Orientation perception-based Gaussian ball single-side rendering method and system

Abstract

The invention provides a single-side rendering method and system of Gaussian balls based on orientation perception, and relates to the technical field of image rendering, and the method comprises the steps: distributing a unit normal vector for each Gaussian ball to be rendered; calculating a unit observation direction of the Gaussian sphere by the camera, and calculating a cosine value between the unit normal vector and the unit observation direction; the opacity modulation weight corresponding to the unit observation direction is obtained through calculation based on the cosine value, finally the final opacity is obtained through calculation according to the opacity modulation weight and the original opacity of the Gaussian balls, and finally each Gaussian ball is rendered based on the final opacity. The method has the beneficial effects that the problem of rendering distortion of the front and back surfaces of a thin-layer object in the prior art is solved, the sense of reality of a rendering result is greatly improved, and the complexity of scene representation and the storage and calculation overhead are also remarkably reduced.

Description

Technical Field

[0001] This invention relates to the field of image rendering technology, and in particular to a single-sided rendering method and system based on an orientation-aware Gaussian sphere. Background Technology

[0002] In recent years, significant progress has been made in 3D scene reconstruction and rendering technologies based on Neural Radiation Fields (NeRF). Among them, 3D Gaussian Splatling (3DGS) technology has attracted much attention due to its fast training speed, high rendering quality, and ability to achieve real-time rendering. 3DGS represents a scene as a large number of 3D Gaussian spheres, each with attributes such as position, covariance (controlling its shape and size), color (spherical harmonic function coefficients), and opacity (alpha value). During rendering, the final pixel color is synthesized by projecting the 3D Gaussian spheres onto a 2D image plane and performing alpha blending.

[0003] However, existing 3DGS technology has an inherent physical flaw: each Gaussian sphere is optically isotropic, meaning its appearance does not depend on the relative relationship between the viewing direction and the surface normal of the object. Specifically, the color and opacity of a Gaussian sphere are exactly the same when viewed from the front and back.

[0004] This assumption is approximately valid for most solid objects, but it produces serious visual errors when rendering many common thin-layered objects. These objects include, but are not limited to: 1. Plant leaves and petals: usually very thin, and the front and back sides may have drastically different colors or textures.

[0005] 2. Paper and fabric: The front and back may be different.

[0006] 3. Signs and murals: They are two-dimensional planes that are attached to three-dimensional surfaces.

[0007] 4. Any geometric solid that can be considered "one-sided" in the physical world.

[0008] Within the existing 3DGS framework, to represent a blade, at least two Gaussian spheres that are spatially very close or even overlapping are typically needed to simulate the front and back sides respectively. In many cases, due to limitations in reconstruction accuracy or viewing angle, the system may only learn one Gaussian sphere to represent the entire blade. In this situation, when the camera observes from the back of the blade, the color of the blade's back side, which should be invisible, will be incorrectly rendered, creating a false visual effect of "transparency" or "uniform color on both sides," severely compromising the realism of the rendering result.

[0009] Therefore, there is an urgent need in this field for an improved technology that can accurately simulate the single-sided optical properties of thin-layer objects while maintaining the original advantages of 3DGS in terms of high efficiency and differentiability. Summary of the Invention

[0010] To address the problems existing in the prior art, this invention provides a single-sided rendering method based on an orientation-aware Gaussian sphere, comprising: Step S1: For each Gaussian sphere to be rendered, assign a unit normal vector to the Gaussian sphere; Step S2: Calculate the unit viewing direction of the camera to the Gaussian sphere, and calculate the cosine value between the unit normal vector and the unit viewing direction; Step S3: Calculate the opacity modulation weight corresponding to the unit viewing direction based on the cosine value, and finally calculate the final opacity based on the opacity modulation weight and the original opacity of the Gaussian sphere. Finally, render each Gaussian sphere based on the final opacity.

