3D Gaussian splash artifact suppression method and system based on high-order regularization and multi-stage pruning

Abstract

The invention provides a 3D Gaussian splash artifact suppression method and system based on high-order regularization and multi-stage pruning, and belongs to the technical field of three-dimensional model reconstruction, and the method comprises the steps: obtaining an initial Gaussian point cloud; and processing the obtained initial Gaussian point cloud by using a pre-trained 3DGS framework to obtain a 3D reconstruction result. According to the method, through polynomial high-order regularization, explicit suppression of high-opacity abnormal points is realized, and the rendering quality is effectively improved. In the rough pruning stage, Gaussian points with low opacity and small contribution are periodically removed to reduce storage, and in the fine pruning stage, spatial abnormal points are further identified and eliminated through joint judgment of local density and anisotropy, so that artifact suppression is realized.

Description

Technical Field

[0001] This invention relates to the field of 3D model reconstruction technology, specifically to a 3D Gaussian splash artifact suppression method and system based on high-order regularization and multi-stage pruning. Background Technology

[0002] 3D Gaussian Splatting (3DGS) is a highly efficient 3D scene representation method that has gained significant attention in recent years. It directly models the scene using Gaussian point clouds and performs splatting and blending on the GPU to achieve high-quality synthesis of novel perspectives. Compared to traditional volume rendering methods, such as Neural Radiation Field (NeRF), 3DGS does not rely on deep neural network inference, significantly improving rendering speed while maintaining high-quality 3D reconstruction. However, in practical applications, 3DGS still faces several technical challenges, particularly in scenes with uneven views, where floating artifacts are easily generated—abnormally high-opacity Gaussian points appearing near the camera. These points cause rendering blur, visual artifacts, and geometric distortion. Furthermore, existing methods fail to fully consider opacity information during optimization, relying primarily on low-order gradients driven by reconstruction errors. This lack of explicit constraints on high-opacity anomalies makes it difficult to effectively suppress such artifacts. Simultaneously, the accumulation of redundant Gaussian points further increases computational and storage overhead, impacting the system's real-time performance and applicability.

[0003] To address the aforementioned issues, existing research has proposed several optimization methods, such as 3DGS and Pixel-GS based on adaptive density control, and Mip-NeRF 360 based on distortion regularization. While these methods have made some progress in density control, splitting control, and artifact suppression, they still have significant shortcomings in constraining high-opacity outliers and in early suppression capabilities. Furthermore, they cannot effectively suppress the negative impact of high-opacity points while preserving the contribution of low-opacity points.

[0004] Existing methods suffer from insufficient gradient constraints on Gaussian point opacity during optimization, primarily relying on low-order linear regularization or reconstruction errors to guide weight adjustments. This approach has limited effectiveness in suppressing high-opacity outliers, especially in the early stages of training. Once outlier Gaussian points appear, they are difficult to decay in time and spread during subsequent splitting and cloning operations, resulting in floating high-opacity artifacts near the camera. This causes rendering blur, geometric distortion, and loss of detail, significantly reducing the realism and stability of 3D reconstruction. Therefore, relying solely on existing density adaptive control or cloning splitting strategies cannot fundamentally solve the problem of outlier Gaussian point accumulation. Summary of the Invention

[0005] The purpose of this invention is to provide a 3D Gaussian splash artifact suppression method and system based on high-order regularization and multi-stage pruning, so as to solve at least one of the technical problems existing in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning, comprising:

[0008] Obtain the initial Gaussian point cloud;

[0009] A pre-trained 3DGS framework is used to process the acquired initial Gaussian point cloud to obtain the 3D reconstruction result. During 3DGS training, Gaussian distribution parameters are initialized based on the input multi-view data, and a basic rendering error is defined to measure the difference between predicted and true colors. In the opacity constraint part, a squared form of higher-order opacity regularization is used. By penalizing the sum of squared opacities, high-opacity points are suppressed. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution parameters and... Opacity distribution; during the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below the threshold are dynamically removed; for the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low importance points are removed after sorting by scores; geometrically aware pruning is adopted, firstly using KDTree to calculate local density features, and then using Grubbs test to detect spatial outliers; the anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously meet the density and anisotropy conditions are identified as outliers and removed.

