Three-dimensional Gaussian sputtering scene reconstruction method based on structure perception refined Gaussian

Abstract

The invention discloses a three-dimensional Gaussian sputtering scene reconstruction method based on structure perception refined Gaussian, and aims to solve the problems of Gaussian drift, edge blur, structure artifacts and the like of a reconstruction model due to the fact that sparse point cloud contains outliers, Gaussian morphology and normal are mismatched and a multi-dimensional optimization target is lacked in an existing three-dimensional Gaussian sputtering reconstruction method. A key frame is extracted by collecting target scene video data, sparse three-dimensional point clouds are reconstructed by using an SfM algorithm, a depth map and a normal map are generated through a Lotus model, three-dimensional Gaussian distribution is initialized after the sparse point clouds are filtered, a Gaussian covariance matrix is adjusted by using a normal consistency regular term, and the sparse point clouds are extracted. And after structure attribute analysis is carried out, a comprehensive scoring function is constructed to screen Gaussian points, and finally, a combined training framework including luminosity, normal consistency and structure continuity loss is adopted to optimize and generate a three-dimensional Gaussian scene model. The method is mainly applied to the field of three-dimensional reconstruction and multi-view rendering, and scene reconstruction precision and geometric consistency can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical fields of computer vision, three-dimensional reconstruction and graphics rendering, and specifically relates to a three-dimensional Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian. Background Art

[0002] Three-dimensional scene reconstruction technology has widespread application in fields such as computer vision, virtual reality, and cultural heritage preservation. Reconstruction methods based on 3D Gaussian Splatting (3DGS) demonstrate unique advantages in real-time performance and detail by representing scenes as a set of anisotropic Gaussian distributions and combining them with efficient rasterization rendering strategies. However, this technology still faces a number of key challenges in practical applications, limiting further improvements in reconstruction accuracy and geometric consistency.

[0003] First, existing 3DGS methods are highly dependent on the quality of the initial sparse 3D point cloud. However, point clouds generated by structure-from-motion (SfM) algorithms often contain a large number of outliers due to incomplete image feature extraction and matching errors. These outliers may be scattered outside the actual structure of the scene or exhibit an abnormal spatial distribution, causing the positions of the subsequently initialized Gaussian points to deviate from the actual geometry, triggering a Gaussian drift phenomenon. For example, in areas with repeated features or missing textures, the SfM algorithm is prone to mismatching feature points. The resulting sparse point cloud cannot accurately reflect the scene's topological structure, making it difficult for the initial Gaussian distribution to fit the actual surface, resulting in artifacts such as "floating points" or "holes" in the reconstructed model.

[0004] Secondly, in the Gaussian rendering process, traditional methods lack the constraints on the consistency of the Gaussian shape and the geometric structure of the scene, resulting in blurred edge areas and loss of high-frequency details. The isotropic assumption of the Gaussian kernel is difficult to adapt to the directional characteristics of complex surfaces (such as object edges and areas where surface normals change). When multiple Gaussians overlap at the boundary, the smoothness of their kernel functions will blur the clear boundaries of geometric mutations. For example, at the junction of the object and the background, if the short axis direction of the Gaussian distribution is not aligned with the surface normal, it will cause a smooth transition of the depth value during rendering and a decrease in edge clarity. At the same time, for high-frequency structures (such as fences and surfaces with rich texture details), existing methods are unable to effectively capture the local curvature and anisotropic characteristics of Gaussian points, and are prone to detail smoothing or redundant fitting, making it difficult to restore subtle geometric changes in real scenes.

[0005] In addition, the existing Gaussian optimization mechanism lacks a means of quantitatively evaluating the stability and credibility of individual Gaussian points. The visibility (frequency of occurrence across frames) and opacity fluctuations of Gaussian points reflect their consistency in multi-view observations, but traditional methods do not incorporate such temporal information into the screening criteria. For example, some Gaussian points may only be visible in a single frame of image, or their opacity may change dramatically due to noise interference in multiple frames. If such points are not eliminated, unstable geometric assumptions will be introduced, affecting the reliability of the overall model. At the same time, due to the lack of analysis of the local geometric properties of Gaussian points (such as curvature and anisotropy indicators), it is impossible to distinguish between plane areas, curved surface areas and edge areas, resulting in insufficient Gaussian density in areas with rich surface details, or blurring in edge areas due to uncontrolled Gaussian scale changes.

[0006] In terms of optimization target design, traditional 3DGS methods often use only photometric loss as a training objective, ignoring the global consistency constraints of the geometric structure. Photometric loss only focuses on the difference between the rendered color and the real image, making it difficult to constrain the rationality of the spatial distribution and normal direction of the Gaussian points. For example, in textureless areas or scenes with drastic lighting changes, relying solely on photometric loss can easily cause the Gaussian points to converge to the wrong spatial position, resulting in "multiple solutions" ambiguity. At the same time, the lack of explicit constraints on the position and color continuity between adjacent Gaussian points can cause breaks or color mutations in the reconstructed surface, affecting the visual coherence of the model.

[0007] In summary, the existing 3DGS technology has deficiencies in sparse point cloud preprocessing, Gaussian geometric constraints, structural attribute analysis, and optimization target design, which makes the reconstructed model prone to outlier interference, edge blur, structural artifacts, and geometric inconsistency. The key to solving these problems lies in: how to effectively filter outliers in sparse point clouds, establish directional constraints between Gaussian morphology and scene geometry, quantitatively evaluate the structural quality and stability of Gaussian points, and design multi-dimensional joint optimization objectives to guide the Gaussian distribution to converge to the real scene structure. However, achieving the above goals requires balancing computational efficiency and the complexity of geometric constraints, avoiding the optimization process from falling into local optimality or a surge in computational costs due to the introduction of too many regularization terms, which places higher demands on the design and implementation of the algorithm. Summary of the Invention

[0008] An object of the present invention is to solve at least the above problems and to provide at least the advantages which will be described hereinafter.

[0009] The present invention also solves the following technical problems:

[0010] The existing three-dimensional Gaussian sputtering reconstruction method solves the problems of Gaussian drift, edge blur, structural artifacts, etc. in the reconstructed model due to sparse point clouds containing outliers, mismatch between Gaussian morphology and normals, and lack of multi-dimensional optimization goals, making it difficult to accurately fit the geometric details and topological structure of the real scene.

[0011] To solve the problem that the direction of the Gaussian covariance matrix is ​​inconsistent with the direction of the scene normal, which will lead to chaotic surface normal vectors and blurred edge transitions, it is necessary to use regularization terms to constrain the Gaussian minor axis to align with the normal to improve the consistency of the geometric structure.

[0012] To solve the problem that traditional methods lack quantitative analysis of the local geometric characteristics of Gaussian points (such as anisotropy and curvature) and cannot distinguish between planes, curved surfaces and edge areas, it is necessary to evaluate structural stability through eigenvalue decomposition and statistical indicators.

[0013] To solve the problem that a single indicator is prone to ignoring the comprehensive influence of multi-dimensional structural properties when screening Gaussian points, it is necessary to construct a scoring function that includes anisotropy, curvature, visibility, and opacity changes to achieve a comprehensive evaluation and dynamic adjustment of the quality of Gaussian points.

