Information processing method, apparatus, and program for three dimensional shape estimation

Abstract

To accurately estimate a three dimensional shape of particles from an observation result of two-dimension.SOLUTION: (A) calculating, from a two-dimension image of a plurality of particles to be estimated, an indicator value in a two-dimension of shapes of the particles, (B) generating, from the two-dimension image, a plurality of estimated three dimensional shapes of a first generation, and (C) calculating, for the plurality of estimated three dimensional shapes of the first generation, a feature parameter indicating a shape feature, (D) generating a plurality of estimated three dimensional shapes of the next generation using a control parameter and a feature parameter based on a relationship between an indicator value in the two-dimension of the plurality of estimated three dimensional shapes of the current generation and an indicator value in the two-dimension of the grain shape, and (E) evaluating the relationship between the indicator value in the two-dimension of the plurality of estimated three dimensional shapes of the next generation and the indicator value in the two-dimension of the grain shape, and further executing a process of generating the plurality of estimated three dimensional shapes of the next generation until a process termination condition is satisfied.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a technique for estimating the three-dimensional shape of a particle. [Background technology]

[0002] Most raw materials in mining and manufacturing are powders and granular materials, and the shape of the particles contained in these powders affects powder handling (transportation, mixing, packing, etc.) as well as the physical and chemical properties of the materials produced from them. Two-dimensional observation devices for powders and granular materials include various microscopes (e.g., Malvern Panalytical's Morphologi 4) and dynamic image analyzers (e.g., Shimadzu Corporation's iSpect DIA-10).

[0003] Two-dimensional observation devices can only obtain two-dimensional shapes, and cannot obtain three-dimensional shape information that actually affects the physical and chemical properties of materials. Methods for obtaining three-dimensional shapes include electron tomography, X-ray CT (Computed Tomography), and 3D scanners, but these methods are more costly and time-consuming than two-dimensional shape acquisition methods.

[0004] Several techniques are known for estimating the shape of particles contained in powders and granular materials from two-dimensional observation results. For example, Non-Patent Document 1 discloses a three-dimensional particle shape estimation technique based on Fourier Shape Descriptors (FSD). However, experiments by the present inventors have shown that the estimation accuracy is not very high. Furthermore, Non-Patent Document 2, for example, discloses a technique that uses spherical harmonic-based principal component analysis to estimate 3D particle size and shape characteristics from measurable 2D characteristics. This technique uses actual particle data as reference data, but there are cases where actual particle data cannot be obtained. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] G. Mollon, J. Zhao, Comput. Methods Appl. Mech. Eng. 279, 46-65 (2014) [Non-patent document 2] Ueda, T., Powder Technol. 404, 117461 (2022) Summary of the Invention [Problem to be solved by the invention]

[0006] Therefore, according to one aspect, it is an object of the present invention to provide a novel technique for accurately estimating the three-dimensional shape of a particle from two-dimensional observation results. [Means for solving the problem]

[0007] The information processing method of the present invention includes the steps of: (A) calculating two-dimensional index values ​​of particle shapes from two-dimensional images of multiple particles to be estimated; (B) generating multiple first-generation estimated three-dimensional shapes from the two-dimensional images; (C) calculating feature parameters representing shape characteristics for the multiple first-generation estimated three-dimensional shapes; (D) generating multiple next-generation estimated three-dimensional shapes using control parameters and feature parameters based on the relationship between the two-dimensional index values ​​for the multiple current-generation estimated three-dimensional shapes and the two-dimensional index values ​​for the particle shapes; and (E) evaluating the relationship between the two-dimensional index values ​​for the multiple next-generation estimated three-dimensional shapes and the two-dimensional index values ​​for the particle shapes, and further executing the process of generating the multiple next-generation estimated three-dimensional shapes until a processing termination condition is met. [Effects of the Invention]

