A voxel-based neural implicit surface generation and interaction method

Abstract

The application discloses a kind of neural implicit surface generation and interaction method based on voxel, belong to computer vision and computer graphics field.The application is decomposed into geometric unit with voxel block as unit by three-dimensional scene, and the geometry and texture information in its interior are stored in the form of feature vector in voxel block, the feature of corresponding three-dimensional point is obtained by interpolation, and signed distance field (SDF) and corresponding color are obtained by geometric analysis network and texture analysis network two parts.On this basis, the application further improves the surface and texture accuracy of model by progressive voxel culling and decomposition;It is proposed to increase the number of effective point sampling by using surface perception sampling.The surface and texture effect after editing can be rendered by the interactive editing of the generated voxel block.

Description

Technical Field

[0001] This invention relates to the fields of computer vision and computer graphics, and more particularly to a voxel-based neural implicit surface generation and interaction method. Background Technology

[0002] Virtual content generation and interaction are crucial components of 3D applications. Typically, virtual content requires professional designers to construct, a process that is both complex and time-consuming. Therefore, automatically reconstructing accurate surfaces from multi-view images is essential for virtual content generation, and this is a significant research topic in computer vision and computer graphics. Before the era of deep learning, image surface reconstruction primarily relied on multi-view stereo geometry (MVS) techniques, which heavily depend on feature detection and matching. While these methods are relatively mature in both academia and industry, their reliance on indirect feature matching and point cloud representation leads to information loss during reconstruction. This information loss poses a challenge for reconstructing complex scenes. For example, in cases of weak textures, repetitive features, or inconsistent brightness, it is difficult to match accurate features, resulting in the generation of incorrect 3D points and ultimately, defects in the reconstructed surface. Furthermore, since the textures corresponding to the meshes are generated separately, discrete triangular meshes and inconsistent texture patches often fail to render realistic scenes.

[0003] In the past two years, works using neural networks to represent scenes have emerged and quickly become a research hotspot. Works such as OccupancyNet and DeepSDF have shown that implicit surfaces can be generated through learning, such as signed distance fields (SDF) or occupancy fields, and stored in multilayer perceptrons (MLPs). These networks can learn continuous scene representations from discrete 3D point samples. Based on this discovery, DVR and IDR have extended this representation to image-based surface reconstruction tasks. However, these methods only learn textures from points on the surface, making it difficult to learn accurate surfaces without sufficient observations.

[0004] With the advent of NeRF-based methods, novel view synthesis tasks have seen significant improvements. NeRF and its extensions have made notable progress by learning the neural radiation field of a scene through volumetric rendering. However, these methods cannot accurately reconstruct surfaces. Subsequently, methods like NeuS, UNISURF, and VolSDF proposed combining SDF and radiation fields to achieve surface reconstruction. These methods can be trained end-to-end directly from multi-view images without introducing additional representations, thus minimizing information loss and achieving higher accuracy than traditional methods.

[0005] However, these methods reconstruct the entire space using only a single network, which limits large-scale reconstruction due to network capacity. Furthermore, the scene is implicitly embedded within the network, making it impossible to perform interactive operations such as scene segmentation and editing. Summary of the Invention

[0006] To address the above issues, this invention employs a hybrid architecture consisting of explicit voxel representation and implicit surface representation. This architecture combines the advantages of both representations, allowing for explicit manipulation of the scene while possessing implicit surface and texture representation capabilities. The proposed Vox-Surf is a voxel-based neural implicit surface rendering framework that combines voxel-based methods with image-based implicit surface reconstruction methods, enabling efficient surface reconstruction and rendering.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention first provides a voxel-based method for generating and interacting with neural implicit surfaces, comprising the following steps:

[0009] Step 1: Divide the scene into multiple non-overlapping voxel blocks aligned with the coordinate axes in advance, and establish an octree structure corresponding to the voxel blocks; store the geometric and texture information inside the voxel blocks in the form of fixed-length optimizable feature vectors in the 8 vertices of the voxel blocks;

[0010] Step 2: By inputting multiple RGB or RGBD images with known camera positions and orientations, generate a ray that passes through pixels on the image from the camera center, and calculate the intersection of the ray with the voxel block. Perform 3D point sampling in the area where the ray intersects with the voxel block, and obtain the feature vector of the voxel block where the point is located through the 3D point coordinates. Then, obtain the signed distance field (SDF) and intermediate information through a geometric analysis network, and finally obtain the color through a texture analysis network using the obtained intermediate information.