[0014] To solve the problem of geometric ambiguity easily caused by relying solely on photometric loss optimization, it is necessary to introduce normal consistency and structural continuity losses, build a multi-dimensional joint training framework, and guide the Gaussian points to converge to the geometric structure of the real scene.

[0015] In order to achieve these objectives and other advantages according to the present invention, a method for reconstructing a three-dimensional Gaussian sputtering scene based on structure-aware refined Gaussian is provided, which comprises the following steps:

[0016] S1: Collect video data of the target scene, extract key frame images at a fixed frame rate, and generate image sequences;

[0017] S2: Based on the image sequence, a sparse 3D point cloud is reconstructed using the SfM algorithm, and a depth map and normal map for each frame are simultaneously generated using the Lotus monocular depth estimation model.

[0018] S3: performing statistical filtering and radius filtering on the sparse three-dimensional point cloud in sequence;

[0019] S4: Based on the filtered sparse 3D point cloud, initialize the 3D Gaussian distribution and assign the position center, scaling rotation matrix, color and opacity attributes to each Gaussian point;

[0020] S5: Using the normal direction in the normal map as a constraint condition, adjusting the direction of the minimum eigenvector of the Gaussian covariance matrix through the normal consistency regularization term so that the Gaussian minor axis direction is aligned with the normal direction; wherein the scaling rotation matrix is ​​used to construct the initial parameters of the covariance matrix, and the position center is used to determine the spatial distribution position of the Gaussian point;

[0021] S6: Perform structural attribute analysis on each Gaussian point: decompose the covariance matrix to obtain eigenvalues, calculate the ratio of the maximum eigenvalue to the minimum eigenvalue as an anisotropy index; calculate the local curvature based on the eigenvalues; count the number of times the Gaussian point is visible in multiple frames of images, and calculate the opacity change variance; the opacity attribute is used to count the opacity change variance;

[0022] S7: Based on the anisotropy index, local curvature, visibility times, and opacity change variance, a comprehensive scoring function is constructed to filter and remove Gaussian points with scores below the set threshold;

[0023] S8: A joint training framework including photometric loss, normal consistency loss, and structural continuity loss is used to optimize the screened Gaussian points. The color attribute is used to calculate the photometric loss, the scaling rotation matrix and the position center are dynamically adjusted through gradient backpropagation, and the opacity attribute is used to calculate the structural continuity loss. Finally, a 3D Gaussian scene model is generated.

[0024] Preferably, in step S2, the sparse point cloud generated by the SfM algorithm is converted from a bin format to a ply format, and statistical filtering and radius filtering are performed on the ply format point cloud using a general point cloud processing tool to filter out outliers and abnormal density distribution points; after the filtering is completed, the optimized point cloud is re-encoded into a bin format to adapt to the input specification of the 3D Gaussian splatter rendering engine;

[0025] Among them, the format conversion ensures that the filtered point cloud data is compatible with the initialization requirements of three-dimensional Gaussian sputtering by retaining the point cloud geometric properties and topological structure, avoiding input errors due to data format differences; the re-encoded bin format contains point cloud coordinates, color and normal information, and directly supports the parametric initialization of the position center, covariance matrix and opacity attributes of three-dimensional Gaussian points, thereby improving the geometric consistency and rendering efficiency of scene reconstruction.

[0026] Preferably, the statistical filter calculates the average Euclidean distance between each point and its neighboring points. If the distance exceeds the threshold range of the sum of the overall average distance and the standard deviation, it is determined to be an outlier and removed. The calculation method of the statistical filter is:

[0027]

[0028] where ||X i -X j || represents point X i to X j The Euclidean distance between global represents the overall density level of the point cloud, and σ is the standard deviation of all points. i Greater than the overall average distance μ globalAdd a certain threshold λσ, then it is considered an outlier and is removed.

[0029] Preferably, the radius filter counts the number of neighboring points within a preset radius of each point. If the number is lower than a set threshold range, it is determined to be an outlier and removed. The calculation method of the radius filter is:

[0030]

[0031] For each point X i , calculate its neighborhood point cloud R within radius r i If R i Less than the set threshold R min , then delete the point.

[0032] Preferably, in step S4, the initialized three-dimensional Gaussian is constructed based on each spatial point in the sparse point cloud, and initial geometric and appearance attributes are assigned to each Gaussian point;

[0033] Among them, the position center of the Gaussian point is: μ j =X j ∈R 3 ; Color c∈R k ;Opacity α∈R;

[0034] Covariance matrix ∑ N for:

[0035]

[0036] Its probability density formula is:

[0037]

[0038] μ j : The position center of the j-th Gaussian point, which is the spatial point X in the sparse point cloud j OK, X j ∈R 3 Indicates that it is in three-dimensional real space;

[0039] c: the color of the Gaussian point, c∈R k Indicates that color is a k-dimensional vector;

[0040] α: opacity of the Gaussian point, α∈R indicates that it is a real number;

[0041] σ x 2 is the variance in the x direction, σ xy is the covariance between x and y directions, σ yx is the covariance between the y and x directions;

[0042] x: Any point in space, used to calculate the probability density under Gaussian distribution;

[0043] μ: the position center of the Gaussian point;

[0044] ∑ -1 : Covariance matrix ∑ N The inverse matrix of

[0045] g(x): probability density of point x under the Gaussian distribution;

[0046] The initial parameters of the scaling rotation matrix are associated with the density distribution of the point cloud after statistical filtering;

[0047] The initialization process ensures that the spatial distribution and anisotropic scale of the Gaussian points strictly correspond to the geometric characteristics of the filtered point cloud, providing a geometrically consistent Gaussian sputtering scene initial model for subsequent normal consistency alignment, comprehensive score screening and joint optimization.

[0048] Preferably, in step S5, based on the covariance matrix of the initialized three-dimensional Gaussian sputtering scene, the direction of the minimum eigenvector of the Gaussian distribution is dynamically adjusted by the normal consistency regularization term so that it is aligned with the normal direction; the loss function of the normal consistency regularization term is:

[0049]

[0050] L normal : The loss function of the normal consistency regularization term, which obtains the overall loss by summing the individual losses of all Gaussian points;

[0051] w i : The weight of Gaussian point i is dynamically adjusted according to the visibility and stability of the point;

[0052] N i : The minimum eigenvector of the Gaussian point covariance matrix, corresponding to the minor axis direction of the Gaussian sphere;

[0053] n i : The normal direction of the point extracted from the normal map estimated by the Lotus model;

[0054] The regularization term forces Ni and n to be i Direction alignment makes the short axis of the Gaussian distribution in the edge area of ​​the Gaussian sputtering scene fit the surface normal, suppressing the edge blurring phenomenon of the sparse area retained by the radius filter; at the same time, the dynamic weight w i Based on the adjustment of visibility and stability indicators, the interference of low-confidence Gaussian points on normal alignment is reduced, ensuring that the geometric structure of the 3D Gaussian sputtering scene is consistent with the real surface topology.