[0008] According to one aspect, it becomes possible to accurately estimate the three-dimensional shape of a particle from two-dimensional observation results. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram showing an example of the configuration of an information processing system according to an embodiment of the present invention. [Figure 2] FIG. 2 is a diagram illustrating a processing flow of the processing according to the embodiment. [Figure 3] FIG. 3 is a diagram showing a processing flow of the three-dimensional processing. [Figure 4] FIG. 4 is a diagram for explaining the FSD analysis. [Figure 5] FIG. 5 is a diagram showing a specific example of a first-generation estimated three-dimensional shape. [Figure 6] FIG. 6 is a diagram showing a processing flow of the spherical harmonic analysis processing. [Figure 7] FIG. 7 is a diagram for explaining the major axis, median axis, and minor axis of an ellipsoid. [Figure 8] FIG. 8 is a schematic diagram for explaining the distance Rd between the base ellipsoid and the surface of the estimated three-dimensional shape. [Figure 9] FIG. 9 is a diagram showing a processing flow of the shape evolution processing. [Figure 10] FIG. 10 shows the experimental results including the 2D error scores (expressed as differences rather than absolute values) for each generation. [Figure 11] FIG. 11 is a diagram comparing the statistical results of MAE between the conventional method and this embodiment. [Figure 12] FIG. 12 is a diagram illustrating an example of a functional configuration of a computer. DETAILED DESCRIPTION OF THE INVENTION

[0010] [Embodiment 1] An example configuration of an information processing system 1000 that performs processing according to an embodiment of the present invention is shown in Fig. 1. The information processing system 1000 includes a first data storage unit 110, a preprocessing unit 120, a second data storage unit 130, a three-dimensionalization processing unit 140, a third data storage unit 150, a shape evolution processing unit 160, a fourth data storage unit 170, and an output unit 180.

[0011] The first data storage unit 110 stores two-dimensional images of particles obtained by a two-dimensional observation device for granular materials. The preprocessing unit 120 performs preprocessing to generate binarized two-dimensional image data for each particle from the two-dimensional images stored in the first data storage unit 110, and stores the resulting data in the second data storage unit 130. The three-dimensional processing unit 140 uses the data stored in the second data storage unit 130 to generate a first-generation estimated three-dimensional shape of the particle and related data, and stores the resulting data in the third data storage unit 150. The shape evolution processing unit 160 generates a second-generation estimated three-dimensional shape of the particle and related data from the data stored in the third data storage unit 150, and stores the resulting data in the fourth data storage unit 170. Upon completion of processing by the shape evolution processing unit 160, the output unit 180 outputs the estimated three-dimensional shape data stored in the fourth data storage unit 170 to an output device such as a display device.

[0012] Next, the processing executed by the information processing system 1000 will be described with reference to FIGS.

[0013] First, the preprocessing unit 120 performs preprocessing to generate binarized two-dimensional image data for each particle from the two-dimensional image stored in the first data storage unit 110, and stores the processing results in the second data storage unit 130 (FIG. 2: step S1). When multiple particles are in contact in the two-dimensional image, the particles are separated and identified using a method such as the watershed method. Furthermore, for binarization, an appropriate brightness value is set as a threshold value, thereby setting different brightness values ​​for the particles and the background.

[0014] Furthermore, the three-dimensional processing unit 140 executes three-dimensional processing using the data stored in the second data storage unit 130 (step S3). Details of the three-dimensional processing will be described with reference to FIGS. 3 to 8.

[0015] First, the three-dimensional processing unit 140 calculates the observed 2D index (sometimes abbreviated as O2DS), which is an index value of the particle shape in two dimensions, from the two-dimensional image data (2D image), and stores it in the third data storage unit 150 (FIG. 3: step S11). In this embodiment, first, the aspect ratio and circularity are calculated for each particle. The aspect ratio is the ratio of the long axis length to the short axis length, and takes a value of 1 or more, being 1 for a circle and increasing for elongated particles. The circularity is calculated as 4π × (area) / (perimeter) 2 It is calculated as follows: and takes a value between 0 and 1, with 1 for a circle and 0 as the shape becomes more distorted. The aspect ratio and circularity are calculated from all 2D images, and the average aspect ratio α ave OBS and standard deviation α SD OBS and the average circularity κ ave OBS and standard deviation κ SD OBS These are calculated as O2DS.

[0016] The three-dimensional processing unit 140 also performs an FSD (Fourier Shape Descriptors) analysis process on each 2D image to calculate an FSD index value, which is then stored in the third data storage unit 150 (step S13). Specifically, the particle contour is divided into N equal points. For example, if N=128, a point is set on the particle contour every time the angle formed by the particle and a reference line passing through the center of the particle increases by approximately 2.8 degrees. Then, as shown schematically in FIG. 4, a radial function r, which is the length from the i-th point (angle ψi) on the contour to the center of the particle, is calculated. i Then, r i From the Fourier coefficients obtained by performing Fourier analysis up to L-th order (for example, L=64) on ψi and ψi, an index value D representing the magnitude of the Fourier coefficient at order i is obtained as follows: i Calculate.

number

[0017] This method assumes that there is only one contour point in a specific direction from the center point of the particle. This condition is generally met for sand and ore particles, but if there are multiple contour points, the shortest one is used.

