure which shows the example of the calculation amount reduction process of an adaptive quantization process in embodiment. It is a figure which shows the example of the process which produces | generates an approximate error reference table in embodiment. It is a figure which shows the 1st encoding method of the conventional high bit depth signal. It is a figure which shows the 2nd encoding method of the conventional high bit depth signal.

Embodiments of the present invention will be described in detail with reference to the drawings.
In the following, symbols (^: hat, ~: tilde) attached to variables etc. in the figure or formula are described before the variables. For example, “c” with “^” on top is expressed as “^ c”. Hereinafter, the subscript symbols and the like are described first in the subscript symbols and the superscript symbols and the like of the variables or symbols in the drawings or formulas. For example, a variable Δ with a subscript “1” and a superscript “*” is expressed as “Δ ₁ ^* ”. For example, a symbol Σ with a subscript “i = 0” and a superscript “m” is expressed as “Σ _{i = 0} ^m ”.

  Hereinafter, K represents the number of levels of the input signal (hereinafter referred to as “number of input levels”). M (M <K) indicates the number of levels of the output signal based on the quantized input signal (hereinafter referred to as “quantization level number”). A histogram (frequency) of the pixel value k is expressed as h [k] (k = 0,..., K−1).

[Quantizer design]
When the image signal (luminance signal) is 8 bits, the possible range of the pixel value k is an integer from 0 to “number of input levels−1”, that is, a value from 0 to 255. Consider a case in which an image signal having an input level number K is quantized into an image signal having a quantization level number. The parameters to be obtained are M parameters that satisfy Expression (1).

Here, L _m is the upper end of the m-th section in the histogram, and is represented by Expression (2).

Here, the delta _m, represents the section width of the m section of the histogram. Further, since each gradation after quantization needs to include at least one gradation before quantization, L _m (0 ≦ m ≦ M−2) is m ≦ L _m ≦ K− ( M-m). Since L _M-1 is fixed to L _M-1 = K-1, for L _m , m = M-1 may be omitted and m ≦ M-2 may be considered.

e (L _m − (Δ _m −1), L _m ) is a value obtained by the following equation, and the histogram section [L _m − (Δ _m −1), L _m ] is represented by a representative value c (L _m − ( It is an approximation error when approximating with Δ _m −1), L _m ).

Further, ^ c (L _m − (Δ _m −1), L _m ) is an integer obtained by rounding off the real value c (L _m − (Δ _m −1), L _m ) obtained by the equation (4). Value.

c (L _m − (Δ _m −1), L _m ) represents the position of the center of gravity in the section [L _m − (Δ _m −1), L _m ] of the histogram. Hereinafter, the histogram interval [L _m − (Δ _m −1), L _m ] is referred to as the m-th quantization class. Since possible combinations of M parameters (Δ ₁ ,..., Δ _m ) increase exponentially with M, an optimal combination (Δ ₁ ,..., Δm) is searched from the round robin. Is computationally difficult.

Therefore, focusing on the fact that the quantization error e (L _m − (Δ _m −1), L _m ) of the m-th quantization class depends on the upper end L _m of the same class and the section width Δm of the same class, The optimal solution is calculated as follows. Further, at that time, the calculation amount is reduced based on the non-significant elements of the histogram.

[Basic solution]
First, the histogram of the interval [0, _{L m]} an approximation error sum during the m + 1 divided ^{_{Σ i = 0 m e (L}} i - (Δ i -1), L i) the minimum value of _S m _(L m) Define as In other words, the optimal ^{_{Δ m, ..., Σ i =}} 0 m e in the case of using the _{Δ 0 (L i - (Δ} i -1), L i) is a minimum for. Here, focusing on the fact that e (L _m − (Δ _m −1), L _m ) depends on the upper end Lm of the m-th quantization class and the section width Δ _m of the same class, S _m (L _m ) is Using S _m−1 (L _m −Δ _m ), it is expressed as in equation (5).

Note that m = 1,..., M-1. Further, L _m = m,..., K− (M−m).
Range of delta _m is as follows. Because it is _{L m-1 = L m -Δ} m, the range of _L m - [delta _{m is, m-1 ≦ L m -Δ} m ≦ K- (M-m + 1) become. Therefore, the range of delta _m is expressed by the equation (6) using the given L _m.

Further, considering that Δ _m ≧ 1, Equation (7) is obtained.

Here, the calculated S _m (L _m ) is stored and used in the calculation of S _{m + 1} (L _{m + 1} ). Further, as an expression of the value of delta _m that minimizes the right-hand side of ^{_{(5) Δ m (Lm)}} , each Lm (= m, ..., K -M + m) with respect to _{^ L m-1 [L m} ] = L Store _m −Δ _m ^(Lm) . The minimization problem of Expression (1) is expressed as Expression (8).

Δ _M−1 that minimizes the expression (8) is expressed as Δ _M−1 ^* . Δ _M-1 ^* is expressed by the equation (9).

Using Δ _M-1 ^* , the optimum value of the upper end of the M-2 class is obtained as L _M−2 = L _M−1 −ΔM ₋₁ ^* = K−1−ΔM ₋₁ ^* . Optimal value of the upper end of the M-3 _{class, L} as the optimal solution for _{M-2, ^ L} since M-3 is stored as _{[L M-2],} 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 class is obtained as ΔM _-2 ^* = LM _-2 ^* -LM _-3 ^* . Hereinafter, the same reference process is repeated as L _M−4 ^* = ^ L _M−4 [L _M−3 ^* ],..., L ₀ ^* = ^ L ₀ [L ₁ ^* ], and the upper end of each class obtained using the ^{_{values, Δ M-3 * = L}} M-3 * -L M-4 *, ..., Δ 0 * = L 0 * calculated as _{-L -1} ^*. Note that L ₋₁ ^* = − 1.

[Computation amount reduction based on non-significant elements of histogram]
Focusing on non-significant elements (elements whose frequency value is zero) in the histogram, a method for reducing the amount of calculation is introduced. Hereinafter, for the histogram h [k] (k = 0,..., K−1), the index k for designating the element is referred to as “element index”. Hereinafter, with respect to the histogram h [k], an index ˜k (˜k = 0,..., ˜K−1) that designates significant elements (˜K) is referred to as a “significant element index”.

When the frequency value h [L _m +1] at the pixel value L _m +1 is zero, that is, when h [L _m +1] = 0, the histogram interval [L _m − (Δ _m −1), L _m The approximation error for +1] is equal to the approximation error for the histogram interval [L _m − (Δ _m −1), L _m ]. Since h [L _m +1] = 0, even if h [L _m +1] is added to the section to be quantized, the approximation by quantization is not affected. Therefore, when h [L _m +1] = 0, the calculation of S (L _m +1) based on Expression (5) can be omitted.

