Fast Quantitative Characterization Method for Three-Dimensional Directional Variance of Fibrous Structures Based on Frequency-Domain Convolution

Abstract

The present invention discloses a fast quantitative characterization method for three-dimensional directional variance of fibrous structures based on frequency-domain convolution, which is used for quantitative analysis of optical images of fibrous structures in biological tissues. The present invention can achieve fast quantitative characterization of the three-dimensional directional variance of fibrous structures at the pixel-level resolution, with high precision and high accuracy; the present invention uses the method of frequency-domain convolution to replace the point-by-point addition calculation, greatly improving the time efficiency; the present invention also uses the pseudo-color coding technology to intuitively reflect the distribution and change of the three-dimensional directional variance of biological tissues, enhancing the information readability; the present invention realizes the quantitative analysis of three-dimensional images, greatly enhancing the application scope and potential of directional features compared with the traditional two-dimensional analysis, and is of great significance for biological microstructure research and disease analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantitative characterization of biological tissues, and particularly relates to a fast quantitative characterization method for three-dimensional directional variance of fibrous structures based on frequency-domain convolution. Background Art

[0002] Fibrous structures widely exist in biological tissues and are the basic structural forms of biological tissues. Common fibrous structures include collagen fibers, elastic fibers, neuronal axons, and blood vessels, etc., which play crucial roles in the biological life activities. The morphological structure of fibrous structures is closely related to physiological functions, and the evolution of diseases is often also closely related to the interaction between fibrous structures. Usually, perturbations between fibrous structures will bring a series of changes, such as intracellular gene regulation, changes in the fibrous skeleton structure, changes in the spatial orientation of collagen fibers, and changes in tissue mechanical properties, etc. Therefore, imaging and precise quantitative characterization of fibrous structures are of great significance for understanding the physiological and pathological evolution processes of biological tissues and are an indispensable part of biomedical research.

[0003] The three-dimensional direction of fibrous structures is one of the important characterization parameters and is widely used in disease diagnosis, wound location, and evaluation of the development of biological tissues, etc. The three-dimensional directional variance of fibrous structures in biological tissues also has important significance. Usually, the physiological processes of biological tissues and the evolution of diseases will bring changes in the three-dimensional directional variance of fibrous structures, that is, the arrangement of fibrous structures may change from disordered to ordered or from ordered to disordered.

[0004] Existing methods for characterizing the three-dimensional directional variance of fibrous structures are few and have certain limitations. First, most current methods for characterizing fibrous structures still remain at the two-dimensional level, and only a few can achieve the characterization of the three-dimensional direction of fibrous structures; second, some existing methods can only give the overall direction information of fibrous structures and cannot characterize the information of local details, let alone give the specific results of each pixel point; third, for the existing technical solutions that can achieve pixel-level three-dimensional directional variance characterization, since the average value of each pixel point of the auxiliary variable is calculated by the method of point-by-point summation and then the three-dimensional directional variance is calculated therefrom, this results in a large amount of time consumption for pixel-level three-dimensional directional variance characterization and cannot achieve fast and accurate quantitative characterization.

[0005] Therefore, a method capable of replacing point-by-point summation is needed to accelerate the speed of quantitative characterization of fibrous biological structures, and combined with the existing three-dimensional directional variance characterization scheme, the three-dimensional directional variance of fibrous structures can be characterized more quickly. Summary of the Invention

[0006] In view of the deficiencies of the prior art, the present invention proposes a fast quantitative characterization method for the three-dimensional direction variance of fibrous structures based on frequency-domain convolution. This method uses weighted vector summation to calculate the three-dimensional direction of the fibrous structure, and uses the three-dimensional direction result to calculate auxiliary variables. The auxiliary variables are subjected to neighborhood averaging by frequency-domain convolution, and the three-dimensional direction variance map of the fibrous structure is calculated according to the convolution result. Finally, the direction variance map is pseudo-color coded to achieve pixel-level visual quantitative characterization. This method avoids the disadvantages of existing methods that can only achieve two-dimensional characterization, cannot characterize local details, and have slow characterization speed. It applies frequency-domain convolution to the pixel-level characterization of direction variance, and while ensuring the accuracy of the characterization result, significantly improves the quantitative characterization speed of the three-dimensional direction variance of fibrous structures.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A fast quantitative characterization method for the three-dimensional direction variance of fibrous structures based on frequency-domain convolution, characterized by comprising the following steps:

