Digital form denture prosthesis generation method based on artificial intelligence technology

Abstract

The invention relates to an artificial intelligence technology-based digital form false tooth restoration generation method, which comprises the following steps of: performing 3D scanning on the oral cavity of a patient to obtain a three-dimensional digital impression of upper and lower jaw teeth, appointing the position of a preparation body, performing local cutting by taking the preparation body as a center, and obtaining a three-dimensional digital impression of the upper and lower jaw teeth; the cut area comprises a preparation body, adjacent teeth and three-dimensional impression information of jaw teeth; inputting the cut impression information into a deep neural network model to generate a restoration digital form matched with the preparation body; in the model training process, impression information of a cut part is used as model input, and a three-dimensional digital form of a repaired false tooth prosthesis is used as a learning target; and measuring the difference between the output of the network model and impression information by defining an energy function. Compared with the prior art, the method has the advantages that the digital denture prosthesis with highly accurate model natural tooth morphological characteristics can be designed and produced, and the efficiency and the accuracy are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of tooth loss restoration, and particularly to a method for generating a digital morphological denture prosthesis based on artificial intelligence technology. Background Art

[0002] Dental diseases or accidental collisions may both lead to tooth loss. For fixed and removable dentures, dental implants have gradually become a widely used method for tooth loss restoration. During the process of dental implants, the design of the shape and appearance of the denture is an important factor affecting the patient experience. The design of the denture needs to consider the spacing from adjacent teeth on the left and right, the occlusion relationship between the upper and lower teeth, and the physiological texture of the occlusal surface, etc., which is highly professional and difficult.

[0003] Existing computer-aided design and manufacturing CAD / CAM technologies, such as the invention with the authorized announcement number CN109350277B, disclose a method for digitally and precisely manufacturing dental prostheses. Using each patient's own dental arch as an articulator, through communication and inspection between the clinician and the patient, and taking the clinically fine-tuned digitally manufactured die crown as a medium, the correct geometric shape, color, marginal adaptation, proximal contact relationship, occlusion relationship, and the shape required for early gingival healing of the prosthesis are established to achieve temporary restoration - the functions of protection, maintenance, and stability; the clinician then performs a second precise scan on the die crown with the adjusted shape, occlusion, and proximal contact relationship, and fuses the second scan data with the previously designed digital wax pattern data to obtain a precise digital design of the dental prosthesis, and precisely replicate a bionic zirconia denture to achieve zero-adjustment and precise restoration at the clinician's end.

[0004] This solution greatly improves the finished product quality of the denture, but still requires a large amount of labor time from professional dentists during the process, and also has disadvantages such as complicated operation, high cost of patient discomfort, etc.

[0005] The method based on artificial neural network, such as the invention with the authorized announcement number CN113520641B, discloses a method for constructing a prosthesis, in which the dental condition is measured by means of a dental camera and a 3D model of the dental condition is generated. In this case, a computer-aided detection algorithm is applied to the 3D model of the dental condition, and the prosthesis type and / or at least the tooth number and / or position of the prosthesis to be inserted are automatically determined.

[0006] This solution is used to determine information such as the prosthesis type, tooth position number, and position of the tooth to be repaired, but still cannot generate an adaptive-shaped personalized prosthesis to adapt to the opposing occlusion situation. Summary of the Invention

[0007] The object of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a method for generating a digital form denture prosthesis based on artificial intelligence technology, which can independently design and produce a digital denture prosthesis with highly accurate model natural tooth morphological characteristics.

[0008] The object of the present invention can be achieved by the following technical solutions:

[0009] A method for generating a digital form denture prosthesis based on artificial intelligence technology, comprising the following steps:

[0010] Perform 3D scanning on the patient's oral cavity to obtain three-dimensional digital impressions of the upper and lower teeth. According to the denture restoration requirements, specify the position of the abutment on the three-dimensional digital impression; perform local cutting on the three-dimensional digital impression with the abutment as the center, so that the cut-out area includes the three-dimensional impression information of the abutment, adjacent teeth, and opposing teeth.

