CN112686878A - Method and device for positioning key points of CBCT (cone-beam computed tomography) image of temporomandibular joint - Google Patents

Method and device for positioning key points of CBCT (cone-beam computed tomography) image of temporomandibular joint Download PDF

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CN112686878A
CN112686878A CN202110010454.7A CN202110010454A CN112686878A CN 112686878 A CN112686878 A CN 112686878A CN 202110010454 A CN202110010454 A CN 202110010454A CN 112686878 A CN112686878 A CN 112686878A
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cbct image
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temporomandibular joint
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李刚
李居朋
王颖慧
马若晗
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Peking University School of Stomatology
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Abstract

The invention provides a method and a device for positioning key points of a CBCT image of a temporomandibular joint, comprising the following steps: acquiring a CBCT image to be processed containing a temporomandibular joint; and positioning key points of the temporomandibular joint in the CBCT image to be processed by adopting the key point positioning model to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed. The method for positioning the key points of the temporomandibular joint CBCT image adopts the key point positioning model to automatically position the key points of the temporomandibular joint in the CBCT image to be processed, improves the positioning efficiency of the key points of the temporomandibular joint in the CBCT image to be processed, has high intelligent degree, and relieves the technical problems of low efficiency and poor intelligent degree of the existing method for manually marking the key point positions in the CBCT image.

Description

Method and device for positioning key points of CBCT (cone-beam computed tomography) image of temporomandibular joint
Technical Field
The invention relates to the technical field of medical image processing, in particular to a method and a device for positioning key points of a temporomandibular joint CBCT image.
Background
The temporomandibular joint is the only left and right linkage joint of the whole body and is one of the most complex joints of the human body. Consists of a temporal bone joint surface of a temporal bone, a condyle process of a mandible, a joint disc between the temporal bone joint surface and the condyle process, a joint capsule around a joint and joint ligaments.
Temporomandibular joint disease refers to the general term for a group of diseases involving the temporomandibular joint and/or the masticatory musculature, causing joint pain, rebound and restricted mouth opening. Cone Beam CT (Cone Beam CT, CBCT) has become a gold standard imaging mode for bone changes in clinical examination of temporomandibular joint diseases, and quantitative analysis of bone structures using CBCT images of temporomandibular joints is an important basis for disease diagnosis.
In order to realize quantitative analysis of the temporomandibular joint bone structure, key points in the CBCT image of the temporomandibular joint need to be located to facilitate subsequent quantitative analysis. In the prior art, when the key points in the CBCT image of the temporomandibular joint are positioned, doctors with abundant experience generally mark the key points in the image manually, and then coordinate information of the key points is obtained.
The method for manually marking the positions of the key points in the CBCT image has low efficiency and poor intelligence degree.
Disclosure of Invention
In view of the above, the present invention provides a method and an apparatus for locating key points in a CBCT image of a temporomandibular joint, so as to alleviate the technical problems of low efficiency and poor intelligence of the existing method for manually marking key point locations in a CBCT image.
In a first aspect, an embodiment of the present invention provides a method for positioning key points in a CBCT image of a temporomandibular joint, including:
acquiring a CBCT image to be processed containing a temporomandibular joint;
and positioning key points of the temporomandibular joint in the CBCT image to be processed by adopting a key point positioning model to obtain position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
Further, acquiring a CBCT image to be processed containing a temporomandibular joint, comprising:
acquiring an initial CBCT image to be processed containing a temporomandibular joint;
if the resolution of the initial CBCT image to be processed is not the preset resolution, adjusting the initial CBCT image to be processed to the preset resolution, and taking the adjusted initial CBCT image to be processed as the CBCT image to be processed;
and if the resolution of the initial CBCT image to be processed is the preset resolution, taking the initial CBCT image to be processed as the CBCT image to be processed.
Further, the method for locating the key points of the temporomandibular joint in the CBCT image to be processed by using the key point location model comprises the following steps:
and inputting the CBCT image to be processed into the key point positioning model, and outputting to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
Further, the keypoint localization model comprises: the device comprises a feature extraction module and a coordinate regression module.
Further, the method further comprises:
deploying an original keypoint localization model of the keypoint localization model;
obtaining a training sample set, wherein the training sample set comprises: the method comprises the steps that CBCT image samples of temporomandibular joints and position coordinates of key points corresponding to the CBCT image samples are obtained;
and carrying out supervision training on the original key point positioning model by using the training sample set to obtain the key point positioning model.
