Nanometer film material in-situ microscopic image characterization method based on deep learning

Abstract

The invention discloses a nano-film material in-situ microscopic image characterization method based on deep learning. The method comprises the following steps: acquiring growth video data of a nano-film material under an in-situ microscopic platform in real time and synchronously performing picture correction processing; a swing-TRANSEM neural network is used to load a pre-training weight, the corrected growth video image is identified, and an identification frame is generated; determining a crystal domain early growth frame position according to the size of the identification frame, and obtaining center position information of crystal domain growth; using an improved image segmentation algorithm to extract discretized edge information of a single crystal domain; calculating the gradient of each edge representative point in the coordinate axis direction by combining the central position information of the crystal domain growth and the edge information of the crystal domain discretization, and obtaining the growth speed information in each direction; drawing a growth heat map, and establishing a growth model. According to the method, the efficiency and the accuracy of growth analysis of the nano-film material can be remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of nano-thin film material growth tracking, and specifically relates to an in-situ microscopic image characterization method of nano-thin film materials based on deep learning. Background Art

[0002] Nanofilm materials have attracted widespread attention due to their unique size effects and interface properties. Such materials, such as indium tin oxide (ITO) and zinc sulfide (ZnS) films, exhibit excellent electrical, optical and mechanical properties. For example, ITO films have important applications in touch screens and optoelectronic devices due to their high transparency and good conductivity; while ZnS films have excellent performance in optical coatings and display technologies due to their excellent optical properties and good chemical stability. As research on nanofilm materials has gradually deepened, understanding their growth mechanisms and interface properties has become particularly important for optimizing their performance and expanding their application areas.

[0003] However, traditional microscopy techniques face many challenges in in situ monitoring of the growth of these materials. For example, the resolution limitations of the microscope and image distortion problems make it difficult to accurately capture complex growth morphologies. Although existing microscopy techniques can provide certain structural information, in the face of microstructural changes in nanofilm materials under different growth conditions, traditional methods are often insufficient in positioning accuracy and data analysis. Therefore, developing an advanced method that can accurately and real-time characterize the growth process of nanofilm materials is crucial to optimizing material properties and understanding their growth mechanisms. Summary of the invention

[0004] Technical problem to be solved: In order to solve the technical problems that the resolution of optical microscope imaging is low and the reaction temperature will cause different degrees of offset and distortion of the field of view, the present invention provides an in-situ microscopic image characterization method of nano film materials based on deep learning. The growth of nano film materials is observed in real time using an optical microscope, and the swin-TRANSEM algorithm based on deep learning is used to perform statistical analysis to help guide the controllable growth of nano film materials, which can significantly improve the efficiency and accuracy of nano film material growth analysis.

[0005] Technical solution:

[0006] A method for characterizing an in-situ microscopic image of a nano-thin film material based on deep learning, the method comprising the following steps:

[0007] S1, real-time acquisition of the growth video data of nano-thin film materials under the in-situ microscopic platform and simultaneous image correction processing;

[0008] S2, using the swin-TRANSEM neural network to load the pre-trained weights, recognize the corrected growth video image, and generate a recognition frame;

[0009] S3, determining the early growth frame position of the crystal domain according to the size of the identification frame and obtaining the center position information of the crystal domain growth;

[0010] S4, using an improved image segmentation algorithm, discretize the edge information into N points according to the angle of the growth center, and extract the discretized edge information of a single crystal domain;

[0011] S5, combining the center position information of the crystal domain growth and the edge information of the crystal domain discretization, calculating the gradient of each edge representative point in the coordinate axis direction and taking the modulus to obtain the growth rate information in each direction;

[0012] S6, draw a growth heat map and establish a growth model.

[0013] Step S1 further comprises:

[0014] Inert impurities are introduced into the central part of the reaction substrate and lowered to be firmly placed in the reaction furnace;

[0015] Fine-tune the lens so that the inert impurities used as the calibration reference are not at the edge of the field of view, and define the area O that deserves attention during calibration;

[0016] The reaction system is heated up and real-time image recording is started, and the image is binarized;

[0017] In the real-time image after binarization, edge detection is performed on area O to find multiple connected areas, and the multiple connected areas are sorted from large to small according to their areas. During the growth process, the center coordinates Oti and area Sti of each connected area Bi at time t are recorded, and some connected areas are filtered out with (Sti+1-Sti) / Sti>5% as the judgment condition. The lens offset matrix Mdrift is calculated based on the average position of the center points of the remaining connected areas that meet the conditions.