[0011] Preferably, in step S1, a pre-trained model is used to assign unit normal vectors, and the training process includes: In each round of training, a set of scenes represented by Gaussian spheres and a set of corresponding training set images are input into the model. The parameters of each Gaussian sphere include a normal vector. Then, the model optimizes the parameters of all Gaussian spheres by stochastic gradient descent with the goal of making the image parameters of the projected images obtained by the camera from each Gaussian sphere consistent with the image parameters of the training set images. After each round of training, the model adjusts the gradient for the next training iteration and performs multiple rounds of iterative training until the deviation between the image parameters of the optimized projected image calculated by the model using the loss function after this round of training and the image parameters of the training set image is less than a preset threshold, thus obtaining the trained model.

[0012] Preferably, step S2 includes: Step S21: The direction from the center point of the Gaussian sphere to the center point of the camera is taken as the unit observation direction; Step S22: Calculate the dot product of the unit viewing direction and the unit normal vector to obtain the cosine value between the unit normal vector and the unit viewing direction.

[0013] Preferably, step S3 includes: Step S31: Substitute the cosine value into the pre-constructed modulation function to calculate the corresponding opacity modulation weight; Step S32: Calculate the product of the opacity modulation weight and the original opacity to obtain the final opacity, and finally render the Gaussian sphere based on the final opacity.

[0014] Preferably, the modulation function is w = (cosθ + 1) / 2; Wherein, cosθ is the cosine value, w is the opacity modulation weight, cosθ=n · v, n is the unit normal vector, and v is the unit viewing direction.

[0015] This invention also provides a single-sided rendering system based on an orientation-aware Gaussian sphere, applying the real-time radiation field rendering method described above, including: The normal vector allocation module is used to allocate a unit normal vector to each Gaussian sphere to be rendered. The cosine calculation module, connected to the normal vector allocation module, is used to calculate the unit viewing direction of the camera to the Gaussian sphere, and to calculate the cosine value between the unit normal vector and the unit viewing direction; The rendering module, connected to the cosine calculation module, is used to calculate the opacity modulation weight corresponding to the unit viewing direction based on the cosine value, and finally calculate the final opacity based on the opacity modulation weight and the original opacity of the Gaussian sphere, and finally render each Gaussian sphere based on the final opacity.

[0016] Preferably, the normal vector allocation module uses a pre-trained model to allocate unit normal vectors, and the normal vector allocation module includes: The model training unit is used to input a set of scenes represented by Gaussian spheres and a set of corresponding training set images into the model in each training round. The parameters of each Gaussian sphere include a normal vector. Then, the model optimizes the parameters of all Gaussian spheres by using stochastic gradient descent, aiming to make the image parameters of the projected images obtained by the camera from each Gaussian sphere consistent with the image parameters of the training set images. After each round of training, the model adjusts the gradient for the next training iteration and performs multiple rounds of iterative training until the deviation between the image parameters of the optimized projected image calculated by the model using the loss function on each Gaussian sphere after the current training and the image parameters of the training set image is less than a preset threshold, thus obtaining the trained model.

[0017] Preferably, the cosine calculation module includes: A direction calculation unit is used to take the direction from the center point of the Gaussian sphere to the center point of the camera as the unit observation direction; The cosine calculation unit, connected to the direction calculation unit, is used to calculate the dot product of the unit viewing direction and the unit normal vector to obtain the cosine value between the unit normal vector and the unit viewing direction.

[0018] Preferably, the rendering module includes: The weight calculation unit is used to substitute the cosine value into the pre-constructed modulation function to calculate the corresponding opacity modulation weight; The rendering unit, connected to the weight calculation unit, is used to calculate the product of the opacity modulation weight and the original opacity to obtain the final opacity, and finally render the Gaussian sphere based on the final opacity.

[0019] Preferably, the modulation function is w = (cosθ + 1) / 2; Wherein, cosθ is the cosine value, w is the opacity modulation weight, cosθ=n · v, n is the unit normal vector, and v is the unit viewing direction.

