An automatic twist calculation method based on image gray scale

Abstract

The application discloses an automatic tortuosity calculation method based on image gray scale, which comprises calculating the direction orientation of each fiber pixel based on image gray scale, then regarding the pixel as a micro-element vector, calculating the local path and displacement to calculate the tortuosity. Compared with the classical blood vessel quantification algorithm, the application does not need to provide the voxel-level quantitative characterization of the local heterogeneous curling level of the fibrous structure in the form of skeletonization, function fitting or fiber tracking, and can be used as a new dimension to describe the morphological aspect of the fiber structure. The method can realize the quantitative characterization of the local heterogeneous curling level of the blood vessel on the voxel scale, and significantly improves the spatial resolution and analysis sensitivity. Direct gray scale analysis is adopted, the processing steps are greatly simplified, the cumulative error is effectively reduced, and the method is especially suitable for the morphological research of blood vessels, microcirculation analysis and functional evaluation of complex fiber networks with extremely high precision requirements.

Description

Technical Field

[0001] This invention belongs to the field of quantitative characterization technology of biological tissues, specifically relating to an automated distortion calculation method based on image grayscale. Background Technology

[0002] Traditional physical sectioning imaging methods require physical slicing of the object, with each slice mounted on a glass slide and stained. This sampling method is destructive and sparsity-prone, limiting quantitative analysis to a two-dimensional level. The advent of optical sectioning microscopy enables three-dimensional imaging of the entire intact sample, achieving rapid, true three-dimensional, non-destructive high-resolution imaging and improving the workflow of tissue analysis. Faced with entangled structures and complex distributions, three-dimensional quantification provides more comprehensive and accurate information, avoiding artifacts and ambiguities. Simultaneously, the data growth and rich information brought by high-resolution three-dimensional optical imaging place demands on quantitative algorithms to be both fast and accurate.

[0003] Vascular networks are among the most important three-dimensional structures in living organisms, and their spatial morphology and distribution characteristics largely determine tissue perfusion capacity and functional status. Bioimaging technology provides a crucial tool for visualizing vascular structures. Quantitative analysis of vascular imaging results allows for an objective description of the geometric morphology, topology, and spatial heterogeneity of blood vessels at a three-dimensional scale. These quantitative analytical parameters sensitively reflect the structural remodeling process of blood vessels under physiological and pathological conditions, serving as important evidence for evaluating tissue status and disease progression.

[0004] Vascular volume density (VVD) and vessel spacing index (VSI) are commonly used quantitative vascular characterization parameters. VVD is a quantitative parameter used to describe the proportion of space occupied by blood vessels in biological tissues. It is defined as the ratio of blood vessel volume to the total volume of the corresponding tissue, and VVD can reflect the density of blood vessels on a three-dimensional scale. However, VVD can only reflect the proportion of the number of blood vessels from a macroscopic perspective, and it is difficult to directly reflect the spatial arrangement or spacing characteristics between blood vessels.

[0005] The vessel spacing index (VSI) is a quantitative parameter used to describe the spatial distribution and spacing characteristics of blood vessels in tissues, primarily reflecting the average distance or spacing scale between vessels. VSI is typically calculated based on vessel segmentation results, measuring the distance from any location in the tissue to the nearest vascular structure, thus reflecting the level of spatial spacing between vessels; a larger VSI indicates sparser vessel distribution. However, VSI calculation depends on the vessel region segmentation results and is easily affected by factors such as noise and image contrast.

[0006] In summary, current quantitative vascular characterization algorithms have the following technical problems:

[0007] (1) Classical blood vessel quantization algorithms rely on the binarization extraction of blood vessels, as well as skeletonization and boundary extraction based on the binarization results. They can only provide a rough representation of blood vessels, and the segmentation of blood vessel regions depends on the selection of thresholds and segmentation parameters. The accuracy and stability of the segmentation results are difficult to guarantee.

[0008] (2) Noise and outliers in existing vascular quantification images can seriously affect the results of edge and skeletonization, thus affecting the accuracy of quantification. In particular, in addition to sparsely distributed blood vessels, there are a large number of collagen fibers in organisms. These fibrous structures are densely distributed and difficult to segment accurately in binary form. Furthermore, it is impossible to distinguish discrete fibers through skeletonization. Therefore, more refined methods are needed to characterize these collagen fibers.