[0018] For each 2D image, i Calculate the average value D i ave and standard deviation D i SD is calculated as the FSD index value.

[0019] Thereafter, the three-dimensional processing unit 140 generates a predetermined number of basic 3D shapes (B3DS: Basic 3D Shapes) from the FSD index values, and stores the data of the B3DS in the third data storage unit 150 (step S15).

[0020] First, the FSD index value D i ave and D i SD Calculate the three-dimensional radial function R (vector) representing B3DS from

[0021] Specifically, R (vector) at M vertices of a mesh structure obtained by dividing the surface of a three-dimensional shape including M vertices (for example, 642 vertices) into triangles is calculated using the following formula.

number

[0022] In equation (2), μ is a vector with r0 values, ξ represents a random number based on a normal distribution, and λ j and φ j are the j-th eigenvalues ​​and j-th eigenvectors of the covariance matrix C defined below.

number

[0023] In this way, R, i.e., B3DS, that reflects the characteristics of the two-dimensional shape is calculated. In this embodiment, a predetermined number of B3DSs, for example, 121, are generated. For example, an example of a B3DS generated for hematite is shown in FIG. 5.

[0024] Then, the three-dimensional processing unit 140 calculates estimated 2D indices (E2DS), which are index values ​​in two dimensions, from the generated B3DS and stores them in the third data storage unit 150 (step S17). Each B3DS is randomly rotated in three dimensions and projected in the Z-axis direction to obtain a two-dimensional image. Then, the aspect ratio and circularity are calculated for each B3DS. Furthermore, the average aspect ratio α ave EST and standard deviation α SD EST and the average circularity κ ave EST and standard deviation κ SD EST These are calculated as E2DS.

[0025] Furthermore, the three-dimensional processing unit 140 executes spherical harmonic function analysis processing (step S19). The spherical harmonic function analysis processing will be described with reference to FIG.

[0026] The three-dimensional processing unit 140 generates a base ellipsoid from all the generated B3DSs (FIG. 6: step S31). In this embodiment, from the viewpoint of accuracy, a base ellipsoid is generated, and the estimated three-dimensional shape is represented by using the distance from this base ellipsoid to the surface of the estimated three-dimensional shape (also called the inter-surface distance). From all the B3DSs, the ratio of the major axis length to the median axis length and the ratio of the median axis length to the minor axis length are calculated, and the average value A of the former is calculated. ab and the latter average value A bc The major axis length, the middle axis length, and the minor axis length have a relationship as shown in FIG.

[0027] The three-dimensional processing unit 140 also calculates the distance Rd between the surface of the base ellipsoid and the surface of each B3DS for each vertex of the base ellipsoid (step S33). More specifically, the surface of the base ellipsoid is divided into a triangular mesh with a total of M vertices. The distance Rd from each vertex to the intersection with the B3DS is calculated in the normal direction, with the outward direction being positive. Figure 8 schematically shows the distance Rd when the base ellipsoid is a two-dimensional base ellipsoid and the B3DS is a particle shape with a two-dimensional outline. Figure 8 shows the length of the arrows extending vertically from each point on the outline of the base ellipsoid and the distance Rd to the intersection with the outline of the B3DS. As a result, the shape of the B3DS is expressed by a combination of the base ellipsoid and the distance Rd. Note that points for which the distance Rd is positive are protruding parts from the base ellipsoid, and points for which the distance Rd is negative are recessed parts from the base ellipsoid.

[0028] Then, the three-dimensional processing unit 140 converts the distance Rd into an SH coefficient a, which is a coefficient of a spherical harmonic function, and stores it in the third data storage unit 150 (step S35). Then, the process returns to the calling process. This calculation is described in Non-Patent Document 2.

[0029] To explain a little, Rd and a are related by the following formula:

number

[0030] Also, Y n m (θ,φ) is expressed as follows: Y n m (θ,φ)=k n |m| P n |m| (cosφ)Qm(θ) (6) P n |m| is the associated Legendre function of the first kind, and k n |m| and Qm(θ) are expressed by the following equations.

number

number

[0031] Then, a is calculated by solving the following equation using a technique such as QR decomposition.

number

[0032] Returning to the explanation of FIG. 3, the three-dimensionalization processing unit 140 generates a matrix by combining the SH coefficients a of all B3DSs, then performs principal component analysis on the matrix, and stores the results of the principal component analysis in the third data storage unit 150 (step S21). Then, the process returns to the calling process. Since principal component analysis is well known, details will be omitted. The results of the principal component analysis are expressed as the k-th principal component value e m k,n and variance σ kIn this embodiment, principal component analysis is performed to pass on the shape features of B3DS derived from two-dimensional images of particle shapes to the next generation through shape evolution processing.

