Image processing system, image processing method, and image processing program

Abstract

To provide an image processing system, an image processing method, and an image processing program capable of easily and accurately evaluating the shapes of primary particles that form an agglomerated particle.SOLUTION: In an image processing system 10, an image acquisition unit 11 acquires a first image indicating a plurality of agglomerated particles each formed by aggregating a plurality of primary particles, and a second image indicating some of the agglomerated particles and having resolution higher than that of the first image. An evaluation unit 14 calculates a correction coefficient on the basis of a shape parameter pertaining to the shapes of some agglomerated particles in each of the first and second images, and calculates a shape parameter for at least one of the multiple agglomerated particles indicated by the first image, on the basis of the correction coefficient.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] One aspect of the present disclosure relates to an image processing system, an image processing method, and an image processing program.

Background Art

[0002] Patent Document 1 describes a method for evaluating the degree of connection of primary particles in porous secondary particles from an observation image.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] A method for easily performing a highly accurate evaluation of the shape of primary particles forming aggregated particles is desired.

Means for Solving the Problems

[0005] An image processing system according to one aspect of the present disclosure includes at least one processor. The at least one processor acquires a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles, acquires a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image, calculates a correction coefficient based on shape parameters regarding the shapes of some of the aggregated particles in each of the first image and the second image, and calculates a shape parameter for at least one of the plurality of aggregated particles shown by the first image based on the correction coefficient.

[0006] The image processing method according to one aspect of the present disclosure is executed by an image processing system including at least one processor. The image processing method includes: obtaining a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles; obtaining a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image; calculating a correction coefficient based on shape parameters regarding the shapes of some of the aggregated particles in each of the first image and the second image; and calculating shape parameters for at least one of the plurality of aggregated particles shown by the first image based on the correction coefficient.

[0007] The image processing program according to one aspect of the present disclosure causes a computer to execute: obtaining a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles; obtaining a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image; calculating a correction coefficient based on shape parameters regarding the shapes of some of the aggregated particles in each of the first image and the second image; and calculating shape parameters for at least one of the plurality of aggregated particles shown by the first image based on the correction coefficient.

[0008] In such an aspect, a correction coefficient is calculated based on the shape parameters of some of the aggregated particles in each of the first image and the second image having different resolutions. Then, based on this correction coefficient, the shape parameters of the aggregated particles in the first image are calculated. By using the correction coefficient obtained based on the two types of images, the shape parameters of any aggregated particle in the first image can be calculated with high accuracy. As a result, it becomes possible to easily perform a highly accurate evaluation of the shape of the primary particles forming the aggregated particles.

Effects of the Invention

[0009] According to one aspect of the present disclosure, it becomes possible to easily perform a highly accurate evaluation of the shape of the primary particles forming the aggregated particles.

Brief Description of the Drawings

[0010]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Embodiments for Carrying Out the Invention

[0011] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same or equivalent elements are denoted by the same reference numerals, and redundant descriptions are omitted.

[0012] [Overview of the System] The image processing system according to the present disclosure is a computer system that executes image processing on an original image showing aggregated particles. In one example, the image processed by the image processing system is used to evaluate the shape of primary particles forming the aggregated particles. The evaluation may be performed by the image processing system or by a computer system different from the image processing system. "Evaluating the shape of primary particles" means a process including at least calculating a value related to the shape of primary particles.

[0013] An aggregated particle refers to a particle formed by the aggregation of a plurality of primary particles. A primary particle refers to a particle that cannot be further divided into finer particles. That is, a primary particle refers to the minimum unit of a particle. As an example, aggregated particles are formed from a plurality of carbon blacks and are used as a conductive agent in a lithium-ion battery. In this example, the smaller the particle size of the carbon black, the more parallel circuits formed by the carbon black, so that a large number of conductive paths can be formed even with a small amount of carbon black. That is, in this example, by evaluating the particle size of the carbon black by an image processing system, the user can grasp the performance of the aggregated particle as a conductive agent. As an example, the particle size of this carbon black is about 22 to 26 nm.

[0014] The computer system calculates the shape parameter regarding the primary particle based on the shape parameter regarding the aggregated particle in order to evaluate the shape of the primary particle. As an example, the shape parameters of the aggregated particle are area, perimeter, perimeter of convex hull, area of convex hull, length, width, equivalent circle diameter, circularity, area circularity, envelope degree, area envelope degree, aspect ratio, elongation, etc. As an example, the shape parameter of the primary particle is the average particle size of the primary particle, etc. The computer system may evaluate the number of primary particles contained in the aggregated particle, the morphology of the aggregated particle, the electron microscope surface area, the fractal dimension of the whole aggregated particle, etc. As described above, the image processing system may perform such calculations and evaluations.

