Transmission electron microscope image atom column center positioning method
The radial symmetry center algorithm solves the accuracy and speed problems of the center positioning of atomic columns in TEM images by calculating the image intensity gradient and fitting straight lines, achieving high-precision and fast center positioning of atomic columns.
Patent Information
- Application Number
- CN202411371929.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-29
- Publication Date
- 2025-01-17
AI Technical Summary
The existing TEM image atomic column center positioning methods have problems such as limited accuracy and slow calculation speed. The center of mass method is not very accurate in noise and complex backgrounds, while the two-dimensional Gaussian fitting method is complex and time-consuming.
The radial symmetric center algorithm is used to calculate the image intensity gradient through the Roberts cross operator, fit the straight line and minimize the distance sum to determine the optimal center point, and use analytical geometric method to confirm the center point position to achieve sub-pixel positioning.
Provides high-precision positioning results in high-noise environments, fast calculation speed, no iterative process is required, and is suitable for processing large data sets.
Smart Images
Figure CN119322187A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of transmission electron microscope data analysis, and in particular to a TEM image atomic column center positioning method for quickly and accurately fitting radial symmetry centers. Background Art
[0002] Transmission electron microscopy (TEM) is a microscopic technique that uses high-energy electron beams to penetrate samples for observation and imaging. TEM has been widely used in fields such as materials science, nanotechnology, and biology. In high-resolution TEM images, accurately determining the center position of atomic columns helps to understand the structure, defects, and dynamic behavior of materials, and plays a critical role in research in related fields. The existing commonly used methods for locating atomic columns include the centroid method and the two-dimensional Gaussian fitting method.
[0003] The centroid method, also known as the mass point method, is a common method for locating the center of an atomic column in an image. Due to its simple steps and fast calculation speed, the centroid method is very effective when analyzing large amounts of data. However, since it relies on the intensity distribution of the image, noise and complex background may affect its accuracy, and its accuracy and precision are not high in practical applications.
[0004] The two-dimensional Gaussian fitting method accurately determines the center position of the atomic column by fitting the atomic intensity distribution in the image. This method performs well in dealing with noise and complex backgrounds and can provide high-precision positioning results. However, this method also has obvious defects. First, the calculation speed is slow and numerical iteration is required to determine the optimal parameters, which is very time-consuming for large-scale data calculations. The multiple parameters of the two-dimensional Gaussian fitting also place high demands on the computing cost. Secondly, the accuracy is low, and the two-dimensional Gaussian optimization fitting may not necessarily converge to the true distribution, and the fitting results often do not match the true distribution.
[0005] In general, the centroid method has limited accuracy and relies on particle symmetry, while the two-dimensional Gaussian fitting method is computationally complex, slow, and time-consuming. There is an urgent need for a new method with high accuracy and short time consumption. Summary of the invention
[0006] In view of the problems existing in the prior art, the present invention provides a method for locating the center of atoms in a TEM image, the purpose of which is to achieve the center positioning of the atomic column in a TEM image with short time consumption and high precision.
[0007] The present invention is implemented by the following technical solution, comprising the following steps:
[0008] Step 1, obtaining atomic column images with different signal-to-noise ratios;
[0009] Step 2: locate the center position of the atomic column in the image of step 1, and use the radial symmetry center algorithm, which includes:
[0010] 2.1) Use Roberts crossover operator to calculate the intensity gradient of each pixel in the image;
[0011] 2.2) For any pixel point (x k ,y k ), calculate the intensity gradient fitting line passing through the pixel point, and calculate all the intensity gradient fitting lines corresponding to each pixel point on the atomic column image based on this;
[0012] 2.3) Let an arbitrary point (x c ,y c ), calculate the distance from the point to each intensity gradient fitting straight line, and calculate (x c ,y c ) to each straight line, minimize the sum and determine the best center point.
[0013] Furthermore, the intensity gradient of step 2.1) in step 2 is:
[0014]
[0015] in, and It is the coordinate axis direction rotated 45 degrees, I is the pixel intensity, and the subscript k represents the gradient.
[0016] Furthermore, in step 2.2) of the calculation of the intensity gradient fitting line, for any pixel point (x k ,y k ), calculate the slope through this point and m k The equation of the line y is:
[0017]
[0018] y=y k +m k (xx k )
[0019] In this way, the intensity gradient fitting line corresponding to each pixel point on the image is calculated.
[0020] Furthermore, the distance in step 2.3) is calculated as follows:
[0021] For any point (x c ,yc ), from this point to the straight line y=y k +m k (xx k ) k for
[0022]
[0023] By analogy, we can calculate any point (x c ,y c ) to the sum of the distances from the intensity gradient fitting line corresponding to each pixel on the image, and determine the optimal center point (x c’ ,y c‘ ).
[0024] Furthermore, determine the optimal center point (x c’ ,y c‘ ) when introducing weight w k , the weight is calculated as follows:
[0025]
[0026] Among them, the distance d k,c Use (x k ,y k )and The distance between the centroids is approximated.