[0020] The above technical solution has the following advantages or beneficial effects: By adding a unit normal vector to each Gaussian sphere and dynamically adjusting the effective opacity of the Gaussian sphere during rendering using the angle between the unit normal vector and the camera's unit viewing direction, a thin surface can be correctly simulated. This avoids the problem of front and back rendering distortion, such as the back color being rendered incorrectly when viewing the thin surface from the front, resulting in transparency or the same color on both sides. This significantly improves the realism of the rendering results and also significantly reduces the complexity of scene representation and storage and computational overhead. Attached Figure Description

[0021] Figure 1 A flowchart illustrating a single-sided rendering method based on an orientation-aware Gaussian sphere, as a preferred embodiment of the present invention. Figure 2 This is a schematic diagram of a sub-process of step S2 in a preferred embodiment of the present invention; Figure 3 This is a schematic diagram of a sub-process of step S3 in a preferred embodiment of the present invention; Figure 4 In a preferred embodiment of the present invention, the modulation function is plotted as follows; Figure 5 This is a schematic diagram of a single-sided rendering system based on an orientation-aware Gaussian sphere, which is a preferred embodiment of the present invention. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The present invention is not limited to this embodiment; other embodiments that conform to the spirit of the present invention may also fall within the scope of the present invention.

[0023] In a preferred embodiment of the present invention, based on the above-mentioned problems existing in the prior art, a single-sided rendering method based on an orientation-aware Gaussian sphere is provided, such as... Figure 1 As shown, it includes: Step S1: For each Gaussian sphere to be rendered, assign a unit normal vector to the Gaussian sphere; Step S2: Calculate the unit viewing direction of the camera to the Gaussian sphere, and calculate the cosine value between the unit normal vector and the unit viewing direction; Step S3: Calculate the opacity modulation weight corresponding to the unit viewing direction based on the cosine value. Finally, calculate the final opacity based on the opacity modulation weight and the original opacity of the Gaussian sphere. Finally, render each Gaussian sphere based on the final opacity.

[0024] Specifically, in this embodiment, based on the existing attributes of 3DGS technology (position, 3D covariance, spherical harmonic color, and opacity), a unit normal vector is added to each Gaussian sphere. This normal vector can be automatically learned through gradient descent during model training, and the effective opacity of the Gaussian sphere is dynamically modulated using the angle between this unit normal vector and the unit viewing direction, thereby achieving single-sided rendering.

[0025] In this way, when two different Gaussian spheres represent the front and back of a leaf, for a Gaussian sphere representing the front of the leaf, when viewed from the front (or the side to be observed), its final opacity α'_i ≈ the original opacity α_i, displaying its color normally; when viewed from the back, its final opacity α'_i ≈ 0, becoming completely transparent, thus contributing nothing to the final color and correctly simulating the physical properties of a single-sided surface. The principle is the same for the Gaussian sphere representing the back of the leaf, and will not be elaborated here. This effectively solves the problem of rendering errors on the front and back of thin-layer objects, significantly improving the realism of the rendering results, and is especially suitable for common scenes such as plants and paper.

[0026] Building upon the aforementioned single-sided rendering principle, its application is further expanded to include mirror reflection scenes. For scenes requiring simulated mirror reflection, such as a mirror constructed from a Gaussian sphere on a bathroom wall, existing methods typically treat the mirror as the center of symmetry, considering the front and back of the mirror as the physical space and the virtual image space, respectively. A Gaussian sphere, identical to those in the physical space, is then placed symmetrically in the virtual image space to simulate the reflected virtual image. However, due to the lack of single-sided rendering capabilities in traditional 3DGS technology, it is impossible to directly observe the virtual image space from the physical space while preserving the mirror surface. Often, the virtual image can only be indirectly presented by removing or partially hollowing out the mirror surface, frequently resulting in distorted rendering effects.