[0015] The original image can be obtained by imaging with an imaging device such as a scanning electron microscope (SEM) or a transmission electron microscope (TEM). As an example, when using SEM, the original image showing the aggregated particles can be obtained by the following procedure. First, the user disperses a plurality of aggregated particles in a solvent such as chloroform to prepare a sample. Next, the user drops the prepared sample onto a substrate and dries the sample. Then, by imaging the aggregated particles on the substrate with an imaging device, an original image showing the aggregated particles is obtained. When using SEM, the occurrence of unevenness in the background region of the original image is suppressed.

[0016] [Configuration of the System] FIG. 1 is a diagram showing the functional configuration of an image processing system 10 according to an example. The image processing system 10 includes, as functional elements, an image acquisition unit 11, a binarization processing unit 12, a generation unit 13, and an evaluation unit 14.

[0017] The image acquisition unit 11 is a functional module that acquires first original images 211 and 212 obtained by an imaging device. The first original image 211 shows a plurality of aggregated particles. The first original image 212 shows some of the aggregated particles among the plurality of aggregated particles in a certain one of the first original images 211. The some aggregated particles refer to aggregated particles that are 1 or more and less than N when the number of aggregated particles shown in the first original image 211 is N. The resolution of the first original image 212 is higher than the resolution of the first original image 211. The resolution refers to a numerical value indicating the density of pixels with respect to the actual length in an image. As the resolution increases, the length per pixel in the image becomes shorter. That is, relatively high resolution means that the length per pixel in the image is relatively short. Due to such a difference in resolution, the first original image 212 can reflect individual aggregated particles more clearly than the first original image 211.

[0018] The binarization processing unit 12 is a functional module that performs binarization processing on the first original images 211 and 212 and the second original images 231 and 232. Binarization processing refers to converting the pixel value of each pixel in an image into a binary value. By performing binarization processing on the original image, a binary image that distinguishes a foreground region composed of aggregated particles from a background region other than the foreground region is generated. The binarization processing unit 12 performs binarization processing on the first original image 211 to generate a first binary image 221, and performs binarization processing on the second original image 231 to generate a second binary image 241. The binarization processing unit 12 performs binarization processing on the first original image 212 to generate a first binary image 222, and performs binarization processing on the second original image 232 to generate a second binary image 242.

[0019] The generation unit 13 is a functional module that generates one or more second original images 231 based on the first original image 211 and the first binary image 221, and generates one or more second original images 232 based on the first original image 212 and the first binary image 222.

[0020] Each second original image 231 shows some of the aggregated particles among the plurality of aggregated particles in the first original image 211. The pixel value of each pixel of the second original image 231 is the pixel value of each pixel of the first original image 211 corresponding to the respective pixel of the second original image 231.

[0021] When a certain first original image 212 shows two or more aggregated particles, each second original image 232 generated based on the first original image 212 shows some of the aggregated particles among the two or more aggregated particles. When a certain first original image 212 shows one aggregated particle, the second original image 232 is consequently the same as the first original image 212. The pixel value of each pixel of the second original image 232 is the pixel value of each pixel of the first original image 212 corresponding to the respective pixel of the second original image 232.

[0022] The evaluation unit 14 is a functional module that evaluates the shape of the primary particles. The evaluation unit 14 acquires the second binary image 241 and the second binary image 242, and calculates the shape parameters of any aggregated particles in these images. Then, the evaluation unit 14 evaluates the shape of the primary particles forming the arbitrary aggregated particles based on the calculated shape parameters.

[0023] FIG. 2 is a diagram showing a general hardware configuration of a computer 100 that can function as an image processing system 10. For example, the computer 100 includes a processor 101, a main memory unit 102, an auxiliary storage unit 103, a communication control unit 104, an input device 105, and an output device 106. The processor 101 executes an operating system and application programs. The main memory unit 102 is composed of, for example, ROM and RAM. The auxiliary storage unit 103 is composed of, for example, a hard disk or a flash memory, and generally stores a larger amount of data than the main memory unit 102. The auxiliary storage unit 103 non-temporarily stores a program 110 for causing at least one computer to function as the image processing system 10. The communication control unit 104 is composed of, for example, a network card or a wireless communication module. The input device 105 is composed of, for example, a keyboard, a mouse, a touch panel, etc. The output device 106 is composed of, for example, a monitor and a speaker.

[0024] Each functional module of the image processing system 10 is realized by causing the processor 101 or the main memory unit 102 to load the program 110 and causing the processor 101 to execute the program 110. The program 110 includes code for realizing each functional element of the image processing system 10. The processor 101 operates the communication control unit 104, the input device 105, or the output device 106 according to the program 110, and reads and writes data in the main memory unit 102 or the auxiliary storage unit 103. Each functional element of the image processing system 10 is realized by this processing. Data or databases necessary for the processing may be stored in the main memory unit 102 or the auxiliary storage unit 103.

