A method, apparatus, and storage medium for locating the center of circular marker points using a deep convolutional neural network.

Abstract

This invention discloses a method for center localization of circular markers using a deep convolutional neural network, along with an apparatus and storage medium for implementing the method. The method includes: acquiring image data of circular markers and constructing test samples; mapping the center of the circular markers using a trained center localization model CPosNet; calculating the true center of the markers based on scaling factors; and reconstructing the marker image. This invention provides a novel and feasible solution for center localization of circular markers under non-ideal conditions, and it exhibits stronger robustness compared to traditional methods. This method, based on an end-to-end model to directly map the marker center, also simplifies the center localization process, effectively reducing the introduction of external noise and lowering the complexity of circular marker center localization.

Description

Technical Field

[0001] This invention relates to a method, apparatus, and storage medium for locating the center of a circular marker point using a deep convolutional neural network, belonging to the field of visual measurement technology. Background Technology

[0002] Computer vision, with its advantages of being non-contact and fast, has become the most widely used method for digitizing physical objects. In this process, to obtain a complete 3D model of the object, multi-view measurements are typically required, and data alignment algorithms are used to transform data from different viewpoints to a global coordinate system. During data alignment, introducing artificial markers to establish strict correspondences is an effective way to reduce alignment errors.

[0003] Among all forms of artificial markers, circular markers are widely used due to their high positioning accuracy and ease of identification. Furthermore, because the markers are made of reflective materials with a high reflectivity, their reflectivity is hundreds or even thousands of times higher than that of ordinary white markers under the same light source.

[0004] For a long time, many researchers have conducted extensive research on locating the center of circular markers, proposing new methods in areas such as pattern design, image processing, and recognition criteria. However, in actual measurement environments, interference is diverse, and traditional image processing methods struggle to effectively address it, easily leading to the failure of marker center localization due to interference. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method, apparatus, and storage medium for locating the center of circular markers using a deep convolutional neural network. This provides a novel and feasible solution for locating the center of circular markers under non-ideal conditions, and is more robust than traditional methods. This method, which directly maps the center of markers based on an end-to-end model, can also simplify the marker centering process, thereby effectively reducing the introduction of external noise and lowering the complexity of locating the center of circular markers.

[0006] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0007] In a first aspect, the present invention provides a method for locating the center of a circular marker point using a deep convolutional neural network, comprising:

[0008] Obtain image data of circular marker points and construct test samples;

[0009] The center of the circular marker points is mapped using the trained center localization model CPosNet.

[0010] The true center of the marker points is calculated based on the scaling factor, and the marker image is reconstructed.

[0011] Furthermore, the method for constructing the center localization model CPosNet includes:

[0012] Extracting features of labeled points based on the HRNet backbone network;

[0013] After feature extraction is completed, a 2D convolution with a kernel size of 1x1 and a stride of 1 is applied to predict the feature map.

[0014] After outputting the feature map, the center of the marker point and the heat map are predicted by introducing the DSNT module proposed by Nibali et al.;

[0015] The predicted marker centers are constrained by MSE Loss respectively. Focal Loss to constrain the predicted heatmap Construct the loss function for the CPosNet model.

[0016] Furthermore, the specific calculation of the loss function for constructing the CPosNet model is as follows:

[0017]

[0018] In the formula, λ is the weighting coefficient, with a default value of 0.02; p and z represent the actual center of the marker point and the heat map, respectively, and the superscript symbol (^) indicates the corresponding predicted value.

[0019] Furthermore, the method for constructing the test sample includes:

[0020] Snake-based edge optimization technology, image stripe-based subpixel extraction technology, and RANSAC-based ellipse fitting algorithm are introduced to capture the center, major and minor axes, and tilt angle of clean marker points.

[0021] For a labeled image with multiple markers, calculate the minimum bounding box that encloses each marker and then crop it.