[0055] Preferably, in step S6, the covariance matrix of each Gaussian point is subjected to eigenvalue decomposition to extract three eigenvalues ​​λ1, λ2, and λ3, where λ1≤λ2≤λ3, and the anisotropy A thereof is calculated according to the eigenvalues, and the calculation formula is: A=(λ3-λ1) / λ3;

[0056] The anisotropy index is used to quantify the directional distribution of Gaussian points. High anisotropy corresponds to edge areas where the normal consistency regularization term needs to be strongly constrained, and low anisotropy corresponds to curved or flat areas.

[0057] Based on the eigenvalue estimation, the local curvature and dimensional characteristics are calculated by combining the eigenvalues ​​of the covariance matrix. The calculation formula is:

[0058]

[0059] C(X i ) is the local curvature index of the i-th Gaussian point;

[0060] The local curvature is used to identify the geometric complexity of the area where the Gaussian point is located. Combined with the normal direction alignment result, the density of Gaussian points is increased in the curvature mutation area to suppress structural artifacts. At the same time, the number of visible times V and the opacity change variance Δα of the Gaussian point in multiple frames are counted. The visible times V is used to calculate the dynamic weight w. i The weight of high-visibility points is increased to strengthen the normal alignment constraint, and the weight of low-visibility points is decreased to reduce noise interference; the opacity change variance Δα is linked with the structural continuity loss to suppress the negative impact of unstable Gaussian points on the joint optimization.

[0061] Preferably, in step S7, the comprehensive scoring function constructed is:

[0062] S(X i )=w1(1-C(X i ))+w2V i -w3Δα i +w4A(X i );

[0063] A(X i ) is an anisotropy index based on the eigenvalue decomposition of the covariance matrix, which is used to quantify the directional distribution of Gaussian points. The high anisotropy region corresponds to the edge structure in the three-dimensional Gaussian sputtering scene, and the edge clarity is maintained by limiting the scale change of Gaussian points;

[0064] C(X i ) is the local curvature, which is used to identify surface details or flat areas. Combined with the density adaptive mechanism of three-dimensional Gaussian sputtering, Gaussian points are interpolated and added at the curvature mutation point to suppress artifacts;

[0065] V iis the number of times the Gaussian point is visible, and the dynamic weight w i Linkage: High-visibility points are prioritized and normal alignment constraints are strengthened, while low-visibility points are treated as noise and removed;

[0066] Δαi is the variance of opacity change, which works together with the structural continuity loss to suppress the destruction of scene rendering consistency caused by Gaussian points with excessively high opacity fluctuations;

[0067] w1~w4 are weight coefficients, which are dynamically adjusted according to the geometric characteristics of the three-dimensional Gaussian sputtering scene:

[0068] In the edge area, w1 is increased to strictly limit the Gaussian point scale and prevent edge blurring;

[0069] In curved areas, increase w2 to enhance detail density;

[0070] In the stable region, increase w3 and w4 to retain high-quality Gaussian points.

[0071] Preferably, in step S8, the structural continuity loss L is calculated. structure When, for each Gaussian point i (i = 1, 2, ..., N) in the Gaussian point set, determine its neighborhood Gaussian point set N(i); for each neighborhood point j∈N(i), calculate the position difference ||x i -x j || and color difference |c i -c j ||, use Measure the weight of the impact of position distance on the loss, and then multiply it by the square of the color difference || c i -c j || 2 ; Finally, the above products of all i and its neighborhood j are accumulated, and the calculation function is:

[0072]

[0073] This loss function constrains the color and position consistency between adjacent Gaussian points to ensure the structural continuity of scene reconstruction.

[0074] Preferably, in step S8, the final loss function of the joint training framework is:

[0075] L=L1+λ normal L normal +λ structure L structure ;

[0076] Where L1 is the luminosity loss, which is used to measure the rendered image I render Compared with the real image I gt The difference is calculated as:

[0077] L1=∑|I render -I gt |;

[0078] Image I is generated by rasterization rendering of 3D Gaussian splattering render , and compared with the real image I gt In contrast, directly optimize the color attribute c of the Gaussian point i With opacity α i ,Ensure that the scene appearance is consistent with the real data;

[0079] For the interpolated Gaussian points, their color values ​​are dynamically adjusted through back propagation to ensure a smooth transition with the photometric characteristics of the neighboring high-scoring points.

[0080] L normal Normal consistency loss is achieved by constraining the minor axis of the Gaussian covariance matrix to align with the normal to ensure the geometric directionality of the three-dimensional Gaussian sputtering scene; in the edge area, the hyperparameter λ is increased normal To strengthen normal alignment and suppress depth blur; in the surface area, through dynamic weight w i Adjust the normal constraint strength to avoid over-smoothing details;

[0081] L structure To reduce the loss of structural continuity, the following optimization is achieved through dynamic neighborhood screening and stability constraints: for high-scoring areas, the neighborhood radius r is expanded and λ is reduced structure , promote the adaptive growth of Gaussian point density and enhance surface continuity; for low-scoring areas, increase λ structure To forcefully remove outliers and reduce their interference with joint optimization; through the hyperparameter λ structuret In conjunction with the scoring weights w1 to w4, spatial consistency is prioritized in edge areas, while color smoothness is emphasized in stable areas.

[0082] The present invention has at least the following beneficial effects:

[0083] Through multi-step processing, this method effectively solves the problems existing in the existing three-dimensional Gaussian sputtering reconstruction, such as sparse point clouds containing outliers, mismatch between Gaussian morphology and normals, and lack of multi-dimensional optimization targets. It can significantly reduce structural artifacts, improve edge clarity and surface fitting accuracy, and generate high-quality three-dimensional Gaussian scene models with clear geometry and consistent rendering, thereby improving the scene reconstruction accuracy and geometric consistency, and is suitable for the fields of three-dimensional reconstruction and multi-view rendering.

[0084] In step S4, a 3D Gaussian distribution is initialized based on the sparse point cloud, assigning each Gaussian point clear geometric and appearance attributes, including location center, color, opacity, and covariance matrix. This initialization process ensures that the spatial distribution and anisotropic scale of the Gaussian points strictly correspond to the geometric characteristics of the filtered point cloud. This addresses the lack of clear definition of geometric and appearance attributes during Gaussian point initialization, making the initial distribution more realistic and providing a geometrically consistent initial model of the Gaussian sputtering scene for subsequent normal consistency alignment, comprehensive scoring screening, and joint optimization. This reduces the geometric positioning error of the initial model and provides a precise starting point for subsequent optimization.

[0085] In step S5, a normal consistency regularization term is introduced, and the normal direction in the normal map is used as a constraint condition to adjust the direction of the minimum eigenvector of the Gaussian covariance matrix so that the direction of the Gaussian minor axis is aligned with the normal direction. This operation solves the problem of chaotic surface normal vectors and blurred edge transitions caused by the inconsistency between the direction of the Gaussian covariance matrix and the direction of the scene normal. By forcing the Gaussian minor axis to be aligned with the normal direction through gradient optimization, the minor axis of the Gaussian distribution in the edge area of ​​the Gaussian sputtering scene fits the surface normal. At the same time, the dynamic weight reduces the interference of low-confidence Gaussian points on the normal alignment, ensuring that the geometric structure of the three-dimensional Gaussian sputtering scene is consistent with the real surface topology, and improving the directional accuracy of the geometric structure.