[0033] 2, next, the shape evolution processing unit 160 executes shape evolution processing (step S5). The shape evolution processing will be described with reference to FIG.

[0034] Shape evolution processing unit 160 calculates control parameters from the O2DS and E2DS stored in third data storage unit 150, and stores them in fourth data storage unit 170 (FIG. 9: step S41).

[0035] In this embodiment, the following three control parameters β, γ, and δ are introduced.

number

number

number

[0036] α ave EST , α SD EST and κ SD EST is initially the value calculated in step S17, but thereafter is the value calculated in step S47.

[0037] β is a parameter that determines the average aspect ratio of the next-generation base ellipsoid, based on the relationship between the average aspect ratio of the E2DS of the current-generation (initially the first-generation) estimated 3D shape (initially the B3DS) and the average aspect ratio of the O2DS. If the average aspect ratio of the E2DS of the current-generation estimated 3D shape is smaller than the average aspect ratio of the O2DS, it increases the average aspect ratio of the E2DS of the next-generation.

[0038] γ is a parameter that determines the variation in the average aspect ratio of the base ellipsoids of the next generation, based on the relationship between the standard deviation of the aspect ratios included in the E2DS of the estimated 3D shape of the current generation (initially the first generation) (initially the B3DS) and the standard deviation of the aspect ratios included in the O2DS. If the standard deviation of the aspect ratios included in the E2DS of the estimated 3D shape of the current generation is smaller than the standard deviation of the aspect ratios of the O2DS, it acts to increase the variation in the average aspect ratio of the base ellipsoids of the next generation.

[0039] δ is based on the magnitude relationship between the standard deviation of circularity included in the E2DS of the current-generation (initially first-generation) estimated three-dimensional shape (initially B3DS) and the standard deviation of circularity included in the O2DS, and is a parameter that affects the variation in the SH coefficient for the next-generation estimated three-dimensional shape. If the standard deviation of circularity included in the E2DS of the current-generation estimated three-dimensional shape is smaller than the standard deviation of circularity included in the O2DS, it has the effect of increasing the variation in the SH coefficient for the next-generation estimated three-dimensional shape, that is, increasing the sphericity.

[0040] In this way, the control parameters are intended to reflect the magnitude relationship between the current generation E2DS and O2DS in the magnitude relationship between the next generation base ellipsoid and SH coefficient. Therefore, equations other than the above equations (10) to (12) can be used as long as they have a similar effect. For example, although equation (11) uses a power of 2, there is no problem with using a power of 3 or another numerical value. The same applies to equation (12).

[0041] Next, the shape evolution processor 160 calculates the control parameter δ and the result of the principal component analysis e m k,n and variance σ k Based on this, the SH coefficients relating to the estimated three-dimensional shape of the next generation (that is, the SH coefficients of the next generation) are calculated and stored in the fourth data storage unit 170 (step S43).

[0042] Specifically, the next-generation SH coefficient a' is calculated using the following formula: mn Calculate.

number

[0043] Furthermore, the shape evolution processing unit 160 calculates the parameters of the next-generation base ellipsoid (i.e., the average aspect ratio of the new base ellipsoid) based on the control parameters β and γ, and calculates the next-generation Rd based on the next-generation SH coefficient, thereby generating an estimated three-dimensional shape for the next generation, and stores the data in the fourth data storage unit 170 (step S45).

[0044] Next-generation average aspect ratio A next ab and A next bc is calculated using the following formula: A next ab =(1+(A curr ab -1)β)(1+ξγ) (14) A next bc =(1+(A curr bc -1)β)(1+ξγ) (15) A curr ab and A curr bc The curr in represents the current generation (initially the first generation).

[0045] ξ represents a normal distribution random number. The parts of these equations other than (1 + ξγ) give the base value of the aspect ratio based on the control parameter β. The part (1 + ξγ) uses the control parameter γ to give variability along with the normal distribution function ξ. Using these equations, A next ab or A next bc If it becomes less than 1, it is corrected to 1. In this way, β and γ control the aspect ratio of the base ellipsoid of the next generation based on the information of the current generation.

[0046] In addition, the next generation SH coefficient a' m n a in Eq. (5) m n The distance Rd is also generated for each estimated 3D shape of the next generation (for example, 121). In this way, the average aspect ratio A next ab and A next bc and distance Rd, the next generation estimated 3D shape is generated.