[0010] As a further limitation of the first aspect of the invention, the error between the currently rendered 3DGS image and the real image is evaluated to measure the reconstruction quality; then, the rendering loss, including pixel-level error and structural similarity error, is calculated to ensure that the output image is as close as possible to the real scene; to enhance the constraint on opacity, an opacity-aware loss function is proposed:

[0011]

[0012] Where, ρ i λ represents the opacity of the i-th Gaussian point; λ2 and λ3 are the weight coefficients for higher-order and linear regularization, respectively.

[0013] As a further limitation of the first aspect of the present invention, during the training iteration, the opacity of all Gaussian points is checked every fixed number of times to ensure the state of the dynamically tracked points; an opacity threshold is set, and Gaussian points with opacity below this threshold are marked as low contribution points; low opacity Gaussian points are removed from the model to prevent them from continuing to occupy GPU memory and storage space.

[0014] As a further limitation of the first aspect of the present invention, for the Gaussian points that have not been deleted, their opacity and Gaussian volume are taken into account, and after normalization, they are multiplied or weighted to generate an importance score for each point, reflecting its contribution to rendering; all Gaussian points are sorted from high to low according to their importance scores, and points with lower contributions are identified; a certain proportion of the Gaussian points with the lowest importance scores are selected from the sorted points for deletion, and after deletion, the Gaussian point data structure and index are updated.

[0015] As a further limitation of the first aspect of the present invention, the KDTree algorithm is used to establish a spatial index structure for all remaining Gaussian points, thereby accelerating subsequent neighbor queries and density calculations; for each Gaussian point, the average distance between it and its k nearest neighbors is calculated to obtain a local density index, which reflects the spatial relationship between the point and its surrounding points; the Grubbs test or similar statistical methods are used to determine whether the local density of each Gaussian point is significantly higher than the average value, thereby identifying spatially isolated points or density anomalies; and the scaling parameters of the Gaussian points are read for shape analysis.

[0016] As a further limitation of the first aspect of the present invention, the scaling parameters are sorted, the ratio of the principal axis to the secondary axis is calculated, the degree of stretching of the shape is quantified, and the anisotropy ratio is obtained; based on the anisotropy ratio distribution of all points, extreme value distribution fitting is used to determine a judgment threshold for identifying abnormally stretched Gaussian points; if a Gaussian point satisfies both "density anomaly" and "anisotropy anomaly", it is marked as an anomaly point; these Gaussian points that are judged as anomalies are deleted from the model to avoid their negative impact on the rendering results; after fine pruning is completed, the KDTree index and Gaussian point array are updated again to ensure the correctness of subsequent rendering and training processes.

[0017] Secondly, the present invention provides a 3D Gaussian splash artifact suppression system based on high-order regularization and multi-stage pruning, comprising:

[0018] The acquisition module is used to acquire the initial Gaussian point cloud;

[0019] The processing and reconstruction module utilizes a pre-trained 3DGS framework to process the acquired initial Gaussian point cloud to obtain the 3D reconstruction result. During 3DGS training, Gaussian distribution parameters are initialized for the scene based on the input multi-view data, and a basic rendering error is defined to measure the difference between predicted and true colors. In the opacity constraint part, a squared form of higher-order opacity regularization is used. By penalizing the sum of squared opacities, high-opacity points are suppressed. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution. The algorithm considers the distribution of Gaussian points and their opacity. During the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below a threshold are dynamically removed. For the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low-importance points are removed after sorting by scores. Geometric perceptual pruning is employed, first using KDTree to calculate local density features, and then using the Grubbs test to detect spatial outliers. The anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously satisfy both density and anisotropy conditions are identified as outliers and removed.

[0020] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described in the first aspect.

