Method for determining coverage

Abstract

A method for obtaining observation images covering a sufficiently wide area for statistical evaluation of a powder having two or more protrusions on the surface of a single particle, and for calculating the proportion of the particle covered by the protrusions. [Solution] A method for determining the coverage rate of the convex portion on the particle surface of the above powder, comprising the following steps. (1) A step of acquiring a microscopic image of a powder having a brightness distribution and resolution, wherein the microscopic image is acquired such that the brightness distribution satisfies a specific range. (2) A step to create a pseudo-binarization model that converts the brightness distribution of the microscope image obtained in (1) into a distribution with peaks at brightness values ​​of 0 and 255. (3) A step of performing binarization detection on the pseudo-binarization model created in (2). (4) A step of image processing to remove extraneous noise from the binarized image detected in (3). (5) A step of calculating the coverage rate, which indicates the proportion of the particles covered by the convex parts, from the image processed in (4).

Description

[Technical Field]

[0001] This invention relates to a method for determining the coverage rate of a powder having two or more protrusions on the surface of a single particle. [Background technology]

[0002] There are specific surface treatment processes that can highly functionalize powders. Examples include methods that create raised areas on the surface of core particles, or methods that create raised areas by coating the surface of core particles with smaller sub-particles. For powders with raised areas on their surfaces as described above, it is preferable to evaluate the powder performance in conjunction with the surface structure. For this purpose, methods for quantitatively and statistically analyzing the surface structure of powders are needed.

[0003] Such powders can be observed using transmission electron microscopes (TEM), scanning electron microscopes (SEM), and optical microscopes. Furthermore, these images can be subjected to detailed analysis through image processing. Image processing includes various operations such as binarization, filtering, dilation, and stenosis, with ImageJ being a well-known image processing software. Image processing using Python libraries is also employed. Regarding binarization, while it is usually performed by selecting a threshold from 256 luminance values, recent advancements in AI have led to attempts to create models using deep learning and apply them to images for binarization.

[0004] Patent Document 1 (Japanese Patent Publication No. 2023-109890) describes an example in which a pigment is physically attached to the surface of a plate-shaped powder. In that document, 10 images showing only the powder surface were taken at 10,000x magnification using a SEM, and the coverage rate (described as "coarse particle area ratio" in the document) was calculated by binarization using a threshold.

[0005] As seen in these cases, in the conventional method for calculating the coverage rate of coatings, the mainstream approach is to simply select a threshold value using 256 gradation luminance values. The analysis range is limited to a part of the particle, and the number of analyses is not very large. Therefore, the calculated value is only an example and it is difficult to say that it represents the coverage rate specific to the sample, and there is concern that the arbitrariness of the observer strongly affects the evaluation result.

[0006] To solve the above problems, it is necessary to analyze the range including particles with statistical quantities. As will be described later as the analysis method of the present invention, in order to analyze the range including particles with statistical quantities, precise separation and division processing of the background and particles, and precise separation and division processing of particles and convex portions are required. Furthermore, in order to improve the accuracy, noise processing is also indispensable. In addition, for a large number of images including particles with statistical quantities, changing the analysis operation for each image requires a great deal of time and labor. Therefore, it is desired that the analysis be completed by performing the same operation on all images.

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] The present invention has been made in view of the above circumstances, and in a powder having two or more convex portions on the surface of one particle, it is possible to obtain an observation image over a sufficiently wide range for statistical evaluation, accurately recognize the particles and convex portions, and calculate the ratio (coverage rate) of the convex portions covering the particles, and an object of the present invention is to provide a method for performing statistically valid analysis by eliminating subjectivity.

Means for Solving the Problems

[0009] As a result of diligent research to achieve the above objective, the inventors have discovered that, by following the steps (1) to (5) below, it is possible to accurately calculate the percentage of a particle covered by protrusions (coverage rate) in a powder having two or more protrusions on the surface of a single particle, and to perform a statistically valid analysis that eliminates subjectivity, thus leading to the present invention. A flowchart of the method for determining this coverage rate is shown in Figure 1.

