JP2009118297A - Quantization method and quantization device for specimen value - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform proper quantization, even when a sample that has a very singular specimen value is included. <P>SOLUTION: The quantization is performed, by associating any quantization value of an (m) stage with respective (n) pieces of samples having a predetermined specimen value. The lower limit value SL larger than the minimum value of the specimen value, the upper limit value SH smaller than a maximum value are set, and sections SL-SH are set as the quantization object range (b). The quantization object range (b) is divided into M stages, and a predetermined quantization value is respectively determined in the respective stages. Although the quantization value of the stage belonging with its specimen value is respectively associated with the respective samples, the quantization value of the stage belonging to a lower limit value SL associated with the sample, having a specimen value less than the lower limit value SL, the quantization value of the stage belonging with the upper limit value SH is associated with the sample, having a specimen value exceeding the upper limit value SH. The lower limit value SL and the upper limit value SH are defined by designating a cumulative distribution function value, when it is assumed that the distribution of the specimen value is a normal distribution. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a sample value quantization method and a quantization apparatus, and more particularly to a quantum value obtained by associating one of m stages of quantized values with each of n samples having a predetermined sample value. It is related to the technology to make.

  A technique for quantizing each sample value with respect to a large number of samples each having a unique sample value is widely used in various industrial fields. In particular, when analog data is converted into digital data and taken into a computer for processing, the analog scalar value is quantized and converted into digital data. For example, image data captured by a scanner or a digital camera is data obtained by quantizing a scalar value of an analog original image and converting it into a digital value. In this case, if the analog original image is captured as an 8-bit gradation image, the scalar value of the analog original image is quantized into any one of 256 digital values.

Various ideas have been proposed for reducing the quantization error that occurs when performing such quantization. For example, in Patent Document 1 below, when an image on a document is captured by a scanner and quantized, the document portion and the photograph portion on the document are handled separately, and quantization is performed using different reference values. Thus, a technique for generating digital image data having an appropriate density change is disclosed. Further, in Patent Document 2 described below, when analog data obtained by measurement, such as a thermal noise signal, is quantized into digital data, the interval between representative points used for quantization is set non-uniformly to be nonlinear. A technique for performing quantization and reducing the quantization error is disclosed.
JP-A-6-125456 JP 2006-46953 A

  In general, when quantizing individual sample values of a large number of samples, the numerical range from the maximum value to the minimum value of the sample values is divided into m stages, and predetermined quantized values are determined for each stage. A process for associating a quantized value at a stage to which the sample value belongs is performed. However, if samples with extremely specific sample values (for example, extremely large values or extremely small values) are included, the numerical range including the specific sample values is divided into m stages and quantized. As a result, the number of effective quantization steps is reduced, and appropriate quantization processing is hindered. In particular, analog signals captured using various measuring devices such as scanners and digital cameras contain noise components, and such noise components often give extremely specific sample values.

  Accordingly, an object of the present invention is to provide a sample value quantization method and a quantization apparatus capable of performing an appropriate quantization process even when a sample having a very specific sample value is included. To do.

(1) In the first aspect of the present invention, a sample value to be quantized by associating one of m stages of quantized values with each of n samples having a predetermined sample value. In the quantization method,
An input step for inputting a sample value of n samples as digital data to a computer and storing it in a predetermined storage location;
A condition setting step for setting a stage number m (m is a natural number of 2 or more) and a parameter value C (0 <C <1) for the computer;
A sorting step in which a computer performs a process of rearranging n sample values stored in a storage location in order of size;
The computer sets the value of the ((n × (1-C)) / 2 + 1) -th sample value from the smallest to the lower limit SL based on the n sample values rearranged in order of magnitude by the sorting step. And an upper and lower limit determination step for determining the value of the (n− (n × (1-C)) / 2) -th sample value from the smaller one as the upper limit value SH;
A stage determination step in which a computer divides a numerical range from a lower limit value SL to an upper limit value SH into m stages and determines a predetermined quantization value for each stage;
A quantization step in which a computer associates the quantized value of the stage to which the sample value belongs for each of the n samples, and stores each associated quantized value in a memory location corresponding to each sample;
And
In the quantization step, for samples having a sample value less than the lower limit SL among the n samples, a sample having a sample value exceeding the upper limit SH is associated with the quantized value of the stage to which the lower limit SL belongs. Is associated with the quantized value at the stage to which the upper limit SH belongs.

(2) According to the second aspect of the present invention, a sample value to be quantized by associating one of m stages of quantized values with each of n samples having a predetermined sample value. In the quantization method,
An input step for inputting a sample value of n samples as digital data to a computer and storing it in a predetermined storage location;
A condition setting step for setting a stage number m (m is a natural number of 2 or more), a parameter value C (0 <C <1), and a balance value P (0 ≦ P ≦ 1) for the computer;
A sorting step in which a computer performs a process of rearranging n sample values stored in a storage location in order of size;
The computer sets the value of the ((n × (1-C)) × P + 1) -th sample value from the smallest to the lower limit SL based on the n sample values rearranged in order of magnitude by the sorting step. And an upper and lower limit determination step for determining the value of the (n− (n × (1-C)) × (1-P))-th sample value from the smaller one as the upper limit value SH;
A stage determination step in which a computer divides a numerical range from a lower limit value SL to an upper limit value SH into m stages and determines a predetermined quantization value for each stage;
A quantization step in which a computer associates the quantized value of the stage to which the sample value belongs for each of the n samples, and stores each associated quantized value in a memory location corresponding to each sample;
And
In the quantization step, for samples having a sample value less than the lower limit SL among the n samples, a sample having a sample value exceeding the upper limit SH is associated with the quantized value of the stage to which the lower limit SL belongs. Is associated with the quantized value at the stage to which the upper limit SH belongs.

(3) According to the third aspect of the present invention, a sample value to be quantized by associating one of m stages of quantized values with each of n samples having a predetermined sample value. In the quantization method,
An input step for inputting a sample value of n samples as digital data to a computer and storing it in a predetermined storage location;
A condition setting step for setting a stage number m (m is a natural number of 2 or more) and a parameter value C (0 <C <1) for the computer;
An average / standard deviation calculation step in which the computer calculates an average value M and a standard deviation σ for n sample values stored in the storage location;
In the normal distribution, the cumulative distribution function value f (z) indicating the proportion of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation” in the normal distribution is the parameter value C. An upper and lower limit determination step for determining an equalized standardized score z and determining an upper limit SH = M + zσ and a lower limit SL = M−zσ using the calculated average value M and standard deviation σ and standardized score z;
A stage determination step in which a computer divides a numerical range from a lower limit value SL to an upper limit value SH into m stages and determines a predetermined quantization value for each stage;
A quantization step in which a computer associates the quantized value of the stage to which the sample value belongs for each of the n samples, and stores each associated quantized value in a memory location corresponding to each sample;
And
In the quantization step, for samples having a sample value less than the lower limit SL among the n samples, a sample having a sample value exceeding the upper limit SH is associated with the quantized value of the stage to which the lower limit SL belongs. Is associated with the quantized value at the stage to which the upper limit SH belongs.

(4) According to a fourth aspect of the present invention, in the sample value quantization method according to the third aspect described above,
Cumulative distribution function value f (z) indicating the proportion of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation”, where z is the standardized score in the normal distribution A correspondence table showing the correspondence between the standardized score z and the standardized score z is prepared in advance in the computer, and in the upper and lower limit determination step, the cumulative distribution function value f (z) equal to the parameter value C is obtained by referring to the correspondence table. The corresponding standardized score z is obtained.

(5) According to a fifth aspect of the present invention, in the sample value quantization method according to the first to fourth aspects described above,
In the quantization stage, for a sample having a sample value S, a calculation value of ((S-SL) / (SH-SL)) × (m−1) is rounded to an integer value “0- ( The quantization is performed by associating the “quantized values indicated by integers within the range of m−1)”.

(6) According to a sixth aspect of the present invention, a sample value to be quantized by associating one of m stages of quantized values with each of n samples having a predetermined sample value. In the quantizer,
An original data storage unit for inputting sample values of n samples as digital data and storing the digital data;
A condition setting unit for setting the number of steps m (m is a natural number of 2 or more) and the parameter value C (0 <C <1) in advance or based on an operator's instruction;
a sort working unit that temporarily holds n sample values for sorting;
A sort processing unit that replicates n sample values stored in the original data storage unit, holds the sample value in the sort operation unit, and performs a process of rearranging the sample values in order of size;
After the rearrangement process by the sort processing unit is completed, the ((n × (1-C)) / 2 + 1) from the smallest one is based on the n sample values arranged in order of size in the sort operation unit. An upper / lower limit determination unit that determines the value of the nth sample value as the lower limit value SL and determines the value of the (n− (n × (1−C)) / 2) th sample value from the smaller value as the upper limit value SH. When,
The numerical value range from the lower limit value SL to the upper limit value SH is divided into m stages, a predetermined quantization value is determined for each stage, and the quantization value of the stage to which the sample value belongs for each of the n samples. A corresponding quantization processing unit;
a quantized data storage unit that stores, as digital data, a quantized value associated with each of n samples;
Provided,
The quantization processing unit associates the quantized value at the stage to which the lower limit value SL belongs with respect to a sample having a sample value less than the lower limit value SL among the n samples, and has a sample value exceeding the upper limit value SH. For the sample, the quantization value at the stage to which the upper limit SH belongs belongs.