[0025] The program 110 corresponds to an image processing program. The program 110 may be provided after being non-temporarily recorded on a tangible recording medium such as a CD-ROM, a DVD-ROM, or a semiconductor memory. Alternatively, the program 110 may be provided via a communication network as a data signal superimposed on a carrier wave.

[0026] The image processing system 10 can be configured by one or more computers. When a plurality of computers are used, the image processing system 10 is configured by connecting these computers to each other via a communication network.

[0027] [Image] Various images processed by the image processing system 10 will be described. As described above, the resolution of the first original image 212 is higher than the resolution of the first original image 211. The resolutions of the first binary image 221, the second original image 231, and the second binary image 241 are the same as the resolution of the first original image 211, and the resolutions of the first binary image 222, the second original image 232, and the second binary image 242 are the same as the resolution of the first original image 212. Therefore, it can be said that each of the first original image 211, the first binary image 221, the second original image 231, and the second binary image 241 is a relatively low-resolution image, and it can be said that each of the first original image 212, the first binary image 222, the second original image 232, and the second binary image 242 is a relatively high-resolution image.

[0028] As described above, assuming that the first original image 211 shows N aggregated particles, the first original image 212 shows 1 or more and less than N aggregated particles, which are part of the N aggregated particles. The image acquisition unit 11 can acquire 2 or more first original images 212 with different imaging ranges for one first original image 211. Among the first original image 211 and the first binary image 221, the plurality of aggregated particles shown are the same. Among the corresponding first original image 212 and the first binary image 222, the 1 or more aggregated particles shown are also the same.

[0029] The second original image 231 shows some of the aggregated particles in the first original image 211. In other words, it can be said that the second original image 231 is an image that captures a part of the subject range of the first original image 211. Each individual second original image 231 may show one aggregated particle or two or more aggregated particles. Assuming that the first original image 211 shows N aggregated particles, the generation unit 13 may generate a plurality of second original images 231 such that all of the N aggregated particles are shown by one of the second original images 231. When each second original image 231 shows one aggregated particle, N second original images 231 are generated. The generation unit 13 may also generate a plurality of second original images 231 such that some of the N aggregated particles are shown by one of the second original images 231. In this case, the remaining aggregated particles are not shown by any of the second original images 231.

[0030] The relationship between the first original image 212 and the second original image 232 may vary depending on the number of aggregated particles shown by the first original image 212.

[0031] When a certain first original image 212 shows two or more aggregated particles, each second original image 232 generated based on that first original image 212 shows some of the two or more aggregated particles. In this case, each second original image 232 may show one aggregated particle or two or more aggregated particles. Assuming that the first original image 212 shows M aggregated particles, the generation unit 13 may generate a plurality of second original images 232 such that all of the M aggregated particles are shown by one of the second original images 232. When each second original image 232 shows one aggregated particle, M second original images 232 are generated. The generation unit 13 may also generate a plurality of second original images 232 such that some of the M aggregated particles are shown by one of the second original images 232. In this case, the remaining aggregated particles are not shown by any of the second original images 232.

[0032] On the other hand, when a certain first original image 212 shows one aggregated particle, the second original image 232 is consequently the same as that first original image 212.

[0033] Between the corresponding second original images 231 and 232 and the second binary images 241 and 242, the one or more aggregated particles shown are the same. Between the corresponding second original images 232 and 232 and the second binary images 242 and 242, the one or more aggregated particles shown are the same.

[0034] [Operation of the System] With reference to FIG. 3, the operation of the image processing system 10 will be described, and an image processing method according to an example will be described. FIG. 3 is a flowchart showing an example of the processing in the image processing system 10 as a processing flow S1. The processing from the first original image 212 through the first binary image 222 and the second original image 232 to the generation of the second binary image 242 is the same as the processing from the first original image 211 through the first binary image 221 and the second original image 231 to the generation of the second binary image 241.

[0035] In step S11, the image acquisition unit 11 acquires first original images 211 and 212 having different resolutions from each other. The image acquisition unit 11 may receive the first original images 211 and 212 from an imaging device or another computer. Alternatively, the image acquisition unit 11 may access a given database or file system to read out the first original images 211 and 212. Alternatively, the image acquisition unit 11 may acquire the first original images 211 and 212 input by the user of the image processing system 10. The acquired first original images 211 and 212 are grayscale images. In a grayscale image, the pixel value of each pixel is any integer value between 0 corresponding to black and 255 corresponding to white. The image acquisition unit 11 may acquire the first original images 211 and 212 by converting a color image into a grayscale image. In one example, the image acquisition unit 11 acquires a SEM image obtained by imaging with a SEM. Since a SEM image can be acquired with high contrast, it is suitable for binarization processing.