[0010] Therefore, the present invention provides a method for determining the following coverage ratio. 1. A method for determining the coverage rate of the protruding portions on the surface of a particle having two or more protrusions on the surface of a single particle, comprising the following steps (1) to (5). (1) A step of acquiring a microscopic image of the powder having a luminance distribution and resolution, wherein each pixel constituting the microscopic image is displayed with a luminance value of 0 to 255 and the luminance distribution is

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[0011] The method of the present invention allows for the accurate recognition of particles and protrusions in a microscopic image of a powder having two or more protrusions on the surface of a single particle, and the calculation of the percentage of the particle covered by the protrusions (coverage rate). This significantly broadens the scope of analysis and enables the efficient calculation of surface coverage rate supported by statistics. [Brief explanation of the drawing]

[0012] [Figure 1] Method flowchart [Figure 2] Conceptual diagram of a set and its elements in process (4) [Figure 3] Conceptual diagram for obtaining set C in process (4)-2-3 [Figure 4] A raised portion formed from the particle (overall view of the particle) [Figure 5] A raised area formed by the elevation of particles (enlarged view of the raised area) [Figure 6] An example of an SEM-linked image of step (1) in the example. [Figure 7] An enlarged image of a portion of the SEM stitched image (Figure 6) from step (1) in the example. [Figure 8] Brightness distribution of the SEM stitched image (Figure 6) from step (1) in the example. [Figure 9] Binarized detection image of "noise-containing particles" by the pseudo-binarization model in step (3) of the example. [Figure 10] Binarized detection image of "noisy protrusions" by the pseudo-binarization model in step (3) of the example. [Figure 11] Particle detection image in step (4) of the example. [Figure 12] Image of "convex portion on particle" detected in step (4) of the example. [Figure 13] Graph showing the variation in CR(j) within the effective error range for step (6) in the example. [Figure 14] An example of a SEM-linked image in Comparative Example 1 [Figure 15] An enlarged image of a portion of an example of a SEM-linked image in Comparative Example 1 (Figure 14). [Figure 16] Brightness distribution of an example of a SEM-stacked image in Comparative Example 1 (Figure 14) [Figure 17] Binarized detection image of "noise-containing particles" using the pseudo-binarization model in step (3) of Comparative Example 1 [Figure 18] Binarized detection image of "convex parts containing noise" by the pseudo-binarization model in step (3) of Comparative Example 1 [Figure 19] Particle detection image in step (4) of Comparative Example 1 [Figure 20] Image of "convex parts on particles" detected in step (4) of Comparative Example 1 [Figure 21] Binarized particle detection image using threshold in Comparative Example 2 [Figure 22] Binarized image of "convex" portion detected by threshold in Comparative Example 2 [Modes for carrying out the invention]

[0013] The present invention will be described in detail below. The present invention provides a method for determining the coverage rate of a convex portion having two or more protrusions on the surface of a single particle, and includes the following steps (1) to (5). A flowchart of this analysis method is shown in Figure 1.

[0014] The "powder having two or more protrusions on the surface of a single particle" that is the subject of evaluation is not particularly limited. Any single particle (powder) can be used, regardless of its material, shape (spherical, needle-shaped, plate-shaped, etc.), particle size (fuzzy, fine particles, pigment-grade, etc.), or particle structure (porous, non-porous, etc.). Examples of materials for a single particle (powder) include inorganic powders, organic powders, surfactant metal salt powders, colored pigments, pearl pigments, metal powder pigments, tar dyes, natural pigments, etc.

[0015] The shape of the protrusions is not particularly limited, but they are preferably particles, and are not particularly limited to spherical, needle-shaped, or plate-shaped. The method of forming the protrusions is not particularly limited; they may be formed by bulging from the particles, or a substance that forms the protrusions may be attached to or adsorbed onto the particles by chemical or physical means. As for the material of the protrusions, the same materials as those listed above for a single particle (powder) can be used as appropriate.

[0016] As described above, the size of each particle, protrusion, and powder is not particularly limited and can be applied to a wide range of average particle diameters, such as 1 nm to 10 mm, or it may be in the range of 10 nm to 1 mm or 100 nm to 100 μm. The protrusion is preferably a sub-particle having an average particle diameter of 0.01 to 50% of the average particle diameter of the main particle. The method for measuring the average particle diameter is the volume median diameter (D 50 The value of the volume median diameter (D) is shown. 50 ) refers to the particle diameter corresponding to 50% of the cumulative distribution when the volume particle size distribution is expressed as a cumulative distribution. In this invention, the volume median diameter refers to the value measured by a laser diffraction / scattering particle size distribution analyzer.