[0009] (3) The cumbersome steps of the classic blood vessel quantification algorithm lead to the accumulation of calculation errors, which weakens the interpretability of the results. Summary of the Invention

[0010] To address the shortcomings of the aforementioned technical solutions, this invention provides an automated distortion calculation method based on image grayscale. This method fully utilizes the grayscale information of high-resolution three-dimensional imaging to achieve a sensitive characterization of vascular distortion, eliminating the need for previous steps such as skeletonization, fiber tracing, or function fitting, while preserving computational interpretability. It provides an important tool for understanding vascular health, disease progression, and treatment response.

[0011] This method is implemented using the following technical solution:

[0012] This invention discloses an automated distortion calculation method based on image grayscale, characterized by the following steps:

[0013] 1) Calculate the fiber pixel-level orientation based on the fluctuations in image grayscale;

[0014] 2) The path L between the two ends of the fiber in the fiber pixel-level orientation calculation window obtained in step 1);

[0015] 3) Calculate the distance between the two ends of the fiber in the fiber pixel-level orientation calculation window obtained in step 1). ;

[0016] 4) The path L between the two ends of the fiber and the distance between the two ends of the fiber The ratio represents the distortion index TI = L / ;

[0017] 5) Normalize the distortion index TI to obtain ;

[0018] 6) Based on the obtained normalized distortion index Numerical pseudo-color encoding of images enables the visualization of fiber twisting degree without altering the original fiber structure.

[0019] As a further improvement, in step 1) of this invention, the fiber pixel-level orientation is calculated as follows: a window is set according to the image fiber diameter, and all two pixels symmetrical about the center of the window are multiplied by a weighting factor as the first and last vectors. and Then add them all together, and the resulting vector orientation is the orientation of the center pixel of the window, where the weight factor is... Represented as:

[0020] ;

[0021] Where L is the length of the vector, and the weighting factor is... Represented as:

[0022] ;

[0023] in These are the values ​​of the first, last, and center pixels of the vector. It is the average value of three pixels.

[0024] As a further improvement, the method for calculating the path L between the two ends of the fiber in step 2) of the present invention is as follows: For a two-dimensional image, the infinitesimal vector at each fiber pixel point calculated in step 1) is:

[0025] ;

[0026] in , The angle between the vector and the x-axis. Let be the length of the infinitesimal vector element, which is approximated as 1. and Let x and y be the basis vectors in the x and y directions, respectively, and L be the scalar sum of all infinitesimal vectors, expressed as:

[0027] ;

[0028] in This represents the infinitesimal vector of the q-th pixel. and These represent the component values ​​of the infinitesimal vector in the x and y directions, respectively, and n represents the number of effective pixels in the selected neighborhood.

[0029] For the 3D image, the infinitesimal vector at each voxel point calculated in step 1) is:

[0030] ;

[0031] in It is the angle between the infinitesimal vector and the z-axis. Let be the angle between the projection of the vector onto the xy-plane and the x-axis. The length of the infinitesimal vector at each voxel point, which can be considered as 1 in the calculation, is represented by L as:

[0032] ;

[0033] in This represents the infinitesimal vector of the q-th pixel. , , These represent the component values ​​of the infinitesimal vector in the x, y, and z directions, respectively, and n represents the number of effective pixels in the selected neighborhood.

[0034] As a further improvement, in step 3) of the present invention, the distance between the two ends of the fiber in the calculation window is... The method is as follows: For a two-dimensional image, displacement Represented as:

[0035] ;

[0036] in This represents the vector of the q-th pixel in the window. and Let x and y represent the component values ​​of the infinitesimal vector in the x and y directions, respectively, and n represent the number of effective pixels within the window. Therefore, the distance... Represented as:

[0037] ;

[0038] For three-dimensional images, displacement Represented as:

[0039] ;

[0040] distance Represented as:

[0041] ;

[0042] in, , , These represent the component values ​​of the q-th infinitesimal vector in the x, y, and z directions, respectively, and n represents the number of valid pixels within the window.