[0018] Furthermore, in step S2, 2, 2, 6 and 2 Swin-Transformer modules are hierarchically used to replace the convolutional layers of the original backbone module of YOLOv8 for feature extraction, and shape-IoU is introduced as the regression loss function to optimize the detection head, and a swin-TRANSEM neural network is constructed. The swin-TRANSEM neural network includes a backbone module, a feature pyramid and a detection head.

[0019] Furthermore, the backbone module splits the input image of shape [H, W, 3], i.e., the three-channel RGB image with height H and width W, into non-overlapping sub-images with height and width P and shape [N0, P, P, 3], Flatten into a token sequence of [N0, P2×3];

[0020] The token sequence is projected into a new token tensor of shape [N1, C] through a linear layer, where N1 = N0, and then input into the Swin-Transformer module for two feature extractions. The output shape remains unchanged, completing the first-level feature extraction.

[0021] By merging adjacent 2×2 subgraphs to form a new subgraph, the token tensor becomes [N2, 2C],

[0022] After 6 and 2 Swin-Transformer module feature extractions respectively, the token tensor becomes [N3, 4C] and [N4, 8C], N0, N2, N3 and N4 are the number of subgraphs in each stage.

[0023] The detection head introduces shape-IoU as the regression loss function, and optimizes the detection accuracy of the early crystal domain period by considering the influence of the shape and angle of the bounding box itself on the detection accuracy. The specific calculation method is:

[0024] L shape-IoU =1-IoU+distance shape +0.5×Ω shape

[0025] in, θ=4,x c and c is the center coordinate of the prediction box, and the subscript represents the center point. and is the center coordinate of the ground-truth box; hh and ww are weights used to adjust the width and height differences; ω t It measures the shape difference in width or height, θ is the adjustment parameter of the shape difference; IoU is the intersection over union ratio, that is, the ratio of the intersection area to the union area between the detection box and the real box (IoU = S 重叠部分 / S 合并面积 ).

[0026] Step S4 further comprises the following steps:

[0027] For a single crystal domain, track its growth in n frames and select the domains with a relative center angle interval of θ * m points as representative points, θ *×m=360±2°, and obtain the position matrix A of all edge representative points; where θ * ∝(ρ×α), ρ = total number of pixels in the frame / maximum number of crystal domains that may appear on average, α is the accuracy requirement.

[0028] Step S5 further comprises the following steps:

[0029] The second-order difference method is used to calculate the gradient of the transformation of points in each direction on the x-axis and y-axis. The specific calculation formula is:

[0030]

[0031] For the boundary, the second-order single-sided difference method is adopted:

[0032]

[0033] f is x or y, used to calculate the two axial gradients, t represents time, and the subscripts represent the time scale (starting from 0).

[0034] Calculate the gradient modulus in the x and y directions at each angle to obtain a growth rate matrix V of shape [n, m-1], where the value of the i-th row and j-th column represents the crystal domain at (j×θ * ) The growth rate at the angle;

[0035] The filtering operation is performed along the time dimension according to the specific conditions of the material growth and the data acquisition equipment.

[0036] Step S6 further comprises the following steps:

[0037] Draw a pixelated 2D growth heat map, draw a continuous 3D growth heat map after linear interpolation, and establish a growth model.

[0038] Furthermore, the process of drawing a pixelated 2D growth heat map includes the following steps:

[0039] Reconstruct the coordinate system with the growth center as the coordinate origin and grid the entire frame with the origin as the center of a square, with a grid side length of L. At the same time, transform the position matrix A to the new coordinate system to obtain a new position matrix A';

[0040] Traverse all points in the position matrix A' and determine the grid to which they belong. At the same time, assign the data in the position matrix V to the corresponding grid, and take the average of the speed values ​​in each grid as the representative value of the grid;

[0041] The color bar is drawn according to the distribution relationship of the representative values, and the holes are filled by box filtering.