[0086] In step S6, the structural properties of each Gaussian point are analyzed, the eigenvalues ​​are extracted by decomposing the covariance matrix, the anisotropy index and local curvature are calculated, and the number of visible times and the variance of opacity changes are counted. These operations solve the problem that traditional methods lack quantitative analysis of the local geometric features of Gaussian points. They can effectively identify the geometric complexity of the area where the Gaussian points are located and distinguish between planes, curved surfaces and edge areas. The anisotropy index quantifies the directional distribution of Gaussian points, the local curvature identifies the geometric complexity, and the number of visible times and the variance of opacity changes measure the stability and credibility. Combined with the normal direction alignment results, the density of Gaussian points can be increased in the curvature mutation area to suppress structural artifacts. The constraints are strengthened by adjusting the visibility weights to suppress the negative impact of unstable Gaussian points on the joint optimization. The structural properties of the Gaussian points are comprehensively evaluated, providing a basis for subsequent screening and optimization.

[0087] The comprehensive scoring function constructed in step S7 combines multi-dimensional indicators such as anisotropy, local curvature, visibility times, and opacity variation variance to address the problem that single-indicator Gaussian point screening tends to overlook the combined effects of multi-dimensional structural properties. This scoring function comprehensively evaluates the structural quality and stability of Gaussian points, removes or downgrades Gaussian points with scores below a set threshold, interpolates high-scoring areas to increase Gaussian point density to enhance surface detail, and limits Gaussian point scale variation in edge regions to maintain edge clarity. The weight coefficient is dynamically adjusted based on the scene's geometric characteristics, making the screening more targeted and effectively removing low-quality Gaussian points, thereby improving the model's geometric expressiveness and reliability.

[0088] When calculating the structural continuity loss in step S8, a set of neighboring Gaussian points is dynamically determined based on the comprehensive score. The constraints of closely spaced neighboring points are enforced using a Gaussian kernel function. The position and color differences are calculated and accumulated to obtain the loss value. This operation addresses the problem of discontinuities in color and position between adjacent Gaussian points, which can cause breaks or sudden changes in the reconstructed surface. It ensures geometric smoothness in dense areas of the 3D Gaussian sputtering scene. Combined with the color attributes in the scoring function, it suppresses rendering color discontinuities caused by sudden opacity changes, improves the visual coherence of the model, and ensures consistency in the spatial distribution and color of adjacent Gaussian points, reducing imperfections in the reconstructed surface.

[0089] The joint training framework used in step S8 includes photometric loss, normal consistency loss, and structural continuity loss, which solves the problem of geometric ambiguity when relying solely on photometric loss optimization. Photometric loss ensures that the scene appearance is consistent with the real data, normal consistency loss constrains the minor axis direction of the Gaussian covariance matrix to be aligned with the normal, and structural continuity loss is optimized through neighborhood dynamic screening and stability constraints. Hyperparameters are linked to scoring weights, focusing on different optimization goals in different areas, guiding Gaussian points to converge to the geometric structure of the real scene. Multi-dimensional joint optimization balances various constraints, avoids optimization deviations caused by a single loss, and improves the overall reconstruction accuracy and visual realism of the three-dimensional Gaussian scene model, so that the model can still maintain high consistency and reliability under complex conditions.

[0090] Other advantages, objectives and features of the present invention will be reflected in part from the following description and will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is an overview of the 3D Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian.

[0092] Figure 2 This is a flow chart of a 3D Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian of the present invention;

[0093] Figure 3 This is a schematic diagram comparing the Gaussian normal and the estimated normal;

[0094] Figure 4 It is a schematic diagram of the three eigenvalue directions of the Gaussian point;

[0095] Figure 5 It is a schematic diagram of Gaussian continuity structure loss. DETAILED DESCRIPTION

[0096] The present invention will be described in further detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0097] It should be understood that terms such as “having”, “including” and “comprising” used herein do not preclude the existence or addition of one or more other elements or combinations thereof.

[0098] It should be noted that the experimental methods described in the following embodiments are conventional methods unless otherwise specified, and the reagents and materials can be obtained from commercial channels unless otherwise specified.

[0099] A three-dimensional Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian can extract key frame images at a fixed frame rate during data acquisition. The frame rate can be selected as 24fps, 30fps, or 60fps. The acquisition device can be a common ordinary camera or industrial camera on the market, which is fixed on a stable bracket to ensure stability during shooting and avoid jitter affecting data quality. The SfM algorithm is used to reconstruct the sparse three-dimensional point cloud, and the depth map and normal map of each frame image are generated by the Lotus monocular depth estimation model. In order to obtain better sparse point cloud input data and perform filtering processing, the sparse point cloud generated by the SfM algorithm is first converted from bin format to ply format so that statistical filtering and radius filtering can be performed using point cloud processing software such as CloudCompare or Meshlab. During statistical filtering, the average Euclidean distance between each point and its neighboring points is calculated. If the distance exceeds the threshold range of the sum of the overall average distance and the standard deviation (such as the overall average distance plus 2 times the standard deviation), it is determined to be an outlier and removed. During radius filtering, the number of neighboring points within a preset radius of each point (such as 0.1-0.5 meters, which can be set according to the scene scale, and 0.2 meters for indoor scenes) is counted. If the number is lower than the set threshold (such as 5-20, set to 10 for indoor scenes), it is determined to be an outlier and removed. After filtering, the point cloud is re-encoded into bin format to match the input requirements of 3D Gaussian rendering. This process can effectively remove obvious outliers and abnormal values, improve the quality of the point cloud, and lay the foundation for subsequent Gaussian initialization.

[0100] A 3D Gaussian distribution is initialized based on the filtered sparse 3D point cloud, and each Gaussian point is assigned a center of position, a scale rotation matrix, a color, and opacity attributes. The center of the Gaussian point is determined by the spatial point in the sparse point cloud, the color is extracted from the RGB value of the corresponding point, the opacity can be initialized to 0.5 or 1, and the covariance matrix can be initially set to a diagonal matrix, such as the identity matrix or a small variance matrix (e.g., diagonal elements are 0.01). This step ensures that the main direction of the Gaussian distribution matches the true surface orientation, improving geometric consistency and effectively suppressing the edge blurring caused by normal confusion in traditional methods.

[0101] Structural properties are analyzed for each Gaussian point. The covariance matrix is ​​decomposed to obtain eigenvalues ​​λ1≤λ2≤λ3. The anisotropy index A = (λ3-λ1) / λ3 and local curvature are calculated. The number of times a Gaussian point is visible across multiple image frames, V, and the variance of its opacity variation, Δα, are counted. A comprehensive scoring function is constructed, where w1, w2, w3, and w4 can be adjusted experimentally (e.g., to 0.2, 0.2, 0.3, and 0.3, respectively). Gaussian points with scores below a set threshold (e.g., 0.5) are removed or downgraded. In regions with high scores, the density of Gaussian points is increased through interpolation to enhance surface detail. Edge clarity is maintained in boundary regions by limiting the scale variation of Gaussian points. Eigenvalue decomposition, index calculation, and scoring function construction can be performed using relevant library functions in programming languages ​​(e.g., Python). Image analysis libraries (e.g., OpenCV) are used to count the number of times a Gaussian point is visible and the opacity variation. By evaluating the stability and credibility of Gaussian points through multi-dimensional indicators, unstable points can be effectively eliminated, the distribution of Gaussian points can be optimized, and the geometric expressiveness and reliability of the model can be improved.