[0017] [Process (1)] (1) A step of acquiring a microscopic image of the powder having a luminance distribution and resolution, wherein each pixel constituting the microscopic image is displayed with a luminance value of 0 to 255 and the luminance distribution is

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[0018] When acquiring images using a scanning electron microscope (SEM) in the above process, it is preferable to adjust the brightness distribution by selecting the energy of the detected signal electrons, the acceleration voltage, and the irradiation current, and to adjust the resolution by selecting the observation magnification, the number of pixels, and the scan time.

[0019] Let G be the set of q image data obtained through the above process, and let Gr be the individual image elements of the set. However, 1 ≤ r ≤ q, and the same applies hereafter. In this invention, the diameter of the protrusion is defined as follows. If the protrusion is formed of sub-particles having a smaller particle size than the powder, the particle size of the sub-particles is defined as the diameter of the protrusion.

[0020] Furthermore, as shown in Figures 4 and 5, if the convex portion is shaped as a protrusion from the powder, the boundary between the space and the convex portion is recognized by a circular arc, the boundary between the particle and the convex portion is recognized by an elliptical arc, the convex portion is detected by a closed curve formed by the combination of these, and the diameter of the circular arc (the major axis of the elliptical arc) is taken as the diameter of the convex portion.

[0021] Regarding the luminance distribution, it refers to the luminance distribution when displayed with luminance values ​​from 0 to 255. If the frequency of luminance values ​​around 0 or 255 is extremely high, it means that a certain area of ​​the image is black or white, which is almost always due to the measurement conditions. Since areas around luminance values ​​of 0 or 255 are difficult to analyze, it is preferable that the frequency of luminance values ​​around 0 or 255 is low. As an example of observation conditions that satisfy the above, when acquiring an image using an SEM, a backscattered electron image with an acceleration voltage of about 1 to 5 kV can be mentioned. However, the above conditions do not limit the observation conditions in this invention.

[0022] When acquiring images using a SEM, the main reason why the brightness of certain areas in the image becomes high, around 255, is the edge effect that occurs when observing the image as a secondary electron image. In SEM observation, when incident electrons are irradiated onto the object being observed, the amount of secondary electrons emitted increases at the slanted parts and edges of the object, resulting in high brightness values ​​at the slanted parts and edges of the object in the secondary electron image. On the other hand, since the backscattered electron emission rate of a backscattered electron image depends on the average atomic number of the sample, the image contrast is less affected by the slanted parts and edges of the sample and more affected by the atomic number of the sample. Therefore, the phenomenon of the slanted parts and edges of the object appearing white due to the edge effect, which was a problem with secondary electron images, is resolved. In addition, if the material has different particles and convex parts, the peaks of their respective brightness values ​​are easier to separate, which is an advantage as it facilitates the binarization process performed in subsequent steps.

[0023] Regarding microscope resolution, when acquiring images using a SEM, it is preferable to adjust the observation magnification, number of pixels, and scan time so that one pixel is 3% or less of the particle size of the smallest particle constituting the composite particle. Regarding particle area ratio, it is preferable that the total projected area of ​​the particles to be analyzed is 20% or more of the total area of ​​the analysis image, and a model that can divide and photograph a selected range and stitch the images together is preferred. Furthermore, it is preferable that the acquired image contains 200 or more particles.

[0024] [Process (2)] (2) A step of creating the following image analysis models (hereinafter referred to as pseudo-binarization models) (A) and (B) based on the results obtained by machine learning, which convert the brightness distribution of the microscope image obtained in step (1) into a distribution with peaks at brightness values ​​of 0 and 255. (A) A pseudo-binarized model that detects particles based on the results of machine learning using sample images in which the particles have been binarized. (B) A pseudo-binarized model that detects convexity based on the results of machine learning using sample images in which the convexity has been binarized.

[0025] From the images obtained in (1), sample images necessary for machine learning to create a pseudo-binarization model using machine learning are prepared. Since the machine learning pseudo-binarization detection model will create two models: one for pseudo-binarization detection of particles and another for pseudo-binarization detection of convex areas, the sample images used for training will also be binarized images of particles and convex areas, respectively. The sample images may be obtained by binarizing several images from the images obtained in (1), or by binarizing images of a specific range extracted from several images. There are no restrictions on the size, number of images, or the number of particles and convex areas contained in the images. There are no specific requirements for the binarization method when preparing the sample images, but it is preferable to manually select the area to be binarized using a stylus or mouse and then binarize it. Specifically, one method is to extract a part of the microscope image, fill in the area to be detected, and then binarize it. Machine learning is performed using the prepared binarized images of particles and convex areas to create pseudo-binarization models for particles and convex areas, respectively. Deep learning is preferred as the machine learning method, and among them, convolutional neural networks are preferred. In this invention, an example is shown in which a binarization model was created using machine learning with the image analysis software MIPAR, but the conditions for machine learning and the software used are not particularly limited. Once a model is created, it can be used to analyze other samples using the same material.