Further, performing supervised training on the original keypoint localization model by using the training sample set, including:
inputting the CBCT image samples in the training sample set into the original key point positioning model, and outputting to obtain the position coordinates of the key points;
substituting the position coordinates of the key points output by the original key point positioning model and the position coordinates of the corresponding key points in the training sample set into a preset loss function to obtain an error value;
and reversely propagating the error value to the original key point positioning model to perform iterative optimization on the original key point positioning model until a preset iteration number is reached, so as to obtain the key point positioning model.
Further, the position coordinates of the key points corresponding to the CBCT image samples are obtained by manual marking.
In a second aspect, an embodiment of the present invention further provides a device for locating key points in a CBCT image of a temporomandibular joint, including:
the acquisition unit is used for acquiring a CBCT image to be processed containing a temporomandibular joint;
and the positioning unit is used for positioning the key points of the temporomandibular joint in the CBCT image to be processed by adopting a key point positioning model to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
In a third aspect, an embodiment of the present invention provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the steps of the method according to any one of the above first aspects when executing the computer program.
In a fourth aspect, an embodiment of the present invention provides a computer-readable medium having non-volatile program code executable by a processor, where the program code causes the processor to perform the steps of the method according to any one of the first aspect.
In an embodiment of the present invention, a method for positioning key points in a CBCT image of a temporomandibular joint is provided, including: acquiring a CBCT image to be processed containing a temporomandibular joint; and then, positioning key points of the temporomandibular joint in the CBCT image to be processed by adopting a key point positioning model to obtain position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed. According to the locating method for the key points of the temporomandibular joint CBCT image, which is disclosed by the invention, the key points of the temporomandibular joint in the CBCT image to be processed are automatically located by adopting the key point locating model, so that the locating efficiency of the key points of the temporomandibular joint in the CBCT image to be processed is improved, the intelligent degree is high, and the technical problems of low efficiency and poor intelligent degree of the existing method for manually marking the key point positions in the CBCT image are solved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a schematic flowchart of a method for locating key points in a temporomandibular joint CBCT image according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method for obtaining a CBCT image to be processed including a temporomandibular joint according to an embodiment of the present invention;
FIG. 3 is a flowchart of a method for training a keypoint localization model according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a training of a keypoint localization model according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a heat map provided by an embodiment of the present invention;
FIG. 6 is a schematic representation of a CBCT image of a temporomandibular joint provided by an embodiment of the present invention;
FIG. 7 is a flowchart of a method for supervised training of an original keypoint localization model using a training sample set according to an embodiment of the present invention;
fig. 8 is a schematic diagram of a device for locating key points in a CBCT image of a temporomandibular joint according to an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the following embodiments, and it should be understood that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to facilitate understanding of the embodiment, a detailed description will be given to a method for locating key points in a CBCT image of a temporomandibular joint disclosed in the embodiment of the present invention.
The first embodiment is as follows:
to facilitate understanding of the embodiment, first, a detailed description is given to a method for positioning key points of a CBCT image of a temporomandibular joint disclosed in the embodiment of the present invention, referring to a schematic flow chart of the method for positioning key points of a CBCT image of a temporomandibular joint shown in fig. 1, which mainly includes the following steps:
step S102, obtaining a CBCT image to be processed containing a temporomandibular joint;
and S104, positioning the key points of the temporomandibular joint in the CBCT image to be processed by adopting the key point positioning model to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
The key point positioning model is obtained by training an original key point positioning model through a training sample in advance.
The key points refer to position points with medical anatomical significance, and generally comprise condylar joint vertexes, external auditory canal vertexes and the like.
In an embodiment of the present invention, a method for positioning key points in a CBCT image of a temporomandibular joint is provided, including: acquiring a CBCT image to be processed containing a temporomandibular joint; and then, positioning key points of the temporomandibular joint in the CBCT image to be processed by adopting a key point positioning model to obtain position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed. According to the locating method for the key points of the temporomandibular joint CBCT image, which is disclosed by the invention, the key points of the temporomandibular joint in the CBCT image to be processed are automatically located by adopting the key point locating model, so that the locating efficiency of the key points of the temporomandibular joint in the CBCT image to be processed is improved, the intelligent degree is high, and the technical problems of low efficiency and poor intelligent degree of the existing method for manually marking the key point positions in the CBCT image are solved.
