Information processing device, information processing method, and information processing program

Abstract

To provide an information processing device, information processing method and information processing program which can accurately obtain the size distribution of particles constituting a material from a material structure image.SOLUTION: An information processing device 10 generates an object image being a binarized image of a material structure image. The information processing device 10 generates a first Fourier transformation result of the object image. The information processing device 10 generates a particle position image being the image expressing the gravity center position of each of a plurality of particles captured in the object image. The information processing device 10 generates a second Fourier transformation result being the Fourier transformation result of the particle position image. The information processing device 10 calculates a division result obtained by dividing the first Fourier transformation result by the second Fourier transformation result. The information processing device 10 sets the division result as the Fourier transformation result after correction of the object image, and generates the size distribution of the plurality of particles captured in the material structure image such that an expectation value in which the Fourier transformation result after correction appears is maximized by using an EM (Expectation-maximization) algorithm on the basis of the Fourier transformation result after correction.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to an information processing device, an information processing method, and an information processing program. [Background technology]

[0002] Conventionally, a microscope test method for steel grain size is known (for example, see Non-Patent Document 1). In the method disclosed in Non-Patent Document 1, the grain size is measured by a microscope on a polished surface of a test piece that has been treated in an appropriate manner depending on the steel type or other information. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] JIS G0551:2013 Japanese Industrial Standard "Steel - Microscopic test method for grain size" Summary of the Invention [Problem to be solved by the invention]

[0004] Incidentally, when calculating the size distribution of particles shown in a material structure image, it is possible to use a Fourier transform, which is an example of a known frequency analysis. However, since the result of the Fourier transform of a material structure image also contains information on the radial distribution between particles, there is a problem that the size distribution of the particles constituting the material cannot be obtained with high accuracy even if the result of the Fourier transform is simply used.

[0005] In consideration of the above, an object of the present invention is to provide an information processing device, an information processing method, and an information processing program capable of accurately obtaining the size distribution of particles constituting a material from a material structure image. [Means for solving the problem]

[0006] The information processing device according to the first aspect includes an acquisition unit that acquires a material structure image of an analysis target, a generation unit that generates a target image that is a binary image of the material structure image by binarizing the material structure image acquired by the acquisition unit, a first Fourier transform unit that generates a first Fourier transform result that is a Fourier transform result of the target image by Fourier transforming the target image generated by the generation unit, an image generation unit that identifies a center of gravity of each of a plurality of particles appearing in the target image generated by the generation unit and generates a particle position image that is an image representing the center of gravity of each of the plurality of particles, and a second Fourier transform unit that generates a Fourier transform result of the particle position image by Fourier transforming the particle position image generated by the image generation unit. a calculation unit that calculates a division result obtained by dividing the first Fourier transform result by the second Fourier transform result, based on the first Fourier transform result obtained by the first Fourier transform unit and the second Fourier transform result obtained by the second Fourier transform unit; and a distribution generation unit that sets the division result obtained by the calculation unit as a corrected Fourier transform result of the target image, and generates a size distribution of a plurality of particles appearing in the material structure image using an EM (Expectation-maximization) algorithm, based on the corrected Fourier transform result, so that an expectation value for the appearance of the corrected Fourier transform result is maximized.

[0007] The information processing device acquires a material structure image of an object to be analyzed, and binarizes the acquired material structure image to generate an object image that is a binarized image of the material structure image. The information processing device performs a Fourier transform on the generated object image to generate a first Fourier transform result that is a Fourier transform result of the object image. The information processing device identifies the position of the center of gravity of each of a plurality of particles appearing in the generated object image, and generates a particle position image that is an image representing the position of the center of gravity of each of the plurality of particles. The information processing device performs a Fourier transform on the generated particle position image to generate a second Fourier transform result that is a Fourier transform result of the particle position image. The information processing device calculates a division result obtained by dividing the first Fourier transform result by the second Fourier transform result, based on the first Fourier transform result and the second Fourier transform result. The information processing device sets the division result as a corrected Fourier transform result of the object image, and generates a size distribution of a plurality of particles appearing in the material structure image based on the corrected Fourier transform result, using an EM (Expectation-maximization) algorithm, so that the expected value of the appearance of the corrected Fourier transform result is maximized. This makes it possible to obtain the size distribution of particles constituting the material with high accuracy from the material structure image. In addition, since the corrected Fourier transform result does not include information on the radial distribution of the particles, the size distribution of the particles shown in the material structure image can be calculated with high accuracy by using the corrected Fourier transform result to calculate the size distribution of the particles shown in the material structure image. In addition, by using a particle position image which is an image showing the position of the center of gravity of each of the multiple particles shown in the material structure image, it becomes unnecessary to perform a Fourier transform of the image of each particle shown in the material structure image, so that the amount of calculation is reduced and the size distribution of the particles constituting the material can be efficiently obtained from the material structure image.