[0027] The single-sided rendering method proposed in this invention effectively solves this problem: when observing the virtual image space through the mirror from the physical space, the Gaussian sphere of the mirror itself can automatically adjust its opacity according to the viewing angle, making it visually "transparent." This allows the observer to clearly observe the reflected content in the virtual image space without deleting or destroying the mirror structure. This mechanism not only preserves the realism of the mirror as a physical object but also significantly improves the accuracy of mirror reflection simulation and the overall scene rendering realism.

[0028] In a preferred embodiment of the present invention, step S1 uses a pre-trained model to assign unit normal vectors, and the training process includes: In each round of training, a set of scenes represented by Gaussian spheres and a set of corresponding training set images are input into the model. The parameters of each Gaussian sphere include the normal vector. Then, the model optimizes the parameters of all Gaussian spheres by stochastic gradient descent with the goal of making the image parameters of the projected images of each Gaussian sphere obtained by the camera consistent with the image parameters of the training set images. After each round of training, the model adjusts the gradient for the next training round and performs multiple rounds of iterative training until the deviation between the image parameters of the optimized projected image calculated by combining the normal vectors of the current training round and the image parameters of the training set image is less than a preset threshold, thus obtaining the trained model.

[0029] Specifically, in this embodiment, a set of extended Gaussian spheres is used to represent the scene. The attributes of each Gaussian sphere Gi are: world coordinate position μ_i, three-dimensional covariance matrix Σ_i (usually parameterized by scaling matrix S_i and rotation matrix R_i), spherical harmonic coefficients SH_i, original opacity α_i, and newly added unit normal vector n_i.

[0030] The training process employs an iterative training approach, including: The training data for the model consists of a training set of scene images with known camera poses. During one training iteration, a training image is selected, and a scene with the same object positions as in the training image is constructed using multiple Gaussian spheres. Then, the camera observes each Gaussian sphere in the scene from the same camera pose as in the training image to obtain a projected image. A standard 3DGS training process is then used, with the goal of optimizing the parameters of all Gaussian spheres (including position, covariance, color, opacity, and the unit normal vector added in this invention) to minimize the difference between the projected image rendered using these parameters and the image parameters of the input training image (specifically, parameters representing the true properties of objects in the image, such as color and morphological features).

[0031] In each training iteration, the system performs forward rendering and calculates the loss value based on the difference between the optimized projected image (obtained through multiple training and optimization processes) and the training set image, calculated using the normal vectors (preferably, this invention employs a combination of the original 3DGS L1 loss and D-SSIM loss). Subsequently, this loss is backpropagated using stochastic gradient descent to simultaneously optimize the parameters of all Gaussian spheres (including the newly added unit normal vector). The normal vector parameters of the Gaussian sphere, representing the thin surface, spontaneously learn the direction perpendicular to the apparent geometry of the object's surface under the drive of the loss signal, without requiring manual supervision by setting the ground truth value of the normal vector.

[0032] Repeat the above iterative optimization process until the overall rendering quality of the model converges, that is, the loss value drops to a predetermined threshold or no longer changes significantly. At this point, the training is considered complete, and a set of Gaussian spheres that can accurately reflect the geometry and appearance of the scene is obtained, including physical normal vectors.

[0033] This invention enhances, rather than overturns, the existing 3DGS framework. For objects whose orientation is irrelevant, their normal vectors converge to a meaningless direction during training, and their volume characteristics are reflected through their own opacity α_i. Therefore, it will not negatively affect the representational capabilities of existing models.

[0034] In a preferred embodiment of the present invention, such as Figure 2 As shown, step S2 includes: Step S21: Use the direction from the center point of the Gaussian sphere to the center point of the camera as the unit observation direction; Step S22: Calculate the dot product of the unit viewing direction and the unit normal vector to obtain the cosine value between the unit normal vector and the unit viewing direction.