[0011] Step 3: Calculate the spatial density value corresponding to the 3D point through SDF, then accumulate the weight of the color on the ray through volume rendering, obtain the color of the pixel corresponding to the predicted ray through volume rendering, and compare it with the real color. This optimizes the feature vectors on the geometry parsing network, texture parsing network and voxel block, and gradually generates the neural implicit surface of the scene through progressive training.

[0012] Step 4: For the neural implicit surface of the scene obtained in Step 3, which contains voxel blocks with geometric and texture information feature vectors, render and interact with the voxel blocks individually.

[0013] Furthermore, the three-dimensional point sampling in step 2 specifically involves:

[0014] A surface-sensing sampling strategy is used to sample regions on the ray that intersect with the voxel block. The process consists of three steps:

[0015] (1) First, sample three-dimensional points p in the region where the ray intersects with the voxel block according to uniform probability, and obtain the feature vector e of p through the feature extraction function.

[0016] (2) Then, the geometric analytical network F is used. σ The SDF of each sampling point is calculated; whether the region contains a surface is determined by whether the SDF of two consecutive 3D points changes from positive to negative along the ray direction, and the voxel blocks containing these points are marked as important voxels.

[0017] (3) Finally, increase the sampling probability inside important voxels and decrease the sampling probability inside other voxel blocks. Resample in areas where the ray intersects with the voxel blocks, but keep the total number of sampling points fixed.

[0018] Furthermore, in step 3, obtaining the color of the pixel corresponding to the predicted ray through volume rendering specifically involves:

[0019] Using S-density function φ s (σ) converts the SDF of a 3D point p into density, φ s (σ) is a unimodal function of the signed distance σ with respect to point p, where

[0020]

[0021] It is the Sigmoid function Φ s The derivative of , s is the scale parameter that controls the shape of the distribution, and the value of points closer to the surface is greater than the weight of points farther away;

[0022] Based on φ s (σ), the opaque density ρ(t) is defined as follows:

[0023]

[0024] Therefore, the volume density function in volume rendering is defined as follows:

[0025]

[0026] The discrete cumulative transmittance in the volume rendering is shown below:

[0027]

[0028] Therefore, for N on the ray p By performing volume rendering on 3D sampling points, the cumulative color C(r) can be obtained:

[0029]

[0030] Where c i Let i be the color of point i on the ray.

[0031] According to a preferred embodiment of the present invention, the progressive training in step 3 specifically comprises:

[0032] Progressive training involves removing and decomposing voxel blocks from coarse to fine. By gradually removing voxel blocks that do not contain surfaces and decomposing the remaining voxel blocks, a more refined surface generation effect can be obtained.

[0033] The voxel block removal process involves: first, uniformly sampling sufficient 3D points within each voxel block; then using a geometric analytical network F... σ Calculate the SDF of the 3D points; define a distance threshold τ to determine whether to keep or discard the voxel block;

[0034]

[0035] Here K i ∈{0,1} is a flag, where 1 indicates a reserved voxel;

[0036] The steps of voxel block decomposition are as follows: decompose the remaining voxel block into 8 sub-voxel blocks, use the feature retrieval function Γ to calculate the feature vectors of the corner vertices of the newly generated sub-voxel blocks, and these feature vectors will be optimized separately later.

[0037] Compared with existing technologies, the advantages of this invention are:

[0038] 1) The proposed 3D representation method, named Vox-Surf, achieves the partitioning and storage of 3D scenes by storing them in multiple disjoint voxel blocks. Vox-Surf combines the advantages of voxel representation and neural implicit surfaces, and can be learned end-to-end. The proposed Vox-Surf is a voxel-based neural implicit surface representation that can be learned end-to-end from multi-view images. Compared with existing technologies, this invention generates independent geometric rendering units based on voxel blocks, making it more suitable for interactive scene editing.