[0102] The selected Gaussian points are optimized using a joint training framework that includes photometric loss, normal consistency loss, and structural continuity loss. Photometric loss measures the difference between the rendered image and the real image, and the calculation formula is the mean square error (MSE); normal consistency loss is the above L normal ; The structural continuity loss constrains the color and position consistency between adjacent Gaussian points. The final loss function of the joint training framework is, where λ normal and λ structureare hyperparameters (e.g., set to 0.1 and 0.5 respectively), which are adjusted to guide the Gaussian points to converge to the geometric structure of the real scene. The color attribute is used to calculate the photometric loss, the scaling rotation matrix and the position center are dynamically adjusted through gradient backpropagation, and the opacity attribute participates in the calculation of the structural continuity loss. The training process can be performed on a computer equipped with a computing device such as an NVDIA GPU, and implemented using an existing 3D Gaussian rendering engine (such as an open source or commercial 3DGS framework). Through the joint optimization of multiple losses, the Gaussian points are made to fit the real scene more closely in terms of spatial distribution, normal direction, color and position continuity, and ultimately generate a high-quality three-dimensional Gaussian scene model with clear geometry, clear boundaries and consistent rendering, which significantly improves the reconstruction accuracy and visual coherence of complex scenes.

[0103] Through the synergistic effect of the above-mentioned technical features, this solution effectively solves the problems existing in the existing three-dimensional Gaussian sputtering reconstruction, such as sparse point clouds containing outliers, mismatch between Gaussian morphology and normals, and lack of multi-dimensional optimization targets. It can improve the scene reconstruction accuracy and geometric consistency, and is suitable for the fields of three-dimensional reconstruction and multi-view rendering.

[0104] In another technical solution, in step S2, the sparse point cloud generated by the SfM algorithm can be converted from bin format to ply format. Regarding numerical selection, parameters such as the point cloud's coordinate system and point cloud density can be maintained during the conversion process. The raw material is a sparse 3D point cloud generated by the SfM algorithm. During functional testing, the converted ply format point cloud can be checked for proper display and editing in the software, ensuring that no geometric attributes are lost.

[0105] After conversion to the ply format, statistical filtering and radius filtering are performed on the sparse point cloud. During statistical filtering, the average Euclidean distance between each point and its neighboring points is calculated. If the distance exceeds the threshold range of the sum of the overall average distance and the standard deviation (such as the overall average distance plus 2 times the standard deviation), it is determined to be an outlier and removed. The number of neighboring points can be selected as 10, and the neighborhood point set is determined by the k-nearest neighbor algorithm of the point cloud processing software. During radius filtering, the preset radius r can be set to 0.2 meters (taking indoor scenes as an example), and the number of neighboring points within the radius r of each point is counted. If the number is lower than the set threshold (such as 10), it is determined to be an outlier and removed. In terms of equipment selection, point cloud processing software with statistical filtering and radius filtering functions can be used. The working process is to import the ply format point cloud into the point cloud processing software, execute the statistical filtering and radius filtering functions in sequence, and the software automatically calculates and filters out outliers and abnormal points. Parameter setting methods can be optimized by observing the distribution of the point cloud and adjusting the threshold (e.g., adjusting the standard deviation multiple from 1.5 to 2.5) and radius (e.g., from 0.1 meter to 0.3 meter) multiple times to achieve optimal filtering results. The raw material is a converted sparse point cloud in ply format. During functional testing, the point count and spatial distribution of the point cloud before and after filtering are compared to verify that outliers and abnormal points have been effectively reduced.

[0106] After filtering, the point cloud is re-encoded into bin format. Regarding numerical selection, the point cloud accuracy can be set to single-precision floating-point according to the input requirements of the 3D Gaussian rendering engine during the encoding process. The ID of the filtered sparse point cloud is compared with the original bin file, and the track data of the original bin file is extracted. Each point in the point cloud is re-IDed and written into a new bin file. During functional testing, the re-encoded bin file is imported into the 3D Gaussian rendering engine to check whether the engine can normally recognize the point cloud data without rendering interruptions or data misalignment.

[0107] This technical solution uses the technical features of format conversion, filtering processing and re-encoding. These operations improve the geometric consistency and rendering efficiency of scene reconstruction, provide a reliable data basis for subsequent Gaussian initialization and optimization, reduce the cost of manual intervention, and ensure the continuity of the reconstruction process.

[0108] In another technical solution, during the statistical filtering process, the average Euclidean distance between each point and its neighboring points is first calculated. In terms of numerical selection, the number of neighboring points can be set to 10 (k=10), and the neighborhood point set is determined by the k-nearest neighbor algorithm of the point cloud processing software. The Euclidean distance from each point to the neighboring point is calculated and averaged to obtain the average distance of the point. The outlier judgment threshold can be set to the overall average distance plus 2 times the standard deviation (+2σ). If the average distance of a point is greater than the threshold, it is judged as an outlier and removed. The working process is: import sparse point cloud data into the software, the software automatically traverses each point, calculates its average Euclidean distance with k neighboring points, and then generates a threshold based on the overall average distance and standard deviation to filter out outliers and remove them. Parameter setting method: Initially, k=10 and the standard deviation multiple can be set to 2. The k value (such as 8-15) and multiple (such as 1.5-2.5) can be adjusted according to the point cloud density. Source of raw materials: sparse three-dimensional point cloud generated in step S2. Functional testing: Use visualization tools to compare the point cloud before and after filtering to check whether outliers are reduced and normal points are more concentrated.

[0109] This technical solution effectively removes global outliers from sparse point clouds through a multi-stage statistical filtering process. The integration of statistical analysis and engine parameters enhances the structural consistency of 3D reconstruction, providing a more reliable point cloud foundation for Gaussian initialization and enabling more accurate geometric constraints in subsequent normal alignment and joint training.

[0110] In another technical solution, radius filtering determines abnormal points by counting the number of neighboring points within a preset radius of each point. In terms of numerical selection, the preset radius r can be set to 0.2 meters (taking indoor scenes as an example), and the threshold of the number of neighboring points R min It can be set to 10. The working process is: import the statistically filtered point cloud data into the software, set the radius r = 0.2 meters, and the software automatically searches for the neighboring points within its radius for each point and counts them. If the number is less than R min = 10, it is determined as an abnormal point and removed. Parameter setting method: Initially, r = 0.2 meters, R min =10, outdoor large scene can be adjusted r = 0.5 meters, R min = 20. Source: Sparse point cloud after statistical filtering in step S3. Functional test: Compare the distribution of point clouds in sparse areas before and after filtering to check whether low-density noise points are reduced and whether point clouds in edge areas are preserved.