(7) According to a seventh aspect of the present invention, a sample value to be quantized by associating one of m stages of quantized values with each of n samples having a predetermined sample value. In the quantizer,
An original data storage unit for inputting sample values of n samples as digital data and storing the digital data;
A condition setting unit for setting the step number m (m is a natural number of 2 or more), the parameter value C (0 <C <1), and the balance value P (0 ≦ P ≦ 1) in advance or based on an instruction from the operator;
a sort working unit that temporarily holds n sample values for sorting;
A sort processing unit that replicates n sample values stored in the original data storage unit, holds the sample value in the sort operation unit, and performs a process of rearranging the sample values in order of size;
After the rearrangement process by the sort processing unit is completed, the ((n × (1-C)) × P + 1) from the smallest one is based on the n sample values arranged in order of size in the sort operation unit. The value of the nth sample value is determined as the lower limit value SL, and the value of the (n− (n × (1−C)) × (1−P)) th sample value from the smaller value is determined as the upper limit value SH. An upper / lower limit determination unit;
The numerical value range from the lower limit value SL to the upper limit value SH is divided into m stages, a predetermined quantization value is determined for each stage, and the quantization value of the stage to which the sample value belongs for each of the n samples. A corresponding quantization processing unit;
a quantized data storage unit that stores, as digital data, a quantized value associated with each of n samples;
Provided,
The quantization processing unit associates the quantized value at the stage to which the lower limit value SL belongs with respect to a sample having a sample value less than the lower limit value SL among the n samples, and has a sample value exceeding the upper limit value SH. For the sample, the quantization value at the stage to which the upper limit SH belongs belongs.

(8) According to an eighth aspect of the present invention, a sample value to be quantized by associating one of m stages of quantized values with each of n samples having a predetermined sample value. In the quantizer,
An original data storage unit for inputting sample values of n samples as digital data and storing the digital data;
A condition setting unit for setting the number of steps m (m is a natural number of 2 or more) and the parameter value C (0 <C <1) in advance or based on an operator's instruction;
An average / standard deviation calculation unit for calculating an average value M and a standard deviation σ for n sample values stored in the original data storage unit;
Cumulative distribution function value f (z) indicating the proportion of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation”, where z is the standardized score in the normal distribution A correspondence table storage unit that stores a correspondence table indicating a correspondence relationship between and a standardized score z;
By referring to the correspondence table, the standardized score z corresponding to the cumulative distribution function value f (z) equal to the parameter value C is obtained, and using the obtained average value M, standard deviation σ, and standardized score z, the upper limit SH = M + zσ and a lower limit SL = M−zσ, an upper / lower limit determining unit;
The numerical value range from the lower limit value SL to the upper limit value SH is divided into m stages, a predetermined quantization value is determined for each stage, and the quantization value of the stage to which the sample value belongs for each of the n samples. A corresponding quantization processing unit;
a quantized data storage unit that stores, as digital data, a quantized value associated with each of n samples;
Provided,
The quantization processing unit associates the quantized value at the stage to which the lower limit value SL belongs with respect to a sample having a sample value less than the lower limit value SL among the n samples, and has a sample value exceeding the upper limit value SH. For the sample, the quantization value at the stage to which the upper limit SH belongs belongs.

(9) According to a ninth aspect of the present invention, in the sample value quantization apparatus according to the sixth to eighth aspects described above,
The quantization processing unit calculates “(0−S−SL) / (SH−SL)) × (m−1) for the sample having the sample value S by rounding it to an integer value“ 0 ”. Quantization is performed by associating “quantized values represented by integers within the range of (m−1)”.

  (10) According to a tenth aspect of the present invention, a program is incorporated into a computer so as to function as the sample value quantization apparatus according to the sixth to ninth aspects described above.

  According to the sample value quantization method and the quantization apparatus according to the present invention, when individual sample values of a large number of samples are quantized, the lower limit value SL instead of the minimum value of the sample values, and the maximum value of the sample values The upper limit value SH is determined, and the numerical range from the lower limit value SL to the upper limit value SH is divided into m stages and the quantization process is performed. For this reason, even when a sample having a very specific sample value such as an extremely large value or an extremely small value is included, an appropriate quantization process is performed. Therefore, even when a noise component is included in the sample value, it is possible to perform appropriate quantization with the noise component removed. Further, since the lower limit value SL and the upper limit value SH can be arbitrarily set by the parameter value C, the parameter value C suitable for each sample group is appropriately set, so that the optimum value for the sample group can be obtained. Quantization processing can be performed.

  Hereinafter, the present invention will be described based on the illustrated embodiments.

<<< §1. Conventional general quantization method and its problems >>
First, a conventional general quantization method and its problems will be described based on a specific example. Consider the case where a histogram as shown in FIG. 1 is obtained for a population of n samples each having a predetermined sample value. The illustrated example is an example in which the sample values are distributed in the range of 0 to 2550, and the minimum value Smin = 0 and the maximum value Smax = 2550 of the sample values. Here, quantization is performed by associating each of the n samples with one of m stages of quantization values.

In this case, in the conventional general quantization method, the quantization value Q associated with a sample having an arbitrary sample value S is:
Q = INT (((S−Smin) / (Smax−Smin)) × (m−1))
It is calculated by the following formula. Here, INT (X) is a function that rounds the value of X to an integer value (may be rounded, rounded up, or rounded down). For example, let us consider an example in which m = 256 and quantized values from 0 to 255 are defined so that the sample value of each sample can be expressed by 8-bit digital data. In this case, in the example of FIG. 1, Smin = 0 and Smax = 2550.
Q = INT (((S-0) / (2550-0)) × 255)
After all,
Q = INT ((S / 2550) × 255)
Any of the 256-level quantized values from 0 to 255 are associated with each other by the following arithmetic expression. A grid of 0 to 255 shown below the histogram of FIG. 1 indicates 256 levels of quantized values that are associated with sample values that take a numerical range of 0 to 2550.

The example shown in FIG. 1 is an example of a population whose sample value distribution state is almost a normal distribution. In such an example, even if a conventional general quantization method is adopted, there is no particular inconvenience. Does not occur. On the other hand, consider a population having a distribution state as shown in FIG. In this population, out of n samples, (n−1) sample values are distributed in the range of 0 to 510, but the last one sample value is 2550. That is, only one of the n samples takes a very specific sample value (an extremely large value). Thus, even if it is one sample, since the sample value is 2550, the entire population is distributed in the range of 0 to 2550. Therefore, since the minimum value Smin = 0 and the maximum value Smax = 2550 of the sample value, when m = 256, the quantized value Q associated with each sample is
Q = INT ((S / 2550) × 255)
Is given by the following equation.

  As a result, as shown in the lower part of the histogram in FIG. 2, the quantized values from 0 to 255 are associated with the sample values taking the numerical range from 0 to 2550. However, since the sample values of (n−1) samples are distributed within the range of 0 to 510, the quantized values associated with these samples are 0 to 51. A quantized value 255 is associated with a sample having a specific sample value 2550. In the end, there are no samples to which the quantization values 52 to 254 are associated, and even though the quantization of 256 steps is performed, it is substantially the same as that of the quantization of 52 steps. Result. That is, as shown in FIG. 2, if even one sample having a very specific sample value is included, the number of effective quantization steps is substantially reduced in the conventional quantization method. The quantization process will be hindered.

  In this way, a situation in which a sample having a very specific specimen value is mixed occurs not a little in the case of image data captured using a measuring device such as a scanner or a digital camera. For example, when electromagnetic noise is mixed in the measurement system, the analog output signal from the measurement pixel affected by the noise may show a very unique value as compared with signals from other pixels. Sample values resulting from such noise components should be excluded when performing quantization.

For example, in the case of the example shown in FIG. 2, if the sample having the sample value 2550 is ignored and the remaining (n−1) samples are quantized, the minimum value Smin = 0 of the sample value, Since the maximum value Smax = 510, when m = 256, the quantized value Q associated with each sample is
Q = INT ((S / 510) × 255)
Quantized values from 0 to 255 are associated with sample values that take a numerical range from 0 to 510.

  Of course, sample values to be excluded when performing quantization are not necessarily limited to sample values caused by noise components. For example, in the example shown in FIG. 2, even if the sample value 2550 does not originate from a noise component but shows an original correct measurement value, such a very specific sample value is quantized. It is better to exclude it.

  The present invention provides a sample value quantization method and a quantization method capable of performing appropriate quantization processing even when a sample having a very specific sample value is included as in the example shown in FIG. The object is to provide an apparatus, and its basic concept will be described below.

<<< §2. Basic concept of the present invention >>
The basic idea of the present invention is that when the sample values of n samples are distributed in the numerical range of the minimum values Smin to Smax, the entire numerical range is not set as the quantization target range, but at both ends thereof. The quantization is performed using the region excluding a part as the quantization target range.

  For example, FIG. 3 is a histogram of a population composed of n samples having sample values distributed in the range of 0 to 2550, as in the example shown in FIG. Therefore, the minimum value of the sample values of this population is Smin = 0, and the maximum value is Smax = 2550. Here, as shown in the figure, a lower limit SL slightly larger than the minimum value Smin = 0 and an upper limit SH slightly smaller than the maximum value Smax = 2550 are set. Divide into b and c. Here, the section a is a section from the minimum value Smin (= 0) to the lower limit value SL, the section b is a section from the lower limit value SL to the upper limit value SH, and the section c is an upper limit value SH to the maximum value Smax. (= 2550). Note that the lower limit value SL and the upper limit value SH serving as boundaries may conceptually belong to both sections.

Here, the interval b is set as the quantization target range, and the numerical range in the quantization target range b is divided into m stages, and predetermined quantization values are determined for each stage. Since the sections a and c are excluded from the quantization target, the section a is hereinafter referred to as a lower exclusion range and the section c is referred to as an upper exclusion range. And about the sample which has the sample value in the quantization object range b, the quantization value of the stage to which the sample value belongs is matched. That is, the quantized value Q associated with a sample having an arbitrary sample value S is
Q = INT (((S−SL) / (SH−SL)) × (m−1))
It is calculated by the following formula. As described above, INT (X) is a function that rounds the value of X to an integer value (may be rounded, rounded up, or rounded down). For example, if m = 256,
Q = INT (((S-SL) / (SH-SL)) × 255)
It becomes. The grids 0 to 255 shown below the histogram in FIG. 3 indicate 256-stage quantized values that are associated with the sample values in the quantization target range b.