[0021] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described in the first aspect.

[0022] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described in the first aspect.

[0023] The beneficial effects of this invention are as follows: The higher-order regularization described in this invention specifically employs an opacity quadratic polynomial regularization method. By introducing an opacity squared term into the loss function, compared to traditional linear regularization or threshold pruning, this higher-order constraint mechanism can apply significantly amplified gradient penalties to high-opacity outliers, accelerating their convergence and decay from the early stages of training, preventing the continuous spread and accumulation of outliers, and constraining their influence from different perspectives. This technical effect is unattainable by existing technologies using low-order regularization, density adjustment, or splitting strategies: on the one hand, existing methods can only rely on local density or reconstruction errors during splitting, failing to form a globally consistent higher-order penalty; on the other hand, linear opacity penalties are insufficiently sensitive to high-opacity outliers, making it difficult to suppress artifact generation in a timely manner. Through polynomial higher-order regularization, this invention achieves explicit suppression of high-opacity outliers, effectively improving rendering quality. Furthermore, in the coarse pruning stage, this invention periodically removes Gaussian points with low opacity and small contribution to reduce storage; in the fine pruning stage, through joint determination of local density and anisotropy, it further identifies and removes spatial outliers, achieving artifact suppression.

[0024] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart of the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described in an embodiment of the present invention. Detailed Implementation

[0027] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0028] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0029] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0030] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0031] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0032] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0033] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0034] This invention aims to address the floating artifact problem caused by anomalous Gaussian points with high opacity during 3D Gaussian Splatting (3DGS) rendering. Such artifacts not only degrade rendering quality and introduce blur, but also significantly increase storage overhead. In existing technologies, 3DGS primarily relies on low-order constraints based on reconstruction errors for opacity optimization, lacking explicit constraints on the opacity gradient. This leads to the continuous accumulation of anomalous high-opacity points during optimization, which then spread to larger areas through cloning and splitting, failing to effectively suppress artifacts. Therefore, this invention proposes a 3D Gaussian Splatting artifact suppression method based on high-order regularization and multi-stage pruning. Specifically, the high-order regularization employs a penalty function on the squared term of opacity. By introducing quadratic polynomial regularization of opacity into the loss function, it effectively amplifies the gradient feedback to high-opacity points. Compared to traditional linear penalties or simple threshold pruning, this method can significantly suppress the accumulation of anomalous Gaussian points in the early stages of training, accelerate convergence, and reduce the probability of floating artifact generation. Compared to existing technologies that only utilize low-order regularization or splitting strategies, this invention achieves explicit constraints on artifact regions through high-order opacity regularization. This allows for the preservation of detail contributions from low-opacity points while suppressing the impact of high-opacity anomalies on the final rendering, achieving a technical effect unattainable by existing technologies. Furthermore, this invention employs a phased dynamic pruning strategy. In the coarse pruning stage, opacity is periodically detected and low-contribution points are removed, reducing storage and computational burden. In the fine pruning stage, local density features and anisotropy indices are combined to identify and further remove spatial anomalies. This effectively reduces floating artifacts and redundant data while preserving the overall and local geometric structure of the scene, improving rendering quality and storage efficiency. This method is widely applicable to scenarios such as autonomous driving, VR / AR, medical imaging, industrial inspection, GIS, and cultural heritage protection. It can significantly improve the realism of 3D reconstruction and optimize storage space, making 3DGS more suitable for efficient new perspective compositing applications. It can enhance reconstruction realism, reduce visual artifact interference, and improve the rendering accuracy of scene data. In summary, this invention achieves efficient suppression and storage optimization of 3DGS rendering artifacts by introducing higher-order regularization of opacity quadratic polynomials and multi-stage pruning collaborative constraints. It exhibits significant technical advantages and wide applicability in multiple practical application scenarios. The key technologies of this invention include constraint techniques for opacity optimization based on higher-order regularization terms, dynamic pruning techniques based on opacity and global importance, and geometry-aware dynamic pruning techniques.