[0009] 1) Extract the fibrous structure image, and use the method of weighted vector summation to calculate the three-dimensional direction of each pixel point on the fibrous structure in the image to obtain a three-dimensional direction map;

[0010] 2) Use the three-dimensional direction map to obtain the auxiliary variables C, S, and Z required for calculating the three-dimensional direction variance;

[0011] 3) Determine the size of the quantization window according to the fibrous structure image, and generate an identity matrix of the window size. Divide the identity matrix by the window size to obtain the convolution kernel K for calculating the average value;

[0012] 4) Use the fast Fourier transform to transform the auxiliary variables C, S, Z, and the convolution kernel K into the frequency domain to obtain the corresponding frequency-domain results C', S′, Z′, and the frequency-domain convolution kernel K';

[0013] 5) Multiply the frequency-domain results C', S′, Z′ and the frequency-domain convolution kernel K' point by point respectively, and then perform an inverse FFT transform on the multiplied calculation result to return to the spatial domain to obtain the neighborhood average results C mean , S mean and Z mean ;

[0014] 6) Calculate the direction consistency result R of the fibrous structure in the neighborhood according to the neighborhood average results C mean , S mean and Z mean , and then calculate the final three-dimensional direction variance map Var from the direction consistency result R;

[0015] 7) Pseudo-color code the Var results of the three-dimensional direction variance map based on the signal intensity of the fibrous structure image to achieve three-dimensional direction variance characterization of the image while preserving the morphology of the fibrous structure.

[0016] As a further improvement, in step 1) of the present invention, the specific implementation method of calculating the three-dimensional direction of each pixel point on the fibrous structure in the image using the weighted vector summation method is as follows: Set a window with a size of 2 to 3 times the fiber diameter, take all pixel points in the neighborhood of each pixel respectively, perform vector weighted summation calculation, and finally obtain the three-dimensional direction of the pixel at the center of the window. θ represents the azimuth angle, represents the polar angle.

[0017] As a further improvement, in step 2) of the present invention, the calculation methods of the auxiliary variables C, S, and Z are as follows: The calculation formula of C is The calculation formula of S The calculation formula of Z The three auxiliary variables reflect the directions of the fibrous structure in different dimensions to some extent.

[0018] As a further improvement, in step 3) of the present invention, the size of the quantization window is more than 2 times the fiber structure diameter in the fibrous structure image. If the size of the quantization window is n*n*n, the specific calculation method of the convolution kernel K used to calculate the average value is: First generate a unit matrix K0 with a size of n*n*n, and then divide K0 by n 3 , to obtain the convolution kernel K. At this time, the size of each element in K is: The specific function of this convolution kernel is to calculate the average values of the auxiliary variables C, S, and Z within the quantization window and assign the average values to the central pixel.

[0019] As a further improvement, in step 6) of the present invention, the calculation formula of the direction consistency result R of the fibrous structure in the neighborhood is Then, the three-dimensional direction variance map Var is obtained from the calculation formula Var = 1 - R. The direction variance range of each pixel point on the fibrous structure is between 0 and 1; when the directions of the fibrous structures within the window are completely consistent, R = 1, and the direction variance of the fibrous structure is 0; when the directions of the fibrous structures within the window become chaotic, R is less than 1, and the direction variance increases.

[0020] As a further improvement, in step 7) of the present invention, the specific implementation method of pseudo-color coding is to use the ind2rgb function in Matlab to convert the atlas spatial orientation atlas from a grayscale image to a color image, and then select the Colormap of JET to convert the colored atlas spatial orientation atlas into a new pseudo-color coded image. By multiplying the corresponding pixel values of each color channel in the original fibrous structure image and the pseudo-color coded image, a characterization result that contains both three-dimensional direction variance information and signal intensity information can be obtained.

[0021] Due to the application of the above technical solutions, the present invention has the following advantages compared with the prior art solutions:

[0022] 1. The present invention calculates the three-dimensional direction of the fibrous structure based on the method of weighted vector summation, which can realize the calculation of the three-dimensional direction at the pixel level. Based on this result, the pixel-level visualization and quantitative characterization of the three-dimensional direction variance can be realized. The present invention is applicable to both two-dimensional and three-dimensional images. While ensuring the accuracy rate, it can realize more multi-dimensional and more detailed quantitative characterization, with high precision and high accuracy rate.