[0011] Input the cut-out impression information into a trained deep neural network model to generate a digital form of the prosthesis adapted to the abutment; the training data of the deep neural network model includes the data assets of the digital form of the denture prosthesis obtained by the expert method, and uses the partial impression information cut with the abutment as the center as the model input, and the three-dimensional digital form of the repaired denture prosthesis as the learning target.

[0012] During the training process of the deep neural network model, define an energy function to measure the difference between the output of the deep neural network and the cut-out impression information. By optimizing the energy function, minimize the difference between the output of the deep neural network and the three-dimensional digital form of the denture prosthesis in the data assets to obtain a trained deep neural network model.

[0013] Further, the process of the local cutting is specifically as follows:

[0014] Take the center of the abutment as the center of the sphere, set the cutting size parameter as the sphere radius, define the cutting sphere, and the cutting size parameter satisfies that the cutting sphere includes the three-dimensional impression information of the abutment, the adjacent teeth of the abutment and the opposing teeth. Then, distinguish the area inside the cutting sphere from the outside area to obtain the cut-out impression information.

[0015] Further, the deep neural network model includes:

[0016] A multi-scale geometric feature hierarchical aggregation network encoding module for calculating, encoding, and extracting the geometric distribution shape of the input impression information.

[0017] A generative decoding network module for predicting and generating the digital form of the denture prosthesis according to the features extracted by the multi-scale geometric feature hierarchical aggregation network encoding module.

[0018] Furthermore, the processing process of the multi-scale geometric feature hierarchical aggregation network coding module includes:

[0019] S201: Input the point cloud features of the impression information into the SA module;

[0020] S202: Multiscale extract the point cloud features through the SA module. For each point cloud feature, select multiple nearest neighbor point cloud features by the k-nearest neighbor method, and then obtain better-quality point cloud features combined with the neighbor point cloud features through the attention module; Upsample the better-quality point cloud features through the FP module;

[0021] S203: After operating step S202 multiple times, an input point cloud of N points is finally obtained as a point cloud feature of N A dimensions, and then the displacement corresponding to each point is obtained through a fully connected layer, and the original input point cloud is displaced to obtain a new output point cloud of N points;

[0022] S204: Repeat the operation of step S203 multiple times, and the displacement distance of each time is gradually decreased through hyperparameter setting, and finally a fully completed point cloud is obtained.

[0023] Furthermore, the training data takes the local cutting impression information of the abutment taken from the oral scan impression of each patient as the model input data x, and takes the digital form of the denture restoration repaired by the expert method from the digital assets as the learning target y, and combines them to form a training data set {x, y}.

[0024] Furthermore, the training data is randomly downsampled before being input into the deep neural network model for training.

[0025] Furthermore, data augmentation is performed on the training data by using data augmentation techniques of random rotation, scaling, and flipping before the training data is input into the deep neural network model for training.

[0026] Furthermore, the energy function is the chamfer distance, the earth mover's distance, or the Wasserstein distance.

[0027] Furthermore, the method also includes setting one or more heuristic rules for the energy function, and the heuristic rules include the definition of similarity measures based on the point cloud distribution density, smoothness, or differentiability of the digital form of the denture restoration;

[0028] The optimization object of the energy function is the parameters of the deep neural network model, so that the output of the deep neural network model is consistent with the 3D digital form of the denture restoration under multiple measure metrics.

