JP2015138271A - Unevenness analysis method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for quantifying unevenness of a characteristic value such as distribution, density, or temperature distribution of components of a composite.SOLUTION: The unevenness analysis method for quantifying unevenness of distribution of a characteristic value from a digital image in which same characteristic value is drawn with same color, comprises: a first step for extracting an analysis area from the digital image; a second step for weighting by a predetermined amount to respective pixel in the analysis area according to color tone of the respective pixel; a third step for extracting a local area where is a spot symmetrical shape smaller than the analysis area, in which the respective pixels in the analysis area serve as a center; a fourth step for calculating average weight in the local area, by dividing total sum of weight of all pixels in the local areas by a total number of pixels of the local areas; a fifth step for making the average weight in the respective local area a parent population; and a sixth step for regarding variation of the parent populations as unevenness, and quantifying the unevenness by a variation coefficient or standard deviation of the parent population.

Description

  The present invention relates to a method for analyzing image unevenness, and more particularly to a method for analyzing distribution unevenness and characteristic value unevenness of components of a composite material.

  A composite material produced by integrally combining two or more different constituent materials has different mechanical characteristics depending on the ratio of the constituent materials. For example, in the case of a carbon fiber reinforced plastic in which carbon fibers are mixed with an epoxy resin as a base material, the higher the ratio of carbon fibers, the higher the rigidity. However, even if it is a composite material mixed in the same ratio as a whole, a composite material in which the constituent materials are homogeneously mixed and a composite in which the distribution of the constituent materials is non-homogeneous and local density exists Mechanical properties differ from materials. The distribution of the constituent material also affects the distribution of characteristic values such as concentration and temperature. The distribution of characteristic values can use an image in which the same characteristic values are drawn with the same color, and can indicate a high or low characteristic value range or a characteristic value range. However, even if the overall average characteristic value is the same, whether or not the characteristics of the composite material are regarded as the same varies depending on whether or not the characteristic values are uniformly distributed.

  As described above, if the non-homogeneity of the components of the composite material and the distribution of characteristic values is defined as unevenness, the cross-sectional image of the composite material and the distribution of characteristic values are shown in order to show the homogeneity and identity of the unevenness. There is a need for a method of quantitatively indicating the degree of unevenness using the obtained images. If the degree of unevenness can be shown quantitatively, it can be effectively used for quality assurance of materials.

  Regarding the method for quantifying unevenness, several techniques are known in the field of image processing. In Patent Document 1, an attempt is made to quantify product gloss and printing color unevenness. The unevenness is quantified by dividing the image to be evaluated into a bright part and a dark part by Fourier transform and calculating the distribution of the area of the detected closed section image region.

  In Patent Document 2, a histogram of the entire color data is created for a glass substrate or painted plate used for a liquid crystal display, and it is determined whether the color data of the divided area is within the allowable range. Provides a method for inspecting unevenness.

  In Patent Document 3, unevenness of an antiglare film used on the surface of a display device such as a liquid crystal display is subjected to multiresolution analysis and multiplied by sensitivity for each frequency of the visual system, thereby mixing both rough unevenness and fine unevenness. Unevenness is quantified. It can also be used to compare unevenness and determine identity.

  As examples of applying the analysis of unevenness to a composite material, Patent Documents 4 to 6 are cited.

  In Patent Document 4, the variation in the mixing ratio between the regions is evaluated based on the difference between the mixing ratio of different constituent materials in the divided areas and the known mixing ratio.

  In patent document 5, about the difference of local content of a constituent material, the cross section of the fiber reinforced resin plastic material by which the fiber was arrange | positioned substantially in parallel is a substantially square area | region of 40-100 equal areas which do not mutually overlap. In each region, the area ratio occupied by the fibers is measured, and the variation of the population when these are used as the population is measured. Not only the fiber distribution in the fiber-reinforced composite material but also various distribution unevenness can be measured in the same manner as this method.

  Patent Document 6 also divides the cross section of the composite material into square regions, counts the number of fibers for each region, and sets the population to evaluate the dispersibility of the population. Quantification of the fiber orientation angle is also possible.