[0023] 2. The present invention uses frequency domain convolution to perform neighborhood averaging calculation on the auxiliary variable, and uses the method of fast Fourier transform, multiplying the frequency domain results, and inverse fast Fourier transform. Such frequency domain convolution calculation is much faster than the point-by-point addition method and the spatial domain convolution method of the existing solutions. While ensuring the accuracy of the calculation results, it greatly reduces the time consumed for the pixel-level three-dimensional direction variance characterization, and greatly improves the time efficiency.

[0024] 3. Compared with the traditional fibrous structure analysis tool that can only obtain an overall numerical result for one image, the three-dimensional direction variance parameter used in the present invention is the quantization information with pixel-level resolution. And the present invention uses the original intensity to perform pseudo-color coding on the three-dimensional direction variance atlas, and the obtained color atlas can intuitively reflect the distribution and change of the three-dimensional direction variance of the biological tissue, greatly enhancing the readability of the information.

[0025] 4. The present invention realizes the quantitative analysis of three-dimensional images, which greatly enhances the application scope and potential of the direction features compared with the traditional two-dimensional analysis, and has important significance for the research of biological microstructures and disease analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a flowchart of a fast quantitative characterization method for the three-dimensional direction variance of a fibrous structure based on frequency domain convolution;

[0027] Figure 2 It is a schematic diagram of the calculation principle of the three-dimensional direction of a fibrous structure;

[0028] Figure 3Characterization result diagrams of simulated fibrous structures with different degrees of neatness;

[0029] Figure 4 Characterization result diagrams of the cervical collagen fiber structures at different stages of mouse pregnancy. Detailed implementation manners

[0030] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings of the specification and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0031] The present invention relates to a fast quantitative characterization method for three-dimensional directional variance of fibrous structures based on frequency-domain convolution, and the specific steps included are as Figure 1 shown:

[0032] 1) Extract the fibrous structure image. As shown in Figure 4 (a), it is an image of the collagen fibers of the mouse cervix. The three-dimensional direction of each pixel point on the fibrous structure in the image is calculated using the method of weighted vector summation. The characterization of the three-dimensional direction is as shown in Figure 2 (a). The weights used in the weighted vector summation method are respectively the reciprocal of the distance and the degree of change in intensity along the vector direction, as shown in Figure 2 (b) and (c). The effect of adding the weights is as shown in Figure 2 (d). Finally, the fiber direction result is obtained, as shown in Figure 2 (e). After the vector weighted summation calculation, the three-dimensional direction of the pixel at the center of the window is finally obtained. θ represents the azimuth angle, represents the polar angle. The three-dimensional direction calculation is performed on the entire fibrous structure image to obtain a three-dimensional direction map. The result of the azimuth angle θ is as shown in Figure 4 (b), and the result of the polar angle is as shown in Figure 4 (c);

[0033] 2) Using the calculation results of the three-dimensional direction of the fibrous structure, obtain the auxiliary variables C, S, and Z required for calculating the three-dimensional direction variance, where These three auxiliary variables can reflect the directions of the fibrous structure in different dimensions to a certain extent.

[0034] 3) Determine the size of the quantization window according to the fibrous structure image, and generate an identity matrix of the window size. Divide the identity matrix by the window size to obtain the convolution kernel K for calculating the average value;

[0035] 4) Use the fftn function in the built-in Matlab for fast Fourier transform to transform the auxiliary variables C, S, Z and the kernel into the frequency domain, obtaining the corresponding frequency domain results C', S′, Z′ and the kernel K';

[0036] 5) Multiply the frequency domain results C', S′, Z′ and the frequency domain convolution kernel K' point by point respectively, and then use the ifftn function to perform the inverse FFT transform on the multiplied calculation results and return them to the spatial domain to obtain the neighborhood average results C mean , S mean and Z mean ;