[0029] Further, the deep neural network model uses the stochastic gradient descent method or the Adam optimization algorithm to adjust the parameters of the deep neural network and gradually reduce the value of the energy function.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] (1) Based on the three-dimensional digital impression of the maxillary and mandibular teeth, the present invention sets a prepared body and performs local cutting centered on the prepared body, and inputs the cutting result into the deep neural network model to automatically generate a digital form of the restoration body adapted to the prepared body; and during the training process of the deep neural network model, an energy function is defined to measure the difference between the output of the deep neural network and the cut part of the impression; by optimizing the energy function, the difference between the output of the deep neural network and the 3D digital form of the denture restoration body manufactured by the dentist is minimized. The energy function can be in various forms such as the chamfer distance, the earth mover's distance, and the Wasserstein distance, and one or more heuristic rules defined based on the point cloud distribution density, smoothness, and differentiability similarity can be set, which can ensure that the output of the neural network is consistent with the 3D digital form of the denture restoration body under various measure metrics.

[0032] (2) The present invention designs and produces a digital denture restoration body with highly accurate model natural tooth morphological features through the deep neural network model, which can not only meet the needs of various types of patients, but also have the physiological texture features of the teeth themselves, etc.; and during this process, there is no need to pre-manually input or predict information such as tooth position numbers and prepared body types; the original design work of dentists for several hours or even several days is reduced to within a few minutes to 1 hour, improving the production efficiency while ensuring the quality and reliability of the restoration body. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic flowchart of a method for generating a digital form denture restoration body based on artificial intelligence technology provided in an embodiment of the present invention;

[0034] Figure 2 It is a schematic diagram of a cutting area of a certain patient including adjacent teeth and opposing teeth provided in an embodiment of the present invention;

[0035] Figure 3 It is a schematic diagram of a generated crown point cloud provided in an embodiment of the present invention;

[0036] Figure 4 It is a schematic diagram of splicing the generated crown point cloud onto the tooth preparation provided in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. Components of the embodiments of the present invention usually described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations.

[0038] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0039] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0040] Embodiment 1

[0041] As Figure 1 shown, this embodiment provides a method for generating a digital morphological denture prosthesis based on artificial intelligence technology, including the following steps:

[0042] S1: Perform a 3D scan on the patient's oral cavity to obtain a three-dimensional digital impression of the upper and lower teeth. According to the denture restoration requirements, specify the position of the abutment on the three-dimensional digital impression; perform local cutting on the three-dimensional digital impression with the abutment as the center, so that the cut-out area includes the three-dimensional impression information of the abutment, adjacent teeth, and opposing teeth;

[0043] In actual operation, first use a high-precision oral 3D scanner to scan the upper and lower jaws of the patient to obtain a complete three-dimensional digital impression. During the scanning process, strictly operate in accordance with the specifications of the dental camera manual to ensure that the obtained digital impression is unified in size, coordinate position, and orientation. This step can provide accurate impression data and lay a solid foundation for subsequent restoration work.

[0044] After obtaining the complete digital impressions of the upper and lower jaws, specify the position of the abutment according to the denture restoration requirements. Take the center of the abutment as the center of the sphere, set the cutting size parameter as the radius of the sphere, and define the cutting sphere of the impression. Subsequently, perform local cutting on the digital impression of the upper and lower jaw occlusion with the abutment as the center, so that the cutting area includes the three-dimensional impression information of the abutment, adjacent teeth, and opposing teeth, as Figure 2 shown. Through this local cutting method, effective spatial constraints can be provided for the subsequent automatic generation of the denture prosthesis.

[0045] Specifically, the center of the preparation body is the average coordinate of the point cloud coordinates of the preparation body. The cutting area needs to consider the differences between each different oral cavity and tooth position. The result of each cutting ensures that the three-dimensional impression information of the preparation body, adjacent teeth, and opposing teeth is included. To ensure the accuracy of the cutting area, appropriate adjustments need to be made according to the individual situation of the patient. For example, when there is a large gap between the preparation body and the adjacent teeth, the radius of the cutting sphere can be appropriately increased to ensure that the cutting area completely covers the required three-dimensional impression information.

[0046] The method of multiple scans can also be adopted. By combining the scan data from different angles and positions, a more comprehensive and accurate three-dimensional impression can be generated. This multiple-scan method can effectively reduce data omission and errors that may be caused by a single scan, and further improve the matching accuracy of the denture restoration.