[0008] The distribution generation unit of the information processing device according to the second aspect calculates the corrected Fourier transform result P(f i ), the size s for each combination of index m for identifying the particle size and index i for identifying the frequency is determined so that the following equation (1) is satisfied: mWhen a particle of frequency f appears in the target image, i The probability P(f i |s m ) and set the probability P(f i |s m ) is selected with probability π m and for each combination of index n for identifying the particle size and index i for identifying the frequency, the probability P(f i |s m ) and the selection probability π m The expected value z is calculated from the following formula (2) in The selection probability π is set so that n Calculate the selection probability π n is generated as a size distribution of a plurality of particles appearing in the material structure image. By using an EM (Expectation-maximization) algorithm, the selection probability π n can be calculated.

[0009]

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[0010] An information processing method according to a third aspect is an information processing method in which a computer executes processes of acquiring a material structure image of an analysis target, binarizing the acquired material structure image to generate a target image which is a binarized image of the material structure image, Fourier transforming the generated target image to generate a first Fourier transform result which is a Fourier transform result of the target image, identifying the positions of the centers of gravity of each of a plurality of particles appearing in the generated target image and generating a particle position image which is an image representing the positions of the centers of gravity of each of the plurality of particles, Fourier transforming the generated particle position image to generate a second Fourier transform result which is a Fourier transform result of the particle position image, calculating a division result obtained by dividing the first Fourier transform result by the second Fourier transform result based on the first Fourier transform result and the second Fourier transform result, setting the division result as a corrected Fourier transform result of the target image, and generating a size distribution of a plurality of particles appearing in the material structure image using an Expectation-maximization (EM) algorithm based on the corrected Fourier transform result, such that an expectation value for the appearance of the corrected Fourier transform result is maximized.

[0011] An information processing program according to a fourth aspect is an information processing program for causing a computer to execute processes of acquiring a material structure image of an analysis target, binarizing the acquired material structure image to generate a target image which is a binarized image of the material structure image, Fourier transforming the generated target image to generate a first Fourier transform result which is a Fourier transform result of the target image, identifying the positions of the centers of gravity of each of a plurality of particles appearing in the generated target image and generating a particle position image which is an image representing the positions of the centers of gravity of each of the plurality of particles, Fourier transforming the generated particle position image to generate a second Fourier transform result which is a Fourier transform result of the particle position image, calculating a division result obtained by dividing the first Fourier transform result by the second Fourier transform result based on the first Fourier transform result and the second Fourier transform result, setting the division result as a corrected Fourier transform result of the target image, and generating a size distribution of a plurality of particles appearing in the material structure image using an Expectation-maximization (EM) algorithm based on the corrected Fourier transform result so that an expectation value for the appearance of the corrected Fourier transform result is maximized. Effect of the Invention

[0012] As described above, the present disclosure has the advantage of being able to accurately obtain the size distribution of particles that make up a material from a material structure image. [Brief description of the drawings]