  On the other hand, for samples having sample values less than the lower limit SL (samples belonging to the lower exclusion range a: the leftmost hatched portion of the histogram in FIG. 3), the quantization value 0 of the stage to which the lower limit SL belongs is associated. For samples having sample values exceeding the upper limit SH (samples belonging to the upper exclusion range c: the rightmost hatched portion of the histogram in FIG. 3), the quantization value 255 at the stage to which the upper limit SH belongs is associated. .

  With this handling, the appearance frequency of the lower exclusion range a is 0 in the quantized histogram, and the appearance frequency of this portion of the sample is added to the appearance frequency for the lower limit value SL. The frequency integration bar B1 shown in the histogram of FIG. 3 indicates the number of samples integrated in this way, and corresponds to the number of samples in the leftmost hatched portion of the histogram. Similarly, the appearance frequency of the upper exclusion range c is also 0, and the appearance frequency of this portion of the sample is added to the appearance frequency for the upper limit SH. The frequency integration bar B2 shown in the histogram of FIG. 3 indicates the number of samples integrated in this way, and corresponds to the number of samples in the rightmost hatched portion of the histogram.

  Thus, when performing the quantization according to the present invention as described above, a result slightly different from the result of the conventional quantization method shown in FIG. 1 is obtained. That is, the quantization target range is changed from the original range of Smin to Smax to the range of SL to SH, and the number of samples for which the quantized value is 0 is equal to the frequency integration bar B1 than the original range. Similarly, the number of samples taking the quantized value 255 is increased by the frequency integration bar B2 from the original. However, except for the samples that take the quantization values at both ends, a result that is not significantly different from the conventional quantization method can be obtained on a global basis, and there is no practical problem.

  The example shown in FIG. 3 is an example of a population in which the distribution state of sample values is almost a normal distribution, and thus the merit of the quantization method according to the present invention is not significant. However, when the present invention is applied to a population having extremely specific sample values, a great merit occurs. Specifically, consider the case where the present invention is applied to a population having a distribution state as shown in FIG. The histogram shown in FIG. 4 is the same as the histogram shown in FIG. 2. In this population, (n−1) sample values out of n samples are distributed in the range of 0 to 510. However, the last one sample value is 2550. Thus, when there is a sample having a very specific sample value 2550, the conventional quantization method has a problem that the number of effective quantization steps is substantially reduced and an appropriate quantization process is hindered. What happens is as already mentioned.

  In the quantization method according to the present invention, the following handling is performed. First, the minimum value of the sample values of this population is Smin = 0, and the maximum value is Smax = 2550. Here, as shown in the drawing, a lower limit value SL slightly larger than the minimum value Smin = 0 and an upper limit value SH considerably smaller than the maximum value Smax = 2550 are set, and the horizontal axis indicating the sample value is represented by the lower exclusion range a. , The range to be quantized b, and the upper exclusion range c. The lower exclusion range a is a section from the minimum value Smin (= 0) to the lower limit value SL, the quantization target range b is a section from the lower limit value SL to the upper limit value SH, and the upper exclusion range c is the upper limit value SH. It is a section of ~ maximum value Smax (= 2550).

  Then, as described above, the numerical range within the quantization target range b is divided into m stages, and predetermined quantization values are determined for the respective stages. For example, when m = 256, 256 levels of quantization values are defined as shown below the histogram of FIG. Then, for a sample having a sample value in the quantization target range b, the quantization value at the stage to which the sample value belongs is associated and a sample having a sample value less than the lower limit SL (belonging to the lower exclusion range a) For the sample: the hatched portion at the left end of the histogram in FIG. 4, a sample having a sample value exceeding the upper limit SH (corresponding to the quantization value 0 at the stage to which the lower limit SL belongs) (sample belonging to the upper exclusion range c: For the rightmost hatched portion of the histogram in FIG. 4 and the sample having the sample value 2550, the quantized value 255 at the stage to which the upper limit SH belongs belongs.

  With this handling, the appearance frequency of the lower exclusion range a is 0 in the quantized histogram, and the appearance frequency of this portion of the sample is added to the appearance frequency for the lower limit value SL. The frequency integration bar B1 shown in the histogram of FIG. 4 indicates the number of samples integrated in this way, and corresponds to the number of samples in the leftmost hatched portion of the histogram. Similarly, the appearance frequency of the upper exclusion range c is also 0, and the appearance frequency of this portion of the sample is added to the appearance frequency for the upper limit SH. The frequency integration bar B2 shown in the histogram of FIG. 4 indicates the number of samples integrated in this way, and corresponds to the number of samples of the sample having the rightmost hatched portion of the histogram and the sample value 2550.

  After all, the quantization target range is changed from the original range Smin to Smax to the range SL to SH, and the number of samples taking the quantized value 0 is equal to the frequency integration bar B1 than the original range. Similarly, the number of samples that take the quantized value 255 is increased by the frequency integration bar B2 from the original, but generally, appropriate quantization is performed.

  If the result based on the conventional quantization method shown in FIG. 2 is compared with the result based on the quantization method according to the present invention shown in FIG. 4, the merit of the present invention is obvious. In the example shown in FIG. 2, quantization values from 0 to 255 are associated with sample values that take a numerical value range from 0 to 2550, so 256 levels of quantization are performed. Regardless, the result is substantially the same as when performing 52-stage quantization. On the other hand, in the example shown in FIG. 4, the quantized values from 0 to 255 for the quantization target range b from the lower limit value SL to the upper limit value SH with respect to the sample value taking the numerical range from 0 to 2550. Therefore, 256 stages of quantization have been performed on the range in which the majority of samples are distributed, and the number of effective quantization stages can be sufficiently secured. Therefore, an appropriate quantization process can be performed.

  Here, it is understood that how to set the lower limit value SL and the upper limit value SH is important in carrying out the present invention. For example, in the case of the example shown in FIG. 4, the lower limit SL = 30 is set as a value +30 with respect to the minimum value Smin = 0, and the upper limit SH is set as a value −30 with respect to the maximum value Smax = 2550. If the setting of = 2520 is performed, it will be understood that the merit of the present invention cannot be sufficiently obtained with such a setting. In this case, although the lower exclusion range a and the upper exclusion range c corresponding to the numerical value range 30 are set, the quantization target range b is a numerical range of 30 to 2520, and the number of effective quantization stages is substantially equal to the numerical range. It cannot be secured sufficiently. Therefore, a setting method in which a predetermined absolute value Δ is set and the lower limit value SL = minimum value Smin + Δ and the upper limit value SL = maximum value Smax−Δ is not an effective method. Similarly, there is a setting method in which a predetermined ratio G% is determined, and the lower limit value SL = minimum value Smin + (Smax−Smin) × G% and the upper limit value SL = maximum value Smax− (Smax−Smin) × G%. It is not an effective method.

  The inventor of the present application has realized that it is best to determine the lower limit value SL and the upper limit value SH based on the ratio of the number of samples in order to make full use of the merits of the present invention. Specifically, for example, when all n samples are arranged in ascending order of the sample values, the samples belonging to the rank n × 0% to n × 5% are included in the lower exclusion range a, and the rank is Samples belonging to n × 5% to n × 95% are included in the quantization target range b, and samples belonging to the rank n × 95% to n × 100% are included in the upper exclusion range c. A lower limit value SL and an upper limit value SH that are boundaries of the ranges a, b, and c are set. Then, 5% of the samples whose sample values are less than the lower limit SL and 5% of the samples whose sample values exceed the upper limit SH are out of the quantization target range b, and the remaining 90%. The sample is a sample within the quantization target range b.

  In other words, some samples with small sample values and some samples with large sample values are excluded, and the distribution range of sample values of “n × 90%” samples with medium sample values is quantized. The quantization is performed as the quantization target range b. When such setting is performed, in the example shown in FIG. 3, the number of samples belonging to the leftmost hatched portion of the histogram is “n × 5%”, the number of samples belonging to the rightmost hatched portion of the histogram is “n × 5%”, The number of samples belonging to the remaining intermediate portion is “n × 90%”. Similarly, in the example illustrated in FIG. 4, the number of samples belonging to the leftmost hatched portion of the histogram is “n × 5%”, and the total number of samples belonging to the rightmost hatched portion of the histogram and the sample value 2550 is “n × 5%”. ”, The number of samples belonging to the remaining intermediate portion is“ n × 90% ”. If the lower limit value SL and the upper limit value SH are set by such a method, quantization that makes full use of the merits of the present invention becomes possible.

  Of course, the ratio of the number of samples belonging to the intermediate portion does not necessarily need to be set to 90%, and may be set to 85% or 80%. In the present invention, the ratio of the number of samples belonging to the intermediate portion (the ratio of the number of samples included in the quantization target range b to the total number of samples n) is set as the parameter value C (0 <C <1). . If C = 90%, the remaining 10% of the samples belong to the lower exclusion range a or the upper exclusion range c, and even if these 10% samples have very specific specimen values, Appropriate quantization will be performed.

  The smaller the parameter value C is set, the more samples having specific sample values can be driven to the exclusion range. However, the quantization target range b is narrowed so much, and the quantization result is the conventional quantum value. The result of quantization is free from the result of quantization, and the obtained quantization result is distorted compared to the original quantization result. Therefore, in practice, for a population that seems to have a relatively large number of samples having unique sample values, the parameter value C is set to a relatively small value, for example, 80%, and is shown in FIG. For a population that seems to be close to such a normal distribution, the parameter value C is appropriately set according to the characteristics of the population, such as 98%, for example. do it.

<<< §3. Basic embodiment of the present invention >>
Next, a basic embodiment of the sample value quantization method according to the present invention will be described with reference to the flowchart of FIG. This quantization method is a method of performing quantization by associating one of m stages of quantization values with each of n samples having a predetermined sample value. It is comprised from the process performed by.