[0026] The number of sample images is preferably 2 to 1,000, and more preferably 4 to 100. These images are used as a sample image set for machine learning. The number of particles in the image set is preferably 5 to 3,000, and more preferably 10 to 300. The number of convex parts in the image set is preferably 10 to 10,000, and more preferably 100 to 1,000.

[0027] [Process (3)] (3) A step of applying the two pseudo-binarization models prepared in step (2) to the microscope image obtained in step (1), respectively, to independently and completely binarize and detect particles containing noise and protrusions containing noise. Step (3) involves applying each pseudo-binarization model to the microscope image obtained in (1) to transform the image so that it has a brightness distribution with peaks at brightness values ​​of 0 and 255, selecting the optimal threshold, and completely binarizing the image to detect particles containing noise and convex parts containing noise. Let pm be the mapping corresponding to the pseudo-binarization model for detecting particles created in (2), let pc be the mapping corresponding to the pseudo-binarization model for detecting convex parts, and let b be the mapping for the binarization process. These transformation processes are combined with the elements Gr of the image set G obtained in (1) to obtain the elements Xr of the set X of "particles containing noise" and the elements Yr of the set Y of "convex parts containing noise". If the mapping transformation is represented by ○, it can be expressed by the following mapping transformation formula.

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[0028] In pseudo-binarization detection using machine learning, if there are areas where machine learning detection is difficult, the luminance values ​​are not completely classified as black (0) and white (255), but rather the luminance distribution has peaks at luminance values ​​of 0 and 255. In such cases, it is necessary to set a threshold to completely binarize the data. While the method of selecting the threshold is not specified, Otsu's binarization method is preferable, which sets a threshold that minimizes the mean variance of the distribution with a peak at luminance value 0 and the distribution with a peak at luminance value 255, and maximizes the separation of the two peaks (Nobuyuki Otsu (1979). “A threshold selection method from gray-level histograms”. IEEE Trans. Sys. Man. Cyber. 9 (1): 62-66. doi:10.1109 / TSMC.1979.4310076).

[0029] [Process (4)] (4) A step of performing image processing to remove extraneous noise from the binarized image detected in step (3). The method is not particularly limited, but specific examples are given below. By performing the image processing described in (4)-1-1 to (4)-1-4 below, extraneous noise is removed from the set of "noise-containing particles" X. A process to remove excess noise from the set Y of "protrusions containing noise" by the image processing described in (4)-2-1 to (4)-2-3 below.

[0030] (4)-1-1 Let map e1 be the erosion process that reduces the number of valid pixels. Let map s1 be the transformation process that temporarily removes detected areas below a specified number of pixels. Combine these transformation processes on the image set element Xr (∈X).

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[0031] The purpose of processing with e1 is to remove small noises and to separate noise that is coupled to the detected area. The number of pixels specified in e1 should preferably be about 2 / 3 of the diameter of the protrusion, ensuring that the protrusion is eliminated without being too large. Since Erosion removes the specified number of pixels from the edge of the detected area, circles with a diameter twice the specified number of pixels, or squares with sides twice the specified number of pixels, or smaller, will be removed. This removes small noises and separates noise that is coupled to the detected area.

[0032] The purpose of processing in s1 is to separate the detection image, which has been reduced in size by e1, into "reduced particles (large)" and "reduced particles (small)" + "reduced noise". It is preferable to specify an area equivalent to a circle with a diameter of about 1 / 3 of the smallest particle size of the base material as the area specified in s1.

[0033] (4)-1-2 Let w1 be the mapping of the separation transformation process using Watershed's algorithm. Let s2 be the mapping of the transformation process that removes detected areas below a specified valid pixel, independently of s1. (4)-1-1 Separated by

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[0034] The purpose of w1 is to separate the parts in the image where "reduced particles (small)" and "reduced noise" are connected. The purpose of s2 is to separate the "reduced particles (small)" and the "reduced noise." It is preferable to specify an area in s2 that corresponds to a circle with a diameter approximately 2 / 3 of the diameter of the circle specified in s1.