[0047] Next, the shape evolution processing unit 160 calculates the next-generation estimated 2D metrics (next-generation E2DS) from the next-generation estimated 3D shape and stores them in the fourth data storage unit 170 (step S47). The calculation content of this step is the same as step S17. The average aspect ratio α ave EST and standard deviation α SD EST and the average circularity κ ave EST and standard deviation κ SD EST and calculate.

[0048] Furthermore, the shape evolution processing unit 160 calculates the 2D error score of the next generation from the O2DS and the E2DS of the next generation (step S49).

[0049] The 2D error score is calculated for each index using the following formula: 2Derror Score=|Estimation-Observation| / Observation (16) In equation (16), Estimation is one of the values ​​calculated in step S47, and Observation is one of the values ​​calculated in step S11. As such, the smaller the absolute value of the difference between the E2DS value and the O2DS value of the next generation, the better the estimation.

[0050] Then, the shape evolution processing unit 160 determines whether or not the termination conditions, including the 2D error scores of the next generation, are satisfied (step S51). For example, the termination conditions are determined to be satisfied when either the condition that all 2D error scores of the next generation are less than a certain value or the condition that the next generation is a predetermined generation or greater, is satisfied. The condition may also be that at least one of the 2D error scores of the next generation is less than a certain value. Alternatively, the condition may also be that one overall error score (e.g., average value) is calculated from the 2D error scores of the next generation, and the one overall error score is less than a certain value.

[0051] If the termination condition is met, the next-generation estimated 3D shape becomes the estimated 3D shape to be output as the solution, and the process returns to the calling process. On the other hand, if the termination condition is not met, the next generation becomes the current generation, and the process returns to step S41.

[0052] In this way, by generating the next-generation estimated three-dimensional shape from the results of the principal component analysis and the control parameters, it becomes possible to estimate a three-dimensional shape with less error from the O2DS. In particular, since the next-generation SH coefficients are calculated from the results of the principal component analysis and the control parameters in step S43, it is possible to estimate a three-dimensional shape with less error from the O2DS while maintaining the shape characteristics of the particle group appearing in the two-dimensional image.

[0053] Returning to the explanation of FIG. 2, the output unit 180 outputs data on the generated estimated three-dimensional shape to an output device or the like (step S7).

[0054] In this step, the estimated three-dimensional shape of the last generation may be output as it is, or the aspect ratio and sphericity may be calculated and output. Note that sphericity is calculated by dividing the surface area of ​​a sphere with the same volume as the target particle by the surface area of ​​the target particle, and takes a value between 0 and 1.

[0055] By performing such processing, it becomes possible to obtain a three-dimensional shape with higher estimation accuracy.

[0056] [Example] The ore was crushed using a hammer crusher to produce particles with a sieve size of 500-850 μm. The sample particles were packed into a polyethylene cylindrical container with a diameter of 7.5 mm and a height of 20.0 mm and imaged using an X-ray CT scanner (inspeXio SMX-100CT, Shimadzu Corporation). The X-ray tube output was 60 kV, 40 μA, and the resolution was 0.017 mm / voxel. Because the 3D voxel data contained multiple particles, the watershed method was used to separate and identify individual particles.

[0057] Projection images (two-dimensional images) along the Z axis were created from the 3D voxel data of each particle and processed using the algorithm described above. Furthermore, three-dimensional shape indices (aspect ratio and sphericity) were calculated from the 3D voxel data to evaluate the accuracy of the experimental validation (for answer checking).

[0058] Figure 10 shows the relationship between the 2D error scores of hematite (here, the molecular weights are shown as simple differences rather than absolute values) and the generation of shape evolution. In other words, in Figure 10, the vertical axis represents the 2D error scores, and the horizontal axis represents the generations. For the first generation, the 2D error scores (mean aspect ratio, mean circularity, standard deviation of aspect ratio, and standard deviation of circularity) and the average 2D error scores for the B3DS obtained by FSD analysis are shown. For the second generation and beyond, the 2D error scores (mean aspect ratio, mean circularity, standard deviation of aspect ratio, and standard deviation of circularity) and the average 2D error scores for the estimated 3D shapes generated by the shape evolution process are shown.

[0059] In the example shown in Figure 10, the 2D error scores and the average 2D error scores for the first generation are widely spread in both the positive and negative directions, indicating a significant difference between O2DS and E2DS. In contrast, the absolute value of the 2D error scores gradually decreases from the second generation onwards. In this case, the calculation was terminated when the 11th generation was reached, even though none of the scores fell below the threshold (0.001 in this case).