[0035] The artifact suppression method of this invention first initializes the data: an initial Gaussian point cloud is generated using SfM and input into the 3DGS framework; then, higher-order regularization optimization is performed: by introducing a square-form higher-order regularization term, an enhanced constraint is applied to the opacity of Gaussian points, focusing on suppressing the abnormal accumulation of high-opacity points, enabling faster convergence during training, thereby effectively reducing floating artifacts and improving rendering stability; next, dynamic pruning based on opacity and global importance is performed: coarse pruning periodically removes low-opacity and low-importance Gaussian points, reducing redundancy and storage overhead while preserving the overall structural integrity of the scene; dynamic pruning based on geometry awareness is performed: fine pruning accurately identifies and removes abnormal Gaussian points using both local density and anisotropy conditions, while preserving necessary local geometric structures; finally, a 3D scene is generated: after the above optimizations, 3DGS is used for the final new perspective rendering, and a high-quality 3D reconstruction result is output.

[0036] Example 1

[0037] In this embodiment 1, a 3D Gaussian splatter artifact suppression system based on high-order regularization and multi-stage pruning is first provided, including: an acquisition module for acquiring an initial Gaussian point cloud; and a processing and reconstruction module for processing the acquired initial Gaussian point cloud using a pre-trained 3DGS framework to obtain a 3D reconstruction result. During 3DGS training, Gaussian distribution parameters are initialized for the scene based on input multi-view data, and a basic rendering error is defined to measure the difference between predicted and true colors. In the opacity constraint part, a squared form of high-order opacity regularization is used to suppress high-opacity points by penalizing the sum of squared opacities. Finally, the rendering error is combined with the regularization term to form a total loss function, which is used to jointly optimize the Gaussian distribution. The algorithm considers the distribution of Gaussian points and their opacity. During the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below a threshold are dynamically removed. For the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low-importance points are removed after sorting by scores. Geometric perceptual pruning is employed, first using KDTree to calculate local density features, and then using the Grubbs test to detect spatial outliers. The anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously satisfy both density and anisotropy conditions are identified as outliers and removed.

[0038] In this embodiment, based on the aforementioned system, a 3D Gaussian splatter artifact suppression method based on higher-order regularization and multi-stage pruning is implemented, including: acquiring an initial Gaussian point cloud; processing the acquired initial Gaussian point cloud using a pre-trained 3DGS framework to obtain a 3D reconstruction result; wherein, during the 3DGS training process, the scene is initialized with Gaussian distribution parameters based on the input multi-view data, and a basic rendering error is defined to measure the difference between the predicted color and the real color; in the opacity constraint part, a squared form of higher-order opacity regularization is adopted, which suppresses high opacity points by penalizing the sum of squares of opacity, and finally the rendering error is combined with the... Regularization terms are combined to form the total loss function, which is used to jointly optimize the Gaussian distribution parameters and opacity distribution. During the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below the threshold are dynamically removed. For the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low-importance points are removed after sorting by scores. Geometric perceptual pruning is adopted. Local density features are first calculated using KDTree, and spatial outliers are detected based on Grubbs test. The anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that satisfy both density and anisotropy conditions are identified as outliers and removed.

[0039] Specifically, such as Figure 1 As shown, the method described in this embodiment specifically includes the following steps:

[0040] S1: Generate an initial Gaussian point cloud using traditional SfM (Structure-from-Motion) or other 3D reconstruction methods, and input it into the 3DGS framework.

[0041] S2: During 3DGS training, the scene is initialized with Gaussian distribution parameters based on the input multi-view data, and a basic rendering error is defined to measure the difference between the predicted color and the real color.

[0042] In the opacity constraint part, this embodiment uses a squared form of high-order opacity regularization. By penalizing the sum of squares of opacity, high opacity points are significantly suppressed in the early stages of training, while the impact on low opacity points is relatively small. This effectively reduces floating artifacts and local dense opacity accumulation while ensuring convergence smoothness. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution parameters and opacity distribution. After multiple rounds of comparative experiments, the squared regularization performs best in reducing the number of artifact pixels, improving training stability, and improving rendering quality compared to linear, exponential, and logarithmic forms. This achieves high-quality rendering effects and geometric consistency that cannot be achieved by existing technologies.