[0035] (4)-1-3 Separated

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[0036] (4)-1-4 Let map d2 be the dilation process (dilation) performed with a number of pixels greater than the number of pixels specified in dilation process d1. Let map e2 be the erosion process (erosion) performed with the same number of pixels as the number of pixels specified in dilation process d2. (4)-1-3 obtained

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[0037] The closing process is an operation in which a reduction transformation is performed for the same number of pixels following the expansion transformation to restore undetected areas within the particle (fill in defects).

[0038] (4)-2-1 Let map e3 be a reduction transformation (erosion) of a specified number of valid pixels, independent of maps e1 and e2. Let map s3 be a transformation that temporarily deletes detected areas smaller than or equal to valid pixels, independently of maps s1 and s2. Then, combine these transformations on the image set element Yr (∈Y).

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[0039] e3 aims to remove small noise and separate the noise combined with the convex part detection area. The number of pixels specified by e3 is preferably a value that does not eliminate the convex part and reduces the diameter of the detected convex part to about 2 / 3. s3 aims to remove the noise that was separated from the convex part detection area by e3 but has not yet been removed. The area specified by s3 is preferably about 2 / 3 of the area of one particle of the reduced convex part so that the convex part reduced by e3 does not disappear. Here, by performing the reduction conversion process first, the specified area can be reduced, and it is not necessary to eliminate what is not desired to be eliminated.

[0040] (4)-2-2 Let the dilation transformation (Dilation) with the same number of pixels as the number of pixels specified in the reduction transformation process e3 be the mapping d3. Separated by (4)-2-1

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[0041] (4)-2-3 Let the set of "particles" obtained by (4)-1-4 be M, and the

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[0042] [Process (5)] (5) A step of calculating a coverage rate, which indicates the proportion of the particles covered by the convex portion, from the image processed in step (4), The total surface area of ​​the "particles" is S M Let S be the total area of ​​the "protrusions on the particle surface". C The proportion of the particles covered by the convex portion (coverage rate) is defined as C RIn this case, the coverage C is given by the following formula (X1). R The process of calculating.

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[0043] Specifically, the total area of ​​the image set "particles" and the total area of ​​the image set "convex parts on particles" are calculated from the images, and the total area of ​​the image set "particles" is S M The total area of ​​the image set "convex parts on particles" is S C That's what I decided.

[0044] Measurable coverage C R It is not particularly limited, 0 <C R It can measure in the range of ≤100, and 5 ≤ C R The range ≤95 is also acceptable, or 10 ≤ C R The range ≤90 is also acceptable.

[0045] In the method for analyzing surface shape from the coverage rate of the convex portion on the particle surface of the present invention, the obtained "coverage rate C R The statistical validity of "[ ]" can be confirmed by the following method [Step (6)]. [Process (6)] (6) A step in which the statistical validity of the coverage rate is evaluated using the microscope images and "particle" detection images obtained in steps (1) to (4) above, and the "protrusions on the particles" detection images, based on the following formulas (X2) to (X4) and the following formula (X5). Let U be a set of n unit images from acquired microscope images. Randomly rearrange the elements of the set and let U(i) be the i-th image (i=1,2,…,n). Image U(i) from which "particles" were detected. M (i) Image U(i) in which "convex parts on the particle" are detected. C (i) Let S be the area of ​​the detected "particle". M (i) The area of ​​the "convex part on the particle" is S C (i) Based on the coverage formula, the cumulative coverage C up to the jth sheet is R (j)

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[0046] The present invention is a method for obtaining the coverage rate of the convex portion, and provides a method for obtaining the coverage rate of the convex portion on the particle surface. Furthermore, analysis of properties, characteristics, etc. may also be possible. According to the analysis method of the present invention, the analysis target range becomes significantly wider, and efficient calculation of the surface coverage rate supported by statistics becomes possible. Such an analysis method is also an effective method for evaluating the properties and characteristics of powders in the fields of cosmetics, foods, pharmaceuticals, electrical and electronic materials, paints, etc.