The above description briefly introduces the method for locating key points in CBCT images of temporomandibular joint according to the present invention, and the details thereof are described in detail below.
In an alternative embodiment of the present invention, referring to fig. 2, the step S102 of acquiring a CBCT image to be processed including a temporomandibular joint specifically includes the following steps:
step S201, obtaining an initial CBCT image to be processed, which comprises a temporomandibular joint;
step S202, if the resolution of the initial CBCT image to be processed is not the preset resolution, adjusting the initial CBCT image to be processed to the preset resolution, and taking the adjusted initial CBCT image to be processed as the CBCT image to be processed;
step S203, if the resolution of the initial CBCT image to be processed is the preset resolution, the initial CBCT image to be processed is taken as the CBCT image to be processed.
The preset resolution is the resolution required by the key point positioning model when the key point positioning model performs key point positioning on the CBCT image, and the preset resolution is the resolution of the CBCT image sample during key point positioning model training.
In an optional embodiment of the present invention, in step S104, locating the keypoints of the temporomandibular joint in the CBCT image to be processed by using the keypoint locating model includes: and inputting the CBCT image to be processed into the key point positioning model, and outputting to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
The key point positioning model comprises: the device comprises a feature extraction module and a coordinate regression module, wherein the coordinate regression module is connected with the feature extraction module.
The above description describes the application process of the keypoint localization model, and the following description describes the training process of the keypoint localization model in detail.
In an alternative embodiment of the present invention, referring to fig. 3, the training process of the keypoint localization model specifically includes the following steps:
step S301, deploying an original key point positioning model of the key point positioning model;
the original key point positioning model is a convolutional neural network formed by two module networks of feature extraction and coordinate regression, the model structure is shown in fig. 4, wherein a network Net-1 of the feature extraction module adopts 3D U-Net, an original CBCT image is used as data input, a heat map corresponding to the position distribution of each key point is generated, and the heat map is represented as:
Figure BDA0002884075160000071
n-0, 1, …, N-1, M-0, 1, …, M-1, a schematic diagram of a heat map (taken on the sagittal plane for example) is shown in fig. 5. The network Net-2 of the coordinate regression module is a network for converting the heat map obtained by the feature extraction module into the position coordinates of the key points, that is, the position coordinates of the key points are generated, and the position coordinates of the key points are expressed as:
Figure BDA0002884075160000072
n is 0,1, …, N-1, M is 0,1, …, M-1, and the above transformation relationship can be expressed as:
Figure BDA0002884075160000073
i denotes CBCT images.
Step S302, a training sample set is obtained, wherein the training sample set comprises: the CBCT image sample of the temporomandibular joint and the position coordinates of key points corresponding to the CBCT image sample;
as shown in FIG. 6, a sample of a tomographic image of the temporomandibular joint in 3 directions (three directions, coronal, sagittal and transverse) is shown, where "+" indicates the location of the critical point of the condylar apex of the mandibular joint.
The position coordinates of the key points corresponding to the CBCT image samples are obtained by manual marking. The method is generally completed by a professional doctor, and the professional doctor firstly gives N key points L with anatomical significance in a CBCT image according to medical application requirementsnN-0, 1, …, N-1, CBCT image samples I of a specific number of temporomandibular joints were randomly selectedmM is 0,1, …, M-1 (defined herein as containing M instances of images). Then, a doctor who has many years of medical film reading experience selects N tools in the CBCT image sample according to personal experienceAnatomically significant Key Point, LnN is 0,1, …, N-1, recording all key points in the M, M is 0,1, …, M-1 cases of CBCT image samples in the training sample set
Figure BDA0002884075160000081
Position coordinates
Figure BDA0002884075160000082
N-0, 1, …, N-1, M-0, 1, …, M-1. Thus, a training sample set for training the temporomandibular joint CBCT image key point location model is obtained, which is expressed here as:
Figure BDA0002884075160000083
generally, the training sample set should contain a certain number of CBCT image samples, where M is recommended to be greater than or equal to 50, so that a better training result can be obtained.
Step S303, the original key point positioning model is supervised and trained by utilizing a training sample set to obtain a key point positioning model.