[0042] Furthermore, the process of drawing a continuous 3D growth heat map includes the following steps:

[0043] Select some frames from n frames, use their time series as the Z axis, relocate the edge feature points in the XY plane according to the information in the position matrix A, smooth the discretized edge information and restore it to a continuous edge, and perform linear interpolation on the velocity matrix V as well;

[0044] Draw the 3D part interactive growth rate heat map according to the correspondence between edge position-edge growth speed-color bar.

[0045] Beneficial effects:

[0046] First, the in-situ microscopic image characterization method of nano-thin film materials based on deep learning of the present invention can accurately capture the growth dynamics process information of nano-thin film materials, which is convenient for combining microscopic molecular theory to better explain the material growth mechanism; at the same time, this method can solve the problem that traditional methods will misjudge the edges and have difficulty in handling drift errors.

[0047] Second, the in-situ microscopic image characterization method of nanofilm materials based on deep learning not only helps to optimize the growth conditions of nanofilm materials, but also provides a deep understanding of their growth mechanism and its relationship with physical and chemical properties. In addition, advances in computer vision technology have made high-throughput data processing and large-scale sample analysis possible, providing a new way to quickly screen for optimal growth conditions and customize nanofilm materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flowchart of the in-situ microscopic image characterization method of nano-thin film materials based on deep learning of the present invention;

[0049] Figure 2 This is a diagram of the swin-TRANSEM algorithm architecture in the present invention;

[0050] Figure 3 A schematic diagram of a smoothed edge image and an edge pixelated 2-D heat map drawn according to an embodiment of the present invention;

[0051] Figure 4 A schematic diagram of a 3-D heat map of continuity at different viewing angles drawn for an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following examples will enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0053] The present invention discloses an in-situ microscopic image characterization method for nano-thin film materials based on deep learning. Taking MoS2 as an example, the in-situ microscopic image characterization method for nano-thin film materials comprises the following steps:

[0054] S1, real-time acquisition of MoS2 growth video data under the in-situ microscopy platform and simultaneous image correction processing;

[0055] S2, using the swin-TRANSEM neural network to load the pre-trained weights, recognize the corrected growth video image, and generate a recognition frame;

[0056] S3, determining the early growth frame position of the crystal domain according to the size of the identification frame and obtaining the center position information of the crystal domain growth;

[0057] S4, using an improved image segmentation algorithm, discretize the edge information into N points according to the angle of the growth center, and extract the discretized edge information of a single crystal domain;

[0058] S5, combining the center position information of the crystal domain growth and the edge information of the crystal domain discretization, calculating the gradient of each edge representative point in the coordinate axis direction and taking the modulus to obtain the growth rate information in each direction;

[0059] S6, draw a growth heat map and establish a growth model.

[0060] The present invention is based on an improved image segmentation and detection algorithm, and integrates machine vision technology to achieve higher throughput and accuracy of automatic positioning and analysis of MoS2 crystal domain growth dynamics. The method first collects MoS2 growth video data through an in-situ optical microscopy imaging platform; solves the camera drift error during the shooting process through an impurity point auxiliary correction method; uses the swin-TRANSEM algorithm to locate the crystal domain, obtain the center point and count the number; then uses the U-net improved by this algorithm to obtain the shape (edge) information of the MoS2 crystal domain; finally, integrates the center point coordinate information and edge information to establish a MoS2 growth rate analysis heat map with morphology reconstruction.

[0061] See also Figure 1 The MoS2 in-situ microscopic image characterization method specifically comprises the following steps:

[0062] S1. Place the reaction substrate containing calibration impurities into the reaction system, obtain the growth effect in real time through a microscope and correct the lens shake. The specific steps are as follows:

[0063] S11, introducing inert impurities into the central part of the reaction substrate and lowering it into the reaction furnace to place it firmly;

[0064] S12, fine-tune the lens to ensure that the inert impurities that can also serve as the calibration reference are at the non-edge of the field of view to prevent the jitter from exceeding the field of view and to define a noteworthy area O during calibration (considering that the size and distribution of the calibration impurities are relatively random, defining a noteworthy area can eliminate a lot of interference and thus improve accuracy);

[0065] S13, start heating the reaction system and start real-time image recording, and binarize the image at the same time, with the threshold set to 125. Perform edge detection on noteworthy areas in the binarized real-time image to find the existing connected areas B1, B2... and sort them by area from large to small. During the growth process, record the center coordinates Oti and area Sti of area Bi at time t. According to the judgment condition of (Sti+1-Sti) / Sti>5%, some connected areas that do not meet the conditions are no longer considered, and finally the lens offset matrix M is calculated from the average position of the center points of the remaining connected areas that meet the conditions. drift .