Examples

[0047] The present invention will be described in more detail below with reference to examples, but the present invention is not limited to these. In this example, the coverage rate of a powder in which silica (protrusions) is attached to titanium mica (particles) was determined by the following steps (1) to (5). The scheme of this analysis is shown in Figure 1. (1) Steps to acquire an SEM image of the powder having a brightness distribution, resolution and particle area ratio. Conductive carbon double-sided tape was attached to the SEM sample stage, a small amount of powder was taken with the tip of a cosmetic brush and attached to the double-sided tape, and excess powder was removed by air blowing. After that, Au-Pt deposition was performed. The prepared sample stage was set in the measuring jig of the instrument and observation was performed under the following conditions. <Observation conditions> Equipment used: FEI Helios NanoLab 600i Detected electrons: Backscattered electrons Acceleration voltage: 5kV Irradiation current: 0.17nA Magnification: 20,000x Pixel count: 1536 pixels x 1024 pixels Scan time: 3 μs Automatic shooting and image stitching software: MAPS manufactured by FEI Corporation Automatic shooting, image stitching conditions: 11 vertical x 11 horizontal (total 121 images) Number of images acquired for concatenation: 10 (equivalent to 10 x 121 = 1,210 individual images)

[0048] Wide-area observation was performed using automated imaging and image stitching software FEI's MAPS. The magnification was set to 20,000x, and 11x11 images of 1,536 pixels × 1,024 pixels (10.35 μm × 6.90 μm) were automatically observed and stitched together. Ten stitched images were acquired under these conditions. Approximately 20-60 powder particles could be identified in each stitched image, and it was confirmed that there were more than 200 powder particles in the 10 stitched images. An example of a stitched image acquired by SEM is shown in Figure 6, and a magnified cropped portion of the stitched image is shown in Figure 7 to illustrate the analysis process of the present invention. Furthermore, the brightness distribution of the stitched image shown in Figure 1 is shown in Figure 8.

[0049] Regarding the brightness distribution of the image in Figure 1 obtained under the above conditions,

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[0050] (2) A step to create two pseudo-binarization models based on the results obtained by machine learning, which convert the brightness distribution of the SEM image obtained in step (1) into a distribution with peaks at brightness values ​​of 0 and 255. (A) A pseudo-binarization model for detecting particles was created using the following procedure, based on the results of machine learning using a set of sample images in which particles have been binarized. From the image obtained in (1), four images of approximately 3,000 pixels × 3,000 pixels (20.22 μm × 20.22 μm, including 2 or 3 particles) were extracted, and the particles were manually filled in using a stylus to prepare binarized images for training. Using the images before and after binarization, deep learning (CNN: Convolutional Neural Network) was performed to create a pseudo-binarized model for detecting particles. The corresponding mapping is p m That's what I decided. (B) A pseudo-binarization model for detecting convex areas was created using the following procedure, based on the results of machine learning with a sample image set in which the convex areas were binarized.

[0051] (1) From the image obtained in (1), 500 pixels × 500 pixels (3.37 μm × 3.37 μm, 1 μm 2Six images were extracted (each image having approximately 6 convex areas, and about 70 convex areas in total). Using a stylus, only the convex areas were manually filled in to prepare binarized images for training. Using the images before and after binarization, deep learning (CNN: Convolutional Neural Network) was performed to create a pseudo-binarization model that detects convex areas. The corresponding mapping is p c That's what I decided. The image analysis software MIPAR was used to create the pseudo-binarization model.

[0052] (3) A step in which the two pseudo-binarization models prepared in step (2) are applied to the SEM image obtained in step (1), respectively, and particles containing noise and protrusions containing noise are independently and completely binarized for detection. • Particle detection process including noise The pseudo-binarization model for particle detection created in (2) was applied to the SEM image acquired in (1), and the "noise-containing particles" were detected by complete binarization using Otsu's binarization method. The magnified image after detection is shown in Figure 9. • Process for detecting protrusions containing noise The SEM image acquired in (1) was subjected to the pseudo-binarization model for convex detection prepared in (2), and the "noise-containing particles" were detected by complete binarization using Otsu's binarization method. The magnified image after detection is shown in Figure 10.

[0053] (4) A step of performing image processing to remove extraneous noise from the binarized image detected in step (3) above. The extraneous noise was removed from the "noise-containing particles" using the following procedure. (4)-1-1 The 10 images of "particles containing noise" obtained in (3) above were subjected to a 30-pixel reduction transformation process e1. Subsequently, a transformation process s1 was performed to delete detection areas of 200,000 square pixels or less, separating them into "reduced particles (large)" and "reduced particles (small)" + "reduced noise".