The following reference tables are prepared as preparations for adaptive processing focusing on non-significant elements of the histogram. Z [k] (k = 0,..., K−1) stores the number of insignificant elements included in the histogram interval [0, k]. F [˜K] stores element indexes corresponding to the first to Kth significant elements (significant elements, not insignificant elements). On the other hand, F ⁻¹ [k] stores a significant element index corresponding to the kth element. When the k-th element is an insignificant element, a value representing “don't care” is substituted for F ⁻¹ [K].

Ψ _u [m] (m = 0,..., M−1) stores the maximum value of the significant element index that can be the upper end of the m-th bin. Ψ _l [m] (m = 0,..., M−1) stores the minimum value of the significant element index that can be the upper end of the m-th bin. Here, Ψ _u [m], Ψ _l [m] (m = 0,..., M−1) are set as follows. The following is a calculation method of Ψ _u [m], Ψ _l [m] (m = 0,..., M−1) when the reference table Z [] is used.

The following is a calculation method of Ψ _u [m], Ψ _l [m] (m = 0,..., M−1) when the reference table F ⁻¹ [] is used.

Here, ~ K-1 represents the maximum value of the significant element index. K-1-Z [K-1] is represented as ~ K-1. ψ _u [m−M + K] is the maximum value of the element index of the significant element in the histogram interval [m, m−M + K], and ψ _l [m] is significant in the histogram interval [m, m−M + K]. The minimum element index of the element. That is, ψ _u [m−M + K] is a significant element closest to the upper limit of the selectable range among significant elements that can be taken as the upper end of the m-th bin, and ψ _l [m] is the upper end of the m-th bin. Is the closest significant element to the lower limit of the selectable range.

FIG. 1 is a diagram illustrating an example of processing for generating the reference table ρ _u [m]. FIG. 2 is a diagram illustrating an example of processing for generating the reference table ρ _l [m]. From Expression (10) to Expression (13), when certain conditions are satisfied, the significant elements indicated by ψ _u [m−M + K] and ψ _l [m] cannot be candidates for the optimum solution. This indicates that it can be excluded from search candidates. Small and the condition, in the case of _{ψ u [m-M + K} ], ρ u index value determined by [m] m-M + K -ρ u [m] is, than the element index represented by _{ψ u [m-M + K} ] it is to take a value, in the case of ψ _{l [m],} ρ _l index value determined by _{[m] m + ρ l [} m] is, is to take a larger value than the element index represented by ψ _{l [m]} . Here, ρ _u [m] represents the maximum value of the section width of the partial section consisting only of insignificant elements in the histogram section [m−M + K, K−1], and ρ _l [m] represents the histogram section [ 0, m] represents the maximum value of the section width of the partial section consisting only of insignificant elements. That is, ρ _u [m] and ρ _l [m] represent the maximum number of consecutive non-significant elements in each designated section. Each is determined as shown in FIG. 1 and FIG.

[Find optimal solution]
In order to omit unnecessary operations on insignificant elements and reduce the amount of calculation, an algorithm for finding an optimal solution using a significant element index is shown below.

Consider a case where the histogram section [0, F [˜L _m ]] with the _m- th significant element at the upper end is divided into m + 1. The partial section [F [˜L _i − (˜Δ _i −1)], F [˜L _i ]] (where i = 0,..., M) obtained by dividing the same section is the i-th bin. . Against the i-th bin, the quantization error e in the case of approximate center of gravity _{(F [~L i - (~Δ} i -1)], F [~L i]) is calculated. Here, ~ L _i is a significant element index corresponding to the upper end of the i-th bin, and ~ Δ _i is the number of significant elements in the i-th bin. Furthermore, the quantization error sum Σ _i ⁼ 0 m e - define _{[~L i (~Δ i -1)} , ~L i] a reference table for storing the minimum value as _{~S m} [~L m]. In other words, the optimal ^{_{~Δ m, ..., σ i =}} 0 m e in the case of using the _{~Δ 0 [~L i - (~Δ} i -1), ~L i] is a minimum for. _{Incidentally,} ~S _m [~L m] is equal to _{S m [F [~L m]} ].

_{Here, ~e (~L m - (~Δ} m -1), ~L m) number significant elements in the section width of the significant element index ~L _m the same class of the upper end of the first m quantized class ～Deruta focusing be dependent on _m, ~S _m (~L _m) by using the _{~S m -1 (~L m -~Δ m} ), is expressed by the equation (14).

Note that m = 0,..., M-1. _{Further, ~L m = Ψ l [m} ], ..., a Ψ _u [m]. Range ～Deruta _m is as follows. Since it is _{~L m-1 = ~L m -~Δ} m, the range of _{~L m -~Δ} m _{is, Ψ l [m-1]} ≦ ~L m -~Δ m ≦ Ψ u [m- 1]. Therefore, the scope of ～Deruta _m can be expressed as in equation (15) using a given ~L _m.

Furthermore, considering that ~ Δ _m ≧ 1, Expression (16) is obtained.

Here, the calculated _{to S} m may be stored a (~L _m), it shall be used in the calculation of _{~S m + 1 (~L m +} 1). Furthermore, the ～Deruta _m to the minimum value of the right side of the equation (14) and ～Deruta _m ^{(to L m),} as the upper end of optimal first m-1 bottle when the upper end of the m bins and ~L _m, ^ L _m−1 [˜L _m ] = ˜L _m −˜Δ _m ^(˜Lm) is ^stored for each of ^−L _m (= Ψ _l [m],..., Ψ _u [m]). Shall. The minimization problem of Equation (1) is expressed as Equation (17).

Here, ~ K = KZ [K-1]. ˜ΔM ₋₁ that minimizes the expression (17) is set to ˜ΔM ₋₁ ^* . Δ _M-1 ^* is expressed by Equation (18).

Since ~ L M-1 can only have a value KZ [K-1] -1, ~ L M-1 = KZ [K-1] -1. Using ~ LM -1 and ~ ΔM -1 * , the optimal value of the significant element index at the upper end of class M-2 is ~ LM -2 * = ~ LM -1- ~ ΔM -1 *. = KZ [K-1] -1--ΔM -1 * . Optimal value of the significant element index of the upper end of the M-3 class, the optimal solution to ~L M-2 *, ^ L M-3 because it is stored as [~L M-2 *], the appropriate values ˜L M−3 * = ^ L M−3 [˜L M−2 * ]. As a result, the number of significant elements within the section width of the M-2 class is obtained as ~ ΔM -2 * = ˜LM -2− ˜LM -3 . Hereinafter, ~L similar reference process M-4 * = ^ L M -4 [~L M-3 *], ..., ~L 0 * = ^ L 0 repeatedly as [~L 1 *], resulting using significant element index of the upper end of each class, ~Δ M-3 * = ~L M-3 * -~L M-4 *, ..., ~Δ 0 * = ~L 0 * -~L -1 * Asking. In addition, it is -L < -1 > * =-1.