[0039] 2) This invention uses progressive training and surface-aware sampling strategies to improve reconstruction quality without increasing memory overhead. Furthermore, the Ray-AABB intersection detection strategy and the use of a smaller network enable this invention to render faster than existing methods. Attached Figure Description

[0040] Figure 1 This is a summary diagram of the Vox-Surf reconstruction process of the present invention;

[0041] Figure 2This is a schematic diagram of the surface sensing sampling process of the present invention;

[0042] Figure 3 This is a schematic diagram illustrating the progressive voxel and surface reconstruction training process proposed in this invention;

[0043] Figure 4 This is a schematic diagram of the interactive editing function of the present invention. Detailed Implementation

[0044] The present invention will now be described in detail with reference to the accompanying drawings. The technical features of each embodiment of the present invention can be combined accordingly without conflict.

[0045] The voxel-based neural implicit surface generation and interaction method of the present invention includes the following steps:

[0046] Step 1: Divide the scene into multiple non-overlapping voxel blocks aligned with the coordinate axes in advance, and establish an octree structure corresponding to the voxel blocks; store the geometric and texture information inside the voxel blocks in the form of fixed-length optimizable feature vectors in the 8 vertices of the voxel blocks.

[0047] Specifically, the scene is represented by a set of bold pixel blocks. The data is divided into segments, each voxel block has 8 corner vertices, and each corner vertex contains encoded geometric and texture information; this information is represented by a fixed-length, optimizable feature vector. It means, L e Let V be the length of the eigenvector; therefore, for any voxel V i any 3D point within Adjacent voxel blocks share the feature vectors of the four corner vertices.

[0048] Step 2: By inputting multiple RGB or RGBD images with known camera positions and orientations, generate a ray that passes through pixels on the image from the camera center, and calculate the intersection of the ray and the voxel block. Perform 3D point sampling in the area where the ray intersects the voxel block, and obtain the feature vector of the voxel block where the point is located through the 3D point coordinates. Then, obtain the symbolic distance field (SDF) and intermediate information through a geometric analysis network, and then obtain the color through a texture analysis network using the obtained intermediate information.

[0049] like Figure 1 As shown, a ray passing through a pixel in the image from the camera center o along the d direction is defined as r(t) = o + dt, where t is the depth along the ray direction. The depth of the intersection point between the ray and the voxel block is calculated using the Ray-AABB intersection detection algorithm, thereby delineating the regions on the ray that intersect with the voxel block.

[0050] In a preferred embodiment of the present invention, step 2, which involves obtaining the symbolic distance field (SDF) and intermediate information through a geometric analytical network, and then using the obtained intermediate information to obtain color through a texture analytical network, specifically involves defining a feature extraction function. Map the 3D point p to a length L e eigenvectors The feature extraction function is implemented through trilinear interpolation. Based on the three-dimensional coordinates of p and its relative position in the voxel block, the feature vectors contained in the eight corner vertices of the voxel block are interpolated to obtain the feature vector of p.

[0051] This invention uses a multilayer perceptron network (MLP) to represent the geometric analytic network F. σ and texture parsing network F c Geometric analytic networks The eigenvector e of p is mapped to its signed distance field and length L f Geometric eigenvectors The sign of σ indicates whether p is inside or outside the surface S. The surface S of the scene can be extracted using the following formula.

[0052]

[0053] Where operation [0] means from F σ The first value is obtained from the data, which in this example is the signed distance field σ of position p. The geometric feature vector f of the 3D point p, the ray direction d of p, and the feature vector e of p are concatenated to form the texture parsing network F. c The input is used to obtain the color c at point p. In practice, this invention adopts the positional encoding algorithm PE proposed in the NeRF method, which encodes the feature vector e before entering the geometric parsing network and the ray direction d before entering the texture parsing network.

[0054] In one embodiment of the present invention, a surface-sensing sampling strategy is proposed to perform three-dimensional point sampling on regions along the ray that intersect with the voxel block. This process can be roughly divided into three steps, such as... Figure 2 As shown: (1) First, three-dimensional points p are sampled in the region where the ray intersects with the voxel block according to uniform probability, and the feature vector e of p is obtained through the feature extraction function. (2) Then, the geometric analytical network F is used. σTo calculate the SDF of each sampling point. By judging whether the SDF of two consecutive three-dimensional points changes from positive (outside) to negative (inside) along the ray direction, it is determined whether this region contains a surface, and the voxel blocks containing these points are marked as important voxels. (3) Finally, the sampling probability inside the important voxels is increased and the sampling probability inside the remaining voxel blocks is decreased. The regions that intersect with the voxel blocks on the ray are resampled, but the total number of sampling points is kept fixed.