[0054] (4)-1-2 The resulting "small reduced particles" + "reduced noise" were subjected to a separation and transformation process w1 using the Watershed algorithm. Subsequently, a transformation process s2 was applied to remove detection areas with an area of ​​80,000 square pixels or less, thereby separating the data into "small reduced particles" and "reduced noise 1".

[0055] (4)-1-3 The separated "large reduced particle" and "small reduced particle" were combined to obtain "large reduced particle" + "small reduced particle". Subsequently, by performing the expansion transformation process d1 at 30 pixels as specified in the reduction transformation process e1, "large particle" + "small particle" was obtained.

[0056] (4)-1-4 The "large particle" + "small particle" obtained above was subjected to an expansion transformation process d2 at 50 pixels, which is larger than the 30 pixels specified in the expansion transformation process d1, followed by a reduction transformation process e2 at the same 50 pixels. This restored the undetected parts within the particle and obtained a "particle". Based on the above, by performing image processing on the "particles containing noise" detection image, a "particle" detection image with the noise removed (Figure 11) was obtained.

[0057] The excess noise was removed from the "noise-containing protrusions" using the following procedure. (4)-2-1 The 10 images obtained by (3) above, which contained noise, were subjected to a 7-pixel reduction transformation process e3. Subsequently, a transformation process s3 was performed to remove detection areas of 50 square pixels or less, separating them into "reduced convex areas" and "reduced noise 2". (4)-2-2 The "reduced convex portion" obtained as described above was subjected to an expansion transformation process d3 of 7 pixels, as specified in the reduction transformation process e3, to obtain a "convex portion". (4)-2-3 A "protrusion on a particle" was obtained, consisting of a common detection portion of the "particle" obtained by (4)-1-4 and the "protrusion" obtained by (4)-2-2. Based on the above, by performing image processing on the "protrusions containing noise" detection image, we obtained a "protrusion detection image on particles" (Figure 12) with the noise removed.

[0058] (5) A step of calculating the coverage rate, which indicates the proportion of the particles covered by the protrusions, from the noise-removed detection image processed in step (4). The total area of ​​the image set "particle" consisting of the 10 noise-removed detection images obtained as described above is S. M The total area of ​​the image set "convex parts on particles" is S C The following formula was used to calculate the percentage of the particles covered by the protrusions (coverage rate) of 49.8%. Note that the volume median diameter (D) of the powder was used. 50 The diameter was 23.4 μm.

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[0059] (6) A step to evaluate the statistical validity of the coverage rate using the SEM images and "particle" detection images obtained in steps (1) and (5) above, and the "protrusions on the particles" detection images. Let U be a set of 1,210 unit images from acquired SEM images. The elements of the set were randomly rearranged, and the i-th image was defined as U(i) (i=1,2,…,1210). Based on the coverage formula, the cumulative coverage C up to the jth layer is calculated. R (j)

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[0060] [Comparative Example 1] Binarization of SEM images using machine learning with secondary electron images As a comparative example of this analysis, we show an example where the conditions for acquiring SEM images in step (1) of the example are changed as follows, and the conditions of (1) are not met. Detected electrons: Secondary electrons Acceleration voltage: 15kV Figure 14 shows an example of a stitched image acquired by SEM, and Figure 15 shows an enlarged cropped portion of the stitched image to illustrate the analysis process of the present invention. Figure 16 also shows the brightness distribution of the stitched image shown in Figure 10. The image obtained as described above has a very strong peak at a brightness value of 255 in its brightness distribution, and as can be seen from Figures 10 and 11, white, bright areas can be observed scattered throughout the image. Regarding the luminance distribution, the peak intensity ratio for a luminance value of 255 was as follows, and it did not satisfy the condition (1) above. That is,

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[0061] Therefore, the peak intensity ratio of the luminance value 255 in this comparative example 1 is as follows:

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[0062] Figure 17 shows particle detection images obtained by performing pseudo-binarization and complete binarization using the same steps (2) and (3) as in the example on the SEM image, and Figure 18 shows the convexity detection image. While particles were detected fairly well, it was difficult to detect the white, glowing parts of the convexity. Next, noise reduction was performed on the particle detection image and the convexity detection image using the same step (4) as in the example. Figure 19 shows the particle detection image after noise reduction, and Figure 20 shows the convexity detection image. Regarding the convexity, the silica in the white, glowing parts in the original SEM image could not be detected. Because detection could not be performed with sufficient accuracy, it was not possible to calculate the coverage rate.