[0035] In a preferred embodiment of the present invention, such as Figure 3 As shown, step S3 includes: Step S31: Substitute the cosine value into the pre-constructed modulation function to calculate the corresponding opacity modulation weight; Step S32: Calculate the product of the opacity modulation weight and the original opacity to obtain the final opacity, and finally render the Gaussian sphere based on the final opacity.

[0036] In a preferred embodiment of the present invention, the modulation function is w=(cosθ+1) / 2; Where cosθ is the cosine value, w is the opacity modulation weight, cosθ=n · v, n is the unit normal vector, and v is the unit viewing direction.

[0037] Specifically, during the rendering process, for each Gaussian sphere i, the unit viewing direction v from its center point to the camera center is calculated.

[0038] Then, calculate the cosine of the angle θ between the unit normal vector n and the unit viewing direction v: cosθ = n · v.

[0039] Design a differentiable modulation function f(cosθ) that satisfies: When viewed from the front (cosθ> 0, i.e., the included angle is less than 90 degrees), f(cosθ) ≈ 1, allowing the Gaussian sphere to be fully visible.

[0040] When viewed from the opposite side (cosθ < 0, i.e., the included angle is greater than 90 degrees), f(cosθ) ≈ 0, making the Gaussian sphere completely transparent.

[0041] A smooth transition is made near cosθ = 0 (grazing angle) to ensure the differentiability of the function and facilitate model training.

[0042] The present invention preferably uses the following function as the modulation function: w = f(cosθ) = (cosθ + 1) / 2 This function maps cosθ ∈ [-1, 1] to w ∈ [0, 1]. w = 1 on the positive side (cosθ = 1) and w = 0 on the negative side (cosθ = -1). It is continuously differentiable within its domain. The graph is shown below. Figure 4 As shown.

[0043] The final opacity α'_i of a Gaussian sphere during rendering is determined by its original opacity α_i and the opacity modulation weight w_i, calculated as follows: α'_i=α_i * w_i=α_i * ((n·v)+1) / 2 This modulated final opacity α'_i will be used in subsequent alpha blending processes, such as real-time rendering: For a given camera pose, sort the Gaussian spheres by depth.

[0044] For each pixel, iterate through the overlapping Gaussian spheres and perform alpha blending.

[0045] Before mixing, perform the following operations on each Gaussian sphere i: a. Calculate the viewing direction v = (camera_position - μ_i).normalize(), where (camera_position - μ_i) represents the direction vector from the center position μ_i of the Gaussian sphere to the camera position camera_position, and .normalize() is a vector normalization function.

[0046] b. Calculate the cosine value cosθ = n·v.

[0047] c. Calculate the opacity modulation weight w_i=(cosθ+1) / 2.

[0048] d. Calculate the final opacity α'_i = α_i * w_i.

[0049] Using α'_i and the color c_i calculated by the Gaussian sphere according to the spherical harmonic function, the standard volume rendering alpha blending formula is executed to synthesize the final pixel color.

[0050] Compared with the prior art, the present invention has the following outstanding advantages: 1. The rendering effect is closer to reality, and it can accurately distinguish the front and back of objects, avoiding the problem of not being able to distinguish the front and back of thin objects (such as plant leaves, paper, etc.) in the rendering, and significantly improving the realism of the picture.

[0051] 2. Facilitates model training and optimization. The opacity modulation function used is smooth and differentiable, and can be seamlessly embedded into the original 3DGS training process without affecting the parameter optimization process based on gradient descent.

[0052] 3. This invention is a functional extension based on the original 3DGS framework. For objects without a clear orientation, their normal vectors are automatically adjusted to random directions during training that do not affect the rendering results, and their three-dimensional characteristics are still reflected through opacity, thus not weakening the performance capability of the original method.

[0053] 4. The additional computational burden is extremely light. The calculation of the dot product of the new normal vector and the view direction, as well as the opacity adjustment operation, are very simple and have virtually no impact on the original real-time rendering performance.