[0013] [Figure 1] 1 is a schematic block diagram of an information processing apparatus according to an embodiment. [Diagram 2] FIG. 1 is a diagram for explaining an overview of an embodiment. [Diagram 3] FIG. 1 is a diagram for explaining an overview of an embodiment. [Figure 4] FIG. 1 is a diagram for explaining a radial distribution function. [Diagram 5] FIG. 13 is a diagram for explaining a process of accumulating the Fourier transform results of an image showing one particle. [Figure 6] FIG. 2 is a diagram for explaining the derivation of a radial distribution function and an overview of the present embodiment. [Figure 7] FIG. 13 is a diagram for explaining a Fourier transform result after correction. [Figure 8] FIG. 1 is a diagram for explaining estimation of size distribution by the EM algorithm. [Figure 9] FIG. 1 is a diagram for explaining estimation of size distribution by the EM algorithm. [Figure 10] FIG. 1 is a diagram for explaining estimation of size distribution by the EM algorithm. [Figure 11] FIG. 2 is a diagram illustrating an example of the configuration of a computer of an information processing device according to an embodiment. [Figure 12] 10 is a flowchart illustrating an example of processing performed by the information processing device according to the embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] <Embodiment>

[0015] Hereinafter, an information processing apparatus according to an embodiment will be described with reference to the drawings.

[0016] Fig. 1 is a block diagram showing an example of a functional configuration of an information processing device 10 according to an embodiment. As shown in Fig. 1, the information processing device 10 functionally includes an acquisition unit 100, a generation unit 102, a first Fourier transform unit 104, an image generation unit 106, a second Fourier transform unit 108, a calculation unit 110, and a distribution generation unit 112.

[0017] Fig. 2 is an explanatory diagram for explaining the information processing device 10 of the embodiment. As shown in Fig. 2, the information processing device 10 of the embodiment calculates a size distribution D of particles appearing in a material structure image Im, which is an image captured when observing a material using a microscope, from the material structure image Im. If it is possible to obtain the size distribution D of particles appearing in the material structure image Im, it is possible to obtain information on the properties of the material corresponding to the material structure image Im based on the size distribution D.

[0018] FIG. 3 is a diagram for explaining the relationship between a material structure image and the frequencies contained in the material structure image. As shown in FIG. 3, a material structure image Im is generated by dividing image signals I f1 ,I f2 ,I f3 These multiple image signals I f1 ,I f2 ,I f3 The superposition of these corresponds to the material structure image Im. In this case, by performing a Fourier transform, which is an example of frequency analysis, on the material structure image Im, a Fourier transform result FFT as shown in FIG. 3 is obtained. Note that the pixel values ​​of the image corresponding to the Fourier transform result FFT in FIG. 3 represent the power spectrum, and the higher the pixel value, the higher the value of the power spectrum. The power spectrum values ​​from A to B shown in FIG. 3 are extracted from the Fourier transform result FFT shown in FIG. 3. At that time, the straight line from A to B is rotated in the R direction, and the value obtained by accumulating the power spectrum values ​​obtained at each position is obtained as the power spectrum integrated value PS. It is also possible to obtain the size distribution of particles captured in the material structure image using such a Fourier transform result.

[0019] On the other hand, the Fourier transform of an image has properties similar to those of small angle scattering (SAS). Considering this, the value of the power spectrum obtained by Fourier transforming an image can correspond to the small angle scattering intensity I(q). The small angle scattering intensity I(q) is expressed by the following formula (1).

[0020]

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[0021] In the above formula (1), N, F(q), S(q), and q represent the physical quantities in small-angle scattering. Specifically, N is the number of repetitions of the unit cell, F(q) represents the shape factor, S(q) represents the structure factor, and q represents the scattering vector.

[0022] When the above formula (1) is applied to the Fourier transform result of the material structure image, I(q) corresponds to the Fourier transform result of the material structure image, N corresponds to the number of particles appearing in the material structure image, and F 2 Here, I(q) corresponds to the size distribution function of the particles in the material structure image, and S(q) corresponds to the radial distribution function of the particles in the material structure image. For the sake of convenience, the Fourier transform result of the material structure image will be referred to as I(q), the number of particles as N, and the size distribution function of the particles in the material structure image as F(q). 2 The radial distribution function of the particles in the material structure image is called S(q).

[0023] The size distribution function of a particle is a function that reflects the size and shape of the particle. On the other hand, the radial distribution function of a particle is a function that represents the spatial distribution of the center of gravity between particles, as shown in Figure 4. Specifically, for example, in the case where particles P1, P2, and P3 exist, the distance r between particle P1 and particle P2 is j and the distance r between particle P1 and particle P3 i In this case, the distance r between each particle is the horizontal axis of the graph, and the vertical axis of the graph is the radial distribution function.