[0055] In practice, resampling is further divided into full-surface-sensing resampling based on whether only the first important voxel is used. Figure 2 (Image 3) and the first surface-sensing resampling ( Figure 2 (Last image). When the shape is unstable, the former is used to optimize all possible surfaces, while the latter is used to optimize the fine structure of the stable shape.

[0056] Step 3: Calculate the spatial density value corresponding to the 3D point through SDF, then accumulate the weight of the color on the ray through volume rendering, obtain the color of the pixel corresponding to the predicted ray through volume rendering, and compare it with the real color. This optimizes the feature vectors on the geometry parsing network, texture parsing network and voxel block, and gradually generates the neural implicit surface of the scene through progressive training.

[0057] Step 3, obtaining the color of the pixel corresponding to the predicted ray through volume rendering, specifically involves:

[0058] This invention employs the S-density function φ s (σ) converts the SDF of a 3D point p into density, φ s (σ) is a unimodal function of the signed distance σ with respect to point p, where

[0059]

[0060] It is the Sigmoid function Φ s The derivative of , s is a scale parameter that controls the shape of the distribution, with the value of points closer to the surface being greater than the weight of points farther away.

[0061] Based on φ s (σ), the opaque density ρ(t) is defined as follows:

[0062]

[0063] Therefore, the volume density function in volume rendering is defined as follows:

[0064]

[0065] The discrete cumulative transmittance in the volume rendering is shown below:

[0066]

[0067] Therefore, for N on the ray p By performing volume rendering on 3D sampling points, the cumulative color C(r) can be obtained:

[0068]

[0069] Where c i Let i be the color of point i on the ray.

[0070] The progressive training in step 3 specifically refers to:

[0071] Progressive training involves removing and decomposing voxel blocks from coarse to fine. By gradually removing voxel blocks that do not contain surfaces and decomposing the remaining voxel blocks, a more refined surface generation effect can be obtained.

[0072] The voxel culling process involves: first, uniformly sampling a sufficient number of 3D points within each voxel block; then, using a geometric analytical network F... σ The SDF of the 3D points is calculated. To determine whether to retain or discard the voxel block, this invention defines a distance threshold τ.

[0073]

[0074] Here K i ∈{0,1} is a flag indicating whether to retain voxels, where 1 indicates that voxels are retained.

[0075] The voxel block decomposition steps are as follows: decompose the remaining voxel block into 8 sub-voxel blocks, and use the feature retrieval function Γ to calculate the feature vectors of the corner vertices of the newly generated sub-voxel blocks. These feature vectors will be optimized separately later.

[0076] The effect after each voxel block removal and decomposition is as follows Figure 3 The four images on the left show the final generated surface and texture as follows: Figure 3 As shown in the two pictures on the right.

[0077] To optimize the feature vector, geometric parsing network, and texture parsing network, this invention utilizes the following loss function. For each ray, the cumulative color C(r) of the ray is first calculated, and then compared with the true color. Calculate the L1 loss.

[0078]

[0079] To constrain the SDF, this invention also adds an eikonal loss term to the sampled 3D point p. This term maintains the stability of the SDF by constraining the normal vectors of adjacent sampled points.

[0080]

[0081] The final loss function used is

[0082]

[0083] If the input includes depth information, this invention additionally uses a depth loss based on occupancy field.

[0084] Occupied field is defined as

[0085] occ(t) = Sigmoid(-scale·F) σ (Γ(r(t)))[0])

[0086] Since the gradient of the occupancy field only peaks near the surface S, this invention divides the ray r(t) with depth information into three intervals, each corresponding to a different loss:

[0087]

[0088] For a given depth For the previous points, δt represents a small noise tolerance depth range. This invention always assumes that these points are outside the surface.

[0089]

[0090] For a given depth The present invention always assumes that these points are within the surface. Experiments have shown that this loss remains effective even when the rays intersect multiple surfaces, provided sufficient observation is made.

[0091]

[0092] for The points between these points are considered to be on the surface, therefore the direct constraint SDF is 0.