Significant element index _{~L M-1} at the upper end of each ^{_{class, ~L M-2 *, ...}} , from ^{_{~L 0 *, F [~L M}} -1], F [~L M-2 *], ..., The upper end of each class is obtained by F [˜L ₀ ^* ].

[Storing quantization error in lookup table]
Depending on the combination of L _m and Δ _m , a quantization error e (L _m − (Δ _m −1), L _m ) is required in different quantization classes (meaning that the value of m is different). It is not a good idea from the viewpoint of calculation cost to calculate the quantization error e (L _m − (Δ _m −1), L _m ) each time. The calculation amount can be reduced by storing the calculation result and calling the storage result as necessary. Therefore, a value that can be taken as e (L _m − (Δ _m −1), L _m ) is stored in a lookup table (M × K element).

FIG. 3 is a diagram illustrating an example of processing (storage processing) stored in the lookup table. Quantization error e (F stored in the lookup table ((K−Z [K−1] −1) × (K−Z [K−1]) element) E [˜i _s , ˜i _e ]. Since there are overlapping calculations in the calculation process of [˜i _s ], F [˜i _e ]), the amount of calculation is reduced by omitting such overlapping parts. First, the following values are defined.

From this, it can be seen that c (~ i _s , ~ i _e ) and e (~ i _s , ~ i _e ) have the following recurrence relationship.

E (~ i _s , ~ i _e ) is calculated based on the recurrence relation, and the calculation result is represented as a lookup table ((K−Z [K−1] −1) × (K−Z [K−1]) element. ).

[Flowchart: Adaptive quantization processing]
An embodiment of adaptive quantization processing will be described with reference to the drawings.
FIG. 4 is a flowchart illustrating an example of adaptive quantization processing. The input signal is read and a histogram of input signal values is generated (step S101). Assuming that the element index of the histogram is k and the significant element index of the histogram is ~ k, F [~ k] is generated as a reference table storing the correspondence between k and ~ k (step S102).

  FIG. 5 is a diagram illustrating an example of processing for generating a reference table that stores the correspondence between element indexes and significant element indexes. A specific method for generating F [˜k] is as shown in FIG. Z [k] is generated as a reference table storing the number of insignificant elements included in the histogram section [0, k] (step S103).

  FIG. 6 is a diagram illustrating an example of processing for generating a reference table storing the number of insignificant elements. A specific method for generating Z [k] is as shown in FIG.

As shown in FIG. 4, the histogram is read as an input, and for m = 0,..., M−1, the maximum value and the minimum value of the element index of the significant element in the histogram section [m, m−M + K] are respectively obtained. And stored in the reference table Ψ _u [m−M + K] and the reference table Ψ _l [m] (step S104-1). Ψ _u [m] (m = 0,..., M−1) is generated as a reference table storing the maximum value of Lm that accompanies skipping insignificant coefficients. Specifically, it sets with Formula (26) and Formula (27) (step S104-2).

The processing up to step S107 is repeated as j = 1,..., KM-1-Z [KM-1] (step S105).
Approximation error to e [0, j] when the histogram section [0, F [j]] is approximated by the representative value (centroid obtained from the equation (4)) is obtained, and the approximation error is set to S ₀ (j). Store (step S106).
The processing up to step S118 is repeated as m = 1,..., M−1 (step S108).

The process up to step S117 is repeated as .about.L _m = Ψ _l [m],..., Ψ _u [m] (step S109).
~Δ the following processing in steps S114 _m = 1, ..., repeated as _{~L m -Ψ l (m-1} ) ( step S110).
Hitoguramu interval _{[F [~L m - (~Δ} m -1)], F [~L m]] is obtained by equation a representative value of (4) (step S111).

Histogram interval _{[F [~L m - (~Δ} m -1)], F [~L m]] from the representative value formula (3) approximation error when approximated by (the value determined in step S111) Ask. The same approximation error _{~e (~L m - (~Δ m} -1), ~L m) to (step S112).
_{~S m-1 (~L m -~Δ} m) + ~e (~L m - (~Δ m -1), ~L m) to calculate the value of (step S113).

_{~S m-1 (~L m -~Δ} m) + ~e (~L m - (~Δ m -1), ~L m) (~Δ m = 1, ..., ~L m - (m- storing the minimum value among the 1)) to _{~S m} (~L m) (step S115).
_{~S m-1 (~L m -~Δ} m) + ~e (~L m - (~Δ m -1), ~L m) (~Δ m = 1, ..., ~L m - (m- 1)) is minimized using ~ Δm, and ~ L _m- ~ Δ _m is stored in ^ L _m-1 (~ L _m ). Hereinafter, ^ L _m−1 (˜L _m ) is referred to as “optimum path tracking reference table” (step S116).

Substitute K-1 for L M-1 * . ZZ [k-1] -1 is substituted for ~ LM -1 * (step S119).
The process up to step S122 is repeated as m = M−1,..., 1 (step S120).
^ L m-1 reads the (~L m *), it is assigned to ~L m-1 *. F [˜L m−1 * ] is read and assigned to L m−1 * (step S121).

[Flow chart: Adaptive quantization processing with reduced amount of computation]
An embodiment of adaptive quantization processing in which an approximation error is stored in a reference table and the approximation error is appropriately read from the reference table will be described with reference to the drawings.

FIG. 7 is a flowchart illustrating an example of a calculation amount reduction type adaptive quantization process.
Step S201 to step S204-2 are the same as step S101 to step S104.
A reference table storing an approximation error when approximating each section of the histogram with a representative value is generated (step S205).
Steps S206 to S212 are the same as steps S105 to S111.

Interval _{[F [~L m - (~Δ} m -1)], F [~L m]] of the histogram reference table E the approximation error in the case of approximating the representative value _{(~L m} - (~Δ m - 1) to L _m ) (Step S213).
_{~S m-1 (~L m -~Δ} m) + E (~L m - (~Δ m- 1), ~L m) to calculate the value of (step S214).