[0027] Furthermore, the best center point (x c’ ,y c‘ ) position, the formula is:
[0028]
[0029]
[0030] Furthermore, other methods are used to locate the image in step 1, and the positioning process time and positioning result errors of the radial symmetry center algorithm and other methods are directly measured multiple times. The difference between the radial symmetry center algorithm and other algorithms is compared, and the results obtained by the radial symmetry center algorithm are evaluated.
[0031] Furthermore, the method is a sub-pixel positioning algorithm based on analytical and non-iterative calculations.
[0032] Furthermore, the atomic column image is obtained by software generation and TEM actual photography.
[0033] Furthermore, the atomic column image is an atomic column image with arbitrary symmetry distribution.
[0034] The radial symmetry center algorithm in the present invention is a powerful method for locating particles or atomic columns. Compared with traditional methods, the radial symmetry center algorithm has the following obvious advantages: (1) High accuracy. The radial symmetry center algorithm can still provide high-precision positioning results in a high-noise environment. It calculates the intensity gradient of each pixel in the image and finds the symmetry center of the intensity distribution. This method can effectively reduce the impact of noise and thus improve positioning accuracy. (2) Short time consumption. The radial symmetry center algorithm is an analytical method that does not require an iterative process. This gives it a significant speed advantage when processing large data sets. Compared with the two-dimensional Gaussian fitting method that requires iterative optimization, the radial symmetry center algorithm can calculate the position of particles or atomic columns more quickly. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 The technical roadmap for the radial symmetry center algorithm.
[0036] Figure 2 Zero noise images and 50 signal-to-noise ratio images were generated using the software Digital Micrograph.
[0037] Figure 3 The result of locating the center of the atomic column using the radial symmetry center algorithm for the image.
[0038] Figure 4 Comparison of atomic column center positioning error and required time among radial symmetry center algorithm, centroid method and two-dimensional Gaussian fitting method at different signal-to-noise ratios.
[0039] against Figure 1 , where (a) is the atomic column image, (b) is an arbitrary point on the image, (c) is the intensity gradient fitting line corresponding to each selected point, and (d) is the center point of the atomic column. DETAILED DESCRIPTION
[0040] The detailed implementation steps of the embodiment of the method of the present invention are described below. The specific steps are as follows:
[0041] Step 1: Obtain atomic column images with different signal-to-noise ratios. This step corresponds to Figure 1 (a) in the technical route. Specifically, Figure 2 As shown, the single-atom column image with a signal-to-noise ratio ranging from 1 to 200 is generated by using the software Digital Micrograph in this embodiment. The image is defined as having an x-direction length and a y-direction length of 31, a center position of 15, and an intensity calculation formula of: intensity = 0.70932 + exp(signal-to-noise ratio / 4.04534). Use "showimage" to display the image with noise.
[0042] Step 2: Use the radial symmetry center algorithm to determine the center position of the atomic column for the image in step 1. Use offset and Gaussian smoothing to calculate the gradient of each pixel in the image, and calculate the weight based on the magnitude of the gradient and the square value of the distance from the center of gravity. Finally, use the least squares method to solve the radial symmetry center of the image and convert it into Figure 3 The image coordinates are shown.
[0043] Specifically, the radial symmetry center algorithm process is as follows:
[0044] 2.1) Intensity gradient calculation. The intensity gradient of each pixel in the image is calculated using the Roberts crossover operator. This step corresponds to Figure 1 (b) in the technical route. For any set of pixels (i,j), (i+1,j), (i,j+1) and (i+1,j+1) in the single-atom column image, we have
[0045]
[0046] in, and It is the coordinate axis direction rotated 45 degrees, I is the pixel intensity, and the subscript k represents the gradient.
[0047] 2.2) Linear fitting. For each gradient point (x k ,y k ), calculate the slope through this point and m k The equation of the line, this step corresponds to Figure 1 (c) in the technical route.
[0048] For any pixel (x k ,y k ), calculate the slope through this point and m k The equation of the line y is:
[0049]
[0050] y=y k +m k (xx k )
[0051] In this way, the fitting straight line corresponding to each pixel point on the image is calculated.
[0052] 2.3) Center estimation. Suppose an arbitrary point (x c ,y c ), calculate the sum of its distances to all straight lines, and determine the best center point by minimizing the sum of all distances. This step corresponds to Figure 1 (d) in the technical route. For any point (x c ,yc ), from this point to the straight line y=y k +n k (xx k ) k for
[0053]
[0054] From the above formula, we can calculate any point (x c ,y c ) to the sum of the distances of the fitted straight line corresponding to each pixel on the image, minimizing the sum of the distances, based on the weight w k and gradient Directly calculate the best center point (x c’ ,y c‘ ) position, the formula is
[0055]
[0056] The best center point (x c’ ,y c‘ ) is located at
[0057]
[0058] Among them, the distance d k,c Use (x k ,y k )and The distance between the centroids is approximated.