[0111] Statistical filtering is combined with radius filtering to process global outliers and local density anomalies respectively. In terms of numerical selection, the outlier judgment threshold of statistical filtering is the overall average distance ±2 times the standard deviation, and the radius filter parameters are as described in Technical Features 1 and 2. Working process: First, statistical filtering is used to remove global distribution anomalies (such as floating points), and then the local point cloud density is optimized through radius filtering, retaining the anisotropic distribution in the curved area and maintaining clarity in the edge area. Parameter setting method: First run the statistical filter, and then adjust the radius filter parameters for local optimization based on the density distribution results of the output point cloud. Source of raw materials: original sparse point cloud generated by SfM. Functional test: Observe the overall structure of the filtered point cloud through a three-dimensional visualization tool to check whether there are obvious outliers, and whether the point cloud density in different geometric areas adapts to the scene characteristics, such as the continuity of the point cloud at the edge of the object and the reasonable distribution of the point cloud of the surface details.

[0112] By dynamically setting the parameters of the radius filter and synergizing it with statistical filtering, the problem of fixed threshold filtering's difficulty adapting to uneven point cloud density is effectively addressed. Differentiated parameter configurations for surface details and edge transition regions capture the anisotropic characteristics of local geometry while suppressing edge blur and scale mutations. This combination reduces optimization conflicts between different loss terms in joint training, improves the stability and structural continuity of the Gaussian covariance matrix, effectively suppresses suspension artifacts and edge blur in the reconstructed scene, and enhances the geometric consistency and visual fidelity of the 3D model.

[0113] In another technical solution, based on the filtered sparse point cloud, each Gaussian point is assigned initial geometric and appearance attributes. In terms of numerical selection, the center of the Gaussian point directly corresponds to the three-dimensional coordinates of the sparse point cloud (such as X j ∈R 3 ), the color can be extracted from the RGB value of the corresponding image pixel (such as c∈R3, with a value range of 0-255), and the opacity α can be initialized to 0.5 or 1.0.

[0114] The initial covariance matrix is ​​a symmetric matrix whose parameters are determined by the scaling and rotation matrix. In terms of numerical selection, the initial covariance matrix can be set to an isotropic diagonal matrix, such as σx 2 =σy 2 =σz 2 =0.01 2 , which corresponds to the ∑ matrix in the probability density formula. For equipment selection, mathematical computing software or programming libraries (such as Python's numpy library) can be used to construct matrices and calculate probability density. The working process is: generate the initial parameters of the covariance matrix by scaling the rotation matrix, combined with the position center μ jConstruct a complete matrix and use the probability density formula g(x) to calculate the density value of the spatial point x for subsequent rendering simulation. Parameter setting method: The initial variance value can be adjusted according to the point cloud density, and the high-density area is set to 0.01 2 , low density area is set to 0.05 2 The raw materials are the center of the Gaussian point and the scaling and rotation matrix parameters. Functional test: Draw the Gaussian distribution probability density curve to check whether the shape conforms to the expected bell-shaped distribution.

[0115] The initial parameters of the scaling rotation matrix are related to the point cloud density distribution. In terms of numerical selection, in the surface detail area (high point cloud density), the covariance matrix variance can be set to 0.01 2 -0.03 2 , to match local high-density features; in the edge area (low point cloud density), the variance can be set to 0.05 2 -0.1 2 , adapted to sparse geometric structures.

[0116] In another technical solution, based on the initialized Gaussian covariance matrix, the loss function of the normal consistency regularization term is constructed, and the formula is: i Can be initialized to 1.0 and dynamically adjusted based on visibility and stability, such as high visibility points w i Set it to 1.5 and set it to 0.5 for low visibility points. For device selection, you can use a deep learning framework (such as PyTorch or TensorFlow), which supports matrix operations and gradient optimization. The working process is: import the normal map generated by the Lotus model into the framework, extract the normal direction n of each point i , get the minimum eigenvector N of the Gaussian covariance matrix i , calculate the loss value of each Gaussian point and sum it up to get L normal , optimize the covariance matrix parameters by back propagation. Parameter setting method: Initially w i Unified to 1.0, and then based on the number of times the Gaussian point is visible in multiple frames V i (If Vi ≥ 5 times, it is considered highly visible.) Dynamic adjustment. Source of raw materials: Gaussian covariance matrix initialized in step S4 and normal map generated in step S2. Functional test: Observe the change in the angle between the Gaussian short axis and the normal direction before and after optimization to ensure that the angle gradually decreases.

[0117] Perform eigenvalue decomposition on the initialized Gaussian covariance matrix and extract the minimum eigenvector N i (corresponding to the direction of Gaussian minor axis). In terms of numerical selection, eigenvalue decomposition can be implemented through a mathematical calculation library (such as Python's numpy library), ensuring that the eigenvalues ​​are sorted according to λ1≤λ2≤λ3, and taking the eigenvector corresponding to λ1 as Ni The working process is: load the covariance matrix in the programming environment, call the eigenvalue decomposition function (such as numpy.linalg.eigh), obtain the sorted eigenvalues ​​and eigenvectors, and use the eigenvector corresponding to the minimum eigenvalue as N i Parameter setting method: Ensure the accuracy of eigenvalue decomposition and set the error tolerance to 1e-6. Source of raw materials: covariance matrix parameters initialized in step S4. Functional test: Observe the Gaussian minor axis direction (N) through the visualization tool. i ) and the normal direction (n i ) to check whether the edge areas fit the surface normals.

[0118] Extract the normal direction n of each point from the normal map estimated by the Lotus model i , n i is a unit vector with a value range of [-1, 1]. Dynamic weight w i According to the visible number V of the Gaussian point i and opacity change Δα adjustment, such as V i Points with ≥5 times and Δα≤0.1 are considered to have high confidence, w i Set to 1.2; V i Points with <3 times or Δα>0.3 are considered to have low reliability, w i Set to 0.8. For device selection, you can use an image processing library (such as OpenCV) to read the normal map and extract pixel values. The working process is: match the normal map with the Gaussian point position, extract n by bilinear interpolation i Statistics V i and Δα, according to the preset threshold (such as V i =5, Δα=0.1) adjust w i Parameter setting method: Determine V through experiments i and the threshold of Δα, such as V in indoor scenes i The threshold is set to 5 frames, and the Δα threshold is set to 0.1. Source of raw materials: normal map generated in step S2 and Gaussian point visibility data statistically calculated in step S6. Functional test: compare the w of high / low confidence Gaussian points. i The value distribution ensures that high-confidence points have higher weights and low-confidence points have lower weights.

[0119] Through the normal consistency regularization term and dynamic weighting mechanism, the minor axis of the Gaussian is forced to align with the normal direction, effectively suppressing blurring in edge areas. Eigenvalue decomposition ensures the directional constraints of the Gaussian morphology, and dynamic weighting reduces the interference of low-confidence points on normal alignment, making the geometric structure of the three-dimensional Gaussian scene closer to the actual surface topology. This process improves the geometric consistency of the Gaussian distribution, provides accurate normal constraints for subsequent structural property analysis and joint optimization, reduces reconstruction errors caused by normal mismatch, and enhances the geometric fidelity and edge clarity of the model.

