Nerve implicit surface dynamic three-dimensional reconstruction method for spacecraft shape and action decoupling

Abstract

The invention discloses a nerve implicit surface dynamic three-dimensional reconstruction method for spacecraft shape and action decoupling, and relates to a nerve implicit surface dynamic three-dimensional reconstruction method. The invention aims to solve the problem that NPMs focus on shape and deformation modeling and cannot directly render a new view angle. The method comprises the following steps: step 1, data acquisition and preprocessing; step 2, static three-dimensional shape coding; step 3, dynamic deformation feature decoupling; and step 4, color rendering. The invention belongs to the technical field of spatial perception, three-dimensional reconstruction and artificial intelligence.

Description

Technical Field

[0001] The present invention relates to a method for dynamic three-dimensional reconstruction of neural implicit surfaces, belonging to the technical fields of spatial perception, three-dimensional reconstruction, and artificial intelligence. Background Art

[0002] With the progress of space technology, dynamic components of satellites and spacecraft (such as solar panels, antennas, robotic arm sampling devices, etc.) have become increasingly important when performing complex tasks. These components need to adjust their attitudes and positions according to mission requirements, and their precise control is crucial for the success of the mission. Dynamic three-dimensional reconstruction technology can provide key support for mission execution by monitoring the motion states and deformations of these dynamic components in real time. First, the extreme conditions or emergencies in the space environment may cause deformations of the components, and dynamic three-dimensional reconstruction can help evaluate these changes in real time. In addition, as the degree of autonomy of space missions continues to increase, dynamic three-dimensional reconstruction technology has also become the core of realizing autonomous mission execution. By providing high-precision spatial perception for robots, robotic arms, or other dynamic components, three-dimensional reconstruction can support complex tasks such as sampling, object grasping, docking, and cooperative operations. Especially in multi-satellite cooperation or networking missions, deformable three-dimensional reconstruction helps to precisely control the dynamic components of each satellite and ensure the smooth progress of the mission. Dynamic three-dimensional reconstruction can not only provide real-time feedback during the mission execution stage, but also provide important support for data analysis, scientific research, and future mission optimization in the later stage of the mission. And dynamic and variable three-dimensional reconstruction can also provide necessary support for the implementation of space dynamic missions in virtual scenarios. Therefore, dynamic three-dimensional reconstruction technology has great application potential in space missions, and it provides certain technical guarantees for ensuring the autonomous mission execution of satellites and spacecraft and the simulation experiments of related scientific research.

[0003] In the existing technical solutions, for the dynamic three-dimensional reconstruction of the target, the time dimension is introduced into the neural network for three-dimensional reconstruction, so that the network encodes both the spatial coordinates (x, y, z) and inputs the information of time, and then combines the dynamic changes of the scene to model the three-dimensional information at each moment and capture the scene motion information at different time points. The existing technologies usually perform two-stage learning on the dynamic scene. In the first stage, the scene is encoded into a canonical space, and in the second stage, this canonical expression is mapped to the deformed scene at a specific time. However, the introduction of time variables also brings certain problems. The deformation of the target over time may cause the model to fail to converge. Specifically, the technology includes an inverse mapping that maps the observed dynamic scene back to a canonical, undeformed spatial representation. This process may introduce complex dynamic changes that are difficult to effectively learn and simulate by the neural network, resulting in the model being difficult to converge during the training process.

[0004] NeuS (Neural Surface Reconstruction) is a neural implicit surface representation method for high-quality 3D reconstruction. Based on volume rendering technology, it represents the scene as an implicit surface, combines surface normal vectors and color information, and achieves precise reconstruction of complex geometric details by optimizing the rendering loss. NeuS performs excellently in processing non-occluded static scenes and can generate high-precision surface models. However, NeuS cannot reconstruct dynamic objects because its core assumption is a static scene, that is, the geometry and appearance of the scene remain unchanged throughout the modeling process. The movement of objects in a dynamic scene causes data consistency problems and cannot meet the temporal continuity requirements of implicit surface representation, so it cannot be directly applied to the reconstruction of dynamic objects.