[0066] S2. Each frame is transmitted in real time to a deep learning network based on the swin-TRANSEM neural network that has been loaded with pre-trained weights for recognition.

[0067] See also Figure 2 , the swin-TRANSEM neural network refers to the YOLO architecture, which is mainly composed of three parts: backbone, feature pyramid, and detection head:

[0068] The backbone uses the Swin-Transformer module instead of traditional convolution for feature extraction, and improves efficiency through the window attention mechanism. First, the input RGB image ([H, W, 3]) is split into several non-overlapping sub-images of size P×P Flatten into a token sequence of [N0, P2×3]. Project the token sequence to a new token tensor of shape [N1, C] (N1=N0) through a linear layer, input into the Swin-Transformer module for two feature extractions, and the output shape remains unchanged, completing the first level of feature extraction. In the second stage, adjacent 2×2 subgraphs are merged to form a new subgraph, and the token tensor becomes [N2, 2C] The third and fourth stages respectively extract features through 6 and 2 Swin-Transformer modules, and the token tensor becomes [N3, 4C] and [N4, 8C] Among them, N0, N2, N3 and N4 are the number of sub-images in each stage. The four stages realize the hierarchical extraction of image features while maintaining the computational efficiency;

[0069] The feature pyramid part adopts the design of YOLOv8, using C2f, convolution and other modules to complete the feature hierarchy;

[0070] Considering that the early crystal domains are small objects compared to the frame size, shape-IoU is introduced as the regression loss function in the detection head. The detection accuracy of the early crystal domains is optimized by considering the influence of the shape and angle of the bounding box itself on the detection accuracy. The specific calculation method is: L shape-Io =1-IoU+distance shape +0.5×Ω shape ,in θ=4,x c and c is the center coordinate of the prediction box, and is the center coordinate of the ground-truth box. hh and ww are weights used to adjust the width and height differences; θ=4,ω t It measures the shape difference in width or height, and θ is the adjustment parameter for the shape difference.

[0071] S3, store the position of the first detection frame (if the overlap between detection frames does not exceed 5%, it is considered a new detection frame) coordinate center matrix M center (M center =M0+M drift , M0 is the directly obtained detection frame center) and the detection frame size information matrix M size , the matrix M center 、M size Corresponding dimensions correspond to corresponding position data.

[0072] S4, through M center 、M size Locate each detection box, segment each detection box using the pre-trained U-net segmentation network and obtain the edge information of the crystal domain.

[0073] Specifically, the segmentation algorithm is used to obtain the edge information of the crystal domain in the identification frame and the edge information is processed in combination with the discretization of the corresponding center coordinates. For a single crystal domain, its growth is tracked in n frames, and m points (θ×m=360±2°) with an angle interval of θ relative to the center are selected as representative points, and finally the position matrix A of all edge representative points is obtained, where θ∝(ρ×α) (ρ=total number of pixels in the frame / maximum number of crystal domains that may appear on average, α is the accuracy requirement).

[0074] S5. Investigate the growth performance of a single crystal domain in n frames (in the example of the present invention, n=59, the starting frame is the 990th frame, the ending frame is the 1860th frame, and the interval is 15 frames). Traverse all frames, from M centerThe center point coordinates are obtained from S4, and the total m (m = 720) directions of the crystal domain in the i-th frame with an angle interval of θ (θ = 0.5°) are obtained, and the edge coordinates Ai corresponding to each direction are stored, and Ai' (Ai' = Ai + Mdrift) are corrected. Thus, the position matrix A (A = [A0, A1, .., A58], the shape is [59, 720, 2]) is obtained.