[0022] An index data table is set up to map the image name (name) of each cropped marker point to its corresponding center coordinate (center), thus forming an n x 2 index matrix, as shown below:

[0023]

[0024] Furthermore, the formula for calculating the minimum rectangular frame is as follows:

[0025] Ax 2 +Bxy+Cy 2 +F=0 (7)

[0026] A = a 2 sin 2 (-θ)+b 2 cos 2 (-θ) (8)

[0027] B = 2(a) 2 -b 2 sin(-θ)cos(-θ) (9)

[0028] C = a 2 cos 2 (-θ)+b 2 sin 2 (-θ) (10)

[0029] F = -a 2 b 2 (11)

[0030]

[0031] Left_Up = (center) x -abs(X),center y -abs(Y)) (13)

[0032] Right_Down=(center x +abs(X),center y +abs(Y)) (14)

[0033] Equation (7) is the calculation equation of the ellipse; equations (8)-(11) respectively represent the calculation of the coefficients A, B, C, and F in the ellipse equation, where a, b, and θ represent the major axis radius, minor axis radius, and inclination angle of the ellipse, respectively; equation (12) represents the width and height of the minimum rectangle; Left_Up and Right_Down in equations (13) and (14) respectively represent the upper left and lower right vertices of the minimum rectangle, (center x ,center y ) corresponds to the center of the ellipse, and abs is the absolute value of the variable.

[0034] Furthermore, in the test sample, 80% of the sample data is randomly selected for training the model, and the remaining 20% ​​is used to test the convergence of the model and whether it is overfitting.

[0035] Furthermore, the step of mapping the center of the circular marker point using the trained center localization model CPosNet includes:

[0036] The input image is scaled using bicubic interpolation to ensure that the size of the input image matches the network input requirements.

[0037] Record the corresponding scaling factor in the restoration index table;

[0038] The scaled image of the marker points is fed into the trained model to map the center of the marker points;

[0039] The restoration index table is shown below:

[0040]

[0041] Where Name is the name of the labeled image, name is the image name of a single labeled point, center is the corresponding center coordinate, left_up is the coordinate of the top left vertex during cropping, and scale is the image scaling factor. Since there are many labeled points in a labeled image, the value of m in the reconstruction matrix is ​​usually less than n.

[0042] Furthermore, the step of calculating the true marker center based on the scaling factor and reconstructing the marker image includes:

[0043] The mapping of the marker center is transformed to the real marker center according to the scaling factor in the restoration index table; then, the left_up recorded in the restoration index table is used to restore the individual markers back to the original marker image, thereby reconstructing the marker image and completing the positioning of the marker center of the entire marker image.

[0044] In a second aspect, the present invention provides a circular marker center localization device that incorporates a deep convolutional neural network, including a processor and a storage medium;

[0045] The storage medium is used to store instructions;

[0046] The processor is configured to operate according to the instructions to perform the steps of the circular marker center localization method incorporating a deep convolutional neural network as described in the first aspect.

[0047] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the circular marker center localization method combined with a deep convolutional neural network as described in the first aspect.

[0048] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0049] In existing technologies, the center localization of circular markers is mostly achieved based on contour edges. However, under non-ideal conditions, interference is diverse, and existing technologies struggle to accurately and explicitly model these interferences, significantly impacting the marker center localization task. Deep convolutional neural networks, with their powerful non-linear mapping capabilities, can automatically discover mapping rules from massive amounts of samples and filter out interference that is difficult to model explicitly. This provides a new solution for center localization of circular markers under non-ideal conditions. Therefore, this invention proposes a circular marker center localization method combining deep convolutional neural networks, offering a novel and feasible solution for center localization of circular markers under non-ideal conditions, and demonstrating greater robustness compared to traditional methods.

[0050] The method described in this invention directly maps the center of the marker point based on an end-to-end model, which can simplify the center positioning process of the marker point, thereby effectively reducing the introduction of external noise and reducing the complexity of center positioning of circular marker points. Attached Figure Description

[0051] Figure 1 This is a flowchart of a method for locating the center of a circular marker point by combining a deep convolutional neural network, provided in Embodiment 1 of the present invention;

[0052] Figure 2 This is the overall architecture diagram of the CPosNet model described in Example 1. Detailed Implementation

[0053] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0054] Example 1:

[0055] Figure 1 This is a flowchart illustrating a method for locating the center of a circular marker point using a deep convolutional neural network, as provided in this embodiment. This flowchart merely shows the logical order of the method described in this embodiment; however, in other possible embodiments of the invention, different methods may be used, provided there are no conflicts. Figure 1 Complete the steps shown or described in the order indicated.

[0056] The circular marker center localization method combined with a deep convolutional neural network provided in this embodiment can be applied to a terminal and can be executed by a circular marker center localization device combined with a deep convolutional neural network. This device can be implemented in software and / or hardware and can be integrated into the terminal, such as any smartphone, tablet, or computer device with communication capabilities. See also Figure 1 The method implemented in this way specifically includes the following steps:

[0057] 1. Construct the center-localization model CPosNet, whose overall architecture is as follows: Figure 2 As shown.