[0005] NPMs (Neural Parametric Models) is a method for modeling 3D shapes and their dynamic deformations through neural networks. It uses implicit representations to capture the geometric features of objects and combines deformation parameters to handle dynamic changes, and is widely used in 3D shape reconstruction and animation production. However, NPMs focus on shape and deformation modeling and cannot directly render new viewpoints. Summary of the Invention

[0006] To solve the problem that NPMs focus on shape and deformation modeling and cannot directly render new viewpoints, the present invention further proposes a neural implicit surface dynamic 3D reconstruction method for decoupling the shape and motion of a spacecraft.

[0007] The technical solution adopted by the present invention to solve the above problems is: The steps of the present invention include:

[0008] Step 1: Data acquisition and preprocessing;

[0009] Step 2: Static 3D shape encoding;

[0010] Step 3: Decoupling of dynamic deformation features;

[0011] Step 4: Color rendering.

[0012] Further, Step 1 specifically includes:

[0013] Step 101: Use a high-precision 3D scanner to perform fine modeling of the static state of the spacecraft, capturing the outer contour, component details, and overall geometric features;

[0014] Step 102: Dynamic data acquisition by recording the geometric change process of the spacecraft in different deformation states;

[0015] Step 103: Adopt a discretized multi-angle sampling strategy to ensure full coverage observation of the spacecraft's morphology;

[0016] Step 104: By adjusting the azimuth angle and elevation angle of the camera, multi-view image and depth map information are uniformly collected within the spherical range.

[0017] Further, step 2 specifically includes:

[0018] Step 201: When dealing with the static shape of the spacecraft, an encoding method based on implicit functions is used to map three-dimensional space coordinates to the shape surface function, generating a continuous geometric representation.

[0019] Step 202: Design an implicit representation network for the static shape. Model the three-dimensional space points through a multi-layer perceptron. The input of the network is the space coordinates, and the output is the probability value indicating whether the point belongs to the spacecraft surface.

[0020] Further, in step 3, the dynamic characteristics and static geometry are decoupled and represented through a parameterization method:

[0021] Step 301: The dynamic deformation network takes the canonical shape and the deformed shape as inputs. By learning the relationship between shape changes, it generates a dynamic deformation vector. This vector describes the dynamic characteristics in the current state and is combined with the static shape representation network to achieve geometric modeling under dynamic conditions.

[0022] Step 302: During model training, first fix the parameters of the static shape network, and then optimize the dynamic network. By comparing the point cloud data and implicit shape representations under various dynamic states, gradually adjust the network parameters so that it can efficiently express geometric changes under different dynamic conditions.

[0023] Step 303: 3D convolutional encoder f Ωs and f Ωp Provide the initialization of the canonical shape and the latent space of the action state shape. Both encoders take the back-projected depth observations in the form of a partial voxel grid V as inputs, and use 3D convolution and a final fully connected layer to output the latent code estimation.

[0024] Shape encoder: Given the shape latent space learned from the canonical space in the training dataset and the set of voxel grids of the P action spaces available in the training dataset, train f Ωs To predict the mapping from the voxel grid to the basic shape latent code of the corresponding identity.

[0025] Action encoder: Given the list of action codes learned from the P action shapes in the dataset and the set of P voxel grids, train f Ωp To predict the mapping from the voxel grid of the pose shape to the corresponding action latent space.

[0026] Step 304: Use the dynamic geometry decoding module to interpolate and combine the static shape latent space and the action latent space to reconstruct the dynamically changing three-dimensional form.

[0027] Furthermore, in step 4, based on the three-dimensional reconstruction, a neural radiance field is used to perform high-quality rendering on the dynamic geometric surface, supporting the synthesis of detailed views; a lighting and color modeling network based on dynamic geometry is designed. By inputting the dynamic surface representation into the color field network and combining the camera view and the light direction, the color and transparency values of each sampling point are generated. Based on the ray tracing algorithm, the dynamic surface is sampled, each ray is divided into several sampling points, and the final perspective image is calculated through the volume rendering formula. The rendering result shows the details of the dynamic scene, including light and shadow, texture, and deformation characteristics.