Ripley's K shown in the following formula (1) as described in Non-Patent Document 1 is used as a method for evaluating the randomness of the fiber from the cross section of the unidirectional fiber reinforced composite material in which the fibers are aligned in one direction. function (K (h)). Here, A is the area of the analysis region, N is the number of fibers in the analysis region, I (d _ij <h) is the number of fibers when the distance d _ij between the i-th fiber and the j-th fiber is smaller than h. Is meant to count. That is, it means the number of fibers contained in a circle with a radius h centered on the i-th fiber. d _ij is the distance between the i th and j th fibers. W indicates the proportion of the area of the circle that overlaps the analysis region when the circle with the radius h protrudes from the analysis region. By this method, if the relationship between h and K (h) is a smooth curve, it can be proved that the fiber arrangement is not regular.

JP-A-6-222002 JP-A-9-210789 JP 2009-229391 A JP-A-8-271402 JP-A-8-164521 JP 2004-28669 A

Generation of random distribution of fibres in long-fiber reinformed composites, A.R. R. Melro, P.M. P. camanho, S .; T. T. et al. Pinho, Composites Science and Technology 68 (2008) 2092-2102

  However, the prior art has the following problems.

  Since Patent Document 1 presupposes binarization, it cannot be applied to unevenness quantification using an image including a color. In addition, since the distribution of the area of the closed region is evaluated, for example, when the fiber is distributed in the cross section of the fiber reinforced plastic, the distribution of the cross sectional area of the fiber can be evaluated, but the density of the fibers generated in the cross section can be evaluated. Cannot be evaluated.

  In Patent Document 2, it is a technique for indicating a portion where unevenness exists, and a difference in unevenness between composite materials cannot be indicated.

  In Patent Document 3, it is possible to analyze unevenness with high accuracy by deriving the relationship between resolution and frequency intensity by multi-resolution analysis. However, since the frequency intensity is compared rather than the characteristic value, it is impossible to quantitatively show the variation in the characteristic value and the content of the constituent material in a local region caused by unevenness in the composite material.

  In the methods disclosed in Patent Document 4, Patent Document 5 and Patent Document 6 in which the area ratio of the distribution in the region is measured by dividing into regions, the range in which the content of the constituent material varies as well as the size of the variation is shown. However, the degree of variation varies depending on how the areas are separated. In addition, although the density of whether or not there is a fiber can be evaluated, it is impossible to quantify the unevenness of characteristic values that change stepwise, such as the concentration of a certain component and the temperature distribution.

  Ripley's K function can prove the randomness of the fiber arrangement of the unidirectional fiber reinforced composite material, but count the number of fibers in the circle created around each fiber, and the fibers in all the circles. Since it is a technique of adding numbers, it is difficult to show the difference between the case where there are sparse and dense regions of fibers and the case where the fibers are uniformly distributed.

  In view of such a background, the present invention provides a method for analyzing unevenness for quantifying unevenness in the distribution of characteristic values and constituent materials while minimizing fluctuations in variation depending on how the regions are separated. Let it be an issue.

  In order to solve the above problems, the method for analyzing unevenness of the present invention has the following configuration. That is, a non-uniformity analysis method for quantifying nonuniformity in distribution of characteristic values from a digital image in which the same characteristic values are drawn in the same color, the first step of extracting an analysis area from the digital image, A second step of giving a predetermined weight to each pixel according to the color tone of each pixel, and a third step of extracting a local region having a point symmetric shape smaller than the analysis region around each pixel in the analysis region The fourth step of calculating the average weight in the local region by dividing the total weight of all the pixels in each local region by the total number of pixels in the local region, and calculating the average weight in each local region as the population And a sixth analysis step of quantifying the unevenness by the variation coefficient or the standard deviation of the population.

  Moreover, in order to solve the said subject, the estimation method of the magnitude | size of the nonuniformity of this invention has the following structure. In other words, this is an unevenness estimation method in which a plurality of populations are prepared by changing the area of the local region, and the above-described unevenness analysis method is executed for each population.

  According to the present invention, taking into account the presence or absence of local unevenness, the distribution of the characteristic value of the object and the distribution of the constituent material of the composite material are quantitatively indicated, and the degree of unevenness is quantitatively indicated from the distribution variation. Can do.