[0036] The resolution of the first original image 212 is higher than that of the first original image 211. That is, if the length per pixel in the first original image 211 is defined as pixel length L1 and the length per pixel in the first original image 212 is defined as pixel length L2, then the pixel length L2 is shorter than the pixel length L1. As an example, the pixel length L1 is 2.48 [nm / pixel], and the pixel length L2 is 0.55 [nm / pixel]. The pixel length L1 may be 1.00 to 5.00 [nm / pixel], or may be 1.50 to 3.00 [nm / pixel]. The pixel length L2 may be 0.10 to 1.00 [nm / pixel], or may be 0.50 to 0.71 [nm / pixel]. The pixel length L2 may be 0.5 times or less, 0.3 times or less, or 0.1 times or less of the pixel length L1. The difference in resolution between the first original image 211 and the first original image 212 may be represented by the difference in magnification of the imaging device when the first original image 211 and the first original image 212 are captured. As an example, the first original image 211 may be an image captured at a magnification of 20,000 times, and the first original image 212 may be an image captured at a magnification of 90,000 times.

[0037] FIG. 4 is a diagram showing an example of the first original images 211 and 212. The first original image 211 captures a plurality of aggregated particles 300 existing in a relatively wide subject range. On the other hand, the first original image 212 captures a part of the subject range at a higher resolution than the first original image 211. Therefore, the first original image 212 shows some of the aggregated particles 300 shown by the first original image 211 more clearly than the first original image 211. FIG. 4 shows two first original images 212 corresponding to the partial regions 211a and 211b of the first original image 211.

[0038] Returning to FIG. 3, in step S12, the binarization processing unit 12 performs a first binarization process on the first original image to generate a first binary image that distinguishes between a foreground region consisting of a plurality of aggregated particles and a background region other than the foreground region. The binarization processing unit 12 performs the first binarization process on the first original image 211 to generate a first binary image 221, and performs the first binarization process on the first original image 212 to generate a first binary image 222. As an example, the first binarization process is a process based on a Gaussian mixture model. The Gaussian mixture model will be described in detail with reference to FIG. 5. FIG. 5 is a diagram showing an example of a histogram of pixel values ​​in the first original image 211.

[0039] As shown in Fig. 5, in the first original image, which is a grayscale image, the histograms in the foreground and background regions each form a mountain-shaped distribution. In Fig. 5, the histogram in the background region is shown as the base of the mountain-shaped distribution. The Gaussian mixture model assumes that each mountain-shaped distribution follows a Gaussian distribution, and calculates each pixel value x i (i=0~255) occurrence frequency F(x i ) is calculated as a weighted linear sum of multiple Gaussian distributions, where x0~x 255 correspond to grayscale pixel values ​​of 0 to 255, respectively. The binarization processing unit 12 calculates the occurrence frequency F(x i ) is calculated. Here, the Gaussian distribution is f1(x i ),f2(x i ) f1(x i ) corresponds to a Gaussian distribution in the foreground region, and f2(x i ) corresponds to a Gaussian distribution in the background region. f1(x i ) has an average of μ1, and f1(x i ) has a variance of σ1 2 f2(x i ) has an average of μ2, and f2(x i ) variance is σ2 2 Also, f1(x i ) is weighted by w1, and f2(x i ) is weighted by w2. Both w1 and w2 are real numbers greater than or equal to 0, and the sum of w1 and w2 is 1.

[0040] [Number]

[0041] Then, the binarization processing unit 12 converts each pixel value into a binary value based on a certain threshold T. As an example, the binarization processing unit 12 converts each pixel value into either 0 or 255 based on the threshold T. As an example, the binarization processing unit 12 calculates the threshold T as follows. First, the binarization processing unit 12 calculates the log-likelihood lnL of the above formula (1) by the following formula (2).

[0042] [Number]

[0043] Then, the binarization processing unit 12 estimates the values of the parameters w1, w2, μ1, σ1, μ2, σ2 that maximize the log-likelihood lnL shown in the above formula (2) based on the EM algorithm (expectation-maximization algorithm) or the like. The binarization processing unit 12 calculates the threshold T based on the estimated parameters. As an example, the binarization processing unit 12 calculates the pixel value at the intersection of the two Gaussian distributions f1(x i ), f2(x i ) as the threshold T. Alternatively, the binarization processing unit 12 calculates the average value of μ1 and μ2 as the threshold T. Then, the binarization processing unit 12 executes the first binarization process by converting the pixel values less than the calculated threshold T to 0 and the pixel values greater than or equal to the threshold T to 255. In a grayscale image, each distribution forming the histogram of pixel values follows a Gaussian distribution or has a shape close to a Gaussian distribution. Therefore, when the first original image is a grayscale image, especially when it is a SEM image, the binarization processing unit 12 can generate the first binary image more accurately based on the mixture Gaussian model.

[0044] Alternatively, the first binarization process may be a process based on Otsu's binarization method. Otsu's binarization process refers to a process of dividing a histogram into two classes, calculating the separation degree between the two classes, and calculating the pixel value at which the separation degree is maximized as the threshold T. Alternatively, the first binarization process may be a process of performing binarization based on the threshold T input by the user.