[0028] The beneficial effects of the present invention are as follows:

[0029] 1. Shape-pose decoupled modeling: Using the NPMs technology, a shape and pose latent space is constructed to accurately capture the geometric features and motion patterns of the dynamic spacecraft;

[0030] 2. Dynamic light field reconstruction and optimization: Input the latent space features extracted by NPMs into NeRF, and generate high-fidelity views of the dynamic scene through light field modeling;

[0031] 3. Cross-time consistency modeling: Adopt a time series constraint method to achieve geometric consistency and dynamic optimization between different time points;

[0032] 4. Real-time dynamic rendering and future prediction: Support real-time dynamic modeling and dynamic view generation, and provide the ability to predict the state at future time points. Description of the Drawings

[0033] Figure 1 is a schematic diagram of the network model architecture of the present invention;

[0034] Figure 2 is a schematic diagram of the acquisition of shape data by surrounding;

[0035] Figure 3 is a schematic diagram of dynamic data;

[0036] Figure 4 is a schematic diagram of the initialization of the shape and pose latent space during testing. Detailed Embodiments

[0037] Detailed Embodiment 1: As Figures 1 to 4 shown, the method for dynamic three-dimensional reconstruction of a neural implicit surface with decoupled spacecraft shape and motion specifically includes the following steps:

[0038] Step 1. Data acquisition and preprocessing; specifically including:

[0039] Step 101: Use a high-precision 3D scanner to finely model the static state of the spacecraft, capturing the outer contour, component details, and overall geometric features;

[0040] Step 102: Dynamic data acquisition records the geometric change process of the spacecraft in different deformation states;

[0041] Step 103: Adopt a discretized multi-angle sampling strategy to ensure a full-coverage observation of the spacecraft's morphology;

[0042] Step 104: By adjusting the camera azimuth and elevation angles, uniformly acquire multi-view image and depth map information within the spherical range;

[0043] Step 2: Static 3D shape encoding; specifically including:

[0044] Step 201: When processing the static shape of the spacecraft, adopt an encoding method based on implicit functions to map 3D space coordinates to the shape surface function, generating a continuous geometric representation;

[0045] Step 202: Design an implicit representation network for the static shape, model 3D space points through a multi-layer perceptron, with the input of the network being the space coordinates and the output being the probability value of whether the point belongs to the spacecraft surface;

[0046] Step 3: Decouple dynamic deformation features; decouple and represent dynamic characteristics from static geometry through a parameterization method:

[0047] Step 301: The dynamic deformation network takes the canonical shape and the deformed shape as inputs, generates a dynamic deformation vector by learning the relationship between shape changes; this vector describes the dynamic characteristics in the current state, combined with the static shape representation network to achieve geometric modeling under dynamic conditions;

[0048] Step 302: During model training, first fix the parameters of the static shape network, and then optimize the dynamic network; by comparing the point cloud data and implicit shape representations under various dynamic states, gradually adjust the network parameters to enable it to efficiently express geometric changes under different dynamic conditions;

[0049] Step 303: 3D convolutional encoder f Ωs and f Ωp Provide the initialization of the canonical shape and the action state shape latent space. Both encoders take the back-projected depth observations in the form of a partial voxel grid V as inputs and use 3D convolution and a final fully connected layer to output the latent code estimate;

[0050] Shape encoder: Given the shape latent space learned from the canonical space in the training dataset and the set of voxel grids of P action spaces available in the training dataset, train fΩs Predict the mapping of the voxel grid to the latent code of the base shape corresponding to the identity;

[0051] Action Encoder: Given a list of action codes learned from P action shapes in the dataset and P sets of voxel grids, train f Ωp Predict the mapping of the voxel grid of the pose shape to the corresponding action latent space;

[0052] Step 304: Use the dynamic geometry decoding module to interpolate and combine the static shape latent space and the action latent space to reconstruct the dynamically changing three-dimensional form;

[0053] Step 4: Color rendering;

[0054] Based on the three-dimensional reconstruction, use the neural radiance field to perform high-quality rendering on the dynamic geometry surface to support the synthesis of detailed views; design a lighting and color modeling network based on dynamic geometry. By inputting the dynamic surface representation into the color field network and combining the camera view and the light direction, generate the color and transparency values of each sampling point. Based on the ray tracing algorithm, sample the dynamic surface, divide each ray into several sampling points, and calculate the final view image through the volume rendering formula. The rendering result shows the details of the dynamic scene, including light and shadow, texture, and deformation characteristics.

