Fast quantitative characterization method for three-dimensional direction variance of fibrous structure based on frequency domain convolution

Abstract

The invention discloses a rapid quantitative characterization method for a three-dimensional direction variance of a fibrous structure based on frequency domain convolution. The rapid quantitative characterization method is used for quantitative analysis of an optical image of a biological tissue fibrous structure. According to the method, the rapid quantitative characterization of the three-dimensional direction variance of the fibrous structure at the pixel-level resolution level can be realized, and the method has high precision and high accuracy; a frequency domain convolution method is used for replacing point-by-point addition calculation, so that the time efficiency is greatly improved; the distribution and change conditions of the three-dimensional direction variance of the biological tissue are intuitively reflected by utilizing a pseudo-color coding technology, and the information readability is enhanced; quantitative analysis of the three-dimensional image is achieved, compared with traditional two-dimensional analysis, the application range and potential of the direction features are greatly enhanced, and the method has great significance in biological microstructure research and disease analysis.

Description

Technical Field

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

[0002] Fibrous structures are widely present in biological tissues and are the basic structural form of biological tissues. Common fibrous structures include collagen fibers, elastic fibers, neuronal axons, and blood vessels, which play a vital role in the life activities of organisms. The morphological structure of fibrous structures is closely related to physiological functions, and the evolution of diseases is often closely related to the interaction between fibrous structures. Often, disturbances between fibrous structures will bring about a series of changes, such as gene regulation inside cells, changes in fibrous skeleton structure, changes in the spatial orientation of collagen fibers, and changes in the mechanical properties of tissues. Therefore, imaging and precise quantitative characterization of fibrous structures are of great significance for understanding the physiological and pathological evolution of biological tissues, and are an indispensable part of biomedical research.

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

[0004] There are few existing methods for characterizing the three-dimensional directional variance of fibrous structures, and they have certain limitations. First, most of the current characterization methods for fibrous structures are still at the two-dimensional level, and only a few can achieve the three-dimensional characterization of fibrous structures; second, some existing methods can only provide the overall directional information of the fibrous structure, and cannot characterize the information of local details, let alone the specific results of each pixel point; third, for the schemes that can achieve pixel-level three-dimensional directional variance characterization in the prior art, since the point-by-point addition and averaging method is used to calculate the average value of each pixel point of the auxiliary variable, and then the three-dimensional directional variance is calculated, this results in a pixel-level three-dimensional directional variance characterization that consumes a lot of time and cannot achieve fast and accurate quantitative characterization.

[0005] Therefore, a method is needed to replace the point-by-point addition method to speed up the quantitative characterization of fibrous biological structures, and to combine the existing three-dimensional directional variance characterization scheme to more quickly characterize the three-dimensional directional variance of fibrous structures. Summary of the invention

[0006] In view of the deficiencies of the prior art, the present invention proposes a method for rapid quantitative characterization of the three-dimensional directional variance of a fibrous structure based on frequency domain convolution. The method uses weighted vector summation to calculate the three-dimensional direction of the fibrous structure, and uses the three-dimensional directional results to calculate auxiliary variables. The auxiliary variables are neighborhood averaged by the frequency domain convolution method, and the three-dimensional directional variance map of the fibrous structure is calculated according to the convolution results. Finally, the directional variance map is pseudo-colored to achieve pixel-level visualized quantitative characterization. The method avoids the shortcomings of the existing methods that can only achieve two-dimensional characterization, cannot characterize local details, and have a slow characterization speed. The frequency domain convolution is applied to the pixel-level characterization of the directional variance, which greatly improves the quantitative characterization speed of the three-dimensional directional variance of the fibrous structure while ensuring the accuracy of the characterization results.