[0120] In another technical solution, the covariance matrix of each Gaussian point is subjected to eigenvalue decomposition, and three eigenvalues ​​λ1, λ2, and λ3 (λ1≤λ2≤λ3) are extracted to calculate the anisotropy index A = (λ3-λ1) / λ3. In terms of numerical selection, eigenvalue decomposition can be implemented through a mathematical calculation library (such as Python's numpy library), ensuring that the eigenvalues ​​are arranged in ascending order and the value range of A is [0, 1]. In terms of equipment selection, programming libraries or software that support matrix operations can be used. The working process is: load the covariance matrix in the programming environment, call the eigenvalue decomposition function (such as numpy.linalg.eigh), obtain the sorted eigenvalues, and substitute them into the formula to calculate A. Parameter setting method: Ensure the accuracy of the eigenvalue decomposition and set the error tolerance to 1e-6. Raw material source: Gaussian covariance matrix initialized in step S4. Functional test: Verify whether the value of A is between 0 and 1, and whether high anisotropy values ​​(such as A>0.7) correspond to Gaussian points in the edge area.

[0121] Calculate the local curvature C(X i )=λ1 / (λ1+λ2+λ3), which is used to identify geometric complexity. In terms of numerical selection, the value range of C(Xi) is [0, 1]. The larger the value, the higher the curvature (e.g., C≈0 in the plane area and C≈0.5 in the corner area). The working process is: extract λ1, λ2, and λ3 from the eigenvalue decomposition result, substitute them into the curvature formula to calculate C(X i ), and judge the dimensional characteristics based on the relative size of the eigenvalues ​​(for example, when λ1<<λ2≈λ3, it is considered a linear structure). Parameter setting method: No additional parameters are required, and it is calculated directly based on the eigenvalues. Source of raw materials: Same as above. Functional testing: Use visualization tools to observe whether high curvature areas (such as C>0.3) correspond to surface details or corners in the scene, and whether low curvature areas (C<0.1) correspond to planes.

[0122] Count the number of times V a Gaussian point is visible across multiple frames, and calculate the variance of the opacity change, Δα. The threshold for the number of visible times can be set to 5 (V ≥ 5 is considered highly visible), and the threshold for the variance of the opacity change, Δα, can be set to 0.1 (Δα ≤ 0.1 is considered stable). For device selection, an image processing library (such as OpenCV) can be used to track the projection of the Gaussian point across each frame to calculate V and Δα. The process is as follows: Project the Gaussian point onto each frame, determine visibility through pixel matching (e.g., the projected point is located within a valid pixel area and has consistent depth), and count V; then collect the opacity values ​​for each frame and calculate the variance, Δα. Parameter Setting: Adjust the threshold for the number of visible times based on the scene frame rate and reconstruction requirements. For example, a setting of 3 can be used for high-frame-rate scenes. Source: The keyframe image sequence extracted in step S1 and the Gaussian opacity attributes initialized in step S4. Functional Testing: Check that low-visibility points (V < 3) and high-fluctuation points (Δα > 0.2) are correctly identified, ensuring that the statistical results reflect the stability of the Gaussian points.

[0123] Through multi-dimensional structural property analysis, the geometric characteristics (anisotropy, curvature) and stability (visibility, opacity fluctuation) of Gaussian points are quantified. Eigenvalue decomposition and curvature calculation effectively identify edges, curved surfaces, and planar regions, providing a basis for adjusting Gaussian point density. Visibility and stability statistics eliminate low-confidence points and reduce noise interference. These operations enable the algorithm to adaptively allocate Gaussian resources, increasing density in areas of sudden curvature changes to suppress artifacts, and retaining high-quality points in stable areas, thereby improving the geometric expressiveness and structural consistency of the reconstructed model, laying the foundation for subsequent comprehensive scoring screening and joint optimization.

[0124] In another technical solution, the comprehensive scoring function S(X i )=w1(1-C(X i ))+w2V i -w3Δα i +w4A(X i ), in terms of numerical selection, the anisotropy index A(X i ) ranges from [0, 1], the local curvature C(Xi) ranges from [0, 1], and the number of visible times V i is a non-negative integer, the opacity change variance Δα i The value range is [0, 1]. The weight coefficients w1~W4 can be initially set to w1=0.3, w2=0.2, w3=0.3, w4=0.2, and dynamically adjusted according to the scene. In terms of equipment selection, programming software (such as Python) or mathematical calculation tools (such as MATLAB) can be used to implement formula calculations. The working process is: input the data of each Gaussian point, call the scoring function to calculate the comprehensive score S(X iParameter Setting Method: Initial weights can be set empirically and subsequently optimized through cross-validation. For example, adjust w1 to 0.4 in edge regions and w2 to 0.3 in curved regions. Source: Anisotropy index, local curvature, visibility times, and opacity variance data calculated in step S6. Functional Testing: Check whether the scoring results match the actual quality of the Gaussian points, for example, whether points with high anisotropy and low visibility have low scores.

[0125] Set the scoring threshold θ = 0.5, and perform elimination or downgrade processing on Gaussian points with scores below the threshold. In terms of equipment selection, data processing software (such as Pandas) or programming libraries (such as NumPy) can be used for data screening. The working process is: traverse S (X i ), S(X i ) < 0.5 are marked as pending points and are removed by deletion or their weights adjusted (e.g., reducing opacity to 0.2). Parameter Setting Method: The threshold can be adjusted based on scene complexity, such as 0.6 for complex scenes and 0.4 for simple scenes. Source of Raw Materials: The comprehensive score data calculated in step S7. Functional Testing: Statistically analyze the change in the number of Gaussian points before and after screening to check whether low-scoring points are effectively reduced and high-scoring points are retained.

[0126] The weight coefficients w1 to w4 are dynamically adjusted according to the geometric characteristics of the three-dimensional Gaussian sputtering scene. In terms of numerical selection, in the edge area, w1 is increased to 0.4-0.5 to strictly limit the scale of Gaussian points; in the curved area, w2 is increased to 0.3-0.4 to enhance the detail density; in the stable area, it is increased to 0.4-0.5 to retain high-quality Gaussian points. In terms of equipment selection, programming software that supports conditional judgment (such as Python) can be used to automatically identify the area type and adjust the weight through the algorithm. The working process is: use the curvature detection algorithm to identify the edge area (such as C(X i )>0.3) and surface areas (such as 0.1<C(X i )<0.3), automatically loading the corresponding weight parameter group based on the region type. Parameter setting method: Preset weight templates for different regions, such as edge template [0.5, 0.2, 0.2, 0.1] and surface template [0.2, 0.4, 0.3, 0.1]. Raw material source: Local curvature and anisotropy index extracted in step S6. Functional test: Comparing the scale changes of Gaussian points in different regions, the scale fluctuation of Gaussian points in edge regions should be reduced, and the surface regions should have richer details.

[0127] Through a comprehensive scoring function and a dynamic weighting mechanism, a multi-dimensional assessment and adaptive screening of the structural quality of Gaussian points is achieved. Anisotropy and curvature metrics effectively identify edge and surface features, visibility and stability metrics eliminate noise points, and dynamic weighting ensures a clear optimization direction for the Gaussian distribution in different geometric regions. This method reduces the interference of unstable Gaussian points on reconstruction, suppresses blur in edge regions, and enhances detail in curved areas. This improves the rationality of the Gaussian point distribution and the overall reliability of the model, significantly improving the geometric accuracy and visual coherence of the reconstructed scene.