[0055] Embodiment

[0056] First, use a three-dimensional spatial scanner to perform high-precision scanning on the static model of the spacecraft to capture the geometric details and global shape features of its components. During the scanning process, all components of the spacecraft are collected under both static and dynamic conditions, and the dynamic data is recorded at a rate of 60 FPS to capture its shape changes under different deformation parameters. Select a canonical pose of the spacecraft as the static reference pose, and the remaining dynamic poses are regarded as posed states, and the dynamic description is realized through deformation parameterization. Observe the non-closed dynamic shape from multiple perspectives, and use the depth information at a specific angle to capture its surface geometry. Let the camera view be θ i , φ i (azimuth angle and elevation angle respectively), the sampling step size is 5 degrees, covering the complete hemisphere space. Then project the three-dimensional geometric structure into a multi-view depth map, and let the depth map be D i (x, y), representing the surface depth at the view θ i , φ i .

[0057] To represent the static shape of the spacecraft, an implicit shape representation method based on a multi-layer perceptron (MLP) is adopted to map the spatial coordinates (x, y, z) to the implicit function values on the shape surface. The input of the shape encoding network is the three-dimensional spatial point coordinates, and the output is the implicit representation of whether the point belongs to the object surface. Let the shape encoding network be MLP shape , and its formula is:

[0058] f(x, y, z) = MLP_shape(x, y, z)

[0059] The output of the implicit function f(x, y, z) is a continuous value, which is used to describe the distance from the point to the object surface. Through subsequent activation functions (such as the Sigmoid function), the continuous value is converted into a probability, indicating whether the point is located on the object surface:

[0060] P_surface(x, y, z) = γ(f(x, y, z))

[0061] where σ is the Sigmoid activation function. This implicit representation is more flexible than traditional polygon meshes and can naturally handle complex geometric structures.

[0062] For the dynamic shape of the spacecraft in each state, a three-dimensional shape surface characterization mapping also needs to be performed first. Similarly, an implicit shape representation method based on a multi-layer perceptron (MLP) is adopted to map the spatial coordinates (x, y, z) to the implicit function values on the shape surface. The shape of the spacecraft in each action state is obtained.

[0063] To characterize the geometric changes of the spacecraft under dynamic conditions, a dynamic deformation modeling network is introduced. Through the multi-layer perceptron MLP deform , the deformation parameters are mapped to the dynamic deformation space of the shape to generate the deformed implicit geometry. The formula is:

[0064] Z deform (t, f) = MLP deform (t, f)

[0065] where Z_deform represents the implicit representation vector in the current dynamic form. Combining it with the implicit representation of the static shape can generate the geometric form after dynamic deformation:

[0066] f deform (x, y, z, t, f) = MLP shape (x + Z deform(t，f) )

[0067] Through the above process, the geometric structure under dynamic conditions is accurately represented as the deformed implicit function. Finally, it is converted into a surface probability representation through the Sigmoid function:

[0068] P surface (x, y, z, t, f) = γ(f deform (x, y, z, t, f))

[0069] After obtaining the dynamic implicit surface representation, the neural radiance field (NeRF) is further utilized to achieve high-quality 3D scene rendering and novel view synthesis. NeRF performs rendering calculations on the dynamic geometric surface and lighting characteristics through volume rendering methods in combination with ray tracing techniques. The rendering inputs include: the dynamic implicit surface representation P_surface(x, y, z, t, f), the ray direction d, and the camera position o. And a geometric decoder is used to decode the implicit surface representation to generate a color field and a density field. The calculation formulas for the color field c and the density field σ are as follows:

[0070] σ(x, y, z) = MLP density (f deform )

[0071] c(x, y, z, d) = MLP color (f deform , d)

[0072] Each ray is divided into p sampling points through the ray tracing algorithm, and the color and transparency are calculated at each point. The final pixel color is calculated through the volume rendering formula.

[0073] The l2-loss for optimizing the flow prediction during training: When training the dynamic deformation modeling network, we use the l2-loss to optimize the flow vector prediction. This loss function measures the difference between the flow vector predicted by the model and the true flow vector, and the formula is as follows:

[0074]

[0075] where f deform is the pose MLP, s is the latent shape code of the spacecraft shape, pj is the latent pose code of the spacecraft action state j, is the point sampled in the canonical shape space.

[0076] The optimization reconstruction loss Lr during inference: During the inference stage, we use the reconstruction loss to optimize the model so that the model can reconstruct the shape of the spacecraft according to the input coordinates. The reconstruction loss can be defined as:

[0077]

[0078] where P surface is the surface probability predicted by the model, and P gt is the ground truth surface probability.