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

[0008] A rapid quantitative characterization method for three-dimensional directional variance of fibrous structures based on frequency domain convolution, characterized in that it comprises the following steps:

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

[0010] 2) Using the three-dimensional directional map, the auxiliary variables C, S and Z required to calculate the three-dimensional directional variance are obtained;

[0011] 3) Determine the size of the quantization window according to the fibrous structure image, generate a unit matrix of the window size, divide the unit matrix by the window size, and obtain the convolution kernel K used to obtain the average value;

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

[0013] 5) Multiply the frequency domain results C', S', Z' by the frequency domain convolution kernel K' point by point, and then perform inverse FFT transformation on the multiplied calculation results and return them to the spatial domain to obtain the neighborhood average result C of the auxiliary variable mean , S mean and Z mean ;

[0014] 6) According to the neighborhood average result C mean , S mean and Z mean The directional consistency result R of the fibrous structure in the neighborhood is calculated, and then the final three-dimensional directional variance map Var is calculated from the directional consistency result R;

[0015] 7) Based on the signal intensity of the fibrous structure image, the three-dimensional directional variance map Var result is pseudo-color-coded to achieve three-dimensional directional variance characterization of the image while maintaining the fibrous structure morphology.

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

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

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

[0019] As a further improvement, in the step 6) of the present invention, the calculation formula of the directional consistency result R of the fibrous structure in the neighborhood is: The three-dimensional directional variance map Var is then obtained by the calculation formula Var=1-R, where the directional variance of each pixel on the fibrous structure ranges from 0 to 1; when the direction of the fibrous structure in the window is completely consistent, R=1, and the directional variance of the fibrous structure is 0; when the direction of the fibrous structure in the window becomes chaotic, R is less than 1, and the directional variance increases.

[0020] As a further improvement, in the step 7) described in 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 map from a grayscale image to a color image, and then use JET's Colormap to convert the color atlas spatial orientation map into a new pseudo-color coded image. The original fibrous structure image is multiplied by the corresponding pixel value of each color channel in the pseudo-color coded image to obtain a characterization result that includes both three-dimensional directional variance information and signal intensity information.

[0021] Due to the application of the above technical solution, the present invention has the following advantages compared with the existing technical solution:

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

[0023] 2. The present invention adopts frequency domain convolution to perform neighborhood average calculation on auxiliary variables, and uses the method of fast Fourier transform, frequency domain result multiplication, and inverse fast Fourier transform. Such frequency domain convolution calculation is much faster than the point-by-point addition method and spatial domain convolution method of the existing scheme. While ensuring the accuracy of the calculation results, it greatly reduces the time required for pixel-level three-dimensional directional variance characterization, greatly improving time efficiency.

[0024] 3. Compared with traditional fibrous structure analysis tools that can only obtain an overall numerical result for an image, the three-dimensional directional variance parameter used in the present invention is quantitative information of pixel resolution, and the present invention uses pseudo-color encoding of the three-dimensional directional variance map based on the original intensity. The obtained color map can intuitively reflect the distribution and changes of the three-dimensional directional variance of biological tissues, 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 directional features compared with traditional two-dimensional analysis, and is of great significance for biological microstructure research and disease analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A flowchart of a method for rapid quantitative characterization of three-dimensional directional variance of fibrous structures based on frequency domain convolution;

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

[0028] Figure 3The characterization results of simulated fibrous structures with different uniformity are shown in the figure;

[0029] Figure 4 This is a diagram showing the characterization results of the cervical collagen fiber structure at different stages of mouse pregnancy. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solution and advantages of the present invention more clear, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0031] The present invention is a method for rapid quantitative characterization of the three-dimensional directional variance of fibrous structures based on frequency domain convolution, which specifically comprises the following steps: Figure 1 As shown:

[0032] 1) Extract fibrous structure images, such as Figure 4 (a) shows the collagen fiber image of the mouse cervix. The weighted vector summation method is used to calculate the three-dimensional direction of each pixel on the fibrous structure in the image. The representation of the three-dimensional direction is as follows: Figure 2 (a) is shown. The weights used in the weighted vector summation method are the inverse of the distance and the subtlety of the intensity change along the vector direction, as shown in Figure 2 As shown in (b) and (c), the effect of adding weights is as follows Figure 2 As shown in (d), the fiber direction result is finally obtained, such as Figure 2 (e) As shown. After the vector weighted summation calculation, the three-dimensional direction of the center pixel of the window is finally obtained. θ represents the azimuth angle, Represents the polar angle, and the three-dimensional direction calculation is performed on the entire fibrous structure image to obtain a three-dimensional direction map, where the result of the azimuth angle θ is as follows Figure 4 (b) shows the polar angle The results are as follows Figure 4 (c)