[0093] Finally, the total depth loss is a combination of the three losses mentioned above:

[0094]

[0095] Step 4: For the neural implicit surface of the scene obtained in Step 3, which contains voxel blocks with geometric and texture information feature vectors, perform individual rendering and interaction on the voxel blocks. Specifically, the individual rendering and interaction in Step 4 means that each voxel block trained in Step 3 can be considered an independent geometric unit. By modifying the position, size, orientation, and other properties of the voxel blocks, the scene can be directly interactively edited, increasing the degree of freedom of interaction. Furthermore, the volume rendering in Step 3 directly generates realistic texture effects from the current viewpoint.

[0096] Example

[0097] This invention was tested on two different types of datasets: the small scene object dataset DTU and the indoor scene dataset ScanNet. For the DTU dataset, the invention first generates initial voxel blocks and corresponding octrees within a unit cube with a voxel size of 0.8. Voxel block culling is performed every 50,000 iterations, with further voxel block decomposition at iterations of 20,000, 50,000, 100,000, 20,000, and 300,000, with a culling threshold of 0.01. Uniform voxel sampling is used before the second segmentation, and a full-surface-aware voxel resampling strategy is used from the second to the fourth segmentation. After the fourth segmentation, first-surface-aware voxel resampling is used to further refine details. The voxel embedding length is 16. The geometry parsing network is a 4-layer MLP with 128 hidden units per layer, and the texture parsing network is also a 4-layer MLP with 128 hidden units per layer. Before inputting the data to the extractor, positional encoding at six frequencies was used on the voxel features, and positional encoding at eight frequencies was used on the ray directions. This invention compares COLMAP, DVR, IDR, and the currently most accurate NeuS method, using the Chamfer metric to evaluate the accuracy of the real 3D model and the reconstructed 3D model. The average accuracy of this invention is higher than that of NeuS and IDR.

[0098] For the Scannet dataset, this invention uses depth-integrated data for training. First, all depth observations are back-projected onto 3D points, and then these points are voxelized using an initial voxel size of 0.4. Since the RGB-D sensor is accurate only within a certain distance, the maximum depth range is limited to 5.0 to reduce noisy samples. This invention also progressively decomposes and removes voxels twice during training, resulting in a minimum voxel size of 0.1. This invention compares with the COLMAP and TSDF methods, and also compares the chamfer metric and F-score, showing significantly better results than the traditional TSDF method.

[0099] This invention can be applied to the editing of scenes and objects, such as... Figure 4 As shown, by modifying the voxel units in this method, aligning and copying, local scaling, segmentation, and other operations, the corresponding realistic scene can be rendered directly.

[0100] The above examples are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for voxel-based neural implicit surface generation and interaction, comprising: The method comprises the following steps: Step 1: pre-divide the scene into a plurality of non-overlapping voxel blocks aligned with the coordinate axes, and establish an octree structure corresponding to the voxel blocks; store the geometric and texture information in the voxel blocks in the form of fixed-length optimizable feature vectors in the 8 vertices of the voxel blocks; Step 2: generate a ray passing through the pixels on the image from the camera center, calculate the intersection of the ray and the voxel block, and perform three-dimensional point sampling in the intersection area of the ray and the voxel block, obtain the feature vector of the voxel block where the three-dimensional point is located through the three-dimensional point coordinates; obtain the signed distance field SDF and intermediate information through the geometric analysis network, and then obtain the color through the texture analysis network; Step 3: calculate the spatial density value corresponding to the three-dimensional point through the SDF, and then perform weight accumulation on the color on the ray through volume rendering, obtain the predicted color of the pixel corresponding to the ray through volume rendering, and compare it with the true color, thereby optimizing the geometric analysis network, the texture analysis network and the feature vector on the voxel block, and gradually generating the neural implicit surface of the scene through progressive training; Step 4: for the neural implicit surface of the scene obtained in step 3, which contains the geometric and texture information feature vectors of the voxel block, render and interact with the voxel block separately.

2. The voxel-based neural implicit surface generation and interaction method of claim 1, wherein, The step 1 is specifically: A scene is represented by a set of coarse voxel blocks Each voxel block has 8 corner vertices, among which the encoded geometry and texture information is contained; this information is represented by fixed-length optimizable feature vectors L e is the length of the feature vector; thus, for any 3D point i inside a voxel V ; neighboring voxel blocks share 4 corner vertices' feature vectors.