[0075] The second-order difference method is used to calculate the gradient of the transformation of points in each direction on the x and y axes. The specific calculation formula is:

[0076]

[0077] For the boundary, the second-order single-sided difference method is adopted:

[0078] f=x,y

[0079] Then, the modulus of the gradient in the x and y directions at each angle is calculated to obtain a growth rate matrix V of the shape [n, m-1]. The value of the i-th row and j-th column represents the growth rate of the crystal domain at the (j×θ) angle in the selected i-th frame. After that, a certain degree of filtering operation can be performed according to the time dimension according to the specific conditions of the material growth and the data acquisition equipment to eliminate or reduce the interference of certain abnormal values. In the example of the present invention, the shape of V is [58,720], and Gaussian filtering is used to filter the second dimension of the matrix V.

[0080] S6. There are two ways to draw the growth heat map, as follows:

[0081] 1. Divide the image into pixel grids with a side length of 2.2, and select any one of them as the center to reconstruct the coordinate system. Take the origin of the coordinate as the growth center, calculate the grid corresponding to the edge point in E and assign the corresponding value in the growth rate matrix V to the corresponding pixel. If multiple points belong to the same pixel, take the average as the representative value of the grid, and draw the color bar according to the representative value. For example, when n>4, m>180, A' 13 and A' 23 In the same grid, the ). Draw the color bar according to the distribution relationship of the representative values. Some holes are filled by box filtering. Some holes are filled by box filtering (kernel is 3×3), and the final result is a 2-D pixelated heat map. Figure 3 shown.

[0082] 2. Select some frames in n frames, use their time series as the Z axis, relocate the edge feature points in the XY plane according to the information in the position matrix A, smooth the discretized edge information and restore it to a continuous edge, and perform linear interpolation on the velocity matrix V. Draw a 3D partial interactive growth rate heat map according to the correspondence between edge position-edge growth velocity-color bar. Allow interactive observation of the growth of the crystal domain from different angles, and manually change the observation direction to obtain more time-related growth information, as shown below: Figure 4 shown.

[0083] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for characterizing in-situ microscopic images of nano-thin film materials based on deep learning, characterized in that: The MoS2 in-situ microscopic image characterization method comprises the following steps: S1, real-time acquisition of the growth video data of nano-thin film materials under the in-situ microscopic platform and simultaneous image correction processing; S2, using the swin-TRANSEM neural network to load the pre-trained weights, recognize the corrected growth video image, and generate a recognition frame; S3, determining the early growth frame position of the crystal domain according to the size of the identification frame and obtaining the center position information of the crystal domain growth; S4, using an improved image segmentation algorithm, discretize the edge information into N points according to the angle of the growth center, and extract the discretized edge information of a single crystal domain; S5, combining the center position information of the crystal domain growth and the edge information of the crystal domain discretization, calculating the gradient of each edge representative point in the coordinate axis direction and taking the modulus to obtain the growth rate information in each direction; S6, draw a growth heat map and establish a growth model.

2. The in-situ microscopic image characterization method of nano-thin film materials based on deep learning according to claim 1, characterized in that: Step S1 further comprises: Inert impurities are introduced into the central part of the reaction substrate and lowered to be firmly placed in the reaction furnace; Fine-tune the lens so that the inert impurities used as the calibration reference are not at the edge of the field of view, and define the area O that deserves attention during calibration; The reaction system is heated up and real-time image recording is started, and the image is binarized; In the real-time image after binarization, edge detection is performed on area O to find multiple connected areas, and the multiple connected areas are sorted from large to small according to their areas. During the growth process, the center coordinates Oti and area Sti of each connected area Bi at time t are recorded, and some connected areas are filtered out with (Sti+1-Sti) / Sti>5% as the judgment condition. The lens offset matrix Mdrift is calculated based on the average position of the center points of the remaining connected areas that meet the conditions.

3. The MoS2 in-situ microscopic image characterization method based on deep learning according to claim 1, characterized in that: In step S2, 2, 2, 6 and 2 Swin-Transformer modules are hierarchically used to replace the convolutional layers of the original backbone module of YOLOv8 for feature extraction, and shape-IoU is introduced as the regression loss function to optimize the detection head to construct a swin-TRANSEM neural network, which includes a backbone module, a feature pyramid and a detection head.