[0043] The beneficial effects of this invention are:

[0044] 1. This method enables quantitative characterization of local heterogeneous vascular coiling at the voxel scale, significantly improving spatial resolution and analytical sensitivity. Compared to the complex multi-step computational process of traditional quantification algorithms, this method employs direct grayscale analysis, greatly simplifying the processing steps and effectively reducing cumulative errors. It is particularly suitable for vascular morphology studies, microcirculation analysis, and functional assessment of complex fibrous networks, which require extremely high precision. This high-precision, low-error characteristic provides a tool for in-depth exploration of the microstructure and functional relationship of the vascular system.

[0045] 2. This method avoids the necessary but easily disturbed vessel segmentation step in traditional vascular analysis. It directly calculates the orientation field of each voxel based on image grayscale information, modeling each voxel as a micro-vector with directional attributes. Local distortion is quantified by calculating the deviation of the micro-vector path from its spatial distance. Traditional methods typically rely on image segmentation and skeleton extraction, whose performance is easily affected by noise, contrast, and parameter settings. Especially in complex vascular or fibrous systems with dense branches and varied morphologies, problems such as breakage and misconnection often occur, seriously affecting the robustness and reproducibility of the analysis. In contrast, this method achieves direct voxel-level distortion mapping without segmentation or fitting, which not only significantly improves computational efficiency but also enhances the intuitiveness of interpretation and the biological relevance of the results. This provides more robust methodological support for quantitative analysis in fields such as vascular morphodynamics, pathological state assessment, and fibrous tissue engineering.

[0046] 3. In addition to providing quantitative indicators, this method also achieves multimodal visualization of tortuosity. By mapping the normalized tortuosity index to pseudocolor and overlaying it with the original structural image, users can intuitively identify high-curvature regions and morphologically heterogeneous areas of blood vessels or fibers while preserving the integrity of the image. This visualization strategy, which integrates structure and function, not only supports visual qualitative assessment but can also be combined with spatial statistical tools for regional heterogeneity analysis, potentially enhancing the depth of image data interpretation and its practicality for scientific research and clinical applications. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the process of the present invention;

[0048] Figure 2 This is a schematic diagram for calculating two-dimensional torsion.

[0049] Figure 3 This is a schematic diagram for calculating three-dimensional torsion.

[0050] Figure 4 Test diagrams for calculating the two-dimensional torsion of curves in different directions;

[0051] (a) is a color-coded map of the orientation of curves in different directions; (b) is a normalized TI color-coded map of the curve in (a); (c) is a histogram of the global normalized distortion in Figure (b); and (d) is a histogram of the local region. Region 1 corresponds to the region in the upper right dashed box in Figure (b), Region 2 corresponds to the region in the upper left dashed box in Figure (b), and Region 3 corresponds to the region in the lower left dashed box in Figure (b).

[0052] Figure 5 Test image showing the results of three-dimensional torsion calculation;

[0053] (a) is a simulation diagram of a three-dimensional double helix structure; (b) is a rose diagram of the corresponding three-dimensional spatial orientation angle; (c) is a normalized TI (Transformation Indicator) plot and histogram distribution of simulated helical structures with the same inner diameter but different lengths; (e) is a normalized TI plot and histogram distribution of simulated helical structures with the same length but different inner diameters; (d) is a statistical analysis chart of the tortuosity of three-dimensional helical fibers with a radius of 10 and lengths of 40, 80, and 120; (f) is a statistical analysis chart of the tortuosity of three-dimensional helical fibers with a length of 80 and radii of 4, 8, and 12. The sample size for each group is n = 6. * p < 0.05; *** p < 0.001. Detailed Implementation

[0054] To describe the present invention in more detail, the technical methods of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] This invention relates to an automated distortion calculation method based on image grayscale, the specific steps of which are as follows: Figure 1 As shown.

[0056] First, the pixel-level spatial orientation of the fiber image is calculated. Then, the path L and distance between the two ends of the fiber in the window are calculated from the pixel-level spatial orientation. Then calculate the distortion index TI = L / And the normalized distortion index is obtained Finally, based on the obtained normalized torsion index value, the image is encoded in pseudo-color to achieve a visual representation of the degree of fiber torsion without changing the original fiber structure.