[0024] In this case, as shown in the above formula (1), the Fourier transform result I(q) of the material structure image is expressed by the size distribution function F 2 It is expressed as the product of the Fourier transform result I(q) and the radial distribution function S(q). Therefore, the radial distribution function S(q) is reflected in the Fourier transform result I(q), and even if one tries to obtain the size distribution of particles in a material structure image simply by using the Fourier transform result I(q), the size distribution cannot be obtained with high accuracy due to the influence of the radial distribution function S(q). Therefore, when trying to accurately calculate the size distribution of particles in a material structure image based on the Fourier transform result I(q), it is necessary to remove the influence of the radial distribution function S(q).

[0025] Here, we consider generating multiple images in which one particle appears based on a material structure image in which multiple particles appear, and removing each of the Fourier transform results of the images in which one particle appears from the Fourier transform result of the material structure image. According to this method, both the particle shape and the particle radial distribution are removed from the Fourier transform result of the material structure image, so that a Fourier transform result corresponding to the size distribution of the particles appearing in the material structure image can be obtained.

[0026] When this method is adopted, first, images Im1, Im2, Im3, Im4, Im5, and Im6 in which one particle is captured are generated from a material structure image, as shown in Fig. 5. Then, Fourier transform results FFT1, FFT2, FFT3, FFT4, FFT5, and FFT6 of images Im1, Im2, Im3, Im4, Im5, and Im6 are generated, as shown in Fig. 5. Note that integrated values ​​PS1, PS2, PS3, PS4, PS5, and PS6 of the power spectrum are calculated from each of the Fourier transform results FFT1, FFT2, FFT3, FFT4, FFT5, and FFT6.

[0027] The Fourier transform result FFT represents the sum of these Fourier transform results FFT1, FFT2, FFT3, FFT4, FFT5, and FFT6. ALL and its Fourier transform result FFT ALL The integrated value PS of the power spectrum corresponding to ALL In the following, the integrated value of the power spectrum PS ALL Let y0.

[0028] The sum of the Fourier transform results of an image showing one particle (FFT) ALL Since is calculated from an image that shows one particle, there is no interference between particles. Therefore, the sum of the Fourier transform results FFT ALL For this, the radial distribution function S(q) can be considered to be 1. Therefore, the sum of the Fourier transform results FFT ALL The Fourier transform result I0(q) corresponding to the above equation (1) has a radial distribution function S(q) of 1 and is expressed by the following equation (2).

[0029]

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[0030] The Fourier transform result FFT of the material structure image corresponds to I(q) in the above formula (1). Therefore, the radial distribution function S(q) can be obtained by dividing both sides of the above formula (1) by both sides of the above formula (2). In practice, the division result y0 / y1 obtained by dividing the integrated value y0 of the power spectrum by the integrated value y1 of the power spectrum corresponds to the radial distribution function S(q), as shown in the following formula.

[0031]

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[0032] On the other hand, when generating multiple images each showing one particle from a material structure image, the amount of calculation required becomes enormous. Therefore, in this embodiment, a particle position image showing the center of gravity of each particle is generated, and the radial distribution function S(q) is obtained by using the Fourier transform result of the particle position image.

[0033] Specifically, the information processing device 10 of this embodiment generates a particle position image Im in which the positions of the centers of gravity of the particles P1, P2, P3, and P4 captured in the material structure image Im are specified, as shown in the lower part of FIG. centers Then, the information processing device 10 of this embodiment generates a particle position image Im centers The Fourier transform result of FFT centers The power spectrum integrated value y1 calculated from centers As shown in FIG. 6, the integrated value y1 of this power spectrum is generated. centers Since it can be said that represents the spatial distribution of the center of gravity between particles, it can be said to be an approximation of the radial distribution function S(q) corresponding to y0 / y1. Therefore, the following equation (3) is established.

[0034]

number

[0035] For this reason, when calculating the size distribution of a plurality of particles appearing in a material structure image, the information processing device 10 of this embodiment uses the corrected Fourier transform result y1 / y1 centers By using this method, the size distribution of multiple particles seen in the material structure image is calculated.

