Titanium dioxide particle size determination method
By identifying and supplementing the boundaries of titanium dioxide particles in SEM images, and utilizing clustering learning and convolutional neural network technologies, the problem of accurate particle size determination of nano-titanium dioxide was solved, achieving rapid and accurate particle size statistics, and improving production efficiency and product quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-29
- Publication Date
- 2026-03-20
AI Technical Summary
Existing technologies struggle to accurately determine the particle size of nano-titanium dioxide, especially in SEM images where particle overlap leads to significant statistical errors in particle size information. Manual statistics are time-consuming and highly subjective, while commercial software exhibits large deviations when faced with images containing a large number of overlapping particles.
By identifying surface particles and non-surface particles in SEM images, clustering learning and boundary completion techniques are used to determine the shape and complete the boundaries of non-surface particles based on the granularity information of surface particles, and convolutional neural networks are combined to improve the accuracy of the determination.
It enables automatic identification and counting of nano-sized titanium dioxide particles, improves the accuracy of particle size determination, reduces manual statistical errors, shortens the statistical time, guides the control of process parameters in actual production lines, and improves production quality.
Smart Images
Figure CN121707906A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of trace substance measurement technology, and in particular to a method for determining the particle size of titanium dioxide. Background Technology
[0002] Titanium dioxide possesses highly stable physicochemical properties, exhibiting high refractive index, optimal opacity, and superior whiteness. It is non-toxic and harmless, making it the world's best white pigment, widely used in coatings, plastics, papermaking, inks, and electronics. With industry development, the trend towards more refined applications of titanium dioxide is becoming increasingly apparent. For example, coating products generally require a particle size average of around 220 nm, while plastic products are generally considered to have an average of 180 nm as optimal. Currently, the particle size of nano-titanium dioxide is typically obtained through statistical analysis of particle information in SEM images. Due to the small particle size and high surface energy of nano-titanium dioxide particles, the interparticle forces are strong, leading to agglomeration. Therefore, the overlap of titanium dioxide particles in SEM images of powder samples is high, posing a significant challenge to the statistical analysis of particle size information. Manual statistical analysis is usually time-consuming and highly subjective; different inspectors may yield particle size average results from the same SEM image that differ by more than 30 nm. In addition, while existing commercial particle size analysis software can automatically determine particle size, these software programs usually require a good degree of dispersion between particles in the image. When faced with images with a large number of overlapping particles, there is still a problem of unclear criteria for determining particle boundaries, resulting in a large deviation between the automatic statistical results and the actual sample particle size information. Summary of the Invention
[0003] The technical problem to be solved by the present invention is to provide a method for determining the particle size of titanium dioxide, with the aim of improving the accuracy of determining the particle size of nano-sized titanium dioxide.
[0004] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:
[0005] A method for determining the particle size of titanium dioxide, the method comprising:
[0006] Obtain SEM images of titanium dioxide particles;
[0007] Based on SEM images, surface particles and non-surface particles in the images are identified, and the particle size information of surface particles is obtained.
[0008] Clustering learning is performed on the particle size information of surface particles. Based on the clustering learning results of surface particles and fragments of non-surface particles, the shape of non-surface particles is determined. Based on the shape of non-surface particles, the boundaries of non-surface particles are supplemented.
[0009] The particle size information of non-surface particles is obtained based on the boundary information after supplementing the edges.
[0010] Furthermore, the identification of surface particles and non-surface particles in the image based on SEM images includes:
[0011] Preprocess the acquired SEM images;
[0012] The particle boundaries in the SEM image are identified based on the gradient magnitude and direction of each pixel in the SEM image.
[0013] If the particle boundary shape in the SEM image is a convex polygon or ellipsoid, then the corresponding particle is a surface particle; if the particle boundary shape is a concave polygon or concave ellipsoid, then the corresponding particle is a non-surface particle.
[0014] 3. The method for determining the particle size of titanium dioxide according to claim 1, wherein the particle size information includes: the major axis a, the minor axis b, the boundary curvature k, and the perimeter p of the particle.
[0015] 4. The method for determining the particle size of titanium dioxide according to claim 1, characterized in that, determining the shape of non-surface particles based on the particle size information clustering learning results of surface particles and fragments of non-surface particles includes:
[0016] Step S1: Perform feature pooling on the particle size information of the surface particles to obtain the clustering features Fe=(ae, be, ke, pe) of ellipsoidal particles and the clustering features Fp=(ap, bp, kp, pp) of convex polygonal particles; ae and ap, be and bp, ke and kp, pe and pp are the major axis, minor axis, boundary curvature and perimeter of the corresponding particle types, respectively.