[0079] For the neural radiance field-based network model, the calculation of its loss is consistent with NeRF.

[0080] The 3D geometric data generated by multi-view scanning, combined with implicit shape encoding and dynamic deformation modeling methods, accurately captures the static and dynamic geometric features of the spacecraft; further uses NeRF to achieve view synthesis and rendering based on dynamic geometry, generating multi-view images with rich details, providing an efficient and flexible solution for 3D reconstruction and visual representation of complex scenes.

[0081] Working principle

[0082] The model designed in this invention includes four core modules, namely: 1) Dynamic spacecraft high-precision full-view image acquisition and multi-modal data generation module; 2) Implicit shape representation module of static geometric structure; 3) High-dimensional feature decoupling modeling module driven by dynamic deformation; 4) View-dependent rendering and geometric reconstruction module based on Neural Radiance Field (NeRF); The overall process covers the dynamic construction of the dataset, offline joint optimization of decoupled shape and deformation models, and online real-time geometric decoding and multi-view image generation steps; This invention is applicable to high-precision and multi-task application scenarios such as in-orbit modeling of spacecraft, fine attitude analysis, intelligent target recognition, and mission simulation execution; The overall process includes three steps: dataset construction, offline model training, and online model testing:

[0083] Dataset construction: Based on the dynamic operation characteristics of the spacecraft, design a comprehensive data acquisition and construction process to support the decoupled design of shape representation, deformation modeling, and view rendering. Use the dynamic model of the spacecraft to perform full-angle multi-view sampling of the spacecraft in different attitudes and deformation states. Through discrete sampling of the altitude and azimuth angles, widely cover and record the morphology of the spacecraft under different dynamic conditions; Then, simulate the complex dynamics of the spacecraft, including solar panel deployment, antenna adjustment, orbit change movement, etc., and record dynamic morphology parameters such as timestamps, node positions, deformation angles, etc.; Generate real point clouds and depth information from the collected images to provide accurate geometric constraints for subsequent training, and label the geometric features and dynamic parameters under each view.

[0084] Decoupled 3D Shape Representation and Deformation Modeling: Decouple the implicit representation of the 3D shape of the spacecraft from the dynamic deformation modeling, and separately process the static features and dynamic changes of the geometric form. The implicit representation of the 3D shape is obtained by a neural network learning the 3D shape of the spacecraft in a static state, encoding the geometric features of the spacecraft as an implicit function f(x, y, z), which represents whether a point is on the surface of the spacecraft. The dynamic deformation modeling is based on the shape representation, designing an independent dynamic deformation network. By inputting dynamic parameters (such as time, deformation angle, etc.), it predicts the deformed shape of the spacecraft under different conditions. The dynamic deformation network outputs an implicit representation vector Z, which is used to describe the dynamic features in the current state. In addition, two stages of optimization are also required. First, train the shape representation module so that it can accurately model the 3D shape of the static spacecraft. Then, on the basis of fixing the shape representation parameters, optimize the dynamic deformation network so that it can capture the dynamic changes.

[0085] Multi-view Rendering and Geometric Decoding: After completing the shape representation and dynamic deformation modeling, the present invention uses the geometric decoding and rendering module to perform multi-view synthesis of the dynamic form. The geometric decoder receives the static shape representation and the dynamic deformation representation Z, and generates the density field and geometric structure of the current dynamic state. The decoding process combines the camera parameters (intrinsic and extrinsic parameters) of each view to generate the point cloud and geometric information corresponding to the view. Then, based on the geometric structure generated by the decoder, volume rendering technology is used for multi-view image synthesis. The rendering result contains high-detail representations of the dynamic form, such as textures, lighting, and dynamic deformations. In addition, continuous rendering is performed on multiple frames of data in the dynamic trajectory of the spacecraft to generate a time-series multi-view dynamic synthesis result.

[0086] The dynamic modeling and rendering method provided by the present invention can efficiently complete the dynamic reconstruction task of the spacecraft and is applicable to various on-orbit modeling requirements. In the training stage, the shape representation module and the dynamic deformation module are optimized separately, and the density field and geometric decoding are accurately constrained through a geometric loss function. In the testing stage, in actual tasks, by inputting the dynamic parameters of the spacecraft and real-time acquired images, the 3D geometric structure of the current state is decoded and a multi-view rendering result is generated.