It is an example of the digital image which drawn the same characteristic value with the same color. It is the schematic of the local area | region centering on the aggregate | assembly of a pixel and a certain pixel. It is an example of the digital image which shows distribution of the core-shell rubber uniformly disperse | distributed to resin. It is an example of the digital image which shows distribution of the core-shell rubber disperse | distributed non-homogeneously to resin. It is a graph which shows the relationship between the radius of the local region obtained from the nonuniformity analysis using FIG. 3 and FIG. 4, and the standard deviation of a population. It is a graph which shows the relationship between the radius of a local area | region obtained from the nonuniformity analysis using FIG. 3 and FIG. 4, and the kurtosis of a population. FIG. 4 is a histogram of the population in FIG. 3 when the radius of the local region is 20 pixels. 5 is a histogram of the population in FIG. 4 when the radius of the local region is 20 pixels. FIG. 5 is a graph showing a relationship between a radius of a local region and a standard deviation of a population when a local region is extracted around a pixel having a weight of 1 or more from FIGS. FIG. 5 is a graph showing the relationship between the radius of a local region and the kurtosis of a population when a local region is extracted around a pixel having a weight of 1 or more from FIGS. FIG. 4 is a histogram of the population in FIG. 3 in a case where a local area centering on a pixel having a weight of 0 or more is extracted when the radius of the local area is 20 pixels. FIG. 5 is a histogram of the population in FIG. 4 when a local region having a radius of 20 pixels and a local region centered on a pixel having a weight of 0 or more is extracted. It is an example of the digital image which binarized the cross section of the composite material in which the carbon fiber was disperse | distributed heterogeneously in the thermoplastic resin. It is an example of the digital image which binarized the cross section of the composite material in which carbon fiber was uniformly disperse | distributed in the thermoplastic resin. It is a graph which shows the relationship between the radius of the local area | region obtained from the nonuniformity analysis using FIG. 13 and FIG. 14, and the standard deviation of a population. It is a graph which shows the relationship between the radius of a local area | region obtained from the nonuniformity analysis using FIG. 13 and FIG. 14, and the kurtosis of a population. 14 is a histogram of the population obtained from the unevenness analysis of FIG. 13 when the radius of the local region is 40 pixels. 15 is a histogram of a population obtained from the unevenness analysis of FIG. 14 when the radius of the local region is 40 pixels. This is the result of evaluating the standard deviation of the population when the analysis area is divided by non-overlapping areas while changing the position of the division. It is sectional drawing of the fiber right angle direction of the unidirectional fiber reinforced composite material in which the fiber is regularly arranged. It is sectional drawing of the fiber right angle direction of the unidirectional fiber reinforced composite material in which the fiber was arrange | positioned at random. It is sectional drawing of the fiber right angle direction of the unidirectional fiber reinforced composite material with which the density difference was large and the fiber was arrange | positioned. It is the result of having evaluated the fiber arrangement | positioning of FIG.20, FIG.21, FIG.22 using a standard deviation. It is the result of having evaluated the fiber arrangement | positioning of FIG.20, FIG.21, FIG.22 using kurtosis. It is the result of having evaluated the fiber arrangement | positioning of FIG.20, FIG.21, FIG.22 using Ripley's K function.

  The present invention relates to a technique for quantifying unevenness of distribution of characteristic values from digital images in which the same characteristic values are drawn with the same color. Since the image is taken into a computer and the unevenness of the image is quantified, it is assumed that the image is a digital image. A digital image can measure the distribution of temperature, concentration, etc. with a measuring device using a sensor or the like. If the obtained image is an analog image, it is digitized and used.

  The unevenness analysis method according to the present invention has the following procedure. First, an analysis area is selected and extracted from a digital image. Next, a predetermined weight is given to each pixel in the analysis region according to the color tone of each pixel. Here, the weight is preferably a characteristic value corresponding to the color tone or luminance of the digital image.

  Next, a local region having a point-symmetrical shape smaller than the analysis region is extracted around each pixel in the analysis region. A local region may overlap another local region. Since the local area can define the center, the local area needs to have a point-symmetric shape represented by a circle or a rectangle.