~ S _m-1 (~ L _m- ~ Δ _m ) + E (~ L _m- (~ Δ _m -1), ~ L _m ) (~ Δ _m = 1, ..., ~ L _m- (m-1) ) Is stored in ~ Sm (~ Lm) (step S216).
_{~S m -1 (~L m -~Δ m} ) + E (~L m - (~Δ m -1), ~L m) (~Δ m = 1, ..., ~L m - (m-1) ) using ～Deruta _m that minimizes the stores _{~L m -~Δ} m _^ L m -1 to (~L _m) (step S217).
Steps S220 to S223 are the same as steps S119 to S122.

FIG. 8 is a flowchart illustrating an example of processing (step S205) for generating an approximate error reference table. A histogram of the input signal is read (step S301).
The reference table Z [k] (k = 0,..., K-1), F [.about.k] (.about.k = 0,..., KZ [K-1] -1) is read (step S302).
The process up to step S305 is repeated as .about.k = 1,..., KZ [K-1] -1 (step S303).
0 is stored in q ₁ [0, ˜k], q ₂ [0, ˜k], q ₃ [0, ˜k] (step S304).
The processing up to step S316 is repeated as ~ i _s = 0,..., KZ [K−1] −2 (step S306).
_{~i s + K-Z [K} -1] by comparing -M-1 and K-Z [K-1] -1, stores the smaller value to the variable U (step S307).

_{Through i} the processes in steps _{S315 e = ~i s + 1,} ..., repeated as U (step S308).
I read reference table F [~i _e], substituting F [~i _e] to _{i e.} The reference table F [˜i _s ] is read, and F [˜i _s ] is substituted for is (step S309).
q ₁ [i _s , i _e −1] and h [i _e ] are read, q ₁ [i _s , i _e −1] + h [i _e ] is calculated, and the calculated result is q ₁ [i _s , i _e ] (step S310).

_{q 2 [i s, i e} -1], h [i e], reads the _{i e, q 2 [i s} , i e -1] + ieh calculates [ie], a calculation result _q 2 _{[i s} , I _e ] (step S311).
_{q 3 [i s, i e} -1], h [i e], reads the _{i e, q 3 [i s} , i e -1] + i e to calculate the 2 h _{[i e],} the calculation result q ₃ [i _s , i _e ] is stored (step S312).

_{q 2 [i s, i e} -1], q 3 [i s, i e -1] _reads, calculates _{q 2 [i s, i e} ] q 1 [i s, i e] the result of the calculation Is stored in c [i _s , i _e ] (step S313).
_{q 1 [i s, i e} -1], q 2 [i s, i e -1], q 3 [i s, i e -1], reads the _{c [i s, i e]} , q 3 [ i _s , i _e ] −2c [i _s , i _e ] q ₂ [i _s , i _e ] + c [i _s , i _e ] ² q ₁ [i _s , i _e ]] Store in [˜i _s , ˜i _e ] (step S314).

[Flow of reference table generation process]
FIG. 9 is a flowchart illustrating an example of processing for generating a reference table for the upper bound in step S104-2 and step S204-2.
The histogram is read as input, the maximum value of the section width of the partial section consisting only of insignificant elements in the section [m−M + K, K−1] of the histogram is obtained, and the reference tables ρ _u [m], ρ _l [m] ( The data is stored in m = 0,..., M-1 (step S401) A specific processing flow is shown in FIG.
The process from step S403 to step S408 is repeated for m = 0,..., M−1 (step S402).
The histogram is read as input, and the maximum value of the element index of the significant element in the histogram interval [m, m−M + K] is read from the reference table Ψ _u [m−M + K]. The reference table is output in step S104-1 in FIG. 2 and step S204-1 in FIG. 7 (step S403).
The value of the reference table ψ _u [m] output in step S401 is read as the maximum value of the section width of the partial section consisting only of insignificant elements in the histogram section [m−M + K, K−1] (step S404).
The value of m−M + K−ρ _u [m] is obtained as a value obtained by subtracting the section width ρ _u [m] read in step S404 from the element index m−M + K corresponding to the upper limit of the selectable range (step S405).
The value obtained in step S403 and step S405 is read as an input, and the smaller value is obtained as min (ψ _u [m−M + K], m−M + K−ρ _u [m]), and this value is added to the new selectable range. An element index corresponding to the upper limit is set (step S406).
The element index obtained in step S406 is read as an input, and a significant element index for the element index is obtained (step S407). When calculating the significant element index stored in the reference table, the equation (10) or the equation (12) is used.
A table Ψ _l [m] (m = 0,..., M−1) storing significant element indexes is output (step S409).

FIG. 10 is a flowchart illustrating an example of processing for generating a lower bound reference table in step S104-2 and step S204-2. The histogram is read, the maximum value of the section width of the partial section consisting only of insignificant elements in the section [0, m] of the histogram is obtained, and the reference tables ρ _l [m], ρ _l [m] (m = 0,. (Step S501) The specific processing flow is shown in Fig. 12. The processing from Step S503 to Step S508 is repeated for m = 0, ..., M-2 (Step S502). ).

The histogram is read, and the minimum value of the element index of the significant element in the histogram section [m, m−M + K] is read from the reference table ψ _l [m] (step S503). The reference table is output in step S104-1 in FIG. 4 and step S204-1 in FIG.

The value of the reference table ρ _l [m] output in step S501 is read as the maximum value of the section width of the partial section consisting only of insignificant elements in the histogram section [0, m] (step S504). The value of m + ρ _l [m] is obtained as a value obtained by adding the section width ρ _l [m] read in step S504 from the element index m corresponding to the lower limit of the selectable range (step S505).

The values obtained in step S403 and step S505 are read, the larger value is obtained as max (ψ _l [m], m + ρ _l [m]), and this value is set as an element index corresponding to a new lower limit of the selectable range ( Step S506). The element index obtained in step S506 is read, and a significant element index for the element index is obtained (step S507). When calculating the significant element index stored in the reference table, the equation (10) or the equation (12) is used.

As the value of the significant elements maximum ~K-1 index Ψ _l [M-1], and stores it in the reference table Ψ _l [M-1] (step S509). A table Ψ _u [m] (m = 0,..., M−1) storing significant element indexes is output (step S510).

FIG. 11 is a flowchart illustrating an example of processing for generating a reference table in step S401. The histogram element h [K-1] is read (step S601). If the element value is not zero, the process proceeds to step S602, and otherwise, the process proceeds to step S604. The variable c is set to 0 (step S602). The element ρ _u [M−1] of the reference table is set to 0 (step S603). The variable c is set to 1 (step S604). The element ρ _u [M−1] of the reference table is set to 1 (step S605).