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

[0034] 3) Determine the size of the quantization window according to the fibrous structure image, generate a unit matrix of the window size, divide the unit matrix by the window size, and obtain the convolution kernel K used to obtain the average value;

[0035] 4) Use the fast Fourier transform (fftn) function of Matlab to transform the auxiliary variables C, S, Z and kernel into the frequency domain to obtain the corresponding frequency domain results C', S', Z' and kernel K';

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

[0037] 6) According to the calculation formula: Use the neighborhood average result C mean , S mean and Z mean Calculate the directional consistency parameter R of the fibrous structure in the neighborhood, and then use the calculation formula Var = 1-R to obtain the three-dimensional directional variance map Var, where the directional consistency parameter R and directional variance Var of each pixel point on the fibrous structure are both between 0 and 1. Figure 3 (a) and (b) show the morphological changes of the fiber structure when the directional variance of the simulated fiber structure gradually increases from 0 to 1. The distribution of the directional variance histogram of the simulated fibrous structure is shown in Figure 3 (c)

[0038] 7) Based on the signal intensity of the original image, the three-dimensional directional variance map result is pseudo-colored by using JET's Colormap, and the original fibrous structure image is multiplied by the pixel value corresponding to each color channel in the pseudo-color coded image, and finally the three-dimensional directional variance characterization of the image is achieved while retaining the fibrous structure morphology. The characterization result is as follows: Figure 4 As shown in (d), the corresponding directional variance histogram distribution is as follows Figure 4 (e) as shown.

[0039] In this process, we used the traditional method (point-by-point addition), spatial domain convolution, and frequency domain convolution to calculate and characterize the directional variance of the collagen fiber image of the mouse cervix (size 512*512*46) to demonstrate the improvement of the frequency domain convolution method in characterization speed. Among them, the traditional method adds the domain pixel value of each pixel point in the auxiliary variables C, S and Z to obtain the average value, that is, C mean , S mean and Z mean ; Spatial convolution is performed by convolving the auxiliary variable with the generated convolution kernel K to obtain the average value, that is, C mean , S mean and Z mean; The frequency domain convolution method is as shown in step 3) to step 5) above. Finally, the feature calculation time required by the three methods is as follows: Figure 4 As shown in (f), the feature calculation time of the traditional method is 370.88 seconds, the spatial domain convolution takes 6.33 seconds, and the frequency domain convolution takes 1.15 seconds. The speed of the frequency domain convolution is increased by 300 times. Combined with a series of preprocessing before feature calculation and subsequent post-processing such as pseudo-color encoding, the frequency domain convolution method shortens the total representation time from 441.99 seconds to 71.20 seconds, and the representation speed is increased by 6.5 times.