  First, in the input step S1, a sample value of n samples is input as digital data to the computer and stored in a predetermined storage location. Here, for example, it is assumed that n digital data S1, S2, S3,..., Sn are input to the computer as sample values.

The next condition setting step S2 is a processing stage for setting the quantization processing conditions for the input n samples, and for the computer, the stage number m (m is a natural number of 2 or more) and parameter value C (0 <C <1) is set. For example, if the quantized sample is expressed by 8-bit data, any of the n samples is associated with one of 256 quantization values 0 to 255. = 256 (2 ⁸ ). On the other hand, as described above, the parameter value C is a value indicating the proportion of samples included in the quantization target range b out of all n samples, and according to the characteristics of the population composed of n samples, An appropriate value (for example, a value such as 90%) may be set.

  The processes in steps S1 and S2 described above are processes that are executed when an operator who operates the computer performs some operation on the computer, and can be said to be a preparation process for quantization. On the other hand, steps S3 to S6 described below are processes automatically executed by the computer.

  First, in the sorting step S3, a process of rearranging the n sample values input in step S1 and stored in the storage location in the computer in order of size is performed. The n pieces of digital data S1, S2, S3,..., Sn input in step S1 are sample values of the respective samples, and these sample values are rearranged in ascending order or descending order. Note that the process of rearranging data having scalar values in the order of size is a known process generally called a sort process, and various algorithms are known. Therefore, a detailed description of the procedure for performing the sorting process is omitted here.

  In the subsequent upper / lower limit determination step S4, the process of determining the lower limit value SL and the upper limit value SH described in §2 is performed. Specifically, the value of the ((n × (1-C)) / 2 + 1) -th sample value from the smaller one is calculated based on the n sample values rearranged in order of magnitude by the sorting step S3. The lower limit value SL is determined, and the process of determining the value of the (n− (n × (1-C)) / 2) th sample value from the smaller value as the upper limit value SH is performed (the calculation result is the integer number). If not, round it up by rounding down or rounding up) By executing the sort step S3, the sample values are stored in the memory in the computer in the order of the size in the order of the addresses. Therefore, the value of the Xth sample value from the smallest is the address corresponding to the Xth. Can be recognized by reading the data stored in the. Therefore, the process of step S4 is a process of reading data from each specific address and setting it to the lower limit value SL and the upper limit value SH.

  Here, for example, consider the case where n = 10000 sample values are input in step S1, and the parameter value C = 90% (0.9) is set in step S2. In this case, the value of the ((n × (1-C)) / 2 + 1) th from the smallest, that is, the value of the 501st sample value from the smallest is the lower limit SL, and the (n− (n × n × The value of the (1-C)) / 2) th, that is, the 9500th sample value from the smallest is the upper limit SH. The actual values of the lower limit SL and the upper limit SH are determined depending on the values of the 501st and 9500th sample values from the smallest. Naturally, the values of the lower limit SL and the upper limit SH are as follows when the population having the distribution shown in FIG. 3 is targeted and when the population having the distribution shown in FIG. 4 is targeted. Different.

  In the next stage determination step S5, the numerical value range from the lower limit value SL to the upper limit value SH is divided into m stages, and processing for determining a predetermined quantized value for each stage is performed. For example, assuming that the number of stages m = 256 is set in step S2, in the case of the above-described specific example, the numerical range of the 501st to 9500th sample values from the smallest is the quantization target range b. Are divided into 256 stages, and a quantization value of 0 to 255 is associated with each stage.

  Then, in the last quantization step S6, for each of the n samples, the quantization value at the stage to which the sample value belongs is associated, and each associated quantization value is stored in a memory location corresponding to each sample. Processing is performed. Specifically, for a sample having the sample value S, “0 (-(S−SL) / (SH−SL)) × (m−1)” is obtained by rounding the calculated value to an integer value. Quantization is performed by associating a “quantized value indicated by an integer within a range of m−1)”. However, for a sample having a sample value less than the lower limit SL, the quantization value at the stage to which the lower limit SL belongs is associated, and for a sample having a sample value exceeding the upper limit SH, the stage to which the upper limit SH belongs. Associate the quantized values of.

That is, for a sample with a sample value S,
Q = INT (((S−SL) / (SH−SL)) × (m−1))
The quantized value Q obtained by the following arithmetic expression is associated. However, INT (X) is a function for rounding the value of X to an integer value (rounding, rounding up, or rounding down). For example, if SL = 50, SH = 460, S = 123, m = 256, and a function that truncates the fractional part of X as INT (X) is used,
Q = INT (((123-50) / (460-50)) × (256-1))
As a result, a quantized value of Q = 45 is obtained. Accordingly, a quantized value of Q = 45 is associated with a sample having a sample value of S = 123.

  Further, since the lower limit value SL = 50, for samples having a sample value less than S = 50, a quantized value of Q = 0 is uniformly associated with the upper limit value SH = 460, so S = 460. For samples having a sample value exceeding 1, a quantized value of Q = 255 is uniformly associated.

  FIG. 6 is a block diagram showing the configuration of the quantization processing apparatus according to the basic embodiment of the present invention. This device is a device that performs quantization by associating one of m stages of quantized values with each of n samples having a predetermined sample value. Each of the samples shown in the flowchart of FIG. It has a function to execute steps. As described above, each step is actually a process executed using a computer. As shown in FIG. 6, this apparatus is referred to as an original data storage unit 10, a sort operation unit 20, a sort processing unit 30, a quantization processing unit 40, an upper / lower limit determination unit 50, a condition setting unit 60, and a quantized data storage unit 70. Each block is composed of a collection of blocks. Actually, each of these components is realized by incorporating a dedicated program into a computer.

  The original data storage unit 10 is a component that inputs the sample values of n samples as digital data and stores them. In the case of the embodiment shown here, the original data storage unit 10 is constituted by a hard disk device for a computer. The operator inputs the sample values S1, S2, S3,..., Sn of the n samples as digital data in a file format having a predetermined data format, and stores it in the original data storage unit 10. Will do.

  The data stored in the original data storage unit 10 includes a data identification code as necessary together with the sample value of each sample. For example, if the population data to be quantized is a measurement of some physical quantity at a number of locations on the earth, it usually identifies which point the individual sample is at. Information is needed. In such a case, for example, digital data as shown in FIG. 7A is input to the original data storage unit 10. The data S1, S2, S3,..., Sn shown in the right column of FIG. 7 (a) are sample values of each sample, that is, in the above example, measured values at individual points. The indicated data D1, D2, D3,..., Dn are data identification codes, that is, data such as latitude and longitude for specifying individual points. Accordingly, the information shown in FIG. 7A is information indicating that the measured value of the i-th point (the point specified by the latitude and longitude Di) is Si among all n points.

  On the other hand, the sort work unit 20 is a component used as a work place for the sort processing performed by the sort processing unit 30 and has a function of temporarily holding n sample values for sorting. In the case of the embodiment shown here, the sort working unit 20 is configured by a computer memory (RAM).

  The sort processing unit 30 is a component that performs a process of copying n sample values stored in the original data storage unit 10 and holding them in the sort operation unit 20 and rearranging them in order of size, Actually, it is realized by causing a CPU of a computer to execute a predetermined sort routine.

  For example, when data as shown in FIG. 7 (a) is stored in the original data storage unit 10, the sort processing unit 30 first selects the sample values S1, S2, S3,. .., Sn are copied to the sort working unit 20. FIG. 7B shows the sample values S1, S2, S3,..., Sn thus copied to the sort operation unit 20. Note that the data identification code is not necessary for the sort operation, and therefore it is not necessary to duplicate the data identification code to the sort operation unit 20.

  In the embodiment shown here, the sort operation unit 20 is a memory, and each sample value is stored as fixed-length data in a continuous address space of this memory. Therefore, the address value indicating the storage location of the i-th sample value stored in this address space can be obtained by a simple calculation.

  As described above, various methods are known for processing (sorting) the fixed-length data stored in the continuous address space on the memory in the order of the size. For example, if the data is to be rearranged in a method called bubble sort, the i-th data is compared with the (i + 1) -th data, and if the former ≦ the latter, the former> In the latter case, a process of sequentially executing the steps of exchanging both from i = 1 to (n−1) may be repeated until no data exchange occurs. There are various other data sorting algorithms known in the art, and a detailed description thereof is omitted here.

  The condition setting unit 60 is a component that sets the step number m (m is a natural number of 2 or more) and the parameter value C (0 <C <1) in advance or based on an operator's instruction. When the values of m and C are fixed and used, for example, fixed values such as m = 256 and C = 90% (0.9) may be set in advance by a program. In this case, the quantization process is always executed under the condition that the number of steps m = 256 and the parameter value C = 90%. However, in practice, the number of steps m and the parameter value C (0 <C <1) can be arbitrarily set based on the operator's instruction in accordance with the characteristics of the population, the use form of the data after quantization, and the like. It is preferable to do so. In that case, an input screen may be presented on the display screen so that the operator can input and set a desired value.

  After the rearrangement process by the sort processing unit 30 is completed, the upper and lower limit determination unit 50 starts from the smallest ((n × n) based on the n sample values arranged in the sort operation unit 20 in order of size. The value of the (1-C)) / 2 + 1) th sample value is determined as the lower limit value SL, and the value of the (n− (n × (1-C)) / 2) th sample value from the smaller one is the upper limit. Processing to determine the value SH is performed. Here, the value of n is the total number of sample values stored in the sort operation unit 20, and the value of C is the value of the parameter value C set in the condition setting unit 60. The meanings of the lower limit value SL and the upper limit value SH thus determined are as described above.