[0057] Figure 2 and Figure 3 These are the calculation processes for the distortion of two-dimensional and three-dimensional images, respectively. For a two-dimensional fiber image, the pixel-level spatial orientation is first calculated. Taking each fiber pixel as the center of a window, the vectors connecting all two pixels symmetrical about the center pixel within the window are weighted and summed. The orientation of the resulting sum vector is the spatial orientation of the center pixel of the window. Calculating the spatial orientation of a two-dimensional image yields the angle between the infinitesimal vector at the fiber pixel and the x-axis. The spatial orientation of the three-dimensional image is calculated to obtain the angle between the projection of the infinitesimal vector at the fiber pixel point onto the xy plane and the x-axis. and the angle with the z-axis .

[0058] Next, the obtained pixel-level spatial orientation is used to calculate the path L between the two ends of the fiber in the window. The total path is the scalar sum of all infinitesimal vectors, represented in a two-dimensional image as...

[0059]

[0060] in This represents the infinitesimal vector of the q-th pixel. , These represent the component values ​​of the infinitesimal vector in the x and y directions, respectively. , where n represents the number of valid pixels in the selected neighborhood.

[0061] In a 3D image, the total path L is represented as...

[0062]

[0063] in This represents the infinitesimal vector of the q-th pixel. , , These represent the component values ​​of the infinitesimal vector in the x, y, and z directions, respectively. n represents the number of valid pixels in the selected neighborhood.

[0064] Then calculate the distance between the two ends of the fiber in the window. The formula for calculating distance in a two-dimensional image is expressed as follows:

[0065]

[0066] The distance formula in a 3D image is represented as

[0067]

[0068] Finally, calculate the distortion index. For a two-dimensional image, the distortion index can be expressed as...

[0069]

[0070] For a 3D image, the distortion index can be expressed as:

[0071]

[0072] Where q represents the infinitesimal vector of the q-th voxel within the neighborhood window, and n represents the number of valid pixels in the calculated neighborhood space. Since the path is always greater than the displacement, the value of TI is greater than 1; a larger TI indicates a more twisted fiber. Figure 2 and Figure 3 These are schematic diagrams illustrating the process of calculating distortion in two-dimensional and three-dimensional images, respectively.

[0073] Finally, to facilitate data visualization, TI is normalized to obtain normalized TI:

[0074]

[0075] After normalization The value range is [0,1], corresponding to the TI value range of [1,+∞], reflecting the change of twist degree from low to high.

[0076] Figure 4 A circular sinusoidal sawtooth fiber is shown. First, the orientation of the fiber pixels is calculated, resulting in the result shown in Figure (a), where the orientation of the pixels is the angle corresponding to the pixel color as shown in the legend. Then, the path L and distance between the two ends of the fiber in the window are calculated. Next, calculate the distortion index TI = L / After normalization, the pseudo-color encoding yields the normalized distortion result shown in Figure (b), where the normalized distortion index of a pixel is the value shown in the legend corresponding to the pixel color. Figure (b) shows that the distortion algorithm has stable calculation results for distortions in different directions, demonstrating robustness to direction; for steep and gentle sine peaks, the distortion algorithm can correspond to values ​​from high to low, demonstrating its ability to distinguish the degree of distortion.

[0077] Figure 5 Different 3D double helix structures were simulated, each simulation being 200×200×200 in size, containing 5 double helix structures. The diameter of each helix is ​​5 voxels, the helix axis is parallel to the z-axis, and it is rotated 4 times in the xy-plane. Angle. The simulation structure is shown in (a). The three-dimensional orientation distribution rose diagram of different three-dimensional double helix structures, calculated according to the orientation of the fiber voxel points, is shown in Figure (b). The angles are evenly distributed in all directions. The angles show a significant distribution around 60 and 120 degrees, corresponding to the two helices in the double helix, generally reflecting that the calculation of the three-dimensional orientation conforms to the correct trend. Next, the path L and distance at both ends of the fiber in the window are calculated. Next, calculate the distortion index TI = L / After normalization, the pseudo-color encoding yields the results shown in Figures (c) and (e), where the normalized distortion index of the voxel is the value shown in the legend corresponding to the pixel color. The calculation results of the algorithm are then discussed. As shown in Figure (c), keeping the inner diameter of the spiral structure at 10, and changing the spiral length to 40, 80, and 120, the corresponding normalized TI spectra and histogram distributions are calculated. It can be seen that axial stretching of the spiral structure causes the peak of the histogram to shift to the left, reducing the distortion. Statistical analysis of the repeated experiments on six groups of data is shown in Figure (d), where the three-dimensional distortion shows significant differences among different groups. As shown in Figure (e), keeping the spiral structure length at 80, and changing the inner diameter of the spiral to 4, 8, and 12, the corresponding normalized TI spectra and histogram distributions are calculated. It can be seen that radial stretching of the spiral structure also causes the peak of the histogram to shift to the left, and the trend of decreasing distortion is more obvious. Statistical analysis of the repeated experiments on six groups of data is shown in Figure (f), where the three-dimensional distortion shows significant differences among different groups.