[0043] S3: During the 3DGS optimization iteration, the opacity of Gaussian points is periodically checked, and Gaussian points with opacity below a threshold are dynamically removed. For the remaining Gaussian points, an importance score is calculated based on opacity and volume, and low-importance points are removed after sorting by score. Coarse pruning effectively removes a large number of redundant points with low opacity while maintaining the overall structural integrity of the scene.

[0044] S4: During the 3DGS optimization iteration process, geometry-aware pruning is employed. First, local density features are calculated using KDTree, and spatial outliers are detected based on the Grubbs test. The anisotropy ratio (measuring the degree of shape stretching) of each Gaussian point is calculated, and the anisotropy threshold is determined through extreme value distribution estimation. Gaussian points that simultaneously satisfy both density and anisotropy conditions are identified as outliers and removed. This strategy ensures that only truly outlier points are removed, improving rendering quality while reducing storage requirements.

[0045] S5: After the above optimizations, use 3DGS to perform the final new perspective rendering and output high-quality 3D reconstruction results.

[0046] Specifically, step S2 includes the following steps:

[0047] S21: First, assess the error between the current 3DGS rendered image and the real image to measure the reconstruction quality. Then, calculate the rendering loss, mainly including pixel-level error and structural similarity error, to ensure the output image is as close to the real scene as possible. These loss values ​​will be used to guide the optimization process.

[0048] S22: In 3DGS training, existing opacity constraints are weak and cannot effectively suppress anomalous Gaussian points with high opacity, causing them to gradually accumulate and form obvious floating artifacts. To enhance the constraint on opacity, a new opacity-aware loss function is proposed:

[0049]

[0050] Where N is the total number of Gaussian points, ρ i Let represent the opacity of the i-th Gaussian point. The loss function includes a higher-order regularization term and a linear term: [Higher-order term...] This is used to apply a stronger penalty to Gaussian points with high opacity, enabling them to converge faster during training and reducing artifacts; the linear term λ3ρ i Then, moderate constraints are applied to Gaussian points with low opacity to prevent unconstrained growth or excessive suppression. Here, λ2 and λ3 are the weighting coefficients for higher-order and linear regularization, respectively, used to adjust the intensity of different constraints.

[0051] S23: The newly proposed opacity regularization loss is combined with the original rendering error loss to form the final training objective. Through this optimization strategy, the opacity distribution during training is more reasonable, and abnormally high opacity points are significantly reduced, thereby effectively suppressing floating artifacts and improving rendering quality.

[0052] Step S3 specifically includes the following steps:

[0053] S31: During training iterations, an opacity check is performed on all Gaussian points every fixed number of iterations (e.g., every 100 iterations) to ensure the state of dynamically tracked points.

[0054] S32: Set an opacity threshold (e.g., 0.05 or 0.1) and mark Gaussian points with opacity below this threshold as low contribution points.

[0055] S33: Remove these low-opacity Gaussian points from the model to prevent them from continuing to occupy video memory and storage space.

[0056] S34: For Gaussian points that have not been deleted, take into account their opacity and Gaussian volume, normalize them respectively, and then multiply or weight them to generate an importance score for each point, reflecting its contribution to the rendering.

[0057] S35: Sort all Gaussian points from highest to lowest importance score and identify points with lower contributions.

[0058] S36: Select a certain proportion of Gaussian points with the lowest importance scores in the sorting process and delete them to further remove redundancy.

[0059] S37: After deletion, update the Gaussian point data structure and index to ensure that subsequent training is not affected.

[0060] Step S4 specifically includes the following steps:

[0061] S41: Use the KDTree algorithm to build a spatial index structure for all remaining Gaussian points, which speeds up subsequent neighbor queries and density calculations.