[0036] Figure 7 shows the integrated value y0 of the power spectrum obtained from the sum of the Fourier transform results of an image showing one particle, the integrated value y1 of the power spectrum obtained from the Fourier transform results of the material structure image, and the integrated value y1 / y1 of the power spectrum obtained as the corrected Fourier transform result. centers As shown in FIG. 7, the integrated value y1 / y1 of the power spectrum centers has a waveform similar to that of the integrated value y0 of the power spectrum. Therefore, the integrated value y1 / y1 of the corrected power spectrum centers is almost equivalent to the result obtained by performing a Fourier transform on each image of a single particle, and the effect of the radial distribution between particles has been removed.

[0037] Therefore, the information processing device 10 of the embodiment identifies the position of the center of gravity of each of the multiple particles appearing in the material structure image, and generates a particle position image in which the position of the center of gravity of each of the multiple particles is identified. The information processing device 10 of the embodiment then obtains a corrected Fourier transform result by correcting the Fourier transform result of the material structure image by dividing the Fourier transform result of the material structure image by the Fourier transform of the particle position image. By dividing the Fourier transform result of the material structure image by the Fourier transform of the particle position image, the influence of the radial distribution function S(q) in the above formula (1) is eliminated, and the corrected Fourier transform result does not include the size distribution function F 2Therefore, the information processing device 10 of the embodiment can efficiently and accurately calculate the size distribution of particles appearing in the material structure image by using the corrected Fourier transform result to calculate the size distribution of particles appearing in the material structure image.

[0038] The specific details will be explained below.

[0039] The acquisition unit 100 acquires a material structure image, which is an image captured when observing a material using a microscope. The material structure image is an image that represents the structure of a material. The material structure image is a grayscale image.

[0040] The generating unit 102 binarizes the material structure image acquired by the acquiring unit 100 to generate a target image which is a binarized image of the material structure image.

[0041] The first Fourier transform unit 104 generates a first Fourier transform result, which is a Fourier transform result of the target image, by performing a Fourier transform on the target image generated by the generation unit 102. Then, the first Fourier transform unit 104 calculates an integrated value y1 of the power spectrum from the first Fourier transform result.

[0042] The image generating unit 106 identifies the center of gravity of each of the plurality of particles appearing in the target image generated by the generating unit 102, and generates a particle position image which is an image representing the center of gravity of each of the plurality of particles.

[0043] Specifically, the image generating unit 106 identifies the center of gravity of each of the plurality of particles captured in the target image using a known image processing technique, and then generates a particle position image that is an image representing the center of gravity of each of the plurality of particles.

[0044] The second Fourier transform unit 108 performs a Fourier transform on the particle position image generated by the image generation unit 106 to generate a second Fourier transform result, which is a Fourier transform result of the particle position image. Then, the second Fourier transform unit 108 calculates an integrated value y1 of the power spectrum from the second Fourier transform result. centers Calculate.

[0045] The calculation unit 110 calculates an integrated value y1 of the power spectrum of the first Fourier transform result obtained by the first Fourier transform unit 104 and an integrated value y1 of the power spectrum of the second Fourier transform result obtained by the second Fourier transform unit 108. centers Based on this, the power spectrum integrated value y1 is calculated. centers The result of division by y1 / y1 centers Calculate.

[0046] The distribution generating unit 112 calculates the division result y1 / y1 centers is set as the corrected Fourier transform result of the target image. Then, based on the corrected Fourier transform result, the distribution generating unit 112 uses an expectation-maximization (EM) algorithm to generate a size distribution of multiple particles appearing in the material structure image such that the expected value of the corrected Fourier transform result is maximized.

[0047] Specifically, the distribution generation unit 112 uses the method disclosed in Patent Application No. 2020-119514 to generate a size distribution of multiple particles appearing in the material structure image based on the corrected Fourier transform result using an EM (Expectation-maximization) algorithm so that the expected value for the appearance of the corrected Fourier transform result is maximized.