[0047] S2: Input the cut impression information into the trained deep neural network model to generate a digital form of the restoration body that fits the preparation body;

[0048] That is, define a deep neural network model. This deep neural network takes the impression information of the cut part as input and outputs the digital form of the 3D denture restoration body, which can automatically generate a digital form of the restoration body that fits the preparation body, as Figure 3 shown, and finally spliced into the three-dimensional digital impression, as Figure 4 shown;

[0049] The deep neural network model includes:

[0050] A multi-scale geometric feature hierarchical aggregation network encoding module for calculating, encoding, and extracting the geometric distribution shape of the input impression information;

[0051] A generative decoding network module for predicting and generating the digital form of the denture restoration body according to the features extracted by the multi-scale geometric feature hierarchical aggregation network encoding module.

[0052] The multi-scale geometric feature hierarchical aggregation network encoding module calculates geometric features on multiple geometric distribution scales of the input 3D impression and fuses them, and outputs a feature encoding that describes the geometric distribution shape of the impression;

[0053] The input of the generative decoding network module is the feature encoding that describes the geometric distribution shape of the impression, and through the decoding network, it outputs the predicted digital form of the generated denture restoration body.

[0054] The processing process of the multi-scale geometric feature hierarchical aggregation network encoding module includes:

[0055] S201: Input the point cloud features of the impression information into the SA module;

[0056] S202: Multiscale point cloud features are extracted through the SA module. For each point cloud feature, the nearest multiple neighbor point cloud features are selected by the k-nearest neighbor method, and then a better quality point cloud feature that combines the neighbor point cloud features is obtained through the attention module; the better quality point cloud feature is upsampled through the FP module;

[0057] S203: After performing the operations in step S202 multiple times, an input point cloud of N points finally obtains a point cloud feature of N points with A dimensions. Then, through a fully connected layer, the displacement corresponding to each point is obtained, and the original input point cloud is displaced to obtain a new output point cloud of N points;

[0058] S204: Repeat the operations in step S203 multiple times. The displacement distance each time is gradually decreased through hyperparameter settings, and finally a fully completed point cloud is obtained.

[0059] Specifically, for the multiscale geometric feature hierarchical aggregation network encoding module, the SA (Set Abstraction) module is constructed by using FPS (FarthestPoint Sampling) farthest point sampling. First, the geometric features of the point cloud are extracted multiscale through the SA module. For example, the number of points in the point cloud set sampled in step one is N, and the feature dimension is 3. After passing through one layer of the SA module, the number of points is reduced to N / 16, and the feature dimension becomes A (A>3). At this time, the point cloud has geometric features of another scale and higher dimension. After passing through multiple layers of the SA module, the point cloud can finally be represented by a high-dimensional vector for all geometric features.

[0060] After the point cloud feature passes through the SA module, it then passes through the attention module. Each abstracted point cloud feature selects the nearest k point cloud features by the k-nearest neighbor method according to the corresponding xyz coordinates, and a better quality point cloud feature that combines the neighbor features is obtained through the attention module.

[0061] After obtaining a high-dimensional vector of the point cloud, the point features are upsampled through the FP (Feature Propagation) module. For example, after passing through one layer of the FP module, the number of points of a high-dimensional feature with dimension B increases to M (M>1), and the feature dimension decreases to A (A<B). After multiple operations of the SA module and the FP module, an input point cloud of N points finally obtains a point cloud feature of N points with A dimensions. Based on this feature, the displacement corresponding to each point is obtained through a fully connected layer, and the original input point cloud is displaced to obtain a new output point cloud of N points.

[0062] Repeat this step K times, with the displacement distance decreasing successively through hyperparameter settings, and finally obtain the fully completed point cloud. The models and modules above step two can be Transformer models, PointNet models, PointNet++ models, etc.