[0054] This invention also provides a single-sided rendering system based on an orientation-aware Gaussian sphere, applying the real-time radiation field rendering method described above, such as... Figure 5 As shown, it includes: Normal vector assignment module 1 is used to assign a unit normal vector to each Gaussian sphere to be rendered. Cosine calculation module 2, connected to normal vector allocation module 1, is used to calculate the unit viewing direction of the camera to the Gaussian sphere, and to calculate the cosine value between the unit normal vector and the unit viewing direction; Rendering module 3 is connected to cosine calculation module 2. It is used to calculate the opacity modulation weight corresponding to the unit viewing direction based on the cosine value. Finally, the final opacity is calculated based on the opacity modulation weight and the original opacity of the Gaussian sphere. Finally, each Gaussian sphere is rendered based on the final opacity.

[0055] In a preferred embodiment of the present invention, the normal vector allocation module uses a pre-trained model to allocate unit normal vectors. The normal vector allocation module 1 includes: The model training unit 11 is used to input a set of scenes represented by Gaussian spheres and a set of corresponding training set images into the model in each training round. The parameters of each Gaussian sphere include a normal vector. Then, the model optimizes the parameters of all Gaussian spheres by using stochastic gradient descent, aiming to make the image parameters of the projected images obtained by the camera from each Gaussian sphere consistent with the image parameters of the training set images. After each round of training, the model adjusts the gradient for the next training iteration and performs multiple rounds of iterative training until the deviation between the image parameters of the optimized projected image calculated by combining the normal vectors of the current training round and the image parameters of the training set image is less than a preset threshold, thus obtaining the trained model.

[0056] In a preferred embodiment of the present invention, the cosine calculation module 2 includes: The direction calculation unit 21 is used to take the direction from the center point of the Gaussian sphere to the center point of the camera as the unit observation direction; The cosine calculation unit 22 is connected to the direction calculation unit 21 and is used to calculate the dot product of the unit viewing direction and the unit normal vector to obtain the cosine value between the unit normal vector and the unit viewing direction.

[0057] In a preferred embodiment of the present invention, the rendering module 3 includes: The weight calculation unit 31 is used to substitute the cosine value into the pre-constructed modulation function to calculate the corresponding opacity modulation weight; The rendering unit 32 is connected to the weight calculation unit 31, which is used to calculate the product of the opacity modulation weight and the original opacity to obtain the final opacity, and finally renders the Gaussian sphere based on the final opacity.

[0058] In a preferred embodiment of the present invention, the modulation function is w = (cosθ + 1) / 2; Where cosθ is the cosine value, w is the opacity modulation weight, cosθ=n · v, n is the unit normal vector, and v is the unit viewing direction.

[0059] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made using the content of this specification and illustrations should be included within the protection scope of the present invention.

Claims

1. A single-sided rendering method based on an orientation-aware Gaussian sphere, characterized in that, include: Step S1: For each Gaussian sphere to be rendered, assign a unit normal vector to the Gaussian sphere; Step S2: Calculate the unit viewing direction of the camera to the Gaussian sphere, and calculate the cosine value between the unit normal vector and the unit viewing direction; Step S3: Calculate the opacity modulation weight corresponding to the unit viewing direction based on the cosine value, then calculate the final opacity based on the opacity modulation weight and the original opacity of the Gaussian sphere, and finally render each Gaussian sphere based on the final opacity.

2. The single-sided rendering method according to claim 1, characterized in that, In step S1, a pre-trained model is used to assign unit normal vectors. The training process includes: In each round of training, a set of scenes represented by Gaussian spheres and a set of corresponding training set images are input into the model. The parameters of each Gaussian sphere include a normal vector. Then, the model optimizes the parameters of all Gaussian spheres by stochastic gradient descent with the goal of making the image parameters of the projected images obtained by the camera from each Gaussian sphere consistent with the image parameters of the training set images. After each round of training, the model adjusts the gradient for the next training iteration and performs multiple rounds of iterative training until the deviation between the image parameters of the optimized projected image calculated by the model using the loss function after this round of training and the image parameters of the training set image is less than a preset threshold, thus obtaining the trained model.