4. The MoS2 in-situ microscopic image characterization method based on deep learning according to claim 3 is characterized in that: The backbone module splits the input three-channel RGB image with a height of H and a width of W into non-overlapping sub-images with a height and a width of P and a shape of [N0, P, P, 3]. Flatten into a token sequence of [N0, P2×3]; The token sequence is projected into a new token tensor of shape [N1, C] through a linear layer, where N1 = N0, and then input into the Swin-Transformer module for two feature extractions. The output shape remains unchanged, completing the first-level feature extraction. By merging adjacent 2×2 subgraphs to form a new subgraph, the token tensor becomes [N2, 2C], After 6 and 2 Swin-Transformer module feature extractions respectively, the token tensor becomes [N3, 4C] and [N4, 8C], N0, N2, N3 and N4 are the number of subgraphs in each stage.

5. The MoS2 in-situ microscopic image characterization method based on deep learning according to claim 3 is characterized in that: The detection head introduces shape-IoU as the regression loss function, and optimizes the detection accuracy of the early crystal domain period by considering the influence of the shape and angle of the bounding box itself on the detection accuracy. The specific calculation method is: L shape-IoU =1-IoU+distance shape +0.5×Ω shape in, θ=4;x c and c is the center coordinate of the prediction box, and the subscript indicates the center point coordinate. and is the center coordinate of the ground-truth box; hh and ww are weights used to adjust the width and height differences; ω t It measures the shape difference in width or height, θ is the adjustment parameter of the shape difference; IoU is the intersection over union ratio, that is, the ratio of the intersection area to the union area between the detection box and the true box.

6. The in-situ microscopic image characterization method of nano-thin film materials based on deep learning according to claim 1, characterized in that: Step S4 further comprises the following steps: For a single crystal domain, track its growth in n frames and select the domains with a relative center angle interval of θ * m points as representative points, θ * ×m=360±2°, and obtain the position matrix A of all edge representative points; where θ * ∝(ρ×α), ρ = total number of pixels in the frame / maximum number of crystal domains that may appear on average, α is the accuracy requirement.

7. The MoS2 in-situ microscopic image characterization method based on deep learning according to claim 1, characterized in that: Step S5 further comprises the following steps: The second-order difference method is used to calculate the gradient of the transformation of points in each direction on the x-axis and y-axis. The specific calculation formula is: For the boundary, the second-order single-sided difference method is adopted: Calculate the gradient modulus in the x and y directions at each angle to obtain a growth rate matrix V of shape [n, m-1], where the value of the i-th row and j-th column represents the crystal domain at (j×θ * ) angle; f is x or y, used to calculate the two axial gradients, t represents time, and the subscripts represent the time scale; The filtering operation is performed along the time dimension according to the specific conditions of the material growth and the data acquisition equipment.

8. The in-situ microscopic image characterization method of nano-thin film materials based on deep learning according to claim 1, characterized in that: Step S6 further comprises the following steps: Draw a pixelated 2D growth heat map, draw a continuous 3D growth heat map after linear interpolation, and establish a growth model.

9. The in-situ microscopic image characterization method of nano-thin film materials based on deep learning according to claim 8, characterized in that: The process of drawing a pixelated 2D growth heatmap consists of the following steps: Reconstruct the coordinate system with the growth center as the coordinate origin and grid the entire frame with the origin as the center of a square, with a grid side length of L. At the same time, transform the position matrix A to the new coordinate system to obtain a new position matrix A'; Traverse all points in the position matrix A' and determine the grid to which they belong. At the same time, assign the data in the position matrix V to the corresponding grid, and take the average of the speed values ​​in each grid as the representative value of the grid; The color bar is drawn according to the distribution relationship of the representative values, and the holes are filled by box filtering.

10. The in-situ microscopic image characterization method of nano-thin film materials based on deep learning according to claim 8, characterized in that: The process of drawing a continuous 3D growth heat map includes the following steps: Select some frames from n frames, use their time series as the Z axis, relocate the edge feature points in the XY plane according to the information in the position matrix A, smooth the discretized edge information and restore it to a continuous edge, and perform linear interpolation on the velocity matrix V as well; Draw the 3D part interactive growth rate heat map according to the correspondence between edge position-edge growth speed-color bar.

Images