[0078] The above description of the examples is provided to enable those skilled in the art to understand and apply the present invention. It will be apparent to those skilled in the art that various modifications can be made to the above examples, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. An automated distortion calculation method based on image grayscale, characterized in that... Includes the following steps: 1) Calculate the fiber pixel-level orientation based on the fluctuations in image grayscale; 2) The path L between the two ends of the fiber in the fiber pixel-level orientation calculation window obtained in step 1); 3) Calculate the distance between the two ends of the fiber in the fiber pixel-level orientation calculation window obtained in step 1). ; 4) The path L between the two ends of the fiber and the distance between the two ends of the fiber The ratio represents the distortion index TI = L / ; 5) Normalize the distortion index TI to obtain ; 6) Based on the obtained normalized distortion index Numerical pseudo-color encoding of images enables the visualization of fiber twisting degree without altering the original fiber structure.

2. The automated distortion calculation method based on image grayscale according to claim 1, characterized in that, In step 1), the fiber pixel-level orientation is calculated as follows: A window is set according to the image fiber diameter, and all two pixels within the window that are symmetrical about the window center are multiplied by a weighting factor as the first and last vectors. and Then add them all together, and the resulting vector orientation is the orientation of the center pixel of the window, where the weight factor is... Represented as: ； Where L is the length of the vector, and the weighting factor is... Represented as: ； in These are the values ​​of the first, last, and center pixels of the vector. It is the average value of three pixels.

3. The automated distortion calculation method based on image grayscale according to claim 1 or 2, characterized in that, The method for calculating the path L between the two ends of the fiber in step 2) is as follows: For a two-dimensional image, the infinitesimal vector at each fiber pixel point calculated in step 1) is: ； in , The angle between the vector and the x-axis. Let be the length of the infinitesimal vector element, which is approximated as 1. and Let x and y be the basis vectors in the x and y directions, respectively, and L be the scalar sum of all infinitesimal vectors, expressed as: ； in This represents the infinitesimal vector of the q-th pixel. and These represent the component values ​​of the infinitesimal vector in the x and y directions, respectively, and n represents the number of effective pixels in the selected neighborhood. For the 3D image, the infinitesimal vector at each voxel point calculated in step 1) is: ； in It is the angle between the infinitesimal vector and the z-axis. Let be the angle between the projection of the vector onto the xy-plane and the x-axis. The length of the infinitesimal vector at each voxel point, which can be considered as 1 in the calculation, is represented by L as: ； in This represents the infinitesimal vector of the q-th pixel. , , These represent the component values ​​of the infinitesimal vector in the x, y, and z directions, respectively, and n represents the number of effective pixels in the selected neighborhood.

4. The automated distortion calculation method based on image grayscale according to claim 3, characterized in that, In step 3), the distance between the two ends of the fiber in the calculation window is... The method is as follows: For a two-dimensional image, displacement Represented as: ； in This represents the vector of the q-th pixel in the window. and Let x and y represent the component values ​​of the infinitesimal vector in the x and y directions, respectively, and n represent the number of effective pixels within the window. Therefore, the distance... Represented as: ； For three-dimensional images, displacement Represented as: ； distance Represented as: ； in, , , These represent the component values ​​of the q-th infinitesimal vector in the x, y, and z directions, respectively, and n represents the number of valid pixels within the window.

Images