[0087] The above are only the preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art, within the scope of the technical solution of the present invention, can make some changes or modifications to the above-disclosed technical content to form equivalent embodiments of equivalent changes. However, as long as it does not depart from the technical solution content of the present invention, and based on the technical essence of the present invention, any simple modification, equivalent replacement, and improvement made to the above embodiments still fall within the protection scope of the technical solution of the present invention.

Claims

1. A neural implicit surface dynamic 3D reconstruction method that decouples spacecraft shape and motion, characterized by: The specific steps include: Step 1: Data collection and preprocessing; Step 2: Static three-dimensional shape encoding; Step 3: Decoupling of dynamic deformation features; Step 4: Color rendering.

2. The neural implicit surface dynamic 3D reconstruction method for decoupling spacecraft shape and motion according to claim 1 is characterized in that: Step 1 specifically includes: Step 101: Use a high-precision 3D scanner to perform static Xingtai fine modeling of the spacecraft, capturing the shape contour, component details and overall geometric features; Step 102, dynamic data acquisition is performed by recording the geometric changes of the spacecraft under different deformation states; Step 103, collect a discretized multi-angle sampling strategy to ensure full coverage observation of the spacecraft morphology; Step 104: uniformly collect multi-view images and depth map information within a spherical range by adjusting the camera azimuth and elevation angles.

3. The neural implicit surface dynamic 3D reconstruction method for decoupling spacecraft shape and motion according to claim 1 is characterized in that: Step 2 specifically includes: Step 201: When processing the static shape of a spacecraft, a coding method based on implicit functions is used to map the three-dimensional space coordinates to the shape surface function to generate a continuous geometric representation; Step 202: Design an implicit representation network for static shapes, and model three-dimensional space points through a multi-layer perceptron. The input of the network is the spatial coordinates, and the output is the probability value of whether the point belongs to the surface of the spacecraft.

4. The neural implicit surface dynamic 3D reconstruction method for decoupling spacecraft shape and motion according to claim 1 is characterized in that: In step 3, the dynamic characteristics are decoupled from the static geometry by parameterization: Step 301: The dynamic deformation network takes the standard shape and the deformed shape as input, and generates a dynamic deformation vector by learning the relationship between shape changes; the vector describes the dynamic characteristics in the current state, and is combined with the static shape representation network to achieve geometric modeling under dynamic conditions; Step 302: during model training, the parameters of the static shape network are first fixed, and then the dynamic network is optimized; by comparing the point cloud data and implicit shape representation under various dynamic states, the network parameters are gradually adjusted so that it can efficiently express geometric changes under different dynamic conditions; Step 303, 3D convolution encoder f Ωs and f Ωp Provides initialization of the canonical shape and action state shape latent spaces. The encoders both take back-projected depth observations in the form of partial voxel grids V as input and use 3D convolutions and a final fully connected layer to output latent code estimates. Shape Encoder: Given a shape latent space learned from the canonical space in the training dataset, and a set of voxel grids of P action spaces available in the training dataset, train f Ωs Predicting a mapping from a voxel grid to an underlying shape latent code for the corresponding identity; Action Encoder: Given a list of action codes learned from P action shapes in the dataset, and a set of P voxel grids, train f Ωp Predicting a mapping from a voxel grid of pose shapes to a corresponding action latent space; Step 304: Using the dynamic geometry decoding module, the static shape latent space and the motion latent space are interpolated and combined to reconstruct a dynamically changing three-dimensional shape.

5. The neural implicit surface dynamic 3D reconstruction method for decoupling spacecraft shape and motion according to claim 1 is characterized in that: In step 4, based on the 3D reconstruction, the neural radiation field is used to render the dynamic geometric surface with high quality, supporting the synthesis of detailed views; a lighting and color modeling network based on dynamic geometry is designed, and the color and transparency values ​​of each sampling point are generated by inputting the dynamic surface representation into the color field network, combining the camera perspective and the light direction. Based on the ray tracing algorithm, the dynamic surface is sampled, each ray is divided into several sampling points, and the final perspective image is calculated through the volume rendering formula. The rendering result shows the details of the dynamic scene, including light and shadow, texture and deformation characteristics.

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