[0062] S42: For each Gaussian point, calculate its average distance to its k nearest neighbors to obtain a local density index, which reflects the spatial relationship between the point and its surrounding points.

[0063] S43: Use the Grubbs test or similar statistical methods to determine whether the local density of each Gaussian point is significantly higher than the average value, and identify spatially isolated points or density anomalies.

[0064] S44: Read the scaling parameters of the Gaussian points (e.g., scale factors in three directions) for shape analysis.

[0065] S45: Sort the scaling parameters, calculate the ratio of the principal axis to the secondary axis, quantify the stretching of the shape, and obtain the anisotropy ratio.

[0066] S46: Based on the anisotropic ratio distribution of all points, use extreme value distribution fitting to determine a judgment threshold for identifying Gaussian points with abnormal stretching.

[0067] S47: If a Gaussian point simultaneously satisfies both "density anomaly" and "anisotropy anomaly," it is marked as an anomalous point. These anomalous Gaussian points are removed from the model to avoid negatively impacting the rendering results. After fine pruning, the KDTree index and Gaussian point array are updated to ensure the correctness of subsequent rendering and training processes.

[0068] Through the aforementioned high-order regularization optimization, dynamic transparency adjustment, and pruning strategies, the accumulation of high-opacity outliers can be effectively reduced, thereby mitigating the impact of floating artifacts. Combining PSNR, SSIM, and LPIPS evaluation metrics further ensures the visual and structural accuracy of the generated 3D scene, meeting high quality standards.

[0069] Example 2

[0070] This embodiment 2 provides a non-transitory computer-readable storage medium for storing computer instructions. When executed by a processor, the computer instructions implement the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described above. The method includes:

[0071] An initial Gaussian point cloud is acquired; the acquired Gaussian point cloud is processed using a pre-trained 3DGS framework to obtain the 3D reconstruction result; during the 3DGS training process, the Gaussian distribution parameters of the scene are initialized based on the input multi-view data, and a basic rendering error is defined to measure the difference between the predicted color and the true color; in the opacity constraint part, a squared form of higher-order opacity regularization is adopted, which suppresses high opacity points by penalizing the sum of squared opacities. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution. The algorithm considers the distribution of Gaussian points and their opacity. During the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below a threshold are dynamically removed. For the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low-importance points are removed after sorting by scores. Geometric perceptual pruning is employed, first using KDTree to calculate local density features, and then using the Grubbs test to detect spatial outliers. The anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously satisfy both density and anisotropy conditions are identified as outliers and removed.

[0072] Example 3

[0073] This embodiment 3 provides a computer device, including a memory and a processor, wherein the processor and the memory communicate with each other, and the memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described above. The method includes:

[0074] An initial Gaussian point cloud is acquired; the acquired Gaussian point cloud is processed using a pre-trained 3DGS framework to obtain the 3D reconstruction result; during the 3DGS training process, the Gaussian distribution parameters of the scene are initialized based on the input multi-view data, and a basic rendering error is defined to measure the difference between the predicted color and the true color; in the opacity constraint part, a squared form of higher-order opacity regularization is adopted, which suppresses high opacity points by penalizing the sum of squared opacities. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution. The algorithm considers the distribution of Gaussian points and their opacity. During the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below a threshold are dynamically removed. For the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low-importance points are removed after sorting by scores. Geometric perceptual pruning is employed, first using KDTree to calculate local density features, and then using the Grubbs test to detect spatial outliers. The anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously satisfy both density and anisotropy conditions are identified as outliers and removed.