[0060] Non-Patent Document 1 is a method that uses only FSD analysis, and is a method that is limited to generating a B3DS for the first generation in this embodiment. Below, we compare the case where a B3DS (first generation) is generated using only FSD analysis with the case where an estimated 3D shape of the final generation (11th generation) is generated by performing shape evolution processing 10 times as in this embodiment.

[0061] That is, using cumulative and frequency distributions, we compared the estimated and measured values ​​of shape indices (two-dimensional aspect ratio and circularity, and three-dimensional aspect ratio and sphericity) in the first and final generations (eleventh generation). In the first generation, which was generated using only conventional FSD analysis, all shape indices were significantly different from the measured values. On the other hand, in the eleventh generation, which used the method according to this embodiment, all shape indices were closer to the measured values ​​than in the first generation, demonstrating improved estimation accuracy.

[0062] We also quantitatively evaluated the estimation accuracy using the mean overall error (MAE), which is defined as follows:

number

[0063] Figure 11 compares the statistical results of the MAE of the two-dimensional aspect ratio and circularity and the three-dimensional aspect ratio and sphericity for all 21 samples from the first and final generations (11th generation). The MAE for the 11th generation is less than one-fifth of that for the first generation, confirming that the method according to this embodiment exhibits estimation accuracy five times or more higher than that of the conventional method using only FSD analysis. A t-test confirmed that there was a statistically significant difference.

[0064] Furthermore, by using the method according to this embodiment, in cases where images can be taken with a probe, such as the ground of a planet, but sample return is difficult, it becomes possible to estimate 3D ground particles and rock shapes from two-dimensional images and use them in computer simulations such as the distinct element method. The distinct element method is used in the design of planetary exploration rovers, and being able to estimate the 3D shape of the planetary ground helps improve design accuracy.

[0065] Although the embodiments of the present invention have been described above, the present invention is not limited to these. For example, the functional configuration example of the information processing system shown in Figure 1 is an example, and may differ from the example module configuration of the program. Furthermore, the processing flow is also an example, and the processing order may be changed or multiple steps may be executed simultaneously as long as the same processing results can be obtained.

[0066] The information processing system 1000 described above is a computer device as shown in FIG. 12 , in which a memory 2501, a CPU 2503, a hard disk drive (HDD) 2505 (which may be a solid state drive (SDD)), a display control unit 2507 connected to a display device 2509, a drive device 2513 for a removable disk 2511, an input device 2515, and a communication control unit 2517 for connecting to a network are connected via a bus 2519. An operating system (OS) and an application program for carrying out the processing of this embodiment are stored in the HDD 2505 and are read from the HDD 2505 to the memory 2501 when executed by the CPU 2503. The CPU 2503 controls the display control unit 2507, the communication control unit 2517, and the drive device 2513 according to the processing content of the application program to perform predetermined operations. Data during processing is mainly stored in the memory 2501, but may also be stored in the HDD 2505. In an embodiment of the present invention, an application program for performing the above-described processing is distributed by being stored on a computer-readable removable disk 2511, and is installed from the drive device 2513 onto the HDD 2505. It may also be installed onto the HDD 2505 via a network such as the Internet and the communication control unit 2517. Such a computer device realizes the above-described various functions through organic cooperation between hardware such as the CPU 2503 and memory 2501 described above and programs such as the OS and application programs.

[0067] Furthermore, instead of implementing all of the functions of the information processing system 1000 in one computer device, the functions may be shared among multiple computer devices. Note that whether the information processing system 1000 is implemented in one computer device or multiple computer devices, the entire system will be referred to as an information processing system.

[0068] The above-described embodiment can be summarized as follows.

[0069] The information processing method of this embodiment includes the steps of: (A) calculating two-dimensional index values ​​of particle shapes from two-dimensional images of multiple particles to be estimated; (B) generating multiple first-generation estimated three-dimensional shapes from the two-dimensional images; (C) calculating feature parameters representing shape characteristics for the multiple first-generation estimated three-dimensional shapes; (D) generating multiple next-generation estimated three-dimensional shapes using control parameters and feature parameters based on the relationship between the two-dimensional index values ​​for the multiple current-generation estimated three-dimensional shapes and the two-dimensional index values ​​for the particle shapes; and (E) evaluating the relationship between the two-dimensional index values ​​for the multiple next-generation estimated three-dimensional shapes and the two-dimensional index values ​​for the particle shapes, and further executing the process of generating the multiple next-generation estimated three-dimensional shapes until a processing termination condition is met.