[0063] S3: Obtain the data assets of the digital morphology of the denture prosthesis by the expert method, and use the partial impression information cut with the prepared tooth as the center as the model input, and use the three-dimensional digital morphology of the repaired denture prosthesis as the learning target to form the training data;

[0064] In this embodiment, the data assets of the digital morphology of the denture prosthesis manually made and accumulated by skilled physicians are used to train the above-mentioned deep neural network model. The specific steps are as follows: Take out the partial impression information cut with the prepared tooth as the center from the oral scan impression of each patient as the model input. The impression information needs to be partially preprocessed before becoming the training set data, such as operations like point cloud conversion, normalization, upsampling, and downsampling.

[0065] For example, if the currently obtained impression data is mesh data, it is necessary to perform preliminary sampling on the mesh surface before inputting it into the model to obtain the standard number of point clouds. If the obtained data is point cloud data, it is necessary to perform upsampling or downsampling on the data before inputting it into the model so that the number of points is the standard number of point clouds, which can be 32768 or 16384, etc. The point clouds can be duplicate points, that is, there can be multiple points at the same position. Here, the standardization process only requires the number of point clouds, so there is no need to perform upsampling methods such as interpolation. After obtaining the point clouds with the standard number, perform a normalization operation on the point clouds, and the data obtained at this time can be used as the training set data.

[0066] Before inputting the training set data into the model, it is also necessary to perform a random downsampling so that the point cloud density input into the model is not too high to reduce the training cost. Take out the three-dimensional digital morphology of the denture prosthesis repaired by the physician as the learning target of the model output. Here, the learning target also needs to go through the above-mentioned preprocessing operations to obtain the standard point cloud data and form the training data set. Through the training of these data, the deep neural network can learn how to automatically generate the digital morphology of the denture prosthesis from the impression information.

[0067] During the training process, data augmentation techniques such as random rotation, scaling, and flipping are adopted to increase the diversity of the training data and improve the generalization ability of the model.

[0068] S4: Define an energy function to measure the difference between the output of the deep neural network and the extracted impression information. By optimizing the energy function, minimize the difference between the output of the deep neural network and the 3D digital form of the denture prosthesis in the data asset, and obtain a deep neural network model with the ability to automatically generate the digital form of the denture prosthesis.

[0069] The composition of the energy function includes optional definition methods such as Chamfer Distance, Earth Mover's Distance (EMD), and Wasserstein Distance.

[0070] The energy function considers one or more heuristic rules, including the definition of similarity measures such as the point cloud distribution density, smoothness, and differentiability based on the digital form of the denture prosthesis.

[0071] The object of optimizing the energy function is the parameters of the deep neural network, so that the output of the neural network is consistent with the 3D digital form of the denture prosthesis under various measure metrics.

[0072] Specifically, the Chamfer Distance is a measure method to measure the geometric similarity between two point cloud sets. By calculating the distance from each point to its nearest neighbor point and then taking the average of all these distances, the geometric similarity between the point clouds is obtained. The Earth Mover's Distance and Wasserstein Distance measure their similarity by calculating the minimum transportation cost between two point cloud sets. These distance measure methods can effectively reflect the geometric differences between the denture prosthesis generated by the deep neural network and the target form.

[0073] To reduce the training cost, the object of the optimization function is the low-density point cloud after randomly downsampling the above training data set. For example, the target point cloud and the point cloud to be completed with 16384 points are randomly downsampled to obtain the point cloud to be completed and the target point cloud with 2048 points. After inputting the point cloud to be completed into the model, 2048 completed point clouds are obtained, and then the target point cloud with 2048 points is used to optimize this completed point cloud.

[0074] During the optimization process, the Stochastic Gradient Descent (SGD) or Adam optimization algorithm can be adopted. By continuously adjusting the parameters of the deep neural network, gradually reduce the value of the energy function, thereby improving the accuracy and robustness of the model. At the same time, an Early Stopping mechanism can be introduced. When the value of the energy function no longer significantly decreases on the validation set, terminate the training in advance to prevent the model from overfitting.