  FIG. 7 (c) is a diagram showing n sample values arranged in the order of size (in this example, in ascending order) after the sorting process by the sort processing unit 30 is completed. is there. As shown in the figure, the minimum value Smin of the sample values is stored in the first in the continuous address space of the memory, and the maximum value Smax of the sample values is stored in the nth. Since the lower limit value SL is determined as the value of the ((n × (1-C)) / 2 + 1) th sample value from the smaller one, the address where the corresponding sample value is stored is obtained by calculation, By reading the sample value stored at the address location, the value of the lower limit SL can be recognized. Similarly, since the upper limit value SH is determined as the value of the (n− (n × (1-C)) / 2) th sample value from the smallest value, the address at which the corresponding sample value is stored. Is obtained by calculation and the value of the upper limit SH can be recognized by reading the sample value stored at the address location. The lower exclusion range a, the quantization target range b, and the upper exclusion range c shown in FIG. 7C correspond to the respective ranges in the histograms shown in FIGS.

  Thus, the lower limit value SL and the upper limit value SH determined by the upper / lower limit determination unit 50 are given to the quantization processing unit 40. The quantization processing unit 40 divides a numerical range from the lower limit value SL to the upper limit value SH into m stages, determines a predetermined quantization value for each stage, and stores n pieces of data stored in the original data storage unit 10. For each sample, a process of associating the quantized value at the stage to which the sample value belongs is performed. Specifically, for a sample having the sample value S, “0 (-(S−SL) / (SH−SL)) × (m−1)” is obtained by rounding the calculated value to an integer value. The process of associating “quantized values indicated by integers within the range of m−1)” is performed. Here, m is the value of the number of steps m set in the condition setting unit 60.

  As already described, in this quantization process, among samples of n samples, samples having a sample value less than the lower limit SL (samples whose sample value falls within the lower exclusion range a in FIG. 7C) For a sample having a sample value that exceeds the upper limit value SH (a sample that falls within the upper exclusion range c in FIG. 7C), associates the quantized value at the stage to which the lower limit value SL belongs, and the upper limit value SH. The process of associating the quantized value at the stage to which the

  In this way, when a predetermined quantized value is associated with each sample, the quantization processing unit 40 uses the quantized value associated with each of the n samples as the digital data as the quantized data storage unit 70. To store. FIG. 7D shows an example of data stored in the quantized data storage unit 70 in this way. In the example shown here, since the data identification code and the sample value are stored in pairs in the original data storage unit 10 as shown in FIG. As shown in FIG. 7D, the data identification code and the quantized value are stored in pairs.

  In other words, the quantization processing unit 40 converts the sample value S into the quantization value Q for the data (original data) shown in FIG. 7A stored in the original data storage unit 10. The replacement process is performed, and the data (quantized data) as shown in FIG. 7D obtained as a result is stored in the quantized data storage unit 70. That is, the sample value Si specified by the data identification code Di of the i-th sample is replaced with the quantized value Qi. In the quantized data storage unit 70, the quantized value Qi is the i-th sample. The data is stored in the storage location corresponding to the second sample (location corresponding to the data identification code Di). The quantized values Q1 to Qn shown in FIG. 7 (d) are a total of n quantized values thus replaced.

  Here, an example has been described in which data identification codes D1 to Dn are added to each sample for handling, but the data identification codes D1 to Dn are not necessarily required. For example, as in the above example, when the population data to be quantized is a measurement of some physical quantity at many points on the earth, it is usually the measurement at which point each sample is measured. Since information specifying whether the value is a value is required, it is preferable to associate the data identification code with the quantized value after the quantization process as in the example shown in FIG. However, depending on the application, a data identification code may not be necessary.

  For example, if it is an application in which the measured value of the physical quantity at each point is simply statistically processed, it is not necessary to specify which point the individual measured value is. In such a case, only the sample values S1, S2, S3,..., Sn are stored in the original data storage unit 10, and the quantized values Q1, Q2, and the like are stored in the quantized data storage unit 70. It is sufficient to store only Q3, ..., Qn.

  Further, in the case of data such as image data in which the sample is specified by the arrangement position of each sample, the data identification code is not necessary. For example, consider the case of quantizing pixel data obtained with a scanner or digital camera. A general digital camera converts display raw data called RAW data to obtain display image data. For example, when 12-bit data obtained as RAW data is converted into 8-bit data to obtain display image data, sample values (12-bit data) having detailed information in 4096 levels are converted into 256 levels. It needs to be quantized.

  Alternatively, the quantization is also performed when creating two-dimensional image data for showing an uneven shape called a so-called height field. For example, when a fine uneven shape such as an animal skin or a plant surface is expressed as a two-dimensional image, a two-dimensional image having dimension measurement values in the depth direction (depth direction) indicating unevenness information as respective pixel values is obtained. Created. In this case, it is necessary to produce two-dimensional image data by quantizing the dimension measurement value.

  When such a two-dimensional image is quantized, for example, data composed of a two-dimensional pixel array as shown in FIG. 8A is input to the original data storage unit 10. A predetermined pixel value is defined for each pixel. In the present invention, these individual pixels are samples, and the individual pixel values are sample values. In the example shown in FIG. 8A, S1, S2, S3,..., Sn indicate pixel values (that is, sample values) of the respective pixels. In the case of the RAW data image in the above example, each pixel value is constituted by a sample value expressed by 12 bits, and in the case of the height field image in the above example, each pixel value is constituted by a dimension measurement value in the depth direction.

  In the case of such image data, since each sample can be specified by its arrangement position, a data identification code for specifying each sample is unnecessary. Therefore, data consisting of a two-dimensional array of sample values as shown in FIG. Further, on the sort operation unit 20, as shown in FIG. 8 (b), the sample values composed of this two-dimensional array may be conceptually arranged in a one-dimensional manner and sorted in order of size. FIG. 8C shows n sample values sorted in this way. The method of determining the lower limit value SL and the upper limit value SH based on such a sort result is exactly the same as the method already described. FIG. 8D is a diagram illustrating a state in which the quantized values Q1 to Qn associated by the quantization processing unit 40 are stored in the quantized data storage unit 70. The quantized values Q1 to Qn are stored in the form of a two-dimensional array that is exactly the same as the two-dimensional array shown in FIG. 8A. The data stored in the quantized data storage unit 70 is The quantized image data is constructed as it is. In short, the quantization processing unit 40 stores the quantization value associated with each sample in a storage location (corresponding position on the two-dimensional array) corresponding to each sample in the quantized data storage unit 70. Processing will be performed.

  In the above, the basic embodiment of the present invention has been described. In this basic embodiment, the operator has sample values S1, S2, S3,. Is input as digital data, and the condition setting unit 60 may be configured to set the number of steps m (m is a natural number of 2 or more) and the parameter value C (0 <C <1).

Here, since the stage number m is a value indicating the stage of quantization, it is generally preferable to set a value such as a power of 2 (for example, 2 ⁸ = 256). Of course, if the number of steps m is fixed in advance, designation by the operator is unnecessary. The parameter value C is a value that specifies what percentage of all the samples is included in the quantization target range b. For example, the parameter value C should be set as an intuitively graspable value such as 90%. Can do. The values necessary for the quantization processing are the lower limit value SL and the upper limit value SH, but these values are automatically calculated by the upper and lower limit determination unit 50 based on the sorting result and the parameter value C. The operator does not need to be aware of it directly. As described above, the major feature of the present invention is that the lower limit value SL and the upper limit value SH are automatically determined by the numerical designation of the parameter value C that can be intuitively grasped. Of course, if the parameter value C is fixed in advance, designation by the operator is unnecessary.

<<< §4. Modified example of upper / lower limit determination method >>>
Here, a modified example in which the determination method of the lower limit value SL and the upper limit value SH in the basic embodiment described so far is slightly changed will be described. As described in §3, in step S4 of FIG. 5, the ((n × (1-C)) / 2 + 1) th value from the smaller value is set as the lower limit value for the sample values after sorting in order of magnitude. SL was performed, and the (n− (n × (1−C)) / 2) value from the smallest value was set to the upper limit value SH. When the lower limit SL and the upper limit SH are determined by such a method, among all n sample values, the sample value of the ratio C belongs to the quantization target range b, and the remaining sample value of the ratio (1-C) Belongs to the lower exclusion range a or the upper exclusion range c. Here, the number of sample values belonging to the lower exclusion range “a” and the number of sample values belonging to the upper exclusion range “c” are set to be equal (strictly speaking, the rounding process is performed when the calculation result does not become an integer number). In some cases, there may be a difference of 1).

  For example, when n = 10000 and the parameter value C = 90% (0.9), the ((n × (1-C)) / 2 + 1) th from the smallest, that is, the 501st sample value from the smallest The value becomes the lower limit SL, and the value of the (n− (n × (1-C)) / 2) th from the smallest, that is, the value of the 9500th sample value from the smallest becomes the upper limit SH. Therefore, 9000 sample values corresponding to 90% belong to the quantization target range b, 500 sample values with small values belong to the lower exclusion range a, and 500 sample values with large values belong to the upper exclusion range c. The lower limit SL and the upper limit SH are determined so as to belong to.

  As described above, if 500 sample values having a small value and 500 samples having a large value are excluded from all 10000 sample values, in general, quantization is performed by excluding sample values having unique values. Is possible. However, depending on the characteristics of the population, a sample value having a unique value tends to take a larger value than other sample values, and conversely, tends to take a small value.

  For example, in a CCD imaging device or the like, a large number of light receiving elements for accumulating charges according to the amount of received light are arranged. However, if the charge leaks for some reason, the amount of accumulated charge falls to zero. In such a case, if a sample value proportional to the amount of accumulated charge is used, the sample value of the light receiving element in which charge leakage has occurred becomes smaller than the sample value of a normal light receiving element. In such a case, from the viewpoint of excluding the sample values of the light receiving element in which the charge leak has occurred, it is better to set the number of sample values belonging to the lower exclusion range a larger than the number of sample values belonging to the upper exclusion range c. It stands to reason. Of course, in the case of a measurement system in which the voltage value is saturated when noise occurs, the sample value affected by the noise is larger than the normal sample value. In such a case, from the viewpoint of excluding sample values affected by noise, it is more reasonable to set the number of sample values belonging to the upper exclusion range c larger than the number of sample values belonging to the lower exclusion range a. It is correct.