[0059] In this embodiment, other methods are also used to locate the image in step 1, and the running time and positioning result errors of the radial symmetry center algorithm and other methods are counted, and the difference between the radial symmetry center algorithm and other algorithms is compared to evaluate the results obtained by the radial symmetry center algorithm. Specifically, the other methods include the centroid method and the two-dimensional Gaussian fitting method.
[0060] In the centroid method, x i and i represents the coordinates of any pixel in the atomic column image, I ij is the peak center of the image intensity atom at pixel (i, j). The calculation formulas for the center positions Cx and Cy of the atomic column are as follows:
[0061]
[0062] The two-dimensional Gaussian fitting method assumes that the intensity distribution of each atom can be described by a two-dimensional Gaussian function and a constant. The form of the two-dimensional Gaussian function is as follows:
[0063]
[0064] Where I0 is the background intensity, A is the Gaussian amplitude, x w and w is the width of the atomic column in the x and y directions, x0 and y0 are the center positions of the atomic column, and σ is the standard deviation. By fitting the above Gaussian function, the position x0 and y0 of each atomic column can be obtained.
[0065] like Figure 4 As shown, the comparison of the atomic column center positioning error and the required time under different signal-to-noise ratios among the radial symmetry center algorithm, the centroid method and the two-dimensional Gaussian fitting method.
[0066] Analysis shows that the radial symmetry center algorithm does not require an iterative process and has a significant speed advantage when processing large data sets. Compared with the two-dimensional Gaussian fitting method that requires iterative optimization, the radial symmetry center algorithm can calculate the position of particles or atomic columns more quickly.
[0067] The radial symmetry center algorithm performs well in dealing with different noise levels and can maintain stable performance under various image quality conditions. Compared with the centroid method which is easily disturbed by background clutter and noise, the radial symmetry center algorithm can calculate the position of particles or atomic columns faster.
[0068] In summary, the present invention provides a method for quickly and accurately locating the center of an atomic column in a TEM image. Compared with the prior art, the method can achieve the center positioning of an atomic column in a TEM image in a short time and with high precision.
Claims
1. A method for locating the center of an atomic column in a transmission electron microscope image, characterized in that: The steps include: Step 1, obtaining atomic column images with different signal-to-noise ratios; Step 2: locate the center position of the atomic column in the image of step 1, and use the radial symmetry center algorithm, which includes: 2.1) Use Roberts crossover operator to calculate the intensity gradient of each pixel in the image; 2.2) For any pixel point (x k ,y k ), calculate the intensity gradient fitting line passing through the pixel point, and calculate the intensity gradient fitting line corresponding to each pixel point on the atomic column image accordingly; 2.3) Let an arbitrary point (x c ,y c ), calculate the distance from the point to each intensity gradient fitting straight line, and calculate (x c ,y c ) to each straight line, minimize the sum and determine the best center point.
2. The atomic column center positioning method according to claim 1, characterized in that: The calculation method of 2.1) in step 2 is: For any set of pixels (i,j), (i+1,j), (i,j+1) and (i+1,j+1) in the atomic column image, we have in, and It is the coordinate axis direction rotated 45 degrees, I is the pixel intensity, and the subscript k represents the gradient.
3. The atomic column center positioning method according to claim 1, characterized in that: The calculation method of the intensity gradient fitting straight line in step 2.2) is: For any pixel point (x k ,y k ), calculate the slope through this point and m k The equation of the line y is: y=y k +m k (x-x k ) In this way, the intensity gradient fitting line corresponding to each pixel point on the image is calculated.
4. The atomic column center positioning method according to claim 1, characterized in that: The distance in step 2.3) is calculated as follows: For any point (x c ,y c ), from this point to the straight line y=y k +m k (xx k ) k for By analogy, we can calculate any point (x c ,y c ) to the sum of the distances from the intensity gradient fitting line corresponding to each pixel on the image, and determine the optimal center point (x c’ ,y c‘ ).
5. The atomic column center positioning method according to claim 4, characterized in that: Determine the optimal center point (x c’ ,y c‘ ) when introducing weight w k , the weight is calculated as follows: Among them, the distance d k,c Use (x k ,y k )and The distance between the centroids is approximated.
6. The atomic column center positioning method according to claim 5, characterized in that: Use analytical geometry to determine the optimal center point (x c’ ,y c‘ ) position, the formula is:
7. The atomic column center positioning method according to claim 1, characterized in that: Use other methods to locate the image in step 1, directly measure the positioning time and positioning result errors of the radial symmetry center algorithm and other methods multiple times, compare the differences between the radial symmetry center algorithm and other algorithms, and evaluate the results obtained by the radial symmetry center algorithm.
8. The atomic column center positioning method according to claim 1, characterized in that: This method is a sub-pixel positioning algorithm based on analytical and non-iterative calculation.
9. The atomic column center positioning method according to claim 1, characterized in that: The atomic column image is obtained by software generation and TEM actual photography.
10. The atomic column center positioning method according to claim 1, characterized in that: The atomic column image is an atomic column image with arbitrary symmetry distribution.