[0017] Step S2: Based on the SEM image, obtain the visible boundary curvature k' and the proportion r of straight lines in the visible boundary of a single non-surface particle fragment;
[0018] Step S3: Calculate the Mahalanobis distance Dk between the visible boundary curvature k' of a single non-surface particle and the boundary curvature ke of a surface ellipsoidal particle; if Dk is less than a set threshold Tv and r is less than a set threshold Tr, then the non-surface particle is an ellipsoidal particle, otherwise it is a convex polygonal particle.
[0019] Furthermore, the thresholds Tk and Tr are determined based on the principle of maximizing F1-score.
[0020] Furthermore, if the non-surface particles are ellipsoidal particles, the process of supplementing the boundaries of the non-surface particles includes:
[0021] Calculate the major and minor axes of the corresponding non-surface particles: major axis ae*=ae·(Lvis / Le), minor axis be*=be·(Lvis / Le), where Lvis is the visible perimeter of the non-surface particle fragment and Le is the average perimeter of the surface ellipsoidal particles.
[0022] Using the line connecting the two ends of the non-surface particle fragment as the major axis, a complete ellipsoid is generated according to the calculated major axis ae* and minor axis be*, and the generated ellipsoid is adjusted based on the least squares method.
[0023] Furthermore, if the non-surface particles are multi-convex polygonal particles, the process of supplementing the boundaries of the non-surface particles includes:
[0024] The average number of sides n of the surface convex polygonal particles is used as the boundary supplement target for the non-surface polyconvex polygonal particles.
[0025] The fragment side length of the non-surface convex polygonal particle is magnified as follows: sidei=(visable_length_i / visable_length)·pp*, where pp*=pp·(Lvis / Lp), Lp is the cluster perimeter pp of the surface convex polygonal particle, sidei is the magnification factor ratio of the i-th side, visible_length_i represents the visible length of the i-th side, and visible_length represents the total visible length of the non-surface convex polygonal particle.
[0026] Starting with the visible edge of the fragment, the interior angle of the polygon is controlled to be between 90° and 150°. n edges are generated sequentially in a counterclockwise direction, and the convexity of the convex polygon is guaranteed based on the Graham scan algorithm.
[0027] Furthermore, after the boundary of non-surface particles is completed, the boundary completion accuracy is judged based on the convolutional neural network. If the loss function is less than the set value, the boundary completion is qualified; otherwise, the boundary fitting needs to be performed again.
[0028] The beneficial effects of this invention are as follows: This invention supplements the particle size information of non-surface particles by using the particle size characteristics of surface particles in SEM images of particles, thereby achieving automatic identification and statistics of nanoscale titanium dioxide particles. This improves the accuracy of automatic particle determination and has advantages such as fast statistical speed, comprehensive particle counting, and low requirement for the number of sample SEM images. It is of positive significance for reducing the tedious statistical work of R&D personnel and reducing manual statistical errors. It can accurately provide feedback and guide the process parameter control of actual production lines, and has high practical value and promising prospects for improving the production quality of titanium dioxide products. Attached Figure Description
[0029] Figure 1 This is a flowchart of a method for determining the particle size of titanium dioxide according to the present invention; Figure 2 The original SEM image of titanium dioxide particles in the embodiments of the present invention; Figure 3 This is an image with the non-surface particle boundary supplemented in an embodiment of the present invention. Detailed Implementation
[0032] The core of the titanium dioxide particle size determination method of the present invention for solving the above-mentioned technical problems is: identifying surface particles and non-surface particles in SEM images, performing cluster learning on the particle size information of surface particles, determining the shape of non-surface particles based on the cluster learning results of surface particle particle size information, supplementing the boundaries of non-surface particles based on the shape of non-surface particles, and obtaining the particle size information of non-surface particles based on the boundary information of non-surface particles after supplementation, thereby achieving accurate discrimination of nanoscale titanium dioxide particle particle size information.
[0033] like Figure 1 As shown, the titanium dioxide particle size determination method of the present invention includes the following process.
[0034] Step S1: Obtain SEM images of nano-titanium dioxide.
[0035] Electron microscopy is used to scan titanium dioxide particles in a sample to obtain SEM images of the titanium dioxide particles. The SEM images are required to include as many particles as possible while ensuring that individual particles can be clearly identified in order to reduce errors. Therefore, the magnification of the images is controlled between 50,000 and 100,000 times.
[0036] Step S2: Determination of surface particles and non-surface particles in SEM images.
[0037] Surface particles refer to particles in a SEM image that are not obscured by other particles and are located on the surface. First, surface particle identification is performed on the SEM image using a computer, specifically including:
[0038] Preprocessing of SEM images includes image smoothing and noise reduction;
[0039] Calculate the gradient magnitude and direction of each pixel to identify all particle boundaries in the SEM image;
[0040] The determination of whether a particle is a surface particle or a non-surface particle is based on the boundary shape. Since the shape of nano-titanium dioxide particles is a convex polygon or an ellipsoid, the specific determination criteria are as follows: if the boundary shape is a convex polygon or an ellipsoid, it is determined to be a surface particle; if the boundary shape is a concave polygon or a concave ellipsoid, it is determined to be a non-surface particle.