3. The voxel-based neural implicit surface generation and interaction method of claim 1, wherein, The calculation of the intersection of the ray and the voxel block in step 2 is specifically: The ray passing through the pixels on the image from the camera center o in the d direction is defined as r(t) = o + dt, t is the depth in the direction of the ray; the depth of the intersection of each ray and the voxel block is calculated through the Ray-AABB intersection detection algorithm, thereby dividing the area on the ray that has intersection with the voxel block.

4. The voxel-based neural implicit surface generation and interaction method of claim 1, wherein, The three-dimensional point sampling in step 2 is specifically: The surface perception sampling strategy is adopted to sample the area on the ray that has intersection with the voxel block, which is divided into three steps: (1) first, sample a three-dimensional point p in the area on the ray that has intersection with the voxel block according to the uniform probability, and obtain the feature vector e of p through the feature extraction function, (2) Then use the geometric analytical network F σ to calculate the SDF of each sampling point; determine whether the region contains the surface by judging whether the SDF of the two three-dimensional points in succession changes from positive to negative along the ray direction, and mark the voxel block containing the points as important voxels; (3) finally, increase the sampling probability in the important voxel and decrease the sampling probability in the remaining voxel, resample in the area on the ray that has intersection with the voxel block, but keep the total number of sampling points fixed.

5. The voxel-based neural implicit surface generation and interaction method of claim 1, wherein, The step 2 is specifically: Defining a feature extraction function : Mapping a three-dimensional point p to a feature vector of length L e The feature extraction function is implemented by trilinear interpolation, and the feature vector of p is obtained by interpolating the feature vectors contained in the eight corner vertices of the voxel block according to the three-dimensional coordinates of p and the relative position of p in the voxel block.​ A multi-layer perceptron network, MLP, is used to represent the geometric analytic network F σ and the texture analytic network F c ; geometric analytic network mapping the feature vector e of p to its signed distance field and length L f geometric feature vector ; the sign of s indicates whether p is inside or outside the surface S; the surface S of the scene can be extracted by the following equation ； where operation [0] means to get the signed distance field σ for position p from F σ ; The geometric feature vector f of the three-dimensional point p, the direction d of the ray on which p lies, and the feature vector e of p are concatenated as the input of the texture analysis network F c to obtain the color c at p.

6. The voxel-based neural implicit surface generation and interaction method of claim 3, wherein, The step 3 is specifically: S-density function converts the SDF of a three-dimensional point p to a density, is a unimodal function of the signed distance to the point p, where ； is the derivative of the sigmoid function Φ s with a scale parameter s that controls the shape of the distribution, with points closer to the surface having greater weight than points farther away. Based on , the opacity density p(t) is defined as follows ； The volume density function in volume rendering is defined as: ； The discrete cumulative transmittance in volume rendering is defined as: ； Thus, volume rendering of N p three-dimensional sample points on the ray can result in a cumulative color C(r): ； where c i is the color of point i on the ray.

7. The voxel-based neural implicit surface generation and interaction method of claim 1, wherein, The step 3 is specifically: The progressive training is a coarse-to-fine elimination and decomposition of the voxel block, which gradually eliminates the voxel blocks that do not contain the surface, and decomposes the remaining voxel blocks to obtain a more fine surface generation effect; wherein the step of voxel block culling is: first, uniformly sampling enough 3D points in each voxel block; then using a geometric analytical network F σ to calculate the SDF of the 3D points; in order to decide whether to keep or discard the voxel block, a distance threshold is defined ; ； Here is a flag where 1 indicates a reserved voxel; The step of voxel block decomposition is to decompose the remaining voxel block into 8 sub-voxel blocks, using a feature retrieval function The feature vectors of the newly generated sub-voxel block corner vertices are computed, which will be subsequently optimized individually.

8. The voxel-based neural implicit surface generation and interaction method of claim 1, wherein, The step 4 is specifically: The trained voxel block in step 3 can be regarded as an independent geometric unit, and the scene can be directly edited interactively by changing the position, size and orientation of the voxel block, thereby improving the degree of freedom of interaction, and real texture effects under the current view angle can be directly generated by volume rendering in step 3.

Images