Referring to fig. 7, the method specifically includes the following steps:
s701, inputting a CBCT image sample in a training sample set into an original key point positioning model, and outputting to obtain the position coordinates of key points;
step S702, substituting the position coordinates of the key points output by the original key point positioning model and the position coordinates of the corresponding key points in the training sample set into a preset loss function to obtain an error value;
the predetermined loss function may be:
Figure BDA0002884075160000084
the first item of the key point position coordinates P restricts the original key point position model outputmPosition coordinates G of key points marked by doctorsm(i.e., the location coordinates of corresponding key points in the training sample set), i.e., the Euclidean distance between the corresponding key points in the training sample set
Figure BDA0002884075160000085
The second term constrains Net-1 output key point distribution probability heat chart H (I)m) So that it tends to predict the keypoint PmCentered at σtIs a Gaussian distribution of variances, i.e.
Figure BDA0002884075160000086
Wherein D (· | ·) represents a specific divergence calculation function, which can be selected as Jensen-Shannon divergence, the parameter λ in the loss function is used for balancing the proportional relation of the two parts of constraint functions, and the parameter setting can be properly adjusted according to the test result, wherein λ is more than 0 and less than 1.
And step S703, reversely propagating the error value to the original key point positioning model to perform iterative optimization on the original key point positioning model until reaching a preset iteration number, thereby obtaining the key point positioning model.
Specifically, defining the Euclidean distance between the position coordinates of the key points output by the original key point positioning model and the position coordinates of the corresponding key points in the training sample set as a training loss function, and performing iterative optimization by an RMSProp method to finally obtain the key point positioning model.
As can be seen from the above description, the present invention utilizes a CBCT image sample I containing M casesmM-0, 1, …, M-1 and their corresponding location coordinates of the physician-annotated keypoints
Figure BDA0002884075160000091
N is 0,1, …, N-1, M is 0,1, …, M-1, through the error gradient back propagation method to realize the training of the whole key point positioning model parameters, set up the suitable iteration number (the change situation of the whole loss function value after each training process is observed through the experimental method, if the value tends to be stable after a certain training number, the training number can be selected as the training iteration number of the whole model), after the whole training process is finished, the key point positioning model after parameter learning is obtained.
The method can realize the positioning of anatomical key points in the CBCT image of the temporomandibular joint and obtain the position coordinates of the key points in the 3D image so as to facilitate the quantitative measurement and application of the jaw joint morphology in clinical medicine.
Example two:
the embodiment of the invention also provides a device for positioning key points of a CBCT image of a temporomandibular joint, which is mainly used for executing the method for positioning key points of a CBCT image of a temporomandibular joint provided by the embodiment of the invention.
Fig. 8 is a schematic diagram of a locating device for key points of a CBCT image of a temporomandibular joint according to an embodiment of the present invention, and as shown in fig. 8, the locating device for key points of a CBCT image of a temporomandibular joint mainly includes: an acquisition unit 10 and a positioning unit 20, wherein:
the acquisition unit is used for acquiring a CBCT image to be processed containing a temporomandibular joint;
and the positioning unit is used for positioning the key points of the temporomandibular joint in the CBCT image to be processed by adopting the key point positioning model to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
In an embodiment of the present invention, a device for locating key points in a CBCT image of a temporomandibular joint is provided, including: acquiring a CBCT image to be processed containing a temporomandibular joint; and then, positioning key points of the temporomandibular joint in the CBCT image to be processed by adopting a key point positioning model to obtain position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed. According to the positioning device for the key points of the temporomandibular joint CBCT image, which is disclosed by the invention, the key points of the temporomandibular joint in the CBCT image to be processed are automatically positioned by adopting the key point positioning model, so that the positioning efficiency of the key points of the temporomandibular joint in the CBCT image to be processed is improved, the intelligent degree is high, and the technical problems of low efficiency and poor intelligent degree of the conventional method for manually marking the key point positions in the CBCT image are solved.
Optionally, the obtaining unit is further configured to: acquiring an initial CBCT image to be processed containing a temporomandibular joint; if the resolution of the initial CBCT image to be processed is not the preset resolution, adjusting the initial CBCT image to be processed to the preset resolution, and taking the adjusted initial CBCT image to be processed as the CBCT image to be processed; and if the resolution of the initial CBCT image to be processed is the preset resolution, taking the initial CBCT image to be processed as the CBCT image to be processed.
Optionally, the positioning unit is further configured to: and inputting the CBCT image to be processed into the key point positioning model, and outputting to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
Optionally, the keypoint localization model includes: the device comprises a feature extraction module and a coordinate regression module.