  Thus, it is convenient if the balance between the number of sample values belonging to the lower exclusion range a and the number of sample values belonging to the upper exclusion range c can be adjusted according to the characteristics of the population. The modification described here adds such an adjustment function.

  Specifically, in the condition setting step S2 of FIG. 5, the balance value P (0 ≦ P ≦ 1) is set together with the step number m (m is a natural number of 2 or more) and the parameter value C (0 <C <1). To do. That is, the condition setting unit 60 of FIG. 6 is provided with a function for setting three numerical values, that is, the number m of steps, the parameter value C, and the balance value P in advance or based on an operator instruction. Here, the balance value P is a factor for adjusting the balance between the number of sample values belonging to the lower exclusion range “a” and the number of sample values belonging to the lower exclusion range “c”. The number of sample values belonging to the range a is larger than the number of sample values belonging to the upper exclusion range c. When P = 0, the number of sample values belonging to the upper exclusion range a is 0, and when P = 1, the number of sample values belonging to the lower exclusion range c is 0.

  In the process of the upper / lower limit determination step S4 (the process performed by the upper / lower limit determination unit 50), the value is small based on the n sample values in the sort operation unit 20 rearranged in order of size by the sort step S3. The value of the ((n × (1-C)) × P + 1) th sample value from the direction is determined as the lower limit value SL, and the (n− (n × (1-C)) × (1− P)) A process of determining the value of the first sample value as the upper limit SH is performed. The point that the balance value P is incorporated in the mathematical formula is different from the basic embodiment described in §3.

  For example, when n = 10000, parameter value C = 90% (0.9), and P = 0.3, the ((n × (1-C)) × P + 1) th from the smallest, that is, from the smallest The value of the 301st sample value becomes the lower limit value SL, and the value of the 9300th sample value from the smaller one is (n− (n × (1-C)) × (1-P)) th, that is, the smaller one. Becomes the upper limit SH. Therefore, the point that 9000 sample values corresponding to 90% belong to the quantization target range b is the same as in the basic embodiment described in §3, but 300 sample values having small values are lower. The lower limit value SL and the upper limit value SH are determined so that 700 sample values belonging to the exclusion range a and having a large value belong to the upper exclusion range c.

  If P = 0 is set, the number of samples belonging to the lower exclusion range a is 0, and 1000 sample values having a large value belong to the upper exclusion range c. On the contrary, when P = 1 is set, the number of samples belonging to the upper exclusion range c is 0, and 1000 sample values having a small value belong to the lower exclusion range a. The basic embodiment described in §3 can be said to be a special case where P = 0.5 in the above formula.

<<< §5. Practical embodiment of the present invention >>>
In the embodiment described so far, in the sorting step S3 in FIG. 5, the process of rearranging n sample values in order of size is an essential process. In the apparatus configuration shown in FIG. The processing unit 30 is an essential component. As described above, a number of algorithms are already known as methods for performing such sort processing. Theoretically, there is no difficulty in executing such sort processing inside a computer.

  However, this sort process is a process in which the processing load increases exponentially as the total number n of the target data increases, and the process requires much calculation time. Of course, a large computer with high processing capability may be able to perform sort processing in a relatively short calculation time even if the total number n of data increases, but the quantization according to the present invention can be performed using a general-purpose personal computer. When the apparatus is configured, or when the quantization apparatus according to the present invention is configured by a dedicated semiconductor chip to be incorporated in a digital camera, it is not possible to expect sort processing that is so fast. In such a case, if the sort process is performed, it may be difficult to complete quantization within a practical processing time.

  Thus, here, an embodiment will be described in which quantization can be completed within a practically sufficient processing time even if an apparatus that does not have sufficient sort processing capability is used. FIG. 9 is a flowchart showing the procedure of the quantization processing method according to such a practical embodiment. The difference from the procedure of the basic embodiment shown in FIG. 5 is that average / standard deviation calculation step S3A is performed instead of sort step S3, and upper / lower limit determination step S4A (name of step) instead of upper / lower limit determination step S4. Is the same). Only this difference will be described below.

First, in the average / standard deviation calculation step S3A, a process of calculating the average value M and the standard deviation σ is executed for the n sample values input in the input step S1 and stored in the storage location. Specifically, the average value M and the standard deviation σ for n sample values S1, S2, S3,.
M = Σ _{i = 1 to n} Si / n
σ = √ ((Σ _{i = 1 to n} (Si-M) ² ) / n)
Is calculated by the following formula.

  On the other hand, the upper and lower limit determination step S4A is the same as the upper and lower limit determination step S4 in the basic embodiment shown in FIG. 5 in that the lower limit value SL and the upper limit value SH are processed. The process is different. In the basic embodiment, the lower limit value SL and the upper limit value SH corresponding to the parameter value C are determined using the sorting result in the sorting step S3. However, the practical embodiment described here is an operation burden. Since the purpose is to omit such a sorting step, the sorting result cannot be used. Instead, the lower limit SL and the upper limit SH corresponding to the parameter value C are determined using the average value M and the standard deviation σ obtained in the average / standard deviation calculation step S3A.

  In order to explain the principle of the determination method of the lower limit value SL and the upper limit value SH performed in the upper and lower limit determination step S4A, first, the characteristics of the statistical normal distribution will be described with reference to the graph of FIG. The graph of FIG. 10 is a histogram with the sample value on the horizontal axis and the frequency of appearance on the vertical axis. In the case of the most common normal distribution in terms of statistics, as shown in the figure, a symmetric gentle mountain shape is shown. Distribution. When the center position on the left and right of the graph is the average value M of all the sample values, and the standard deviation is σ, samples having sample values in the range of (M−σ) to (M + σ) Samples with sample values in the range of 68.26% (M-2σ) to (M + 2σ) account for about 95.44% of the total.

  In general, a value z = Δ / σ obtained by dividing the difference Δ between the sample value S and the average value M by the standard deviation σ is called a standardized score (or z-score), and is a horizontal value in the histogram shown in FIG. It is used as a parameter indicating the position on the axis. For example, the standardized score z = 1 indicates a position where the difference Δ from the average value M is equal to one time the standard deviation σ, that is, the position of (M−σ) and the position of (M + σ) in FIG. The standardized score z = 2 indicates a position where the difference Δ from the average value M is equal to twice the standard deviation σ, that is, the position of (M−2σ) and the position of (M + 2σ) in FIG.

  Therefore, a range of (M−zσ) to (M + zσ) is set for an arbitrary standardized score z value, and the ratio of the number of samples that fall within this range to the total number of samples is the cumulative distribution function value f. (Z) is defined. Then, this cumulative distribution function value f (z) is the ratio of the number of samples in the hatched area shown in FIG. 10 to the total number of samples, in other words, the area of the hatched portion with respect to the total area of the mountain histogram. Will be shown. In the case of the normal distribution, as described above, the cumulative distribution function value f (1) for z = 1 = approximately 68.26%, and the cumulative distribution function value f (2) for z = 2 = approximately 95.44%.

  As described above, the cumulative distribution function value f (z) is a function value that is uniquely determined when the standardized score z is determined. In particular, when the distribution of the sample values is a normal distribution, each standardized score z It is known that the value of the cumulative distribution function value f (z) corresponding to the value of is obtained by calculation using the calculation formula of FIG. 11, and the standard normal distribution table illustrated in FIG. 12 is a constant table or the like. It is published in. The term of Σ in the calculation formula of FIG. 11 is a sum from k = 0 to infinity, but in practice it is sufficient to perform an operation from k = 0 to a predetermined finite value.

  The standard normal distribution table of FIG. 12 is created by calculation using the calculation formula of FIG. The leftmost column indicates the value of the upper digit (digits up to the first decimal place) of the standardized score z, and the uppermost row indicates the value of the lower digit (second digit of the decimal point) of the standardized score z. Yes. The numerical value drawn by the table of FIG. 12 is a numerical value indicating the ratio of the number of samples (the hatched portion of the histogram shown in the upper part of FIG. 12) of the sample value within the range of M to (M + zσ) to the total number of samples. Thus, the relationship with the cumulative distribution function value f (z) defined in the present invention is a numerical value corresponding to f (z) / 2. For example, in the table of FIG. 12, since the numerical value corresponding to z = 1.00 is 0.3413, the cumulative distribution function value f (1) defined in the present invention is a value obtained by doubling this value. 0.6826. Similarly, in the table of FIG. 12, since the numerical value corresponding to z = 2.00 is 0.4772, the cumulative distribution function value f (2) defined in the present invention is doubled. The value is 0.9544.

  The standard normal distribution table as shown in FIG. 12 is a table for subtracting the corresponding cumulative distribution function value f (z) from the value of the standardized score z. In addition, a table for subtracting the corresponding standardized score z from the cumulative distribution function value f (z) can be prepared. FIG. 13 shows an example of a correspondence table having such a function. In the left column of the correspondence table shown in FIG. 13, the cumulative distribution function value f (z) is listed in increments of 0.1 from 0 to 1.0, and the corresponding standardized score z value is displayed. It is listed in the right column. Of course, it is also possible to prepare a table in which the cumulative distribution function value f (z) with finer steps is posted as necessary.

  Based on a general standard normal distribution table (table for subtracting the corresponding cumulative distribution function value f (z) from the standardized score z value) as shown in FIG. In order to create a table for subtracting the corresponding standardized score z from the cumulative distribution function value f (z), a standard normal distribution table calculated with a sufficient number of significant digits is prepared in advance. The standardized score z corresponding to the value closest to the cumulative distribution function value f (z) is reversed.

  Now, considering the meaning of the cumulative distribution function value f (z) in relation to the basic embodiment described in §3, the cumulative distribution function value f (z) is the condition shown in FIG. It can be seen that the value corresponds to the parameter value C set in the setting step S2. The parameter value C (0 <C <1) in the present invention specifies the ratio of the number of samples included in the quantization target range b to the total number of samples n, and if C = 90%, all samples The lower limit SL and the upper limit SH are determined so that 90% of the number n is included in the quantization target range b and the remaining 10% is included in the lower exclusion range a or the upper exclusion range c. Become.