  As m = M−2,..., 0, the processing from step S607 to step S613 is repeated (step S606). The histogram element h [m−M + K] is read (step S607). If the element value is not zero, the process proceeds to step S608, and otherwise, the process proceeds to step S609. The variable c is set to 0 (step S608). The value of variable c is incremented (step S609).

It is determined whether or not the value of the variable c is larger than the (m + 1) th element ρ _u [m + 1] of the reference table (step S610). When the value of the variable c is larger than the (m + 1) th element ρ _u [m + 1] of the reference table, the process proceeds to step S611. Otherwise, the process proceeds to step S612. The value of the variable c is set to the m-th element ρ _u [m] of the reference table (step S611). The value of the (m + 1) th element ρ _u [m + 1] of the reference table is set in the m-th element ρ _u [m] of the reference table (step S612). The reference table ρ _u [m] (m = 0,..., M−1) is output (step S613).

FIG. 12 is a flowchart illustrating an example of processing for generating a reference table in step S501. The histogram element h [0] is read. If the element value is not zero, the process proceeds to step S702. Otherwise, the process proceeds to step S704 (step S701). The variable c is set to 0 (step S702). The element ρ _l [0] of the reference table is set to 0 (step S703). The variable c is set to 1 (step S704). The element ρ _l [0] of the reference table is set to 1 (step S705). As m = 1,..., M−1, the processing from step S707 to step S713 is repeated (step S706).

The histogram element h [m] is read (step S707). If the element value is not zero, the process proceeds to step S708, and otherwise the process proceeds to step S709. The variable c is set to 0 (step S708). The value of the variable c is incremented (step S709). It is determined whether or not the value of the variable c is larger than the m−1 element ρ _l [m−1] of the reference table (step S710).

If the value of the variable c is larger than the m−1th element ρ _l [m−1] of the reference table, the process proceeds to step S711. Otherwise, the process proceeds to step S712. The value of the variable c is set to the m-th element ρ _l [m] of the reference table (step S711). The value of the (m−1) th element ρ _l [m−1] of the reference table is set in the mth element ρ _l [m] of the reference table (step S712). The reference table ρ _l [m] (m = 0,..., M−1) is output (step S713).

[Adaptive quantizer]
FIG. 13 is a diagram illustrating an example of the configuration of the quantization device 1a (adaptive quantization device). The quantization device 1a is an information processing device such as a personal computer, a tablet terminal, a smartphone terminal, or a server device. The quantizing device 1a approximates the histogram of the input signal representing the value expressing the range with the first number of levels (the number of gradations) with the histogram of the output signal representing the value expressing the range with the second number of levels. Quantization processing (adaptive quantization) is executed.

  The quantization device 1a includes a histogram generation unit 10, a first element number storage unit 11, a class number storage unit 12, an index reference table generation unit 13, an index storage unit 14, and an element number reference table generation unit 15. , Second element number storage unit 16, upper bound value reference table generation unit 17, upper bound value storage unit 18, lower bound value reference table generation unit 19, lower bound value storage unit 20, and approximate error minimum value determination unit 21, an approximate error minimum value storage unit 22, an upper end storage unit 23, and an upper end tracking unit 24.

  Histogram generator 10, index reference table generator 13, element count reference table generator 15, upper bound reference table generator 17, lower bound reference table generator 19, and approximate error minimum value determiner 21 Part or all of the upper end tracking unit 24 is a software function unit that functions when a processor such as a CPU (Central Processing Unit) executes a program stored in the storage unit. Some or all of these functional units may be hardware functional units such as LSI (Large Scale Integration) and ASIC (Application Specific Integrated Circuit).

  First element number storage unit 11, class number storage unit 12, index storage unit 14, second element number storage unit 16, upper bound value storage unit 18, lower bound value storage unit 20, and approximate error minimum value Part or all of the storage unit 22 and the upper end storage unit 23 are configured using a storage device having a non-volatile storage medium (non-temporary recording medium) such as a magnetic hard disk device or a semiconductor storage device. The Each storage unit may include, for example, a volatile storage medium such as a RAM (Random Access Memory) or a register.

The histogram generator 10 reads an input signal. The histogram generator 10 generates a histogram of the input signal. The histogram generation unit 10 stores the histogram of the input signal and the number K of input signal levels in the first element number storage unit 11.
The first element number storage unit 11 (histogram / input signal element number storage unit) stores (stores) an input signal histogram and an input signal level number K.
The class number storage unit 12 stores a quantization class number M.

The index reference table generating unit 13 sets the histogram element index to k, the histogram significant element index to k, and stores the correspondence between the histogram element index k and the histogram significant element index to k as a reference table. [˜k] are generated. The index reference table generation unit 13 stores the reference table storing the correspondence between k and ˜k in the index storage unit 14. A specific method for generating the reference table F [˜k] is as shown in step S102 of FIG.
The index storage unit 14 stores a reference table that stores the correspondence relationship between the element index k of the histogram and the significant element indexes ˜k of the histogram.

The element number reference table generation unit 15 generates Z [k] as a reference table storing the number of insignificant elements included in the histogram interval [0, K]. The reference table is stored in the second element number storage unit 16. A specific method for generating the reference table Z [k] is as shown in step S103 of FIG.
The second element number storage unit 16 (insignificant element number storage unit) stores a reference table Z [k].

The upper bound value reference table generation unit 17 generates Ψ _u [m] (m = 0,..., M−1) as a reference table storing the maximum value of the m-th class significant element index. The upper bound value reference table generation unit 17 stores the reference table Ψ _u [m] in the upper bound value storage unit 18. A specific method for generating the reference table Ψ _u [m] is as shown in step S104 of FIG.
The upper bound value storage unit 18 stores a reference table Ψ _u [m].

The lower bound value reference table generation unit 19 generates Ψ _l [m] (m = 0,..., M−1) as a reference table storing the minimum value of the m-th class significant element index. The lower bound value reference table generation unit 19 stores the reference table Ψ _l [m] in the lower bound value storage unit 20. A specific method for generating the reference table Ψ _l [m] is as shown in step S104 of FIG.
The lower bound value storage unit 20 stores a reference table Ψ _l [m].

  The approximate error minimum value determination unit 21 includes an input signal histogram, the number of levels of the input signal, the number of quantization classes, an element index reference table, an insignificant element number reference table, and an upper bound of the quantization class. A reference table of values and a reference table of lower bound values of the quantization class are acquired.