[0048] Fig. 8 is a diagram showing a schematic diagram of a method for estimating the size distribution of a plurality of particles appearing in a target image. As shown in Fig. 8, the size of the particles appearing in the target image is determined by a certain selection probability π n According to size S n The size s nA particle with frequency f i The probability corresponding to P(f i |s n ), then the probability P(f i |s n ) is expressed by the following equation I(s,f):

[0049]

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[0050] P(f i |s n ) is the Bayesian s n can be regarded as the posterior probability with the prior condition. Under this premise, i The probability of occurrence of P(f i ) is the probability P(f i |s n ) can be obtained as the sum of

[0051] In Figure 9, a certain frequency f i The probability of occurrence of P(f i 9 is a diagram for explaining the frequency f i The probability of occurrence of P(f i ) is size S m is the frequency f i The probability P(f i |s m ) and its selection probability π m and is expressed by the following formula:

[0052]

number

[0053] FIG. 10 is a diagram for explaining a method for calculating the selection probability from the frequency distribution. As shown in FIG. 10, at a certain frequency f i The particle corresponding ton The corresponding probability is P(s n |f i ) This probability P(s n |f i ) is expressed by the following formula by applying the known Bayes' theorem:

[0054]

number

[0055] P(s n ) is the selection probability π n Also, at a certain frequency f i The probability of occurrence of P(f i ) is calculated using the above formula (2A). Therefore, at a certain frequency f i The particle size corresponding to n The probability P(s n |f i ) is obtained by substituting (2A) above for the denominator of the right-hand side of the above formula (3A) and calculating P(s n ) with probability π n By replacing z in the following equation (4), in is the probability P(s n |f i )

[0056]

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[0057] Also, the selection probability π n is expressed by the following formula. Note that c in the following formula (5A) i ,c j is a predetermined coefficient.

[0058]

number

[0059] The distribution generation unit 112 calculates z in As the M step of the EM algorithm, the distribution generation unit 112 calculates the selection probability π n Calculate.

[0060] Specifically, the distribution generating unit 112 calculates the corrected Fourier transform result P(f i ), so that the above formula (2A) is satisfied, for each combination of index m for identifying the particle size and index i for identifying the frequency, the size s m When a particle of frequency f appears in the target image, i The probability that appears in the corrected Fourier transform result is P(f i |s m ) and set the probability P(f i |s m ) is selected with probability π m Set.

[0061] Next, the distribution generation unit 112 calculates the probability P(f i |s m ) and the selection probability π m The expected value z calculated from the above formula (4A) in The selection probability π is maximized. n Then, the distribution generation unit 112 calculates the selection probability π n is generated as a size distribution of multiple particles seen in the material structure image.

[0062] The distribution generation unit 112 repeats the E and M steps of the EM algorithm until a predetermined convergence condition is satisfied. Then, the distribution generation unit 112 calculates the size s n The selection probability of πn is generated as a size distribution of multiple particles in the target image. Selection probability π n Available in multiple sizes n The probability P(s n ), so the selection probability is π n Available in multiple sizes n This corresponds to a size distribution of (n=1 to N').

[0063] A display unit (not shown) outputs the result of the size distribution generated by the distribution generating unit 112. The user of the information processing device 10 checks the result of the size distribution displayed on the display unit (not shown).

[0064] The information processing device 10 can be realized by, for example, a computer 50 as shown in Fig. 11. The computer 50 realizing the information processing device 10 includes a CPU 51, a memory 52 as a temporary storage area, and a non-volatile storage unit 53. The computer also includes an input / output interface (I / F) 54 to which an input / output device or the like (not shown) is connected, and a read / write (R / W) unit 55 that controls reading and writing of data from and to a recording medium 59. The computer also includes a network I / F 56 that is connected to a network such as the Internet. The CPU 51, the memory 52, the storage unit 53, the input / output I / F 54, the R / W unit 55, and the network I / F 56 are connected to one another via a bus 57.

[0065] The storage unit 53 can be realized by a hard disk drive (HDD), a solid state drive (SSD), a flash memory, etc. The storage unit 53 as a storage medium stores a program for making the computer function. The CPU 51 reads the program from the storage unit 53, expands it in the memory 52, and sequentially executes the processes contained in the program.

[0066] Next, the operation of the information processing device 10 of the embodiment will be described.

[0067] When a material structure image to be analyzed is input to the information processing device 10, the information processing device 10 executes an information processing routine shown in FIG.