[0037] 6) According to the calculation formula Use the neighborhood average results C mean , S mean and Z mean to calculate the direction consistency parameter R of the fibrous structure in the neighborhood, and then obtain the three-dimensional direction variance map Var from the calculation formula Var = 1 - R. The range of the direction consistency parameter R and the direction variance Var for each pixel point on the fibrous structure is between 0 and 1. Figure 3 (a) and (b) show the morphological changes of the fibrous structure when the direction variance of the simulated fibrous structure gradually increases from 0 to 1. The histogram distribution of the direction variance of the simulated fibrous structure is as Figure 3 (c) shown;

[0038] 7) Based on the signal intensity of the original image, select the JET Colormap to perform pseudo-color coding on the three-dimensional direction variance map results, and multiply the corresponding pixel values of each color channel in the original fibrous structure image and the pseudo-color coded image. Finally, realize the three-dimensional direction variance characterization of the image while maintaining the morphology of the fibrous structure. The characterization results are as Figure 4 (d) shown, and the corresponding histogram distribution of the direction variance is as Figure 4 (e) shown.

[0039] In this process, we used three methods: the traditional method (point-by-point addition), spatial domain convolution, and frequency domain convolution to calculate and characterize the direction variance of the collagen fiber image (size 512*512*46) of the mouse cervix respectively, to show the improvement in the characterization speed of the frequency domain convolution method. Among them, the traditional method obtains the average value by adding the neighborhood pixel values of each pixel point in the auxiliary variables C, S and Z, that is, C mean , S mean and Z mean ; The spatial domain convolution obtains the average value through the spatial domain convolution of the auxiliary variables and the generated convolution kernel K, that is, C mean , S mean and Z mean; The method of frequency-domain convolution is as shown in the above steps 3) to 5). Finally, the feature calculation times required by the three methods are as Figure 4 (f). The feature calculation time of the traditional method is 370.88 seconds, the spatial-domain convolution is 6.33 seconds, and the frequency-domain convolution is 1.15 seconds. The speed of the frequency-domain convolution has increased by 300 times. Adding a series of preprocessings before feature calculation and postprocessings such as pseudo-color coding later, the frequency-domain convolution method shortens the total characterization time from 441.99 seconds to 71.20 seconds, and the characterization speed has increased by 6.5 times.

[0040] The frequency-domain convolution method can greatly improve the characterization speed in the three-dimensional direction of fibrous structures. It is worth mentioning that the multiple of the improved characterization speed is related to the size of the quantization window in step 3). In the generated simulated fibrous structure, the image size is 500*500*500, and the diameter of each fiber is 12 pixels. If a quantization window of 25*25*25 is taken, the final feature calculation time is as Figure 3 (d). The characterization speed of the frequency-domain convolution method has increased by 850 times compared with the traditional method. On this basis, we use quantization windows of sizes 7*7*7, 13*13*13, 19*19*19, 25*25*25, and 31*31*31 to characterize the simulated fibers. The final feature calculation times required by each method are as Figure 3 (e). It can be seen that the time required by the traditional method increases rapidly with the increase of the window, and the time of the spatial-domain convolution algorithm also increases with the increase of the window. When the window size is more than 19, the time required by the spatial-domain convolution is greater than that of the frequency-domain convolution, while the time of the frequency-domain convolution always remains around 10 seconds. Note that all the above tests of calculation times are based on the same computing power, that is, CPU: Intel Xeon Platinum 8383C CPU@2.70GHz; memory: 383 grams; GPU: Nvidia GeForce RTX 4080 graphics card, 16GB memory. Therefore, the fast quantitative characterization method of the three-dimensional direction variance of fibrous structures based on frequency-domain convolution is very suitable for the characterization of high-resolution fibrous structure images. As the image resolution is further improved, the required quantization window size will also increase, and this method will also show stronger superiority.

[0041] Based on this idea, through steps such as image extraction, three-dimensional direction calculation, generation of auxiliary variables and convolution kernels, frequency-domain convolution, and pseudo-color coding, the present invention finally obtains a fast quantitative characterization method of the three-dimensional direction variance of fibrous structures based on frequency-domain convolution. Judging from the results, this method can process and analyze high-resolution fibrous structure images, can more quickly realize the visualization characterization of the three-dimensional direction variance of fibrous structures, and can more accurately analyze the morphological changes of fibrous structures, which is of great significance for biological microstructure research and disease analysis.