  FIG. 1 shows an example of a digital image. a is an analysis region selected from the digital image, b is a correspondence between a color and a characteristic value, and c and d are local regions. It is preferable that all the local areas have the same size and shape. However, as an exception, when a part of the local area protrudes from the analysis area as in the local area d, the overlapping area e between the analysis area and the local area is defined as the local area. Treat as. Next, in each local region, the total weight of all the pixels included in the local region is divided by the total number of pixels in the local region by the following equation (2) to calculate an average weight in the local region. Then, an average weight in each local region is set as a population. The pixel included in the local region may be a pixel in which the center of the pixel is included in the local region. Alternatively, when the pixel is considered to be a square having an area, a pixel that overlaps with the local region may be included in the local region, and in that case, the area included in the local region out of the area of the pixel A value obtained by multiplying the ratio by the pixel weight may be used as the pixel weight.

  FIG. 2 is an example of an enlarged view of a digital image, in which pixels f are gathered. g is the edge of the analysis region. In this image, it is assumed that density is weighted, density is given according to the luminance of the pixel, and the density is high at a dark part. h and i indicate local regions centered on a certain pixel. Each pixel has a color tone, and the color tone means a density corresponding to the correspondence j between the color and density of the pixel. Here, density is a weight. If the center of the pixel is included in the local region and the pixel is considered to be included in the local region, there are nine pixels in the local region h, and the weight of the nine pixels Is divided by 9, and the average weight in the local region is calculated to be 2. As described above, when part of the edge of the analysis region protrudes from the edge g, the region where the analysis region overlaps with the local region is defined as the local region, the total number of pixels in the local region i is 3, and the average weight is 1. .

  By extracting the local area while allowing overlap with each pixel as the center, it is possible to evaluate the average weight in an arbitrary area without depending on the number and position of the local areas. Finally, the coefficient of variation or standard deviation of the population is calculated and the variation of the population is evaluated as unevenness. The larger the coefficient of variation and the standard deviation, the larger the unevenness, and the smaller the variation coefficient, the more uniform and uniform.

  In the present invention, the characteristic values in the local region are extracted evenly by allowing the overlapping of the local regions, and in particular, as the digital image, the distribution of the characteristic value of the composite material composed of two or more kinds of components is shown. If used, it is effective in evaluating the unevenness of the characteristic value of the composite material. Unlike single materials, the difference in discontinuous property values that occur between different components is significant in composite materials, and local property values are uneven by extracting local property values uniformly. Can be extracted.

  The present invention may be applied to the quantification of the distribution unevenness of some constituent materials by using the content of some constituent materials of the composite material as a characteristic value. Even if it is a single material, when it contains pores, it can be said to be a composite material with air, and it can also be used for the purpose of quantifying the pore distribution unevenness. In quantifying the distribution unevenness of the constituent material, it is necessary to use a cross-sectional image of the composite material and use an image in which pixels showing some constituent materials and pixels showing other constituent materials are clearly distinguished by binarization. preferable. In this case, if the weights of the pixels indicating some constituent materials are 1 and the weights of the pixels indicating other constituent materials are 0, the average weight in the local region is the content of the partial constituent materials. Equivalent. The present invention is a method that is executed based on a digital image. Even if it is not a cross-sectional image obtained from a cut surface, an image of one cross-section inside a composite material is obtained using an apparatus capable of transmitting and photographing the inside such as an X-ray CT apparatus. May be.

  In principle, in the analysis method of the present invention, a local region is created centering on all pixels in the analysis region. However, the local region is created and extracted centering on the pixels limited to pixels indicating a part of the weight range. May be. For example, when a foreign substance exists in the analysis area, it is preferable not to create a local area centered on a pixel indicating the foreign substance and include it in the population. In this case, it is preferable to calculate the average weight in the local region from the weights of the pixels excluding foreign substances, not all the pixels in the local region. In addition, if the distribution unevenness of some constituent materials is evaluated and the content of some constituent materials is very small, a local region is created around only the pixels indicating some constituent materials as a population. Also good. A reduction in the number of local regions extracted increases the calculation speed.

  Evaluation of variation in the population can be basically performed using a coefficient of variation or standard deviation, but if the coefficient of variation and standard deviation are similar, unevenness can be evaluated using kurtosis. The greater the kurtosis, the more the population is closer to the average value, so the unevenness is smaller. The lower the kurtosis, the greater the unevenness. The kurtosis can be obtained by the following equation (3) using the average weight Xi in each local region (i = 1 to the total number of pixels N in the analysis region), the average value μ of the population, and the variance σ. . The kurtosis is greater than 3 when the population distribution is closer to the average value than the normal distribution, and the kurtosis is less than 3 when the population distribution is wider than the normal distribution.