[0070] As described above, the next generation of estimated three-dimensional shapes is generated using control parameters and feature parameters based on the relationship between the two-dimensional index values ​​of the current generation of estimated three-dimensional shapes and the two-dimensional index values ​​of the particle shapes, thereby improving the estimation accuracy of the three-dimensional shapes of particles.

[0071] The process for calculating the characteristic parameters described above may include (c1) converting the inter-surface distance between a base ellipsoid defined from the average aspect ratio of the first-generation estimated three-dimensional shapes and each of the first-generation estimated three-dimensional shapes into coefficients of spherical harmonic functions of the first-generation estimated three-dimensional shapes, and (c2) performing principal component analysis on a matrix obtained from the coefficients of the spherical harmonic functions to calculate the characteristic parameters. Such principal component analysis allows particle shape characteristics to be summarized into characteristic parameters.

[0072] Furthermore, the process of generating the plurality of estimated three-dimensional shapes of the next generation described above may include the following processes: (d1) calculating coefficients of a plurality of spherical harmonic functions for the plurality of estimated three-dimensional shapes of the next generation based on a first control parameter and a feature parameter that are based on the magnitude relationship between the two-dimensional index values ​​for the plurality of estimated three-dimensional shapes of the current generation and the two-dimensional index values ​​for the particle shapes; (d2) calculating an average aspect ratio for the plurality of estimated three-dimensional shapes of the next generation by applying a second control parameter that is based on the magnitude relationship between the two-dimensional index values ​​for the plurality of estimated three-dimensional shapes of the current generation and the two-dimensional index values ​​for the particle shapes to the average aspect ratio for the plurality of estimated three-dimensional shapes of the current generation; and (d3) calculating the surface-to-surface distance between the next-generation base ellipsoid and each of the plurality of estimated three-dimensional shapes of the next generation, which is defined by the average aspect ratio for the plurality of estimated three-dimensional shapes of the next generation, from the coefficients of the plurality of spherical harmonic functions for the plurality of estimated three-dimensional shapes of the next generation.

[0073] Through this processing, multiple estimated three-dimensional shapes of the next generation can be generated while appropriately reflecting the feature parameters derived from the two-dimensional image of the particle, while correcting errors appearing in the two-dimensional index values ​​of the current generation with control parameters based on the above-mentioned magnitude relationships.

[0074] In addition, the first control parameter mentioned above may be a parameter that adjusts the variation in the coefficients of the spherical harmonic function based on the magnitude relationship between the standard deviation of the circularity in two dimensions for multiple estimated three-dimensional shapes of the current generation and the standard deviation of the circularity in two dimensions of the particle shape.

[0075] In addition, the second control parameter mentioned above may include a first parameter based on the relationship between the two-dimensional aspect ratios of the multiple estimated three-dimensional shapes of the current generation and the two-dimensional aspect ratios of the particle shapes, and a second parameter based on the relationship between the standard deviation of the two-dimensional aspect ratios of the multiple estimated three-dimensional shapes of the current generation and the standard deviation of the two-dimensional aspect ratios of the particle shapes.

[0076] Furthermore, the process of generating the first-generation multiple estimated three-dimensional shapes described above may include the process of (b1) calculating, for each of the multiple particles in the two-dimensional image, the angle between a line passing through the center of the particle and a reference line and the distance from the center, performing Fourier analysis on the angle and distance to calculate an index value representing the magnitude of the Fourier coefficient, and (b2) using the calculated index value to generate the first-generation multiple estimated three-dimensional shapes based on a predetermined three-dimensional radial function.

[0077] A program for causing a processor to perform the above-described processing can be created, and the program is stored in a computer-readable storage medium or storage device, such as a flexible disk, an optical disk such as a CD-ROM (Read Only Memory), a magneto-optical disk, a semiconductor memory (e.g., a ROM), a hard disk, etc. Data during processing is temporarily stored in a storage device such as RAM (Random Access Memory). [Explanation of symbols]

[0078] 1000 Information Processing Systems 110 First data storage unit 120 Preprocessing unit 130 Second data storage unit 140 Three-dimensional processing unit 150 third data storage unit 160 shape evolution processing unit 170 fourth data storage unit 180 output unit