  The approximate error minimum value determination unit 21 calculates the minimum value of the approximate error when the histogram is divided into the number of classes specified by the number of quantization classes. The approximate error minimum value determination unit 21 stores, in the approximate error minimum value storage unit 22, the minimum value of the approximate error when the histogram is divided into the number of classes specified by the number of quantization classes. The approximate error minimum value determination unit 21 stores a significant element index representing the upper end of the class that minimizes the accumulated value of the approximate error in each quantization class as the optimum path tracking reference table in the upper end storage unit 23. Specific processing is as shown in steps S105 to S118 shown in FIG. The approximate error minimum value storage unit 22 stores the minimum value of the approximate error when the histogram is divided into the number of classes designated by the number of quantization classes. The upper end storage unit 23 stores an optimum path tracking reference table.

  The upper end tracking unit 24 acquires the number of levels of the input signal, the number of quantization classes, the element index reference table, the significant element number reference table, and the optimal path tracking reference table. The upper end tracking unit 24 calculates an element index representing the upper end of the class when realizing the minimum value of the approximation error. The specific process is as shown in steps S119 to 122 shown in FIG.

[Computational Complexity Reduced Adaptive Quantizer]
A configuration of an adaptive quantization apparatus with a reduced amount of computation will be described in which the approximation error is stored in a reference table and the approximation error is appropriately read from the reference table storing the approximation error.

  FIG. 14 is a diagram illustrating an example of the configuration of the quantization device 1b (computation reduction type adaptive quantization device). The quantization device 1b is an information processing device such as a personal computer, a tablet terminal, a smartphone terminal, or a server device. The quantizing device 1b approximates the histogram of the input signal representing the value expressing the range with the first number of levels (number of gradations) with the histogram of the output signal representing the value representing the range with the second number of levels. Quantization processing (adaptive quantization) is executed.

  The quantization device 1b includes a histogram generation unit 10, a first element number storage unit 11, a class number storage unit 12, an index reference table generation unit 13, an index storage unit 14, and an element number reference table generation unit 15. , Second element number storage unit 16, upper bound value reference table generation unit 17, upper bound value storage unit 18, lower bound value reference table generation unit 19, lower bound value storage unit 20, and approximate error minimum value determination unit 21, an approximate error minimum value storage unit 22, an upper end storage unit 23, an upper end tracking unit 24, an approximate error determination unit 25, and an approximate error storage unit 26.

  Histogram generator 10, index reference table generator 13, element count reference table generator 15, upper bound reference table generator 17, lower bound reference table generator 19, and approximate error minimum value determiner 21 Part or all of the upper end tracking unit 24 and the approximate error determination unit 25 is a software function unit that functions when a processor such as a CPU executes a program stored in the storage unit. Some or all of these functional units may be hardware functional units such as an LSI or an ASIC.

  First element number storage unit 11, class number storage unit 12, index storage unit 14, second element number storage unit 16, upper bound value storage unit 18, lower bound value storage unit 20, and approximate error minimum value Part or all of the storage unit 22, the upper end storage unit 23, and the approximate error storage unit 26 include, for example, a nonvolatile storage medium (non-temporary recording medium) such as a magnetic hard disk device or a semiconductor storage device. It is configured using a storage device. Each storage unit may have, for example, a volatile storage medium such as a RAM or a register.

  The approximate error minimum value determination unit 21 includes an input signal histogram, the number of levels of the input signal, the number of quantization classes, an element index reference table, an insignificant element number reference table, and an upper bound of the quantization class. A value reference table and a quantization table lower bound value reference table approximation error reference table are acquired.

The approximate error minimum value determination unit 21 includes an input signal histogram, the number of levels of the input signal, the number of quantization classes, an element index reference table, an insignificant element number reference table, and an upper bound of the quantization class. Based on the value reference table and the quantization table lower bound reference table approximation error reference table, the minimum value of the approximation error when the histogram is divided into the number of classes specified by the number of quantization classes is calculated. . The approximate error minimum value determination unit 21 stores the minimum value of the approximate error in the approximate error minimum value storage unit 22. The approximate error minimum value determination unit 21 stores a significant element index representing the upper end of the class that minimizes the accumulated value of the approximate error in each quantization class as the optimum path tracking reference table in the upper end storage unit 23. Specific processing is as shown in steps S206 to S219 in FIG.
The approximate error minimum value storage unit 22 stores the minimum value of the approximate error.
The upper end storage unit 23 stores an optimum path tracking reference table.

  The upper end tracking unit 24 acquires the number of levels of the input signal, the number of quantization classes, the element index reference table, the significant element number reference table, and the optimal path tracking reference table. The upper end tracking unit 24 realizes the minimum value of the approximation error based on the number of levels of the input signal, the number of quantization classes, the element index reference table, the significant element number reference table, and the optimal path tracking reference table. Calculate the element index that represents the top of the class. Specific processing is as shown in steps S220 to S223 in FIG.

The approximate error determination unit 25 acquires an input signal histogram, the number of levels of the input signal, the number of quantization classes, an element index reference table, and an insignificant element number reference table. The approximate error determination unit 25 calculates an approximate error based on the histogram of the input signal, the number of levels of the input signal, the number of quantization classes, the reference table of element indexes, and the reference table of the number of insignificant elements. . The approximation error determination unit 25 stores the calculated approximation error in the approximation error storage unit 26 as an approximation error reference table. The specific processing is as shown in FIG.
The approximate error storage unit 26 stores an approximate error reference table.

  FIG. 15 is a diagram illustrating an example of basic processing of adaptive quantization processing. A flow of basic processing of adaptive quantization processing in which unnecessary processing for insignificant coefficients is deleted will be described. Note that the conditions for repetition of processing (for sentence) are as shown in FIG.

The histogram generator 10 generates a histogram (number of classes K) of the input signal. The class number storage unit 12 reads the class number M after quantization. Reference table Z [k] (k = 0,..., K−1), Ψ _l [m], Ψ _u [m] (m = 0,..., M−1), F [˜k] (˜k = 0,..., KZ [K-1] -1) are generated.

An approximation error is approximated when the histogram section [0, F [j]] is approximated by a representative value (the center of gravity obtained by the equation (4)), and the approximation error when approximated is stored in S ₀ (j). Hereinafter, the process of storing the approximation error in the case of approximation in S ₀ (j) is referred to as “first storage process”.

An approximation error is obtained when the histogram section [F [˜L _m − (˜Δ _m −1)], F [˜L _m ]] is approximated with a representative value. The representative value is obtained from equation (4), and the approximation error is obtained from equation (3). The same approximation error _{~e (~L m - (~Δ m} -1), ~L m) and. _{~S m-1 (~L m -~Δ} m) + ~e (~L m - (~Δ m -1), ~L m) to calculate the value of. _{~S m-1 (~L m -~Δ} m) + ~e (~L m - (~Δ m -1), ~L m) (~Δ m = 1, ..., ~L m - (m- The minimum value in 1)) is stored in ~ S _m (~ L _m ). _{~S m-1 (~L m -~Δ} m) + ~e (~L m - (~Δ m -1), ~L m) (~Δ m = 1, ..., ~L m - (m- 1)) using the ～Deruta _m that minimizes the stores _{~L m -~Δ} m _^ to L _m -1 (~L m).