[0045] FIG. 6 is a diagram showing an example of the first binarization process by the binarization processing unit 12. The first original image 211 shown in this example is a grayscale SEM image. The first binary image 221 is an image after the first binarization process is executed, and the pixel value of each pixel of the first binary image 221 is 0 or 255. In the first binary image 221, the shape of the agglomerated particles 300 can be discriminated more clearly than in the first original image 211. Similarly to this example, in the first binary image 222, the shape of the agglomerated particles can be discriminated more clearly than in the first original image 212.

[0046] Returning to FIG. 3, in step S13, the generation unit 13 generates one or more second original images based on the first original image and the first binary image. The generation unit 13 generates one or more second original images 231 based on the first original image 211 and the first binary image 221, and generates one or more second original images 232 based on the first original image 212 and the first binary image 222. The details of step S13 will be described with reference to FIG. 7. FIG. 7 is a flowchart showing an example of a method for generating a second original image.

[0047] In step S131, the generation unit 13 generates one or more partial images from each of the first binary images 221 and 222. Each partial image is a part of the first binary image and shows some of the aggregated particles among the plurality of aggregated particles. The generation unit 13 may generate a partial image showing one aggregated particle for each of the first binary images 221 and 222, or may generate a partial image showing two or more aggregated particles. As an example, the generation unit 13 may generate a plurality of partial images, each of which shows one aggregated particle, for at least one of the first binary images 221 and 222. In this example, the number of partial images corresponding to the number of aggregated particles shown in the first binary image 221 (or the first binary image 222) is obtained from the first binary image 221 (or the first binary image 222). Note that the generation unit 13 may not generate a partial image showing the aggregated particle after determining that the aggregated particle with a small size is noise.

[0048] In step S132, the generation unit 13 converts the pixel value of each pixel for one or more partial images to generate one or more second original images. For each of the one or more partial images obtained from the first binary image 221, the generation unit 13 converts the pixel value of each pixel of the partial image to the pixel value of the pixel of the first original image 211 corresponding to the pixel, and generates the second original image 231. For each of the one or more partial images obtained from the first binary image 222, the generation unit 13 converts the pixel value of each pixel of the partial image to the pixel value of the pixel of the first original image 212 corresponding to the pixel, and generates the second original image 232. The pixel value of each pixel of the second original image is the pixel value of each pixel of the first original image corresponding to each pixel of the second original image. The second original image is generated from the partial image. Therefore, the second original image shows some of the aggregated particles among the plurality of aggregated particles. For example, each second original image shows one aggregated particle.

[0049] FIG. 8 is a diagram showing an example of a method for generating a second original image, and shows an enlarged part of the first binary image 221. In this example, the generation unit 13 shows two partial images 251 and two second original images 231 corresponding to the partial regions 211c and 211d of the first binary image 221.

[0050] Alternatively, in step S13, the generation unit 13 may directly generate one or more second original images from at least one of the first original images 211 and 212. In this case, first, the generation unit 13 refers to the first original image and the first binary image to identify the region in the first original image corresponding to the region indicating some aggregated particles in the first binary image. Then, the generation unit 13 cuts out the identified region from the first original image to generate the second original image 231. In this way, the generation unit 13 can generate one or more second original images from the first original image without going through the generation of partial images.

[0051] Regarding step S13, when a certain first binary image 222 indicates one aggregated particle, the generation unit 13 may generate the second original image 232 from the first binary image 222 based on the pixel values of the corresponding first original image 212 without generating a partial image from the first binary image 222 or performing cutting out from the first original image 212.

[0052] Returning to FIG. 3, in step S14, the binarization processing unit 12 performs second binarization processing on each of the one or more second original images to generate one or more second binary images that distinguish a foreground region composed of some aggregated particles from a background region other than the foreground region. The binarization processing unit 12 generates one or more second binary images 241 from the one or more second original images 231 and one or more second binary images 242 from the one or more second original images 232 by the second binarization processing. The second binarization processing may be a process based on a mixture Gaussian model or a process based on Otsu's binarization method, similar to the first binarization processing. Alternatively, the second binarization processing may be a process of performing binarization based on a threshold value T input by the user. The binarization method used for the second binarization processing may be the same as or different from the first binarization processing.

[0053] Even if the same binarization is adopted in the first binarization process and the second binarization process, the results of the first binarization process and the second binarization process for a single aggregated particle may be different from each other. This is because the histograms of the pixel values of the first original image and the second original image may be different from each other. The first original image 211 depicts a relatively large number of aggregated particles, and the range or distribution of pixel values may be different among individual aggregated particles. On the other hand, the second original image depicts some of the aggregated particles. Therefore, the histogram of pixel values in the entire image is different between the first original image and the second original image. Due to the difference in the histograms, the threshold value T in the binarization process is also different. Therefore, the results of the first binarization process and the second binarization process for a single aggregated particle may be different from each other.