[0068] In step S100, the acquisition unit 100 acquires an input material structure image.

[0069] In step S102, the generator 102 binarizes the material structure image acquired in step S100 above, thereby generating a target image which is a binarized image of the material structure image.

[0070] In step S104, the first Fourier transform unit 104 performs a Fourier transform on the target image generated in step S102 to generate a first Fourier transform result, which is a Fourier transform result of the target image. Then, the first Fourier transform unit 104 calculates an integrated value y1 of the power spectrum from the first Fourier transform result.

[0071] In step S106, the image generating unit 106 identifies the center of gravity of each of the plurality of particles appearing in the target image generated in step S104 above, and generates a particle position image which is an image representing the center of gravity of each of the plurality of particles.

[0072] In step S108, the second Fourier transform unit 108 performs a Fourier transform on the particle position image generated in step S106 to generate a second Fourier transform result, which is a Fourier transform result of the particle position image. Then, the second Fourier transform unit 108 calculates an integrated value y1 of the power spectrum from the second Fourier transform result. centers Calculate.

[0073] In step S110, the calculation unit 110 calculates an integrated value y1 of the power spectrum of the first Fourier transform result obtained in step S108 and an integrated value y1 of the power spectrum of the second Fourier transform result obtained in step S110. centers Based on this, the power spectrum integrated value y1 is calculated. centers By dividing by y1, the result is y1 / y1centers Calculate.

[0074] In step S112, the distribution generating unit 112 calculates the division result y1 / y1 calculated in step S110. centers is set as the corrected Fourier transform result of the target image. Then, based on the corrected Fourier transform result, the distribution generating unit 112 uses an expectation-maximization (EM) algorithm to generate a size distribution of multiple particles appearing in the material structure image such that the expected value of the corrected Fourier transform result is maximized.

[0075] In step S114, the distribution generating unit 112 outputs the particle size distribution generated in step S112 as a result.

[0076] As described above, the information processing device 10 according to the embodiment acquires a material structure image of an analysis target. The information processing device 10 binarizes the acquired material structure image to generate a target image that is a binarized image of the material structure image. The information processing device 10 performs a Fourier transform on the generated target image to generate a first Fourier transform result that is a Fourier transform result of the target image. The information processing device 10 identifies the position of the center of gravity of each of a plurality of particles appearing in the generated target image, and generates a particle position image that is an image representing the position of the center of gravity of each of a plurality of particles. The information processing device 10 performs a Fourier transform on the generated particle position image to generate a second Fourier transform result that is a Fourier transform result of the particle position image. The information processing device 10 calculates a division result obtained by dividing the first Fourier transform result by the second Fourier transform result, based on the first Fourier transform result and the second Fourier transform result. The information processing device 10 sets the division result as the corrected Fourier transform result of the target image, and generates a size distribution of multiple particles appearing in the material structure image based on the corrected Fourier transform result using an EM (Expectation-maximization) algorithm so that the expected value of the corrected Fourier transform result is maximized. This makes it possible to obtain the size distribution of particles constituting the material from the material structure image with high accuracy. In addition, by using a particle position image that is an image showing the position of the center of gravity of each of multiple particles appearing in the material structure image, it is no longer necessary to perform a Fourier transform of the image of each particle appearing in the material structure image, so the amount of calculation is reduced and the size distribution of particles constituting the material can be efficiently obtained from the material structure image.

[0077] In the above embodiment, the processes performed by each device have been described as software processes performed by executing a program, but they may be hardware processes. Alternatively, they may be a combination of both software and hardware processes. Furthermore, the programs stored in the ROM may be stored in various storage media and distributed.

[0078] Furthermore, the present invention is not limited to the above, and it goes without saying that various modifications can be made without departing from the spirit and scope of the present invention.

[0079] For example, in the above embodiment, granular objects, needle-shaped objects, fibrous objects, holes, etc. that make up the material are given as examples of particles that make up the material, but the particles may have structures different from these.