  Here, if the sample values of the population have a perfectly normal distribution and the average value M and the standard deviation σ are calculated, an arbitrary parameter value can be obtained using the correspondence table of FIG. It is possible to determine the lower limit SL and the upper limit SH according to C. That is, the standardized score z corresponding to the cumulative distribution function value f (z) equal to the designated parameter value C is obtained using the correspondence table of FIG. 13, and the lower limit value SL = M−zσ and the upper limit value SH = M + zσ. Calculate as follows. In the case of a population having a complete normal distribution, as shown in FIG. 10, the ratio of the number of samples having sample values within the range of (M−zσ) to (M + zσ) to the total number of samples is the cumulative distribution function value. Since it is given by f (z), the number of samples whose sample values fall within the range of (M−zσ) to (M + zσ) calculated using the cumulative distribution function value f (z) equal to the desired parameter value C The ratio to the total number of samples is equal to the specified parameter value C.

  For example, when the parameter value C = 90% (0.9) is designated, the standardized score z = 1.645 corresponding to f (z) = 0.9 is obtained by drawing the table of FIG. . Therefore, in the upper / lower limit determination step S4A, the lower limit value SL and the upper limit value SH = M + 1.645σ are calculated by using the average value M and the standard deviation σ obtained in step S3A, and the upper limit value SH = M + 1.645σ. The upper limit value SH can be obtained.

  In short, in step S4A, in a general normal distribution, the cumulative distribution function value f (z) indicating the proportion of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation”. ) Is equal to the parameter value C, and the upper limit SH = M + zσ and the lower limit SL = M−zσ may be determined using the average value M, the standard deviation σ, and the standardized score z. Specifically, when the standardized score in a general normal distribution is set to z, the ratio of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation” is shown. A correspondence table (correspondence table as shown in FIG. 13) indicating the correspondence between the cumulative distribution function value f (z) and the standardized score z is prepared in advance in the computer, and the parameter is obtained by referring to this correspondence table. A standardized score z corresponding to the cumulative distribution function value f (z) equal to the value C may be obtained.

  As described above, when it is assumed that the sample values of the population to be quantized have a complete normal distribution, the processing in steps S3A and S4A in FIG. 9 is equivalent to the processing in steps S3 and S4 in FIG. I explained that. That is, when the sample value of the population is a complete normal distribution, the cumulative distribution function value f (z) equal to the parameter value C can be obtained by calculation without performing the sort process described in §3. The possible numerical range (M−zσ) to (M + zσ), that is, the upper limit value SH and the lower limit value SL can be determined.

  However, the distribution of the sample values of the population actually given as the quantization target, that is, the total n samples input in step S1, is not necessarily a normal distribution. In general, it is considered that there are many cases where the distribution is close to the normal distribution to some extent, but the distribution of actual sample values varies from case to case, and cases that exactly match the normal distribution are rather rare. It is. However, even if the quantization method according to the processing procedure shown in the flowchart of FIG. 9 is applied to various cases, there is no practical problem. This is because the lower limit value SL and the upper limit value SH determined in step S4A do not necessarily have an absolute meaning.

  That is, the lower limit value SL and the upper limit value SH have meanings as boundaries of the lower exclusion range a, the quantization target range b, and the upper exclusion range c. Even if these boundary positions are slightly shifted, the quantization process is performed. There is no significant hindrance in doing this. In the first place, the parameter value C itself that is a factor for determining the lower limit value SL and the upper limit value SH is a value that is arbitrarily set by the operator or an arbitrary value that is set in advance. It should not be set.

  Actually, when the population is not a normal distribution, the ratio of the number of samples included in the quantization target range from the lower limit value SL to the upper limit value SH determined in step S4A to the total number of samples is accurate to the parameter value C. Will not match. For example, even if the parameter value C is set to 90%, the ratio of the number of samples actually included in the quantization target range to the total number of samples will be 92% or 87%. However, even if the values of the lower limit value SL and the upper limit value SH do not become accurate values according to the designated parameter value C, the quantization process itself does not have a serious problem.

  Therefore, the processing procedure shown in the flowchart of FIG. 9 is a sufficiently practical procedure even when the population is not normally distributed. And since this processing procedure does not include sort processing with a large calculation burden, it is not so sophisticated such as a quantizer configured using a general-purpose personal computer or a quantizer configured using a chip for a digital camera. It is most suitable for applying the present invention to an apparatus having no processing function.

  FIG. 14 is a block diagram showing the configuration of the quantization processing apparatus according to the practical embodiment described above. This apparatus has a function of executing each step shown in the flowchart of FIG. 9, and includes an original data storage unit 10, an average / standard deviation calculation unit 80, a correspondence table storage unit 90, a quantization processing unit 40, upper and lower limits. It consists of a collection of block constituent elements: a determination unit 50A, a condition setting unit 60, and a quantized data storage unit 70. Again, each of these components is realized by incorporating a dedicated program into the computer.

  Of the components shown in FIG. 14, the original data storage unit 10, the quantization processing unit 40, the condition setting unit 60, and the quantized data storage unit 70 are the same as the components in the apparatus shown in FIG. Exactly the same. In other words, the quantization processing device according to the practical embodiment shown in FIG. 14 includes the sort operation unit 20, the sort processing unit 30, and the upper and lower limit determination units in the quantization processing device according to the basic embodiment shown in FIG. It can be said that 50 is replaced with the average / standard deviation calculation unit 80, the correspondence table storage unit 90, and the upper and lower limit determination unit 50A. In the apparatus shown in FIG. 6, the upper and lower limits are determined by the sorting process, whereas in the apparatus shown in FIG. 14, the upper and lower limits are determined by calculation using the average value M and the standard deviation σ. To do.

The average / standard deviation calculation unit 80 has a processing function for calculating the average value M and the standard deviation σ for n sample values stored in the original data storage unit 10. Specifically, an average value M and standard deviation σ for n sample values S1, S2, S3,.
M = Σ _{i = 1 to n} Si / n
σ = √ ((Σ _{i = 1 to n} (Si-M) ² ) / n)
The process which calculates with the type | formula is performed. The average value M and the standard deviation σ obtained as a calculation result are delivered to the upper / lower limit determination unit 50A.

  On the other hand, the correspondence table storage unit 90 has a sample value in the range of “average value−z × standard deviation” to “average value + z × standard deviation” when the standardized score is z in a general normal distribution. It is a component that stores a correspondence table showing the correspondence between the cumulative distribution function value f (z) indicating the proportion of samples and the standardized score z. Specifically, a correspondence table as shown in FIG. 13 is stored.

  The upper / lower limit determination unit 50A is a component that performs processing for determining the upper limit value SH and the lower limit value SL, similarly to the upper / lower limit determination unit 50 shown in FIG. 6, but the determination process is different. In other words, the upper and lower limit determination unit 50A refers to the correspondence table in the correspondence table storage unit 90, and thereby the standardized score corresponding to the cumulative distribution function value f (z) equal to the parameter value C set in the condition setting unit 60. z is obtained, and an upper limit SH = M + zσ and a lower limit SL = M−zσ are determined using the average value M, the standard deviation σ, and the obtained standardized score z.

  When the distribution of the n sample values S1, S2, S3,..., Sn stored in the original data storage unit 10 does not have a normal distribution, the upper limit value SH determined by the upper / lower limit determination unit 50A. The lower limit SL is not the original correct value specified by the parameter value C, but as described above, there is no practical problem.

  Using the upper limit value SH and the lower limit value SL determined in this way, the quantization processing by the quantization processing unit 40 is executed, and the resulting quantized values Q1 to Qn are stored in the quantized data storage unit 70. The point is exactly the same as the operation of the apparatus according to the standard embodiment described in §3.

It is a histogram which shows an example of the conventional general quantization process. It is a histogram which shows another example of the conventional general quantization process. 2 is a histogram showing quantization processing when the present invention is applied to the example shown in FIG. 1. It is a histogram which shows the quantization process at the time of applying this invention to the example shown in FIG. It is a flowchart which shows the procedure of the quantization processing method which concerns on basic embodiment of this invention. It is a block diagram which shows the structure of the quantization processing apparatus which concerns on fundamental embodiment of this invention. It is a figure which shows the example of the transition in the example of the sample value processed with the quantization processing apparatus shown in FIG. 6, and its quantization process. It is a figure which shows another example of the sample value processed with the quantization processing apparatus shown in FIG. 6, and an example of the transition in the quantization process. It is a flowchart which shows the procedure of the quantization processing method which concerns on practical embodiment of this invention. It is a graph which shows the relationship between the standardization score z and the cumulative distribution function value f (z) in a general normal distribution. It is a formula which shows the relationship between the standardized score z and the cumulative distribution function value f (z) in a general normal distribution. It is a figure which shows an example of a well-known standard normal distribution table. It is a figure which shows the corresponding | compatible table which shows the corresponding | compatible relationship between the standardized score z and the cumulative distribution function value f (z) in a general normal distribution. It is a block diagram which shows the structure of the quantization processing apparatus which concerns on practical embodiment of this invention.