[0041] Step S3: Extraction of surface particle size information.
[0042] After identifying the surface particles in the SEM image, the major axis a, minor axis b, boundary curvature k, and perimeter p of the surface particles are calculated using the scale bar in the SEM image and the number of pixels occupied by the surface particles.
[0043] Step S4: Based on the granularity information of surface particles, clustering learning results and fragments of non-surface particles determine the shape of non-surface particles, specifically including:
[0044] a. Perform feature pooling on the particle size information of surface particles to obtain the clustering features Fe=(ae, be, ke, pe) for ellipsoidal particles and the clustering features Fp=(ap, bp, kp, pp) for convex polygonal particles; ae and ap, be and bp, ke and kp, pe and pp are the major axis, minor axis, boundary curvature and perimeter of the corresponding particle types, respectively.
[0045] b. Obtain the visible boundary curvature k' and the proportion r of straight lines in the visible boundary of a single non-surface particle fragment based on SEM images;
[0046] c. Calculate the Mahalanobis distance Dk between the visible boundary curvature k' of a single non-surface particle and the boundary curvature ke of a surface ellipsoidal particle; if Dk is less than a set threshold Tk and r is less than a set threshold Tr, then the non-surface particle is an ellipsoidal particle, otherwise it is a convex polygonal particle.
[0047] In this embodiment, the thresholds Tk and Tr are determined based on the principle of maximizing F1-score.
[0048] Step S5: Complete the boundary of the non-surface particles based on their shape.
[0049] If the non-surface particles are ellipsoidal, the process of supplementing the boundaries of the non-surface particles includes:
[0050] Calculate the major and minor axes of the corresponding non-surface particles: major axis ae* = ae·(Lvis / Le), minor axis be* = be·(Lvis / Le), where Lvis is the visible perimeter of the fragment, and Le is the average perimeter of the surface ellipsoidal particles. Using the line connecting the two ends of the fragment as the major axis, generate a complete ellipse according to ae* and be*, and fine-tune it by least-squares fitting with the fragment.
[0051] If the non-surface particles are multi-convex polygonal particles, the process of supplementing the boundaries of the non-surface particles includes:
[0052] The average number of sides n of the surface convex polygonal particles is used as the boundary supplement target for the non-surface polyconvex polygonal particles.
[0053] The fragment side length of the non-surface convex polygonal particle is magnified as follows: sidei=(visable_length_i / visable_length)·pp*, where pp*=pp·(Lvis / Lp), Lp is the cluster perimeter pp of the surface convex polygonal particle, sidei is the magnification factor ratio of the i-th side, visible_length_i represents the visible length of the i-th side, and visible_length represents the total visible length of the non-surface convex polygonal particle.
[0054] Starting with the visible edge of the fragment, the interior angle of the polygon is controlled to be between 90° and 150°. n edges are generated sequentially in a counterclockwise direction, and the convexity of the convex polygon is guaranteed based on the Graham scan algorithm.
[0055] After the boundaries of non-surface particles are filled in, a fast screening is performed using CNN feature consistency loss. If the loss is greater than δ (δ takes the 95th percentile in the validation set), the boundary filling of non-surface particles is repeated. If the loss exceeds the limit, the particles are marked as unfillable and are not processed further.
[0056] Step S6: Particle size information statistics.
[0057] Granularity information statistics are performed on the characteristic information of surface particles and non-surface particles after boundary completion to obtain the mean value of each granularity information.
[0058] Example:
[0059] In this example, the original SEM image obtained is as follows: Figure 1 As shown, after identifying surface particles in the SEM image using the methods in steps S1 and S2, the average major axis of the surface particles was 247 nm, the average minor axis was 169 nm, the average aspect ratio was 1.42, and the average perimeter was 890 nm. The specific results for boundary supplementation of non-surface particles are as follows... Figure 2 As shown in Table 1, after using a convolutional neural network to learn the major and minor axes, particle boundary curvature, and perimeter information of surface particles for clustering and supplementing the boundaries of non-surface particles, the average major axis of all particles was 256 nm, the average minor axis was 151 nm, the average aspect ratio was 1.38, and the average perimeter was 876 nm. Simultaneously, particle size information was statistically analyzed based on manual statistics and commercial automated determination software, as shown in Table 1.
[0060] Table 1. Statistical analysis of particle size information from different SEM images of the same titanium dioxide sample using different methods.