[0075] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in this technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A method for generating a digital morphological denture restoration based on artificial intelligence technology, characterized in that: The following steps are involved: The patient's oral cavity is 3D scanned to obtain a 3D digital impression of the upper and lower teeth. According to the needs of denture restoration, the position of the preparation is specified on the 3D digital impression; local cutting is performed on the 3D digital impression with the preparation as the center, so that the cut area includes the 3D impression information of the preparation, adjacent teeth, and opposing teeth; The cut impression information is input into the trained deep neural network model to generate a digital morphology of the restoration that matches the preparation. The training data of the deep neural network model includes data assets of the digital form of the denture restoration obtained by the expert method, and partial impression information cut around the preparation as the center is used as the model input, and the 3D digital form of the restored denture restoration is used as the learning target; During the training process of the deep neural network model, an energy function is defined to measure the difference between the deep neural network output and the cut impression information. By optimizing the energy function, the difference between the deep neural network output and the 3D digital form of the denture restoration in the data asset is minimized to obtain a trained deep neural network model.

2. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: The process of local cutting is specifically as follows: The center of the preparation is taken as the center of the sphere, the cutting size parameter is set as the sphere radius, and a cutting sphere is defined. The cutting size parameter satisfies the 3D impression information of the preparation, the adjacent teeth of the preparation, and the opposing teeth. Then, the area inside the cutting sphere is distinguished from the external area to obtain the cut impression information.

3. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: The deep neural network model includes: Multi-scale geometric feature hierarchical aggregation network coding module, used for calculating the geometric distribution shape of the input impression information and extracting features; The generative decoding network module is used to predict and generate the digital morphology of the denture restoration based on the features extracted by the hierarchical aggregation network encoding module of multi-scale geometric features.

4. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 3, characterized in that: The processing process of the multi-scale geometric feature hierarchical aggregation network coding module includes: S201: inputting the point cloud features of the impression information into the SA module; S202: extracting point cloud features at multiple scales through the SA module, selecting multiple nearest neighbor point cloud features for each point cloud feature through the k-nearest neighbor method, and then obtaining a better point cloud feature combining the neighbor point cloud features through the attention module; upsampling the better point cloud features through the FP module; S203: After multiple operations of step S202, an input point cloud of N points finally obtains a point cloud feature of N A dimensions, and then a displacement corresponding to each point is obtained through a fully connected layer, and the original input point cloud is displaced to obtain a new output point cloud of N points; S204: Repeat the operation of step S203 multiple times, and the displacement distance each time is gradually reduced through the hyperparameter setting, and finally a completely completed point cloud is obtained.

5. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: The training data uses the partial cutting impression information of the prepared body taken from the oral scan impression of each patient as the model input data x, and the digital form of the denture restoration restored by the expert method from the digital assets as the learning target y, and combines them to form a training data set {x, y}.

6. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: Before the training data is input into the deep neural network model for training, the training data is also randomly downsampled.

7. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: Before the training data is input into the deep neural network model for training, data augmentation techniques such as random rotation, scaling and flipping are used to expand the data.

8. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: The energy function is chamfer distance, bulldozer distance or Wasserstein distance.

9. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: The method further comprises setting one or more heuristic rules for the energy function, wherein the heuristic rules comprise a definition of a similarity measure based on the point cloud distribution density, smoothness or differentiability of the digital morphology of the denture restoration; The optimization object of the energy function is the parameters of the deep neural network model, so that the output of the deep neural network model is guaranteed to be consistent with the 3D digital form of the denture restoration under multiple measurement metrics.

10. The method for generating a digital morphological denture restoration based on artificial intelligence technology according to claim 1, characterized in that: The deep neural network model adopts the stochastic gradient descent method or the Adam optimization algorithm to adjust the parameters of the deep neural network and gradually reduce the value of the energy function.

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