[0058] 1.1 The model is based on the HRNet backbone network to extract features of the labeled points.

[0059] 1.2 After feature extraction, a 2D convolution with a kernel size of 1x1 and a stride of 1 is applied to predict the feature map. Simultaneously, L2 regularization is added to constrain the network and prevent overfitting. The final output feature map size is [32, 128, 128, 1].

[0060] 1.3. After the output feature map, the DSNT module proposed by Nibali et al. is introduced to predict the center of the marker points and the heatmap. The corresponding calculation process is as follows:

[0061]

[0062]

[0063]

[0064] Where FM and HM represent the output feature map and heatmap, respectively. Additionally, in equation (2)... X represents the predicted center of the marker point. i,j and Y i,j Let X and Y be the matrices generated by equation (3), respectively, with symbols... This is represented as a dot product operation. For equation (3), M and N represent the width and height of the heatmap, respectively, and i and j represent the indices along the x-axis and y-axis of the two-dimensional image, respectively.

[0065] As shown in equation (1), for the input feature map, its corresponding heatmap (HM) is first mapped through the Softmax activation function. Then, the created X and Y matrices are multiplied by the heatmap to obtain the final marker center (in equation (2)). This center prediction method is not only computationally differentiable, but it can also compensate for the theoretical lower bound of error, which will help improve the positioning accuracy of the marker center.

[0066] 1.4 The predicted marker centers are constrained by MSE Loss respectively. Focal Loss to constrain the predicted heatmap The loss function for the CPosNet model is then constructed. The specific calculation is as follows:

[0067]

[0068] In the formula, λ is the weighting coefficient, with a default value of 0.02; p and z represent the actual center of the marker point and the heat map, respectively, while the superscript symbol (^) represents the corresponding predicted value.

[0069] and The specific loss calculation is as follows:

[0070]

[0071]

[0072] Where N represents the number of labeled point images. In addition, in equation (6), α and β are the hyperparameters for calculating the corresponding loss, with the default value of α being 2 and the default value of β being 4.

[0073] 2. Obtain image data of circular marker points and construct test samples.

[0074] 2.1. Snake-based edge optimization technology, image stripe-based subpixel extraction technology, and RANSAC-based ellipse fitting algorithm are introduced to capture the center, major and minor axes, and tilt angle of clean marker points.

[0075] The implementation steps are as follows:

[0076] Step 1: Extract the Canny edges of the input image;

[0077] Step 2: Obtain the minimum area bounding box for each side and filter out sides with a diagonal length less than 10 pixels or a major axis greater than 3 times the minor axis.

[0078] Step 3: Optimize edge positions using the Snake algorithm;

[0079] Step 4: Obtain sub-pixel edges based on image stripes;

[0080] Step 5: Fit the center using the RANSAC algorithm.

[0081] 2.2 Calculate and crop the minimum bounding box that encloses each marker point in a marked image with multiple marker points. The formula for calculating the minimum bounding box is as follows:

[0082] Ax2 +Bxy+Cy 2 +F=0 (7)

[0083] A = a 2 sin 2 (-θ)+b 2 cos 2 (-θ) (8)

[0084] B = 2(a) 2 -b 2 sin(-θ)cos(-θ) (9)

[0085] C = a 2 cos 2 (-θ)+b 2 sin 2 (-θ) (10)

[0086] F = -a 2 b 2 (11)

[0087]

[0088] Left_Up = (center) x -abs(X),center y -abs(Y)) (13)

[0089] Right_Down=(center x +abs(X),center y +abs(Y)) (14)

[0090] Equation (7) is the calculation equation of the ellipse; equations (8)-(11) respectively represent the calculation of the coefficients A, B, C, and F in the ellipse equation, where a, b, and θ represent the major axis radius, minor axis radius, and inclination angle of the ellipse, respectively; equation (12) represents the width and height of the minimum rectangle; Left_Up and Right_Down in equations (13) and (14) respectively represent the upper left and lower right vertices of the minimum rectangle, (center x ,center y ) corresponds to the center of the ellipse, and abs is the absolute value of the variable.

[0091] Given the center, major and minor axes, and tilt angle of the marker point, the extended margin (12) can be calculated using the general equation (7) of the ellipse and the calculation formulas (8)-(11) for each parameter. Then, the minimum rectangle is expanded outward from the center of the marker point to the x-axis and y-axis to obtain the upper left vertex (13) and lower right vertex (14) of the minimum rectangle, thus forming the minimum rectangle surrounding the marker point.