[0061]
[0062] As shown in Table 1, the mean particle size obtained by the manual statistical method is significantly larger than the preset value (220 nm) for production, and the standard deviation of the mean is also relatively large. Although the standard deviation of the mean is reduced by using a commercial automatic particle size determination software, there is still a certain discrepancy in the particle size mean statistics. In summary, the particle size statistics obtained by the method described in this invention are closer to the preset value of the produced product in terms of particle size mean, and the standard deviation of the mean is the smallest.
Claims
1. A method for determining the particle size of titanium dioxide, characterized in that, The method includes: Obtain SEM images of titanium dioxide particles; Based on SEM images, surface particles and non-surface particles in the images are identified, and the particle size information of surface particles is obtained. Clustering learning is performed on the particle size information of surface particles. Based on the clustering learning results of surface particles and fragments of non-surface particles, the shape of non-surface particles is determined. Based on the shape of non-surface particles, the boundaries of non-surface particles are supplemented. The particle size information of non-surface particles is obtained based on the boundary information after supplementing the edges.
2. The method for determining the particle size of titanium dioxide according to claim 1, characterized in that, The identification of surface particles and non-surface particles in an image based on SEM images includes: Preprocess the acquired SEM images; The particle boundaries in the SEM image are identified based on the gradient magnitude and direction of each pixel in the SEM image. If the particle boundary shape in the SEM image is a convex polygon or ellipsoid, then the corresponding particle is a surface particle; if the particle boundary shape is a concave polygon or concave ellipsoid, then the corresponding particle is a non-surface particle.
3. The method for determining the particle size of titanium dioxide according to claim 1, characterized in that, The particle size information includes: the major axis a, minor axis b, boundary curvature k, and perimeter p of the particle.
4. The method for determining the particle size of titanium dioxide according to claim 1, characterized in that, Based on the granularity information of surface particles, clustering learning results are used to determine the shape of non-surface particles from fragments, including: Step S1: Perform feature pooling on the particle size information of the surface particles to obtain the clustering features Fe=(ae, be, ke, pe) of ellipsoidal particles and the clustering features Fp=(ap, bp, kp, pp) of convex polygonal particles; ae and ap, be and bp, ke and kp, pe and pp are the major axis, minor axis, boundary curvature and perimeter of the corresponding particle types, respectively. Step S2: Based on the SEM image, obtain the visible boundary curvature k' and the proportion r of straight lines in the visible boundary of a single non-surface particle fragment; Step S3: Calculate the Mahalanobis distance Dk between the visible boundary curvature k' of a single non-surface particle and the boundary curvature ke of a surface ellipsoidal particle; if Dk is less than a set threshold Tv and r is less than a set threshold Tr, then the non-surface particle is an ellipsoidal particle, otherwise it is a convex polygonal particle.
5. The method for determining the particle size of titanium dioxide according to claim 4, characterized in that, The thresholds Tk and Tr are determined based on the principle of maximizing F1-score.
6. The method for determining the particle size of titanium dioxide according to claim 4, characterized in that, If the non-surface particles are ellipsoidal, the process of supplementing the boundaries of the non-surface particles includes: Calculate the major and minor axes of the corresponding non-surface particles: major axis ae*=ae·(Lvis / Le), minor axis be*=be·(Lvis / Le), where Lvis is the visible perimeter of the non-surface particle fragment and Le is the average perimeter of the surface ellipsoidal particles. Using the line connecting the two ends of the non-surface particle fragment as the major axis, a complete ellipsoid is generated according to the calculated major axis ae* and minor axis be*, and the generated ellipsoid is adjusted based on the least squares method.
7. The method for determining the particle size of titanium dioxide according to claim 4, characterized in that, If the non-surface particles are multi-convex polygonal particles, the process of supplementing the boundaries of the non-surface particles includes: The average number of sides n of the surface convex polygonal particles is used as the boundary supplement target for the non-surface polyconvex polygonal particles. The fragment side length of the non-surface convex polygonal particle is magnified as follows: sidei=(visable_length_i / visable_length)·pp*, where pp*=pp·(Lvis / Lp), Lp is the cluster perimeter pp of the surface convex polygonal particle, sidei is the magnification factor ratio of the i-th side, visible_length_i represents the visible length of the i-th side, and visible_length represents the total visible length of the non-surface convex polygonal particle. Starting with the visible edge of the fragment, the interior angle of the polygon is controlled to be between 90° and 150°. n edges are generated sequentially in a counterclockwise direction, and the convexity of the convex polygon is guaranteed based on the Graham scan algorithm.
8. A method for determining the particle size of titanium dioxide according to claim 6 or 7, characterized in that, After the boundary of non-surface particles is completed, the boundary completion accuracy is judged based on the convolutional neural network. If the loss function is less than the set value, the boundary completion is qualified; otherwise, the boundary fitting needs to be performed again.