[0075] Example 4

[0076] This embodiment 4 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions to implement the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described above. The method includes:

[0077] An initial Gaussian point cloud is acquired; the acquired Gaussian point cloud is processed using a pre-trained 3DGS framework to obtain the 3D reconstruction result; during the 3DGS training process, the Gaussian distribution parameters of the scene are initialized based on the input multi-view data, and a basic rendering error is defined to measure the difference between the predicted color and the true color; in the opacity constraint part, a squared form of higher-order opacity regularization is adopted, which suppresses high opacity points by penalizing the sum of squared opacities. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution. The algorithm considers the distribution of Gaussian points and their opacity. During the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below a threshold are dynamically removed. For the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low-importance points are removed after sorting by scores. Geometric perceptual pruning is employed, first using KDTree to calculate local density features, and then using the Grubbs test to detect spatial outliers. The anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously satisfy both density and anisotropy conditions are identified as outliers and removed.

[0078] In summary, the 3D Gaussian splatter artifact suppression method and system based on high-order regularization and multi-stage pruning described in this invention have significant advantages in terms of floating artifact suppression, opacity optimization, computational cost control, and stability of opacity gradient optimization. Existing methods, such as Pixel-GS, optimize the Gaussian point distribution through an adaptive density adjustment strategy, but their constraints on high-opaque outliers are insufficient, failing to completely suppress the accumulation of local high opacity, resulting in the continued presence of floating artifacts. Mip-NeRF360 employs distortion regularization to optimize artifact problems in NeRF volume rendering, but this method relies on density distribution assumptions in volume rendering, making it difficult to directly apply to 3DGS optimization based on Gaussian point clouds. To address these shortcomings, the artifact suppression method of this invention effectively solves the problems of floating artifacts, storage redundancy, and insufficient opacity optimization in 3D Gaussian splatter synthesis from new perspectives.

[0079] This invention addresses the shortcomings of traditional linear or first-order opacity regularization, which only imposes constant or linear constraints on opacity and struggles to adequately penalize high-opacity points. This leads to a rapid accumulation of localized high-opacity points during training, resulting in floating artifacts. In contrast, this invention introduces a quadratic higher-order regularization method. The quadratic term imposes an exponential penalty on high-opacity points, effectively reducing the weight of outliers in the early stages of training and preventing the formation of irreversible artifact regions later. The linear term ensures a gentle constraint on low-opacity points, preventing slow convergence or loss of expressive power in transparent regions. This combined higher-order regularization offers advantages that existing methods cannot achieve: firstly, it significantly improves training convergence speed, resulting in a smoother and more uniform opacity distribution, avoiding the violent oscillations or local extrema that traditional linear regularization produces during opacity gradient optimization. Furthermore, to further improve storage and geometric structure fidelity, this invention introduces a multi-stage pruning mechanism based on high-order regularization. In the coarse pruning stage, low-importance Gaussian points are dynamically removed based on global contribution, reducing storage and computational burden. In the fine pruning stage, local density and anisotropy are used as dual criteria to accurately remove abnormal Gaussian points while retaining key geometric features, ensuring structural consistency and detail integrity of the reconstruction results.

[0080] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0081] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0082] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0083] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0084] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A method for suppressing 3D Gaussian splash artifacts based on high-order regularization and multi-stage pruning, characterized in that, include: Obtain the initial Gaussian point cloud; A pre-trained 3DGS framework is used to process the acquired initial Gaussian point cloud to obtain the 3D reconstruction result. During 3DGS training, Gaussian distribution parameters are initialized based on the input multi-view data, and a basic rendering error is defined to measure the difference between predicted and true colors. In the opacity constraint part, a squared form of higher-order opacity regularization is used. By penalizing the sum of squared opacities, high-opacity points are suppressed. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution parameters and... Opacity distribution; during the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below the threshold are dynamically removed; for the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low importance points are removed after sorting by scores; geometrically aware pruning is adopted, firstly using KDTree to calculate local density features, and then using Grubbs test to detect spatial outliers; the anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously meet the density and anisotropy conditions are identified as outliers and removed.

2. The 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning according to claim 1, characterized in that, The error between the current 3DGS rendered image and the real image is evaluated to measure the reconstruction quality; then the rendering loss, including pixel-level error and structural similarity error, is calculated to ensure that the output image is as close as possible to the real scene. To enhance the constraint on opacity, an opacity-aware loss function is proposed: Where, ρ i λ represents the opacity of the i-th Gaussian point; λ2 and λ3 are the weight coefficients for higher-order and linear regularization, respectively.