Optionally, the apparatus is further configured to: deploying an original key point positioning model of the key point positioning model; obtaining a training sample set, wherein the training sample set comprises: the CBCT image sample of the temporomandibular joint and the position coordinates of key points corresponding to the CBCT image sample; and carrying out supervision training on the original key point positioning model by utilizing a training sample set to obtain a key point positioning model.
Optionally, the apparatus is further configured to: inputting CBCT image samples in a training sample set into an original key point positioning model, and outputting to obtain position coordinates of key points; substituting the position coordinates of the key points output by the original key point positioning model and the position coordinates of the corresponding key points in the training sample set into a preset loss function to obtain an error value; and reversely propagating the error value to the original key point positioning model to carry out iterative optimization on the original key point positioning model until the preset iteration times are reached, thereby obtaining the key point positioning model.
Optionally, the apparatus is further configured to: the position coordinates of the key points corresponding to the CBCT image samples are manually marked.
The device provided by the embodiment of the present invention has the same implementation principle and technical effect as the method embodiments, and for the sake of brief description, reference may be made to the corresponding contents in the method embodiments without reference to the device embodiments.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the foregoing systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again. The locating device for the key points of the CBCT image of the temporomandibular joint provided by the embodiment of the application has the same technical characteristics as the locating method for the key points of the CBCT image of the temporomandibular joint provided by the embodiment, so that the same technical problems can be solved, and the same technical effects can be achieved.
In addition, in the description of the embodiments of the present invention, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. A method for positioning key points of a CBCT image of a temporomandibular joint is characterized by comprising the following steps:
acquiring a CBCT image to be processed containing a temporomandibular joint;
and positioning key points of the temporomandibular joint in the CBCT image to be processed by adopting a key point positioning model to obtain position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
2. The method of claim 1, wherein acquiring the CBCT image to be processed containing the temporomandibular joint comprises:
acquiring an initial CBCT image to be processed containing a temporomandibular joint;
if the resolution of the initial CBCT image to be processed is not the preset resolution, adjusting the initial CBCT image to be processed to the preset resolution, and taking the adjusted initial CBCT image to be processed as the CBCT image to be processed;
and if the resolution of the initial CBCT image to be processed is the preset resolution, taking the initial CBCT image to be processed as the CBCT image to be processed.
3. The method of claim 1, wherein locating the keypoints of the temporomandibular joint in the CBCT image to be processed using a keypoint localization model comprises:
and inputting the CBCT image to be processed into the key point positioning model, and outputting to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
4. The method of claim 1, wherein the keypoint localization model comprises: the device comprises a feature extraction module and a coordinate regression module.
5. The method of claim 1, further comprising:
deploying an original keypoint localization model of the keypoint localization model;
obtaining a training sample set, wherein the training sample set comprises: the method comprises the steps that CBCT image samples of temporomandibular joints and position coordinates of key points corresponding to the CBCT image samples are obtained;
and carrying out supervision training on the original key point positioning model by using the training sample set to obtain the key point positioning model.
6. The method of claim 5, wherein supervised training of the raw keypoint localization model using the training sample set comprises:
inputting the CBCT image samples in the training sample set into the original key point positioning model, and outputting to obtain the position coordinates of the key points;
substituting the position coordinates of the key points output by the original key point positioning model and the position coordinates of the corresponding key points in the training sample set into a preset loss function to obtain an error value;
and reversely propagating the error value to the original key point positioning model to perform iterative optimization on the original key point positioning model until a preset iteration number is reached, so as to obtain the key point positioning model.
7. The method of claim 5, wherein the location coordinates of the keypoints corresponding to the CBCT image samples are manually labeled.
8. A locating device for key points of CBCT images of temporomandibular joints is characterized by comprising:
the acquisition unit is used for acquiring a CBCT image to be processed containing a temporomandibular joint;
and the positioning unit is used for positioning the key points of the temporomandibular joint in the CBCT image to be processed by adopting a key point positioning model to obtain the position coordinates of the key points of the temporomandibular joint in the CBCT image to be processed.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the steps of the method of any of the preceding claims 1 to 7 are implemented when the computer program is executed by the processor.
10. A computer-readable medium having non-volatile program code executable by a processor, characterized in that the program code causes the processor to perform the steps of the method of any of the preceding claims 1 to 7.
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