Store K-1 in LM -1 * . Store KZ [K-1] -1 in ~ LM -1 * . ^ L m−1 (˜L m * ) is read. ^ L m-1 the (~L m *) is stored in the ~L m-1 *. F [˜L m−1 * ] is stored in L m−1 * .

  FIG. 16 is a diagram illustrating an example of the calculation amount reduction process of the adaptive quantization process. An example of an adaptive quantization process that executes a calculation amount reduction process in the case of a method that refers to the lookup table described above will be described. Note that the conditions for repetition of processing (for sentence) are as shown in FIG.

The histogram generator 10 generates a histogram (number of classes K) of the input signal. The class number storage unit 12 reads the class number M after quantization. Reference table Z [k] (k = 0,..., K−1), Ψ _l [m], Ψ _u [m] (m = 0,..., M−1), F [˜k] (˜k = 0,..., KZ [K-1] -1) are generated.

Based on the process shown in FIG. 17 (flow of approximate error reference table generation process), a reference table E [˜i _s , ˜i _e ] storing the approximate error is generated. E [0, j] is stored in S ₀ (j). In the process shown in FIG. 15 (flow of basic process of adaptive quantization process), a process after the first storage process is executed.

  FIG. 17 is a diagram illustrating an example of processing for generating an approximate error reference table. Note that the conditions for repetition of processing (for sentence) are as shown in FIG.

0 is stored in q ₁ [0,... k]. 0 is stored in q ₂ [0, ˜k]. 0 is stored in q ₃ [0, to k]. Substituting F [~i _e] to i _e. Substituting F [~i _s] to i _{s.
q 1 [i s, i e} ] to _{q 1 [i s, i e} -1] stores + h _{[i e].} q ₂ [i _s , i _e −1] + i _e h [i _e ] is stored in q ₂ [i _s , i _e ]. _{q 3 [i s, i e} ] to _{q 3 [i s, i e} -1] + i e 2 h [i e] stores. q ₂ [i _s , i _e ] / q ₁ [i _s , i _e ] is stored in c [i _s , i _e ]. _{E [~i} s, ~i _e] to _{q 3 [i s, i e} ] -2c [i s, i e] q 2 [i s, i e] + c [i s, i e] 2 q 1 [ i _s , i _e ] are stored.

  As described above, in the quantization method, the histogram of the input signal representing the value that can take the range expressed by the first number of levels (number of input signal levels) is expressed as the second level smaller than the first number of levels. A quantization method in a quantization apparatus that approximates a histogram of an output signal that represents a value that can take a range expressed by a number (quantization level number), and includes a storing step and a selecting step. The approximate error minimum value determination unit 21 determines a class that is a set of elements of the histogram of the input signal, restricts class boundary candidates that are class boundaries to significant elements, and sets upper and lower limits to significant elements that can be class boundaries. Significant elements included in the range from the upper limit to the lower limit are determined as class boundary candidates, and the insignificant elements in each section with the upper limit of the selectable range as the lower end of the upper limit of the selectable range of the class boundary Compare the position of the significant element corresponding to the value obtained by subtracting the maximum value of the consecutive number and the position of the significant element that is closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class. Significant elements indicating the new limit of the class boundary selectable range are defined, and the quantized value that minimizes the approximate error accumulated value up to the class boundary and the minimum approximate error accumulated value are stored in memory. To. When selecting the class boundary, the upper end tracking unit 24 excludes the insignificant element from the calculation of the cumulative value of the approximation error, acquires the stored minimum value from the memory, and calculates the minimum value for the calculation of the approximation error in the selection of the class boundary. Is used to select a class boundary that minimizes the sum of approximation errors for all elements of the class boundary.

  As a result, the quantization method can reduce the amount of calculation required for quantization even when the conversion error that occurs when performing gradation conversion of a signal is minimized. In other words, the quantization method can reduce the amount of calculation while maintaining the optimality of the bit depth conversion error by considering the sparseness of the pixel value.

  In the quantization method, a histogram of an input signal representing a value that can take a range expressed by a first number of levels (number of input signal levels) is expressed by a second number of levels (quantization level) smaller than the first level number. A quantization method in a quantization apparatus that approximates with a histogram of an output signal that represents a value that can take a range expressed by a number), and includes a storing step and a selecting step. The approximate error minimum value determination unit 21 determines a class that is a set of elements of the histogram of the input signal, restricts class boundary candidates that are class boundaries to significant elements, and sets upper and lower limits to significant elements that can be class boundaries. Define significant elements included in the range from the upper limit to the lower limit as class boundary candidates, and set the non-significant elements in each section with the lower limit of the selectable range as the upper limit relative to the lower limit of the selectable range of the class boundary. Compare the position of the significant element corresponding to the value obtained by subtracting the maximum value of the consecutive number and the position of the significant element closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class. Significant elements that indicate the value are defined as the new lower limit of the class boundary selectable range, and the quantized value that minimizes the approximate error accumulated value up to the class boundary and the minimum approximate error accumulated value are stored in memory. To. When selecting the class boundary, the upper end tracking unit 24 excludes the insignificant element from the calculation of the cumulative value of the approximation error, acquires the stored minimum value from the memory, and calculates the minimum value for the calculation of the approximation error in the selection of the class boundary. Is used to select a class boundary that minimizes the sum of approximation errors for all elements of the class boundary.

  As a result, the quantization method can reduce the amount of calculation required for quantization even when the conversion error that occurs when performing gradation conversion of a signal is minimized. In other words, the quantization method can reduce the amount of calculation while maintaining the optimality of the bit depth conversion error by considering the sparseness of the pixel value.

  You may make it implement | achieve at least one part of the quantization apparatus in embodiment mentioned above with a computer. In that case, a program for realizing this function may be recorded on a computer-readable recording medium, and the program recorded on this recording medium may be read into a computer system and executed. Here, the “computer system” includes an OS and hardware such as peripheral devices. The “computer-readable recording medium” refers to a storage device such as a flexible medium, a magneto-optical disk, a portable medium such as a ROM and a CD-ROM, and a hard disk incorporated in a computer system. Furthermore, the “computer-readable recording medium” dynamically holds a program for a short time like a communication line when transmitting a program via a network such as the Internet or a communication line such as a telephone line. In this case, a volatile memory inside a computer system serving as a server or a client in that case may be included and a program held for a certain period of time. Further, the program may be a program for realizing a part of the above-described functions, and may be a program capable of realizing the functions described above in combination with a program already recorded in a computer system. You may implement | achieve using programmable logic devices, such as FPGA (Field Programmable Gate Array).