  The size of the local area may be determined empirically according to the content and resolution of the distribution, and a plurality of populations may be created from the local areas having a plurality of areas. After changing the area of the local area and repeatedly executing the method of analyzing unevenness for each population, the relationship between the area of the local area and variations such as the standard deviation and kurtosis of the population was derived. The size of the unevenness may be estimated by comparing the variation of the population with other samples. It is also possible to quantify the size of unevenness from the area of the local area where the difference between samples is large, comparing the relationship between the size of the unevenness and the coefficient of variation, standard deviation, and kurtosis in two or more samples. is there.

  By using the unevenness analysis method described above, it is possible to quantify unevenness from a digital image or a cross-sectional image of a composite material that shows the same characteristic values in the same color.

  Hereinafter, the present invention will be described more specifically with specific examples.

Example 1
3 and 4 are digital images in which the weight of each pixel is determined from the brightness of a cross-sectional photograph of the resin in which the core-shell rubber is dispersed. In FIG. 3, the core-shell rubber is uniformly dispersed, and in FIG. 4, the distribution of the core-shell rubber is uneven. It is assumed that the darker the color, the more the core shell rubber is agglomerated and has a higher weight. The relationship between the local area area and unevenness was quantified while changing the radius of the local area, that is, changing the local area area.

  FIGS. 5 and 6 show the results of evaluation of the variation of the population with the standard deviation and the kurtosis in FIGS. 3 and 4, respectively. Although the standard deviation of the partially aggregated image of FIG. 4 is higher, the kurtosis is also higher.

  7 and 8 show histograms of the population obtained by analyzing the unevenness of the images of FIGS. 3 and 4 in the local region having a radius of 20 pixels. In FIG. 8, the mode value comes to the left end of the histogram, because the content of the core-shell rubber is small, and the average value in the local area including many pixels with a weight of 0 in the area where the core-shell rubber is sparse. This is because the weight is dominant in kurtosis. In such a case, even when the standard deviation is similar, in order to perform comparison by kurtosis, it is limited to only a local region centered on a pixel having a weight of 1 or more, that is, a pixel showing a partial weight range. Thus, it is preferable to analyze the unevenness by extracting a local region around the pixel and creating a population. At this time, a pixel having a weight of 0 is also taken into consideration for the total number of pixels in the local region.

  FIGS. 9 and 10 show the relationship between the area of the local region, the standard deviation, and the kurtosis, respectively. FIGS. 11 and 12 show the histograms of the populations in FIGS. 3 and 4 when the radius of the local region is 20 pixels, respectively. Indicated. From this graph, it can be seen that in the image of FIG. 4, the standard deviation is large and the kurtosis is low, and the histogram is not affected by the region where the mode is sparse, and the variation of the population is large. Thereby, the homogeneity of FIG. 3 and the non-homogeneity of FIG. 4 were shown about distribution of the core-shell rubber disperse | distributed to resin which is a base material. Further, from the population, the concentration is distributed in the range from the maximum value 0 to the minimum value 0.8 in FIG. 3, and in FIG. 4, the concentration is distributed in the range from the maximum value 0 to the minimum value 1.2. I understand that.

(Example 2)
13 and 14 show digital images obtained by binarizing a cross-sectional photograph of a composite material composed of thermoplastic resin and short fibers of carbon fibers. White indicates the fiber, and black indicates the resin part. In the cross section of FIG. 13, the fibers are locally bundled, whereas in the cross section of FIG. 14, the fibers are uniformly dispersed. In both cases, the image size is 512 pixels in the horizontal direction and 384 pixels in the vertical direction, and unevenness analysis was performed on these two cross-sectional images. When the weight of the white pixel is 1 and the weight of the black pixel is 0, the average weight in the local region is the same as the fiber area content in the cross-sectional image.

  The cross-sectional images of FIGS. 13 and 14 are obtained by changing the radius of the local region and repeatedly analyzing the unevenness, and showing graphs showing the relationship between the radius of the local region, the standard deviation, and the kurtosis, respectively. As shown in FIG. From this graph, it can be seen that FIG. 13 shows that the standard deviation is large and the unevenness is large regardless of the size of any local region. Also from the kurtosis, FIG. 13 is small and shows that the unevenness is large.