[0054] In step S15, the evaluation unit 14 calculates a correction coefficient based on the shape parameters of some of the aggregated particles in each of one or more second binary images 241 and one or more second binary images 242. Hereinafter, the second binary image 241 is also referred to as the first image, and the second binary image 242 is also referred to as the second image. In the following description, an example is illustrated in which a set of one or more second binary images 241 (first images) shows a plurality of aggregated particles, and a set of one or more second binary images 242 (second images) shows some of the plurality of aggregated particles. In this example, some of the aggregated particles are shown in both the second binary image 241 (first image) and the second binary image 242 (second image).

[0055] As an example, the evaluation unit 14 analyzes each of one or more first images and one or more second images to obtain shape parameters. Then, the evaluation unit 14 calculates a correction coefficient based on these shape parameters.

[0056] FIG. 9 is a diagram for explaining an example of a method for calculating a correction coefficient. First, for each of the one or more aggregated particles shown in the second image that is 1 or more, the evaluation unit 14 acquires the shape parameter obtained by analyzing the first image and the shape parameter obtained by analyzing the second image. The association between the first image and the second image indicating a common single aggregated particle may be performed in advance by the user or may be performed by the evaluation unit 14. Then, the evaluation unit 14 approximates the relationship between the shape parameters of some of the aggregated particles obtained from the first image and the shape parameters of the some of the aggregated particles obtained from the second image with a linear function G, and calculates the slope of the linear function G as the correction coefficient. The linear function G can be expressed as y = ax, where one of the shape parameters obtained from the first image and the shape parameter obtained from the second image is taken as x and the other is taken as y.

[0057] Explain the technical significance of the calculated correction coefficient. By using the first image with low resolution, information on many aggregated particles can be obtained, but the accuracy of the shape parameters obtained from the first image tends to be lower than the accuracy of the shape parameters obtained from the second image with high resolution. As an example, the perimeter length of the aggregated particle obtained from the first image tends to be shorter than the perimeter length of the aggregated particle obtained from the second image with high resolution. It can be said that the correction coefficient calculated as described above indicates the degree of difference in the shape parameters between such a first image and a second image.

[0058] Returning to FIG. 3, in step S16, the evaluation unit 14 calculates the shape parameter for at least one of the aggregated particles shown by the one or more first images based on the correction coefficient. For each of the at least one aggregated particle, the evaluation unit 14 multiplies the shape parameter obtained by analyzing the first image by the correction coefficient corresponding to the shape parameter to calculate the corrected shape parameter for the aggregated particle.

[0059] In step S17, the evaluation unit 14 evaluates the shape of the primary particles of at least one aggregated particle among the aggregated particles indicated by one or more first images based on the calculated shape parameters. For example, the evaluation unit 14 evaluates the shape of the plurality of primary particles forming each aggregated particle for each aggregated particle.

[0060] The evaluation unit 14 outputs the evaluation result. The evaluation unit 14 may display the processing result on a display device, may store the processing result in a predetermined storage device such as a memory or a database, or may transmit the processing result to another computer system.

[0061] The evaluation unit 14 may calculate the perimeter of each of some of the aggregated particles as a shape parameter based on a correction coefficient. The evaluation unit 14 may calculate the average particle size of the plurality of primary particles forming each of the some aggregated particles based on its perimeter. As an example, the evaluation unit 14 calculates the average particle size of the plurality of primary particles forming an aggregated particle based on the area of the aggregated particle and the calculated perimeter of the aggregated particle. The evaluation unit 14 may calculate the area of the aggregated particle using the correction coefficient, or may obtain the area of the aggregated particle without using the correction coefficient. As an example, the evaluation unit 14 calculates the average particle size of the primary particles in accordance with the standard of ASTM D3849. In this example, the evaluation unit 14 calculates the average particle size of the primary particles by the following formula (3). The evaluation unit 14 may calculate the number of primary particles forming one aggregated particle by the following formula (4). In formulas (3) and (4), let the perimeter of the aggregated particle be P and the area of the aggregated particle be A. α is an aggregation coefficient, dp is the average particle size of the primary particles, and n is the number of primary particles. Note that when the calculated value of α is less than 0.4, the evaluation unit 14 sets the value of α to 0.4.

[0062]

Equation

[0063]

Equation

[0064] The evaluation unit 14 may execute the above processing for each of two or more types of shape parameters. In this regard, the evaluation unit 14 may calculate a correction coefficient for each type of shape parameter.