Explanation of symbols

10: Original data storage unit 20: Sort operation unit 30: Sort processing unit 40: Quantization processing unit 50, 50A: Upper / lower limit determination unit 60: Condition setting unit 70: Quantized data storage unit 80: Average / standard deviation calculation unit 90: correspondence table storage unit a: lower exclusion range b: quantization target range c: upper exclusion range B1, B2: frequency integration bar C: parameter values D1 to Dn: data identification code f (z): cumulative distribution function value M : Average value m: Number of quantization stages n: Total number of samples Q1 to Qn: Quantized value Qi: i-th quantized values S1 to S6, S3A, S4A: Steps S1 to Sn of the flowchart: Sample value Si : I-th sample value SH: upper limit value SL: lower limit value Smax: maximum value Smin: minimum value z: standardized score σ: standard deviation

Claims (10)

A method of performing quantization by associating one of m stages of quantized values with each of n samples having a predetermined sample value,
An input step for inputting a sample value of n samples as digital data to a computer and storing it in a predetermined storage location;
A condition setting step for setting a stage number m (m is a natural number of 2 or more) and a parameter value C (0 <C <1) for the computer;
A sorting step in which the computer performs a process of rearranging the n sample values stored in the storage location in order of size;
The computer sets the value of the ((n × (1-C)) / 2 + 1) -th sample value from the smallest to the lower limit value based on the n sample values rearranged in order of magnitude by the sorting step. An upper and lower limit determination step for determining SL and determining the value of the (n− (n × (1-C)) / 2) -th sample value from the smaller one as the upper limit value SH;
A stage determination step in which a computer divides a numerical range from the lower limit value SL to the upper limit value SH into m stages, and determines a predetermined quantization value for each stage;
A computer that associates, for each of the n samples, a quantization value at a stage to which the sample value belongs, and stores each associated quantization value in a memory location corresponding to each sample;
Have
In the quantization step, among the n samples, a sample having a sample value less than the lower limit SL is associated with a quantized value at a stage to which the lower limit SL belongs, and exceeds the upper limit SH. A sample value quantization method, wherein a sample value having a sample value is associated with a quantized value at a stage to which the upper limit SH belongs. A method of performing quantization by associating one of m stages of quantized values with each of n samples having a predetermined sample value,
An input step for inputting a sample value of n samples as digital data to a computer and storing it in a predetermined storage location;
A condition setting step for setting a stage number m (m is a natural number of 2 or more), a parameter value C (0 <C <1), and a balance value P (0 ≦ P ≦ 1) for the computer;
A sorting step in which the computer performs a process of rearranging the n sample values stored in the storage location in order of size;
The computer sets the value of the ((n × (1-C)) × P + 1) -th sample value from the smallest to the lower limit value based on the n sample values rearranged in order of magnitude by the sorting step. An upper and lower limit determination step for determining SL and determining the value of the (n− (n × (1-C)) × (1-P))-th sample value from the smaller one as the upper limit value SH;
A stage determination step in which a computer divides a numerical range from the lower limit value SL to the upper limit value SH into m stages, and determines a predetermined quantization value for each stage;
A computer that associates, for each of the n samples, a quantization value at a stage to which the sample value belongs, and stores each associated quantization value in a memory location corresponding to each sample;
Have
In the quantization step, among the n samples, a sample having a sample value less than the lower limit SL is associated with a quantized value at a stage to which the lower limit SL belongs, and exceeds the upper limit SH. A sample value quantization method, wherein a sample value having a sample value is associated with a quantized value at a stage to which the upper limit SH belongs. A method of performing quantization by associating one of m stages of quantized values with each of n samples having a predetermined sample value,
An input step for inputting a sample value of n samples as digital data to a computer and storing it in a predetermined storage location;
A condition setting step for setting a stage number m (m is a natural number of 2 or more) and a parameter value C (0 <C <1) for the computer;
An average / standard deviation calculation step in which a computer calculates an average value M and a standard deviation σ for n sample values stored in the storage location;
The cumulative distribution function value f (z) indicating the proportion of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation” in the normal distribution is the parameter value C. An upper and lower limit determination step for determining an upper limit SH = M + zσ and a lower limit SL = M−zσ using the average value M, the standard deviation σ, and the standardized score z;
A stage determination step in which a computer divides a numerical range from the lower limit value SL to the upper limit value SH into m stages, and determines a predetermined quantization value for each stage;
A computer that associates, for each of the n samples, a quantization value at a stage to which the sample value belongs, and stores each associated quantization value in a memory location corresponding to each sample;
Have
In the quantization step, among the n samples, a sample having a sample value less than the lower limit SL is associated with a quantized value at a stage to which the lower limit SL belongs, and exceeds the upper limit SH. A sample value quantization method, wherein a sample value having a sample value is associated with a quantized value at a stage to which the upper limit SH belongs. The quantization method according to claim 3, wherein
Cumulative distribution function value f (z) indicating the proportion of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation”, where z is the standardized score in the normal distribution A correspondence table showing the correspondence between the standardized score z and the standardized score z is prepared in advance in the computer, and in the upper and lower limit determination step, the cumulative distribution function value f (z) equal to the parameter value C is referred to by referring to the correspondence table. A sampled-value quantization method characterized by obtaining a standardized score z corresponding to. In the quantization method in any one of Claims 1-4,
In the quantization stage, for a sample having a sample value S, a calculation value of ((S-SL) / (SH-SL)) × (m−1) is rounded to an integer value “0- ( A sample value quantization method, wherein quantization is performed by associating a “quantized value indicated by an integer within a range of m−1)”. An apparatus for performing quantization by associating one of m stages of quantized values with each of n samples having a predetermined sample value,
An original data storage unit for inputting sample values of n samples as digital data and storing the digital data;
A condition setting unit for setting the number of steps m (m is a natural number of 2 or more) and the parameter value C (0 <C <1) in advance or based on an operator's instruction;
A sorting unit that temporarily holds the n sample values for sorting;
A sort processing unit that duplicates n sample values stored in the original data storage unit, holds the sample value in the sort operation unit, and performs a process of rearranging the sample values in order of size;
After the rearrangement process by the sort processing unit is completed, the ((n × (1-C)) /) from the smallest one is based on the n sample values arranged in order of size in the sort operation unit. The upper and lower limits for determining the value of the (2 + 1) th sample value as the lower limit SL and determining the value of the (n− (n × (1-C)) / 2) th sample value from the smaller value as the upper limit SH A decision unit;
The numerical range from the lower limit value SL to the upper limit value SH is divided into m stages, a predetermined quantization value is determined for each stage, and the quantum value of the stage to which the sample value belongs for each of the n samples. A quantization processing unit for associating quantization values;
A quantized data storage unit that stores quantized values associated with the n samples as digital data;
Have
The quantization processing unit associates a quantized value at a stage to which the lower limit value SL belongs for a sample having a sample value less than the lower limit value SL among the n samples, and sets the upper limit value SH. An apparatus for quantizing a sample value, characterized by associating a quantized value at a stage to which the upper limit SH belongs with respect to a sample having a sample value that exceeds the sample value. An apparatus for performing quantization by associating one of m stages of quantized values with each of n samples having a predetermined sample value,
An original data storage unit for inputting sample values of n samples as digital data and storing the digital data;
A condition setting unit for setting the step number m (m is a natural number of 2 or more), the parameter value C (0 <C <1), and the balance value P (0 ≦ P ≦ 1) in advance or based on an instruction from the operator;
A sorting unit that temporarily holds the n sample values for sorting;
A sort processing unit that duplicates n sample values stored in the original data storage unit, holds the sample value in the sort operation unit, and performs a process of rearranging the sample values in order of size;
After the rearrangement processing by the sort processing unit is completed, the ((n × (1-C)) × The value of the (P + 1) -th sample value is determined as the lower limit value SL, and the value of the (n− (n × (1-C)) × (1-P))-th sample value from the smaller value is set as the upper limit value SH. An upper / lower limit determination unit to determine;
The numerical range from the lower limit value SL to the upper limit value SH is divided into m stages, a predetermined quantization value is determined for each stage, and the quantum value of the stage to which the sample value belongs for each of the n samples. A quantization processing unit for associating quantization values;
A quantized data storage unit that stores quantized values associated with the n samples as digital data;
Have
The quantization processing unit associates a quantized value at a stage to which the lower limit value SL belongs for a sample having a sample value less than the lower limit value SL among the n samples, and sets the upper limit value SH. An apparatus for quantizing a sample value, characterized by associating a quantized value at a stage to which the upper limit SH belongs with respect to a sample having a sample value that exceeds the sample value. An apparatus for performing quantization by associating one of m stages of quantized values with each of n samples having a predetermined sample value,
An original data storage unit for inputting sample values of n samples as digital data and storing the digital data;
A condition setting unit for setting the number of steps m (m is a natural number of 2 or more) and the parameter value C (0 <C <1) in advance or based on an operator's instruction;
An average / standard deviation calculation unit for calculating an average value M and a standard deviation σ for n sample values stored in the original data storage unit;
Cumulative distribution function value f (z) indicating the proportion of samples whose sample values fall within the range of “average value−z × standard deviation” to “average value + z × standard deviation”, where z is the standardized score in the normal distribution A correspondence table storage unit that stores a correspondence table indicating a correspondence relationship between and a standardized score z;
By referring to the correspondence table, a standardized score z corresponding to the cumulative distribution function value f (z) equal to the parameter value C is obtained, and using the average value M, the standard deviation σ, and the standardized score z, An upper and lower limit determination unit for determining an upper limit SH = M + zσ and a lower limit SL = M−zσ;
The numerical range from the lower limit value SL to the upper limit value SH is divided into m stages, a predetermined quantization value is determined for each stage, and the quantum value of the stage to which the sample value belongs for each of the n samples. A quantization processing unit for associating quantization values;
A quantized data storage unit that stores quantized values associated with the n samples as digital data;
Have
The quantization processing unit associates a quantized value at a stage to which the lower limit value SL belongs for a sample having a sample value less than the lower limit value SL among the n samples, and sets the upper limit value SH. An apparatus for quantizing a sample value, characterized by associating a quantized value at a stage to which the upper limit SH belongs with respect to a sample having a sample value that exceeds the sample value. In the quantization apparatus in any one of Claims 6-8,
The quantization processing unit calculates “(0−S−SL) / (SH−SL)) × (m−1) for the sample having the sample value S by rounding it to an integer value“ 0 ”. A sample value quantization apparatus that performs quantization by associating a “quantized value represented by an integer within a range of (m−1)”.   A program for causing a computer to function as the sample value quantization apparatus according to claim 6.

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