[0092] 2.3 After sample preparation, an index data table is set up to map the image name (name) of each cropped marker point to its corresponding center coordinate (center), thus forming an n x 2 index matrix:

[0093]

[0094] For example, when feeding data into the model, the images of marked points can be read in batches according to their names; during the training process, when calculating the descent gradient of the model, the corresponding center coordinates can be indexed and calculated by the image name of the marked point.

[0095] 2.4 Randomly select 80% of the sample data for training the model, and use the remaining 20% ​​to test the convergence of the model and whether it is overfitting.

[0096] 2.5. Set the batch size to 32, and the input image data format to [B,W,H,C]. Here, B represents the batch size, W and H represent the width and height of the image, respectively, and C represents the number of channels in the image. In the training of the CPosNet model, the input image size is [32,128,128,3].

[0097] 2.6. The Adam optimizer is used to optimize the model parameters, and the learning rate is set to 1e-4 until the loss no longer decreases within 10 consecutive epochs, thereby obtaining a set of optimal model parameters, i.e., a well-trained optimal model.

[0098] 3. Use the trained model to map the center of the marked points and calculate their true center based on the scaling factor to reconstruct the marked image.

[0099] 3.1 Before feeding image data into the network model, the input image is scaled using bicubic interpolation to ensure its size matches the network's input requirements. Then, the corresponding scaling factors are recorded in the restoration index table. The restoration index table used is shown below:

[0100]

[0101] The reconstruction index table is represented by an n x 5 reconstruction matrix. From left to right, the elements of the matrix represent the name of the labeled image, the image name of a single labeled point, the corresponding center coordinates, the coordinates of the top-left vertex during cropping, and the image scaling factor. Furthermore, since a labeled image contains many labeled points, the value of m in the reconstruction matrix is ​​usually less than n.

[0102] 3.2. The scaled image of the marker points is fed into the trained model to map the center of the marker points.

[0103] 3.3. The center of the mapped marker point is converted to the center of the real marker point according to the scaling factor in the restoration index table. Then, the left_up recorded in the restoration index table is used to restore the individual marker point back to the original marker image, thereby reconstructing the marker image and completing the positioning of the marker point center of the entire marker image.

[0104] Example 2:

[0105] This invention also provides a circular marker center localization device combining a deep convolutional neural network, including a processor and a storage medium;

[0106] The storage medium is used to store instructions;

[0107] The processor is configured to operate according to the instructions to execute the steps of the circular marker center localization method combined with a deep convolutional neural network as described in Embodiment 1.

[0108] Example 3:

[0109] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the circular marker center localization method combined with a deep convolutional neural network as described in Embodiment 1.

[0110] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0111] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0112] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0113] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0114] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A circular marker center positioning method combined with a deep convolutional neural network, characterized in that, The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. ； The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. respectively, to constrain the predicted marker point centers (MSE Loss) , to constrain the predicted heat maps (Focal Loss) , to construct the loss function of the CPosNet model. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network.

2. The method of claim 1, wherein, The application relates to a circular mark point center positioning method based on a deep convolutional neural network. (4) In the formula, is a weight coefficient, and the default value is 0.02; p and z respectively represent the real marker center and the heat map with a superscript symbol is represented as the corresponding predicted value.

3. The method of claim 1, wherein, The application relates to a circular mark point center positioning method based on a deep convolutional neural network. (7) (8) (9) (10) (11) (12) (13) (14) wherein, Equation (7) is a calculation equation of the ellipse; Equations (8) - (11) respectively represent calculations of coefficient terms A, B, C, F in the ellipse equation, wherein a, b, θ respectively represent a long axis radius, a short axis radius, and an inclination angle of the ellipse; Equation (12) represents a width and a height of the minimum rectangular frame; Left_Up and Right_Down in Equations (13) and (14) respectively represent a left upper vertex and a right lower vertex of the minimum rectangular frame, abs corresponds to a center of the ellipse, and abs is an absolute value of a variable.

4. The method of claim 1, wherein, The application relates to a circular mark point center positioning method based on a deep convolutional neural network.

5. The method of claim 1, wherein, The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. ； The application relates to a circular mark point center positioning method based on a deep convolutional neural network. 6.A circular marker center positioning device combined with a deep convolutional neural network, characterized in that, The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network.

7. A computer readable storage medium having stored thereon a computer program, characterized in that The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point center positioning method based on a deep convolutional neural network. The application relates to a circular mark point

Images