[0065] [Evaluation Example] Table 1 below shows an example of the calculation results of the average particle size of primary particles by the image processing system 10. The image processing system 10 acquired a first original image 211 with a pixel length L1 of 2.48 [nm / pixel] and a first original image 212 with a pixel length L2 of 0.55 [nm / pixel]. Both the first original images 211 and 212 were SEM images. The image processing system 10 executed a first binarization process and a second binarization process based on a mixture Gaussian model. The image processing system 10 acquired the area and the perimeter for each of 15 aggregated particles, and corrected the perimeter acquired from the first original image 211 with a correction coefficient. Then, the image processing system 10 substituted the above area and the corrected perimeter into the above formulas (3) and (4) to calculate the average particle size and the number of primary particles in each aggregated particle. Then, the image processing system 10 calculated the average value of the average particle size of primary particles and the average value of the number of primary particles in the whole of the 15 aggregated particles. When the particle sizes of a plurality of primary particles forming one of the 15 aggregated particles were manually measured to obtain the average particle size of the primary particles, the average particle size was 25 nm. That is, the average value of the average particle size of the primary particles obtained in this evaluation example was close to the average particle size obtained by manual measurement. Therefore, in this evaluation example, it can be said that the image processing system 10 was able to evaluate the average particle size of primary particles with high accuracy.

[0066]

Table 1

[0067] [Modification Example] As described above, the technology according to the present disclosure has been described in detail based on various examples. However, the present disclosure is not limited to the above examples. Various modifications are possible for the technology according to the present disclosure without departing from its gist.

[0068] In the above example, the image processing system 10 calculates the correction coefficient based on the shape parameters of the aggregated particles in each of the first image and the second image, using the second binary images 241 and 242 as the first image and the second image respectively, and then calculates the shape parameters of the aggregated particles. However, other images may be used as the first image and the second image. For example, the image processing system may calculate the correction coefficient based on the shape parameters of the aggregated particles in each of the first original images 211 and 212, and then calculate the shape parameters of the aggregated particles. Alternatively, the image processing system may calculate the correction coefficient based on the shape parameters of the aggregated particles in each of the first binary images 221 and 222, and then calculate the shape parameters of the aggregated particles. Alternatively, the image processing system may calculate the correction coefficient based on the shape parameters of the aggregated particles in each of the second original images 231 and 232, and then calculate the shape parameters of the aggregated particles. In these examples, the image processing system may not include a binarization processing unit or a generation unit.

[0069] In the above example, the image processing system 10 approximates the relationship between the shape parameters of the aggregated particles obtained from the first image and the shape parameters of the aggregated particles obtained from the second image by a linear function, and calculates the slope of the linear function as the correction coefficient. However, the image processing system may approximate the relationship by a non-linear function and calculate the highest-order coefficient of the non-linear function as the correction coefficient.

[0070] The processing steps of the method executed by at least one processor are not limited to the above examples. For example, some of the above steps may be omitted, or each step may be executed in a different order. Also, any two or more of the above steps may be combined, or a part of a step may be modified or deleted. Alternatively, other steps may be executed in addition to each of the above steps.

[0071] In the comparison of the magnitude relationship between two numerical values in the present disclosure, either of the two criteria of "greater than or equal to" and "greater than" may be used, and either of the two criteria of "less than or equal to" and "less than" may be used.

[0072] In the present disclosure, the expression "at least one processor executes a first process, executes a second process,..., executes an L-th process." or a corresponding expression indicates a concept including a case where the execution subject of the L processes from the first process to the L-th process, that is, the processor, changes midway. That is, this expression indicates a concept including both a case where all of the L processes are executed by the same processor and a case where the processor changes in an arbitrary manner in the L processes.

[0073] [Appendix] As can be understood from the various examples above, the present disclosure includes the aspects shown below. (Appendix 1) Comprising at least one processor, The at least one processor, Obtaining a first image showing a plurality of aggregated particles each formed by aggregation of a plurality of primary particles, Obtaining a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image, Calculating a correction coefficient based on shape parameters regarding the shape of the some of the aggregated particles in each of the first image and the second image, Calculating the shape parameter for at least one of the plurality of aggregated particles shown by the first image based on the correction coefficient. An image processing system. (Appendix 2) The length per pixel in the second image is 0.5 times or less the length per pixel in the first image. The image processing system according to Appendix 1. (Appendix 3) For each of the at least one aggregated particle, calculate the perimeter length of the aggregated particle as the shape parameter. For each of the at least one aggregated particle, calculate the average particle size of the plurality of primary particles forming the aggregated particle based on the perimeter length of the aggregated particle. For each of the at least one aggregated particle, approximate the relationship between the shape parameter of the part of the aggregated particles in the first image and the shape parameter of the part of the aggregated particles in the second image by a linear function, and calculate the slope of the linear function as the correction coefficient. The image processing system according to Appendix 1 or 2. (Appendix 4) For each of the at least one aggregated particle, approximate the relationship between the shape parameter of the part of the aggregated particles in the first image and the shape parameter of the part of the aggregated particles in the second image by a linear function, and calculate the slope of the linear function as the correction coefficient. The image processing system according to any one of Appendices 1 to 3. (Appendix 5) Each of the first image and the second image is a binary image in which the pixel value of each pixel is converted to binary. The image processing system according to any one of Appendices 1 to 4. (Appendix 6) An image processing method executed by an image processing system including at least one processor, Obtaining a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles; Obtaining a second image showing a part of the plurality of aggregated particles and having a higher resolution than the first image; Calculating a correction coefficient based on shape parameters regarding the shape of the part of the aggregated particles in each of the first image and the second image; Based on the correction coefficient, calculating the shape parameter for at least one of the plurality of aggregated particles shown in the first image; An image processing method including the above. (Appendix 7) Obtaining a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles; Obtaining a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image; Calculating a correction coefficient based on shape parameters regarding the shape of some of the aggregated particles in each of the first image and the second image; Based on the correction coefficient, calculating the shape parameter for at least one of the plurality of aggregated particles shown in the first image; An image processing program for causing a computer to execute the above.