[0063] [Comparative Example 2] Threshold binarization of SEM images using backscattered electron images As a comparative example of this analysis, we present an example in which step (1) is performed in the same manner as in the example, step (2) of the example is omitted, and in step (3) of the example, the pseudo-binarization model is not applied, and binarization using a normal threshold is applied instead. In the SEM-linked image obtained in the example (Figure 1), we searched for the threshold that best binarized the particles visually, but the background was detected before the particles could be fully detected, making particle detection impossible. Figure 21 shows the binarized image with a threshold of 122. Similarly, we searched for the threshold that best binarized the convex parts visually, but the background and particle areas were detected before the convex parts could be fully detected, making accurate detection impossible. Figure 22 shows the binarized image with a threshold of 130. With binarization using thresholds, neither particles nor convex parts could be detected accurately, and we were unable to calculate the coverage rate.

[0064] Table 1 below summarizes the differences between the example and Comparative Examples 1 and 2. [Table 1] Explanation of symbols in Table 1 ○: Same process as in the example. ×: Different process from the example. -: This step was not performed because analysis was not possible.

Claims

1. A method for determining the coverage rate of the protruding portions on the surface of a powder having two or more protrusions on the surface of a single particle, comprising the following steps (1) to (5). (1) A step of acquiring a microscopic image of the powder having a luminance distribution and resolution, wherein each pixel constituting the microscopic image is displayed with a luminance value of 0 to 255 and the luminance distribution is [Math 1] and, [Math 2] Satisfying the conditions, The aforementioned resolution [Math 3] A process for acquiring a microscope image that satisfies the following conditions. (2) A step of creating the following image analysis models (hereinafter referred to as pseudo-binarization models) (A) and (B) based on the results obtained by machine learning, which convert the brightness distribution of the microscope image obtained in step (1) into a distribution with peaks at brightness values ​​of 0 and 255. (A) A pseudo-binarization model that detects particles based on the results of machine learning using sample images in which the particles have been binarized. (B) A pseudo-binarization model that detects convex parts based on the results of machine learning using sample images in which the convex parts have been binarized. (3) A step of applying the two pseudo-binarization models prepared in step (2) to the microscope image obtained in step (1), respectively, to independently and completely binarize and detect particles containing noise and protrusions containing noise. (4) A step of performing image processing to remove extraneous noise from the binarized image detected in step (3). (5) A step of obtaining the total area of ​​the particles and the total area of ​​the protrusions on the particle surface from the image processed in step (4), and calculating the coverage rate which indicates the proportion of the particles that are covered by the protrusions, The total surface area of ​​the "particles" is S M Let S be the total area of ​​the "protrusions on the particle surface". C The proportion of the particles covered by the protrusions (coverage rate) is defined as C. R In this case, the coverage C is given by the following formula (X1). R The process of calculating. [Math 4]

2. A method for determining the coverage of a convex portion according to claim 1, wherein the brightness distribution is adjusted by selecting the energy of the signal electrons to be detected, the acceleration voltage, and the irradiation current in the image acquisition using a scanning electron microscope as the microscope in step (1) above.

3. A method for determining the coverage of a convex portion according to claim 1, wherein the resolution is adjusted by selecting the observation magnification, the number of pixels, and the scan time when acquiring an image using a scanning electron microscope as the microscope in step (1) above.

4. The method for determining the coverage of a convex portion according to claim 1, wherein in step (2) above, the sample image is obtained by cutting out a part of a microscope image, filling in the area to be detected, and binarizing it.

5. The method for determining the coverage of a convex portion according to claim 1, wherein the machine learning method in step (2) is a convolutional neural network.

6. A method for determining the coverage of a convex portion according to claim 1, wherein in step (3) above, when completely binarizing the image after applying the pseudo-binarization model, a method is used to select a threshold such that the mean variance of the distribution having a peak at a brightness value of 0 and the distribution having a peak at a brightness value of 255 is minimized and the degree of separation is maximized.

7. A method for determining the coverage rate of a protruding portion according to claim 1, wherein the protruding portion of the powder is formed by being raised from the particles.

8. A method for determining the coverage rate of a protruding portion according to claim 1, wherein the protruding portion of the powder is composed of sub-particles having an average particle diameter of 0.01 to 50% of the average particle diameter of the main particle.

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