[0040] The frequency domain convolution method can greatly improve the characterization speed of fibrous structures in three dimensions. It is worth mentioning that the multiple of the characterization speed increase is related to the size of the quantization window in step 3). In the generated simulated fiber structure, the image size is 500*500*500, and the diameter of each fiber is 12 pixels. If the quantization window is 25*25*25, the final feature calculation time is as follows: Figure 3 As shown in (d), the characterization speed of the frequency domain convolution method is 850 times faster than that of the traditional method. On this basis, we use quantization windows of 7*7*7, 13*13*13, 19*19*19, 25*25*25, and 31*31*31 to characterize the simulated fiber. The feature calculation time required by each method is shown in the following figure. Figure 3 As shown in (e), it can be seen that the time required for the traditional method increases rapidly as the window size increases, and the time of the spatial domain convolution algorithm also increases as the window size increases. When the window size is greater than 19, the time required for spatial domain convolution is greater than that for frequency domain convolution, while the time for frequency domain convolution remains around 10 seconds. Note that all the above calculation time tests are based on the same computing power, namely 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 directional 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, the present invention finally obtains a method for rapid quantitative characterization of the three-dimensional directional variance of fibrous structures based on frequency domain convolution through the steps of image extraction, three-dimensional direction calculation, auxiliary variable and convolution kernel generation, frequency domain convolution, and pseudo color coding. 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 directional 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 skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. 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 rapid quantitative characterization method for three-dimensional directional variance of fibrous structures based on frequency domain convolution, characterized by: The steps include: 1) Extracting the fibrous structure image, using the weighted vector summation method to calculate the three-dimensional direction of each pixel on the fibrous structure in the image, and obtaining a three-dimensional direction map; 2) Using the three-dimensional directional map, the auxiliary variables C, S and Z required to calculate the three-dimensional directional variance are obtained; 3) Determine the size of the quantization window according to the fibrous structure image, generate a unit matrix of the window size, divide the unit matrix by the window size, and obtain the convolution kernel K used to obtain the average value; 4) Use fast Fourier transform to transform the auxiliary variables C, S, Z and convolution kernel K into the frequency domain to obtain the corresponding frequency domain results C', S', Z' and frequency domain convolution kernel K'; 5) Multiply the frequency domain results C', S', Z' by the frequency domain convolution kernel K' point by point, and then perform inverse FFT transformation on the multiplied calculation results and return them to the spatial domain to obtain the neighborhood average result C of the auxiliary variable mean , S mean and Z mean ; 6) According to the neighborhood average result C mean , S mean and Z mean The directional consistency result R of the fibrous structure in the neighborhood is calculated, and then the final three-dimensional directional variance map Var is calculated from the directional consistency result R; 7) Based on the signal intensity of the fibrous structure image, the three-dimensional directional variance map Var result is pseudo-color-coded to achieve three-dimensional directional variance characterization of the image while maintaining the fibrous structure morphology.

2. The method for rapid quantitative characterization of three-dimensional directional variance of fibrous structures based on frequency domain convolution according to claim 1, characterized in that: In the step 1), the specific implementation method of using the weighted vector summation method to calculate the three-dimensional direction of each pixel on the fibrous structure in the image is as follows: a window with a size of 2 to 3 times the fiber diameter is set, all the pixels in the neighborhood of each pixel are taken, and vector weighted summation is performed to finally obtain the three-dimensional direction of the center pixel of the window θ represents the azimuth angle, Indicates the polar angle.

3. The method for rapid quantitative characterization of three-dimensional directional variance of fibrous structures based on frequency domain convolution according to claim 2, characterized in that: In step 2), the calculation method of the auxiliary variables C, S and Z is as follows: The calculation formula of C is The calculation formula of S The calculation formula of Z The three auxiliary variables reflect, to some extent, the orientation of the fibrous structure in different dimensions.

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

5. The method for rapid quantitative characterization of three-dimensional directional variance of fibrous structures based on frequency domain convolution according to claim 4, characterized in that: In step 6), the calculation formula of the directional consistency result R of the fibrous structure in the neighborhood is: The three-dimensional directional variance map Var is then obtained by the calculation formula Var=1-R, where the directional variance of each pixel on the fibrous structure ranges from 0 to 1; when the direction of the fibrous structure in the window is completely consistent, R=1, and the directional variance of the fibrous structure is 0; when the direction of the fibrous structure in the window becomes chaotic, R is less than 1, and the directional variance increases.

6. The rapid quantitative characterization method for three-dimensional directional variance of fibrous structure based on frequency domain convolution according to claim 1, 2, 3 or 5, characterized in that: In the step 7), the specific implementation method of pseudo-color coding is to use the ind2rgb function in Matlab to convert the atlas spatial orientation map from a grayscale image to a color image, and then use JET's Colormap to convert the color atlas spatial orientation map into a new pseudo-color coded image. The original fibrous structure image is multiplied by the pixel value corresponding to each color channel in the pseudo-color coded image to obtain a characterization result that contains both three-dimensional directional variance information and signal intensity information.

Images