[0080] In the above embodiment, the input data to the EM algorithm is an integrated value of the power spectrum calculated from the Fourier transform result, but the present invention is not limited to this. Any data may be used as the input data to the EM algorithm as long as the data reflects the Fourier transform result. [Explanation of symbols]

[0081] 10. Information processing device 50 Computer 100 Acquisition Department 102 Generation part 104 First Fourier Transform Unit 106 Image Generation Unit 108 Second Fourier Transform Unit 110 Calculation Department 112 Distribution generator

Claims

1. an acquisition unit for acquiring a material structure image of an object to be analyzed; a generation unit that generates a target image, which is a binarized image of the material structure image by binarizing the material structure image acquired by the acquisition unit; a first Fourier transform unit that performs a Fourier transform on the target image generated by the generation unit to generate a first Fourier transform result that is a Fourier transform result of the target image; an image generating unit that identifies a center of gravity position of each of a plurality of particles appearing in the target image generated by the generating unit and generates a particle position image that is an image representing the center of gravity position of each of the plurality of particles; a second Fourier transform unit that generates a second Fourier transform result, which is a Fourier transform result of the particle position image, by performing a Fourier transform on the particle position image generated by the image generation unit; a calculation unit that calculates a division result obtained by dividing the first Fourier transform result obtained by the first Fourier transform unit and the second Fourier transform result obtained by the second Fourier transform unit, a distribution generating unit that sets the division result obtained by the calculating unit as a corrected Fourier transform result of the target image, and generates a size distribution of a plurality of particles appearing in the material structure image using an expectation-maximization (EM) algorithm based on the corrected Fourier transform result so that an expectation value for the appearance of the corrected Fourier transform result is maximized; An information processing device comprising:

2. The distribution generation unit calculates the corrected Fourier transform result P(f ｉ ), the size s for each combination of index m for identifying the particle size and index i for identifying the frequency is determined so that the following equation (1) is satisfied: ｍ When a particle of frequency f appears in the target image, ｉ The probability P(f ｉ |s ｍ ), and the probability P(f ｉ |s ｍ ) is selected with probability π ｍ Set The probability P(f) for each combination of index n for identifying the particle size and index i for identifying the frequency is ｉ |s ｍ ) and the selection probability π ｍ The expected value z is calculated from the following formula (2): ｉｎ The selection probability π is set so that ｎ Calculate The selection probability π ｎ as a size distribution of a plurality of particles appearing in the material structure image; The information processing device according to claim 1 . [0010] （１） 【number】 （２）

3. Acquire an image of the material structure to be analyzed, generating a target image, which is a binarized image of the material structure image, by binarizing the acquired material structure image; generating a first Fourier transform result that is a Fourier transform result of the target image by performing a Fourier transform on the generated target image; Identifying the center of gravity of each of the plurality of particles appearing in the generated target image, and generating a particle position image which is an image representing the center of gravity of each of the plurality of particles; generating a second Fourier transform result, which is a Fourier transform result of the particle position image, by performing a Fourier transform on the generated particle position image; calculating a division result obtained by dividing the first Fourier transform result by the second Fourier transform result, based on the first Fourier transform result and the second Fourier transform result; the division result is set as a corrected Fourier transform result of the target image, and a size distribution of a plurality of particles appearing in the material structure image is generated based on the corrected Fourier transform result using an expectation-maximization (EM) algorithm so that an expectation value of the corrected Fourier transform result is maximized. An information processing method in which processing is performed by a computer.

4. Acquire an image of the material structure to be analyzed, generating a target image, which is a binarized image of the material structure image, by binarizing the acquired material structure image; generating a first Fourier transform result that is a Fourier transform result of the target image by performing a Fourier transform on the generated target image; Identifying the center of gravity of each of the plurality of particles appearing in the generated target image, and generating a particle position image which is an image representing the center of gravity of each of the plurality of particles; generating a second Fourier transform result, which is a Fourier transform result of the particle position image, by performing a Fourier transform on the generated particle position image; calculating a division result obtained by dividing the first Fourier transform result by the second Fourier transform result, based on the first Fourier transform result and the second Fourier transform result; the division result is set as a corrected Fourier transform result of the target image, and a size distribution of a plurality of particles appearing in the material structure image is generated based on the corrected Fourier transform result using an expectation-maximization (EM) algorithm so that an expectation value of the corrected Fourier transform result is maximized. An information processing program for causing a computer to execute processing.

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