[0042] The above description of the embodiments is to facilitate the understanding and application of the present invention by those of ordinary skill in the art. It is obvious that those who are familiar with the technology in this field can easily make various modifications to the above embodiments, and apply the general principles described herein to other embodiments without creative labor. Therefore, the present invention is not limited to the above embodiments, and all improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A fast quantitative characterization method for three-dimensional directional variance of fibrous structures based on frequency-domain convolution, characterized in that: The steps are as follows: 1) Extract the fibrous structure image, and calculate the three-dimensional direction of each pixel point on the fibrous structure in the image by using the method of weighted vector summation to obtain a three-dimensional direction map; 2) Use the three-dimensional direction map to obtain the auxiliary variables C, S, and Z required for calculating the three-dimensional direction variance; 3) Determine the size of the quantization window according to the fibrous structure image, and generate an identity matrix with the size of the window. Divide the identity matrix by the window size to obtain the convolution kernel K for calculating the average value; 4) Use the fast Fourier transform to transform the auxiliary variables C, S, Z, and the convolution kernel K into the frequency domain to obtain the corresponding frequency domain results C′, S′, Z′, and the frequency domain convolution kernel K′; 5) Multiply the frequency-domain results C′, S′, and Z′ point by point with the frequency-domain convolution kernel K′ respectively, and then perform an inverse FFT transformation on the calculation results after multiplication to return to the spatial domain, obtaining the neighborhood average results C mean , S mean and Z mean ; 6) According to the neighborhood average result C mean , S mean and Z mean calculate the direction consistency result R of the fibrous structure in the neighborhood, and then calculate the final three-dimensional direction variance map Var from the direction consistency result R; Based on the signal intensity of the fibrous structure image, perform pseudo-color coding on the three-dimensional direction variance map Var result to realize the three-dimensional direction variance characterization of the image while maintaining the morphology of the fibrous structure; In the said step 1), the specific implementation method for calculating the three-dimensional direction of each pixel point on the fibrous structure in the image by using the method of weighted vector summation is as follows: A window with a size of 2 to 3 times the fiber diameter is set, and all pixel points in the neighborhood of each pixel are taken respectively, and vector weighted summation calculation is carried out, and finally the three-dimensional direction of the pixel at the center of the window is obtained. represents the azimuth angle, represents the polar angle; In step 2), the calculation methods of the auxiliary variables C, S, and Z are as follows: The calculation formula of C is The calculation formula of S The calculation formula of Z To some extent, the three auxiliary variables reflect the directions of the fibrous structure in different dimensions.

2. The rapid quantitative characterization method of the three-dimensional directional variance of fibrous structures based on frequency domain convolution according to claim 1, characterized in that: In step 3), the size of the quantization window is more than twice the diameter of the fiber structure in the fibrous structure image. If the size of the quantization window is n*n*n, the specific calculation method of the convolution kernel K used to calculate the average value is as follows: first generate a unit matrix K0 with a size of n*n*n, and then divide K0 by n 3 , to obtain the convolution kernel K. At this time, the size of each element in K is: The specific function of this convolution kernel is to calculate the average values of the auxiliary variables C, S, and Z within the quantization window and assign the average values to the central pixel.

3. The rapid quantitative characterization method of three-dimensional directional variance of fibrous structures based on frequency domain convolution according to claim 2, characterized in that: In the step 6), the calculation formula of the direction consistency result R of the fibrous structure in the neighborhood is Then, the three-dimensional direction variance map Var is obtained from the calculation formula Var = 1 - R, where the direction variance range of each pixel point on the fibrous structure is between 0 and 1; when the directions of the fibrous structures in the window are completely consistent, R = 1, and the direction variance of the fibrous structure is 0; when the directions of the fibrous structures in the window become chaotic, R is less than 1, and the direction variance increases.

4. The rapid quantitative characterization method of the three-dimensional directional variance of the fibrous structure based on frequency domain convolution according to claim 1 or 2 or 3, characterized in that: In step 7), the specific implementation method of pseudo-color coding is to use the ind2rgb function in Matlab to convert the map spatial orientation map from a grayscale image to a color image, and then select the JET Colormap to convert the colored map spatial orientation map into a new pseudo-color coded image. Multiply the pixel values corresponding to each color channel in the original fibrous structure image and the pseudo-color coded image to obtain a characterization result that contains both three-dimensional direction variance information and signal intensity information.

Images