3. The 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning according to claim 1, characterized in that, During training iterations, the opacity of all Gaussian points is checked every fixed number of times to ensure the dynamic tracking of the point state; an opacity threshold is set, and Gaussian points with opacity below this threshold are marked as low contribution points; low opacity Gaussian points are removed from the model to prevent them from continuing to occupy GPU memory and storage space.

4. The 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning according to claim 3, characterized in that, For Gaussian points that are not deleted, their opacity and Gaussian volume are considered together, and after normalization, they are multiplied or weighted to generate an importance score for each point, reflecting its contribution to rendering. All Gaussian points are sorted from high to low according to their importance scores to identify points with lower contributions. A certain proportion of Gaussian points with the lowest importance scores are selected from the sorted points and deleted. After deletion, the Gaussian point data structure and index are updated.

5. The 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning according to claim 1, characterized in that, The KDTree algorithm is used to establish a spatial index structure for all remaining Gaussian points, accelerating subsequent neighbor queries and density calculations. For each Gaussian point, the average distance to its k nearest neighbors is calculated to obtain a local density index, reflecting the spatial relationship between the point and its surrounding points. The Grubbs test or similar statistical methods are used to determine whether the local density of each Gaussian point is significantly higher than the average, identifying spatially isolated points or density anomalies. The scaling parameters of the Gaussian points are read for shape analysis.

6. The 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning according to claim 5, characterized in that, The scaling parameters are sorted, the ratio of the principal axis to the secondary axis is calculated, the degree of stretching of the shape is quantified, and the anisotropy ratio is obtained. Based on the anisotropy ratio distribution of all points, an extreme value distribution is used to fit and determine a judgment threshold to identify abnormally stretched Gaussian points. If a Gaussian point satisfies both "density anomaly" and "anisotropy anomaly", it is marked as an anomaly point. These Gaussian points that are judged as anomalies are removed from the model to avoid their negative impact on the rendering results. After fine pruning, the KDTree index and Gaussian point array are updated again to ensure the correctness of subsequent rendering and training processes.

7. A 3D Gaussian splash artifact suppression system based on high-order regularization and multi-stage pruning, characterized in that, include: The acquisition module is used to acquire the initial Gaussian point cloud; The processing and reconstruction module utilizes a pre-trained 3DGS framework to process the acquired initial Gaussian point cloud to obtain the 3D reconstruction result. During 3DGS training, Gaussian distribution parameters are initialized for the scene based on the input multi-view data, and a basic rendering error is defined to measure the difference between predicted and true colors. In the opacity constraint part, a squared form of higher-order opacity regularization is used. By penalizing the sum of squared opacities, high-opacity points are suppressed. Finally, the rendering error is combined with the regularization term to form the total loss function, which is used to jointly optimize the Gaussian distribution. The algorithm considers the distribution of Gaussian points and their opacity. During the 3DGS optimization iteration, the opacity of Gaussian points is periodically detected, and Gaussian points with opacity below a threshold are dynamically removed. For the remaining Gaussian points, importance scores are calculated based on opacity and volume, and low-importance points are removed after sorting by scores. Geometric perceptual pruning is employed, first using KDTree to calculate local density features, and then using the Grubbs test to detect spatial outliers. The anisotropy ratio of each Gaussian point is calculated, and the anisotropy threshold is determined by extreme value distribution estimation. Gaussian points that simultaneously satisfy both density and anisotropy conditions are identified as outliers and removed.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described in any one of claims 1-6.

9. A computer device, characterized in that, The system includes a memory and a processor, which communicate with each other. The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described in any one of claims 1-6.

10. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions that implement the 3D Gaussian splash artifact suppression method based on high-order regularization and multi-stage pruning as described in any one of claims 1-6.

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