  The embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and includes designs and the like that do not depart from the gist of the present invention.

DESCRIPTION OF SYMBOLS 1a ... Quantizer, 1b ... Quantizer, 10 ... Histogram generation part, 11 ... 1st element number storage part, 12 ... Class number storage part, 13 ... Index reference table generation part, 14 ... Index storage part, 15 ... Element number reference table generation unit, 16 ... second element number storage unit, 17 ... upper bound value reference table generation unit, 18 ... upper bound value storage unit, 19 ... lower bound value reference table generation unit, 20 ... lower bound value storage unit, DESCRIPTION OF SYMBOLS 21 ... Approximate error minimum value determination part, 22 ... Approximate error minimum value memory | storage part, 23 ... Upper end memory | storage part, 24 ... Upper end tracking part, 25 ... Approximation error determination part, 26 ... Approximation error memory | storage part

Claims (4)

A histogram of an input signal representing a value that can take a range expressed by the first number of levels is represented by an output signal that represents a value that can take a range expressed by the second number of levels less than the first number of levels. A quantization method in a quantization device approximating with a histogram,
Defining a class that is a set of histogram elements of the input signal, limiting class boundary candidates that are boundaries of the class to significant elements, determining upper and lower limits for the significant elements that can be the class boundary, and from the upper limit The significant element included in the range up to the lower limit is determined as the candidate for the class boundary, and the insignificant element in each section having the upper limit of the selectable range as the lower end with respect to the upper limit of the selectable range of the class boundary The position of the significant element corresponding to the value obtained by subtracting the maximum value of the consecutive number of the number of the significant element and the position of the significant element closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class are compared. Quantifying the significant element showing a relatively large value as a new upper limit of the selectable range of the class boundary, and minimizing the cumulative value of the approximation error up to the class boundary And storing the minimum value of the cumulative value of the values and the approximation error in the memory,
When selecting the class boundary, the non-significant element is excluded from calculation of the cumulative value of the approximation error, the stored minimum value is obtained from the memory, and the approximation error is calculated in the selection of the class boundary. Selecting the class boundary that minimizes the sum of the approximation errors for all elements of the class boundary by using a minimum value;
Including a quantization method. A histogram of an input signal representing a value that can take a range expressed by the first number of levels is represented by an output signal that represents a value that can take a range expressed by the second number of levels less than the first number of levels. A quantization method in a quantization device approximating with a histogram,
Defining a class that is a set of histogram elements of the input signal, limiting class boundary candidates that are boundaries of the class to significant elements, determining upper and lower limits for the significant elements that can be the class boundary, and from the upper limit The significant element included in the range up to the lower limit is determined as the class boundary candidate, and the non-significant element in each section whose upper end is the lower limit of the selectable range with respect to the lower limit of the selectable range of the class boundary The position of the significant element corresponding to the value obtained by adding the maximum value of the consecutive number of the number of the significant element is compared with the position of the significant element closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class. Quantifying the significant element showing a relatively small value as a new lower limit of the selectable range of the class boundary, and minimizing the cumulative value of the approximation error up to the class boundary And storing the minimum value of the cumulative value of the values and the approximation error in the memory,
When selecting the class boundary, the non-significant element is excluded from calculation of the cumulative value of the approximation error, the stored minimum value is obtained from the memory, and the approximation error is calculated in the selection of the class boundary. Selecting the class boundary that minimizes the sum of the approximation errors for all elements of the class boundary by using a minimum value;
Including a quantization method. A histogram of an input signal representing a value that can take a range expressed by the first number of levels is represented by an output signal that represents a value that can take a range expressed by the second number of levels less than the first number of levels. A quantization device approximating with a histogram,
Defining a class that is a set of histogram elements of the input signal, limiting class boundary candidates that are boundaries of the class to significant elements, determining upper and lower limits for the significant elements that can be the class boundary, and from the upper limit The significant element included in the range up to the lower limit is determined as the candidate for the class boundary, and the insignificant element in each section having the upper limit of the selectable range as the lower end with respect to the upper limit of the selectable range of the class boundary The position of the significant element corresponding to the value obtained by subtracting the maximum value of the consecutive number of the number of the significant element and the position of the significant element closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class are compared. Quantifying the significant element showing a relatively large value as a new upper limit of the selectable range of the class boundary, and minimizing the cumulative value of the approximation error up to the class boundary An approximate error minimum value determining unit for storing the minimum value of the cumulative value of the values and the approximation error in the memory,
When selecting the class boundary, the non-significant element is excluded from calculation of the cumulative value of the approximation error, the stored minimum value is obtained from the memory, and the approximation error is calculated in the selection of the class boundary. An upper end tracking unit that selects the class boundary that minimizes the sum of the approximation errors for all elements of the class boundary by using a minimum value;
A quantization apparatus comprising: A histogram of an input signal representing a value that can take a range expressed by the first number of levels is represented by an output signal that represents a value that can take a range expressed by the second number of levels less than the first number of levels. To the computer of the quantizer that approximates with a histogram,
Defining a class that is a set of histogram elements of the input signal, limiting class boundary candidates that are boundaries of the class to significant elements, determining upper and lower limits for the significant elements that can be the class boundary, and from the upper limit The significant element included in the range up to the lower limit is determined as the candidate for the class boundary, and the insignificant element in each section having the upper limit of the selectable range as the lower end with respect to the upper limit of the selectable range of the class boundary The position of the significant element corresponding to the value obtained by subtracting the maximum value of the consecutive number of the number of the significant element and the position of the significant element closest to the upper limit of the selectable range among the significant elements that can be taken as the upper limit of the class are compared. Quantifying the significant element showing a relatively large value as a new upper limit of the selectable range of the class boundary, and minimizing the cumulative value of the approximation error up to the class boundary A step of storing the minimum value of the cumulative value of the values and the approximation error in the memory,
When selecting the class boundary, the non-significant element is excluded from calculation of the cumulative value of the approximation error, the stored minimum value is obtained from the memory, and the approximation error is calculated in the selection of the class boundary. Selecting the class boundary that minimizes the sum of the approximation errors for all elements of the class boundary by using a minimum value;
Quantization program to execute.

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