  17 and 18 show the histograms of the population obtained from the unevenness analysis of FIGS. 13 and 14 when the radius of the local region is 40 pixels. From the histograms, FIG. 13 shows the fiber area content rate. Is distributed in a range from a maximum value of 0.8 to a minimum value of 0.3, and in FIG. 14, a maximum value of 0.5 to a minimum value of 0.23. In FIG. 13, the kurtosis is smaller than that of FIG. It can be seen that there is a large possibility that the rate varies depending on the location of the local region, and the unevenness is large. Further, it can be seen that when the radius of the local region is around 30 pixels, the difference in kurtosis between FIG. 13 and FIG. 14 is large, and if the radius is 30 pixels, the average weight in the extracted local region tends to vary. Therefore, it can be estimated that a circle with a radius of 30 pixels is uneven.

(Comparative Example 1)
13 and 14 are divided into square local regions that do not overlap each other as shown in Patent Literature 4, Patent Literature 5, and Patent Literature 6, and the area content of fibers in the local region is defined as a population. Quantification was performed. The method of dividing the area was selected from five different places, and the variation of the population variation was evaluated. The result is shown in FIG. As a result, in FIG. 14 where the unevenness is small, the difference due to the position of the region is small, but in FIG. Therefore, it can be seen that, in a composite material with large unevenness, the method in which the divided region is a local region is not suitable for quantifying unevenness.

(Example 3)
20, FIG. 21, and FIG. 22 assume a cross-section in the direction perpendicular to the fiber of a unidirectional fiber-reinforced composite material, and assume a regular fiber arrangement, a random fiber arrangement, and a fiber arrangement with a large difference in density. .

  The results of evaluating the unevenness in fiber arrangement of the unidirectional fiber-reinforced composite material using the present invention based on standard deviation and kurtosis are shown in FIGS. 23 and 24, respectively.

  In the standard deviation and kurtosis in the present invention, the irregularity is small in the regular arrangement, and the large irregularity is obtained in FIG. 22, which is effective in evaluating the density difference of the fiber arrangement. It can be seen that it is.

(Comparative Example 2)
FIG. 25 shows a case where Ripley's K function (K (h)) is used for the cross-sectional images of FIGS.

  In FIG. 25, h is the radius of the local region (micrometer) and R is the radius of the fiber (micrometer). In Ripley's K function, the difference between the regular arrangement and the arrangement in the other case is shown, but the difference between FIG. 21 and FIG. 22 is not shown. Therefore, Ripley's K function It turns out that it is not applicable to evaluation.

a: Analysis region b: Correspondence between color and characteristic value c: Example of local region d: Example of local region partially protruding from analysis region a e: Region where analysis region a and local region d overlap f: Pixel g : Edge of analysis area h: Example of local area centered on pixel i: Local area partially protruding from edge g of analysis area j: Correspondence between color and density of pixel

Claims (6)

An unevenness analysis method for quantifying unevenness of distribution of characteristic values from a digital image in which the same characteristic values are drawn in the same color, the first step of extracting an analysis area from the digital image, and each pixel in the analysis area On the other hand, a second step of giving a predetermined weight according to the color tone of each pixel, a third step of extracting a local region having a point symmetric shape smaller than the analysis region around each pixel in the analysis region, The fourth step of calculating the average weight in the local area by dividing the sum of the weights of all the pixels in the local area by the total number of pixels in the local area, and the average weight in each local area as the population An unevenness analysis method having five steps and a sixth step of quantifying the unevenness by a variation coefficient or a standard deviation of the population, with the variation of the population being the unevenness. The method for analyzing unevenness according to claim 1, wherein the digital image shows a distribution of characteristic values of a composite material composed of two or more kinds of constituent materials. The method for analyzing unevenness according to claim 1 or 2, wherein the digital image is an image obtained by binarizing a cross-sectional image of a composite material composed of two or more kinds of constituent materials. The unevenness analysis method according to any one of claims 1 to 3, wherein in the third step, a local region is extracted centering on a pixel that is limited to a pixel indicating a partial weight range. The method for analyzing unevenness according to any one of claims 1 to 4, wherein in the sixth step, unevenness is quantified by the kurtosis of the population. An unevenness size estimation method, wherein a plurality of populations are prepared by changing the area of the local region, and the unevenness analysis method according to any one of claims 1 to 5 is executed for each population.