[0074] According to Appendices 1, 6, and 7, a correction coefficient is calculated based on the shape parameters of some of the aggregated particles in the first image and the second image having different resolutions from each other. Then, based on this correction coefficient, the shape parameter of the aggregated particles in the first image is calculated. By using the correction coefficient obtained based on the two types of images, the shape parameter of any aggregated particle in the first image can be calculated with high accuracy. As a result, it becomes possible to easily perform a highly accurate evaluation of the shape of the primary particles forming the aggregated particles.

[0075] According to Appendix 2, from a second image having a resolution sufficiently higher than that of the first image, shape parameters of some of the aggregated particles with sufficiently higher accuracy than the first image are obtained, and a correction coefficient is calculated based on the shape parameters. Based on this correction coefficient, the shape parameter of the aggregated particles in the first image can be calculated with higher accuracy.

[0076] According to Appendix 3, by using the perimeter length of the aggregated particles calculated with high accuracy in the first image, the average particle diameter of the plurality of primary particles forming the aggregated particles can be calculated with high accuracy.

[0077] According to Supplementary Note 4, the correction coefficient can be easily calculated. As a result, it becomes possible to more easily perform a highly accurate evaluation of the shape of the primary particles forming the aggregated particles.

[0078] According to Supplementary Note 5, the shape of the aggregated particles in each of the first image and the second image is more clearly discriminated. As a result, more accurate shape parameters of some of the aggregated particles can be obtained from each of the first image and the second image, and thus, the shape parameters of the aggregated particles in the first image can be calculated with higher accuracy.

Explanation of Reference Signs

[0079] 10… Image processing system, 11… Image acquisition unit, 12… Binarization processing unit, 13… Generation unit, 14… Evaluation unit, 241… Second binary image (first image), 242… Second binary image (second image).

Claims

1. comprising at least one processor, wherein the at least one processor obtains a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles, obtains a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image, calculates a correction coefficient based on shape parameters regarding the shapes of the some of the aggregated particles in each of the first image and the second image, calculates the shape parameter for at least one of the plurality of aggregated particles shown by the first image based on the correction coefficient, an image processing system.

2. wherein a length per pixel in the second image is 0.5 times or less of a length per pixel in the first image, the image processing system according to claim 1.

3. wherein the at least one processor calculates, for each of the at least one aggregated particle, a perimeter length thereof as the shape parameter, calculates, for each of the at least one aggregated particle, an average particle diameter of the plurality of primary particles forming the aggregated particle based on the perimeter length of the aggregated particle, the image processing system according to claim 1 or 2.

4. wherein the at least one processor approximates a relationship between the shape parameter of the some of the aggregated particles in the first image and the shape parameter of the some of the aggregated particles in the second image by a linear function, and calculates a slope of the linear function as the correction coefficient, the image processing system according to claim 1 or 2.

5. wherein each of the first image and the second image is a binary image in which pixel values of each pixel are converted into binary values, The image processing system according to claim 1 or 2.

6. An image processing method executed by an image processing system including at least one processor, comprising: obtaining a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles; obtaining a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image; calculating a correction coefficient based on shape parameters regarding the shapes of the some of the aggregated particles in each of the first image and the second image; calculating the shape parameters for at least one of the plurality of aggregated particles shown by the first image based on the correction coefficient; An image processing method including the above steps.

7. obtaining a first image showing a plurality of aggregated particles respectively formed by aggregation of a plurality of primary particles; obtaining a second image showing some of the plurality of aggregated particles and having a higher resolution than the first image; calculating a correction coefficient based on shape parameters regarding the shapes of the some of the aggregated particles in each of the first image and the second image; calculating the shape parameters for at least one of the plurality of aggregated particles shown by the first image based on the correction coefficient; An image processing program causing a computer to execute the above steps.

Images