Claims

1. calculating a two-dimensional index value of particle shape from two-dimensional images of a plurality of particles to be estimated; generating a plurality of first-generation estimated three-dimensional shapes from the two-dimensional images; calculating feature parameters representing shape features for the plurality of first-generation estimated three-dimensional shapes; generating a plurality of next-generation estimated three-dimensional shapes using the feature parameters and a control parameter based on a relationship between the two-dimensional index values ​​of the plurality of current-generation estimated three-dimensional shapes and the two-dimensional index values ​​of the particle shapes; The relationship between the two-dimensional index values ​​for the plurality of estimated three-dimensional shapes of the next generation and the two-dimensional index values ​​for the particle shapes is evaluated, and the process of generating the plurality of estimated three-dimensional shapes of the next generation is further performed until a process termination condition is satisfied. A computer-implemented information processing method including the process.

2. The process of calculating the feature parameters includes: converting a surface distance between a base ellipsoid defined from the average aspect ratio of the first-generation estimated three-dimensional shapes and each of the first-generation estimated three-dimensional shapes into coefficients of a plurality of spherical harmonic functions of the first-generation estimated three-dimensional shapes; Calculating the feature parameters by performing principal component analysis on a matrix obtained from the coefficients of the plurality of spherical harmonic functions.

2. The information processing method according to claim 1, further comprising the steps of:

3. The process of generating the next generation of estimated three-dimensional shapes includes: calculating coefficients of a plurality of spherical harmonic functions for a plurality of estimated three-dimensional shapes of a next generation based on a first control parameter based on a magnitude relationship between two-dimensional index values ​​for the plurality of estimated three-dimensional shapes of the current generation and two-dimensional index values ​​of the particle shapes, and the characteristic parameters; calculating an average aspect ratio for the plurality of estimated three-dimensional shapes of the next generation by applying a second control parameter to the average aspect ratio for the plurality of estimated three-dimensional shapes of the current generation, the second control parameter being based on a magnitude relationship between a two-dimensional index value for the plurality of estimated three-dimensional shapes of the current generation and a two-dimensional index value for the particle shape; Calculating a surface distance between a base ellipsoid of the next generation, which is defined by an average aspect ratio of the plurality of estimated three-dimensional shapes of the next generation, and each of the plurality of estimated three-dimensional shapes of the next generation, from coefficients of a plurality of spherical harmonic functions for the plurality of estimated three-dimensional shapes of the next generation.

2. The information processing method according to claim 1, further comprising the steps of:

4. The first control parameter is is a parameter for adjusting the variation in the coefficients of the spherical harmonic function based on the magnitude relationship between the standard deviation of the circularity in two dimensions for the plurality of estimated three-dimensional shapes of the current generation and the standard deviation of the circularity in two dimensions of the particle shape.

4. The information processing method according to claim 3.

5. The second control parameter is a first parameter based on a magnitude relationship between the two-dimensional aspect ratios of the plurality of estimated three-dimensional shapes of the current generation and the two-dimensional aspect ratio of the particle shape; a second parameter based on the magnitude relationship between the standard deviation of the aspect ratios in two dimensions for the plurality of estimated three-dimensional shapes of the current generation and the standard deviation of the aspect ratios in two dimensions of the particle shape; The information processing method according to claim 3, further comprising:

6. The process of generating the first generation of estimated three-dimensional shapes includes: For each of a plurality of particles in the two-dimensional image, an angle formed by a line passing through the center of the particle with a reference line and a distance from the center are calculated, and a Fourier analysis is performed on the angle and the distance to calculate an index value representing the magnitude of a Fourier coefficient; Using the calculated index values, the first generation of estimated three-dimensional shapes is generated based on a predetermined three-dimensional radial function.

2. The information processing method according to claim 1, further comprising the steps of:

7. 7. A program for causing a computer to execute the information processing method according to claim 1.

8. a means for calculating a two-dimensional index value of particle shape from two-dimensional images of a plurality of particles to be estimated; means for generating a plurality of first-generation estimated three-dimensional shapes from the two-dimensional images; means for calculating feature parameters representing shape features for the plurality of first-generation estimated three-dimensional shapes; a means for generating a plurality of next-generation estimated three-dimensional shapes using control parameters based on the relationship between two-dimensional index values ​​for a plurality of current-generation estimated three-dimensional shapes and two-dimensional index values ​​for the particle shapes and the characteristic parameters; and A means for generating the plurality of next-generation estimated three-dimensional shapes operates by evaluating a relationship between the two-dimensional index values ​​of the plurality of next-generation estimated three-dimensional shapes and the two-dimensional index values ​​of the particle shapes until a processing termination condition is satisfied. Information processing system.

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