3. The single-sided rendering method according to claim 1, characterized in that, Step S2 includes: Step S21: The direction from the center point of the Gaussian sphere to the center point of the camera is taken as the unit observation direction; Step S22: Calculate the dot product of the unit viewing direction and the unit normal vector to obtain the cosine value between the unit normal vector and the unit viewing direction.

4. The single-sided rendering method according to claim 1, characterized in that, Step S3 includes: Step S31: Substitute the cosine value into the pre-constructed modulation function to calculate the corresponding opacity modulation weight; Step S32: Calculate the product of the opacity modulation weight and the original opacity to obtain the final opacity, and finally render the Gaussian sphere based on the final opacity.

5. The single-sided rendering method according to claim 4, characterized in that, The modulation function is w = (cosθ + 1) / 2; Wherein, cosθ is the cosine value, w is the opacity modulation weight, cosθ=n · v, n is the unit normal vector, and v is the unit viewing direction.

6. A single-sided rendering system based on an orientation-aware Gaussian sphere, characterized in that, The single-sided rendering method described in any one of claims 1-5 includes: The normal vector allocation module is used to allocate a unit normal vector to each Gaussian sphere to be rendered. The cosine calculation module, connected to the normal vector allocation module, is used to calculate the unit viewing direction of the camera on the Gaussian sphere, and to calculate the cosine value between the unit normal vector and the unit viewing direction; The rendering module, connected to the cosine calculation module, is used to calculate the opacity modulation weight corresponding to the unit viewing direction based on the cosine value, and finally calculate the final opacity based on the opacity modulation weight and the original opacity of the Gaussian sphere, and finally render each Gaussian sphere based on the final opacity.

7. The single-sided rendering system according to claim 6, characterized in that, The normal vector allocation module uses a pre-trained model to allocate unit normal vectors. The normal vector allocation module includes: The model training unit is used to input a set of scenes represented by Gaussian spheres and a set of corresponding training set images into the model in each training round. The parameters of each Gaussian sphere include a normal vector. Then, the model optimizes the parameters of all Gaussian spheres by using stochastic gradient descent, aiming to make the image parameters of the projected images obtained by the camera from each Gaussian sphere consistent with the image parameters of the training set images. After each round of training, the model adjusts the gradient for the next training iteration and performs multiple rounds of iterative training until the deviation between the image parameters of the optimized projected image calculated by the model using the loss function on each Gaussian sphere after the current training and the image parameters of the training set image is less than a preset threshold, thus obtaining the trained model.

8. The single-sided rendering system according to claim 6, characterized in that, The cosine calculation module includes: A direction calculation unit is used to take the direction from the center point of the Gaussian sphere to the center point of the camera as the unit observation direction; The cosine calculation unit, connected to the direction calculation unit, is used to calculate the dot product of the unit viewing direction and the unit normal vector to obtain the cosine value between the unit normal vector and the unit viewing direction.

9. The single-sided rendering system according to claim 6, characterized in that, The rendering module includes: The weight calculation unit is used to substitute the cosine value into the pre-constructed modulation function to calculate the corresponding opacity modulation weight; The rendering unit, connected to the weight calculation unit, is used to calculate the product of the opacity modulation weight and the original opacity to obtain the final opacity, and finally render the Gaussian sphere based on the final opacity.

10. The single-sided rendering system according to claim 9, characterized in that, The modulation function is w = (cosθ + 1) / 2; Wherein, cosθ is the cosine value, w is the opacity modulation weight, cosθ=n · v, n is the unit normal vector, and v is the unit viewing direction.

Images