[0128] In another technical solution, the neighborhood Gaussian point set N(X i ). In terms of numerical selection, the neighborhood radius r can be set to 0.2-0.5 meters (taking indoor scenes as an example), and adjusted according to the complexity of the scene. The working process is: after filtering the Gaussian point cloud data, set the neighborhood radius r, and automatically search for each Gaussian point X according to the comprehensive score. i The neighborhood point set N(X i ), prioritizing points with higher scores as neighborhood points. Parameter Setting Method: Initially set r = 0.3 meters for indoor scenarios and r = 0.5 meters for large outdoor scenarios. Source: Gaussian point cloud filtered in step S7. Functional Testing: Observe the distribution of the neighborhood point set to ensure that the density and quality of the points within the neighborhood match those of the central Gaussian point. For example, the neighborhood points surrounding a high-scoring point should also have high scores.

[0129] Calculate the structural continuity loss L structure In terms of numerical selection, the bandwidth parameter σ of the Gaussian kernel function K can be set to 0.1-0.3 meters and adjusted according to the scene scale. In terms of device selection, programming libraries (such as Python's numpy library) can be used for matrix operations and summation calculations. The working process is: after loading the neighborhood point set N(X i ) and the position of the Gaussian point X i With color c i Data, calculate the structural continuity loss value of each Gaussian point and its neighboring points according to the formula, and then add them up to get L structure Parameter Setting Method: Experimentally adjust the bandwidth parameter σ and observe changes in the loss value. For example, set σ = 0.1 meters for small-scale scenes and σ = 0.3 meters for large-scale scenes. Source: Position and color information of the Gaussian point cloud filtered in step S7. Functional Testing: Compare the loss values ​​under different bandwidth parameters to check whether the loss values ​​change reasonably with parameter adjustments. For example, the loss value should decrease as the bandwidth increases.

[0130] Optimize the structural continuity loss L through gradient backpropagation structureFor device selection, you can use deep learning frameworks (such as PyTorch or TensorFlow), which support automatic differentiation and gradient optimization. The working process is: define the structural continuity loss function L in the deep learning framework structure , take the position and color of the Gaussian point as variables, set the optimizer (such as Adam optimizer) and learning rate (such as α=0.001), automatically calculate the gradient and update the variables through the back propagation algorithm, so that L structure Gradually decrease. Parameter Setting Method: Adjust the learning rate based on the training results. For example, if the loss value decreases slowly, reduce the learning rate to α = 0.0001. Source of Raw Materials: The structural continuity loss value and the position and color information of the Gaussian points calculated in step S8. Functional Testing: Observe the changing trend of the loss value during the optimization process to ensure that the loss value continues to decrease and that the position and color adjustments of the Gaussian points are as expected, such as the distance and color difference between adjacent Gaussian points gradually decrease.

[0131] By optimizing the dynamic neighborhood point set and structural continuity loss, the team ensured geometric smoothness and color consistency between adjacent Gaussian points in the 3D Gaussian sputtering scene. The dynamic neighborhood search made the local environment of the Gaussian points more representative, while the Gaussian kernel function strengthened the constraints of nearby neighborhood points. The calculation and optimization of the structural continuity loss effectively suppressed positional and color abrupt changes between adjacent Gaussian points, improving the model's visual coherence and geometric stability, reducing imperfections and discontinuities in the reconstructed surface, and making the final 3D Gaussian scene model more realistic and natural.

[0132] In another technical solution, a joint training framework including photometric loss, normal consistency loss and structural continuity loss is used to optimize the screened Gaussian points. In terms of numerical selection, the weight coefficient of photometric loss can be set to 0.5, the weight coefficient of normal consistency loss is set to 0.3, and the weight coefficient of structural continuity loss is set to 0.2. In terms of equipment selection, a deep learning framework (such as PyTorch or TensorFlow) can be used to build and train the model. The working process is: define a joint training framework in the deep learning framework, combine the photometric loss, normal consistency loss and structural continuity loss according to the set weight coefficients, and obtain the final loss function. The screened Gaussian points are used as input, and the model is trained through the backpropagation algorithm. The parameters of the Gaussian points are continuously adjusted to gradually reduce the loss function. Parameter setting method: Determine the optimal value of the weight coefficient through experiments and debugging. For example, the weight coefficients can be set to 1 first, and then adjusted according to the training results. Source of raw materials: Gaussian points screened in step S7. Functional testing: Observe the changing trend of the loss function during training to ensure that the loss function can gradually converge to a smaller value.

[0133] To calculate the luminosity loss, for numerical selection, the color value can be in RGB format with a value range of 0-255. For device selection, image processing software (such as OpenCV) can be used to read and process images. The working process is: load the real image and the rendered image into the image processing software, extract the color values ​​of the Gaussian points in the real image and the rendered image, and calculate the luminosity loss according to the formula. Parameter setting method: No additional parameter setting is required. Source of raw materials: The key frame image sequence extracted in step S1 and the Gaussian points filtered in step S7. Functional test: Compare the color values ​​of the Gaussian points in the real image and the rendered image to check whether the luminosity loss can reflect the difference between the two.

[0134] The joint training framework optimizes the Gaussian points to ensure they more closely align with the real scene in terms of spatial distribution, normal orientation, color, and positional continuity. For numerical selection, the learning rate can be set to 0.001, and the number of training rounds can be set to 100-200 rounds. The process is as follows: Set up the joint training framework and optimizer in the deep learning framework, take the Gaussian points as input, and begin training. During training, continuously adjust the parameters of the Gaussian points to gradually reduce the loss function. Simultaneously, observe changes in the spatial distribution, normal orientation, color, and positional continuity of the Gaussian points to ensure they more closely align with the real scene. Parameter Setting Method: Determine the optimal values ​​for the learning rate and number of training rounds through experimentation and debugging. For example, you can initially set the learning rate to 0.01 and the number of training rounds to 50, then adjust them based on the training results. Source of raw materials: Gaussian points filtered in step S7. Functional Testing: Observe whether the optimized Gaussian points more closely align with the real scene in terms of spatial distribution, normal orientation, color, and positional continuity. For example, you can use visualization tools to visualize the distribution of the Gaussian points.

[0135] By constructing and optimizing a joint training framework, the Gaussian points are made to more closely align with the real scene in multiple aspects, resulting in a high-quality 3D Gaussian scene model. A photometric loss ensures that the scene's appearance is consistent with the real data, a normal consistency loss constrains the alignment of the minor axis of the Gaussian covariance matrix with the normal, and a structural continuity loss ensures color and position consistency between adjacent Gaussian points. By adjusting weight coefficients and hyperparameters, the Gaussian points are guided to converge to the real scene's geometric structure, improving the accuracy and visual coherence of the 3D reconstruction.

[0136] <Application Examples>

[0137] like Figure 1-5 As shown, the present invention provides a 3D Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian, comprising the following steps:

[0138] Data collection and point cloud preprocessing:

[0139] The target indoor scene is captured by an industrial camera at 30fps, and key frames are extracted to generate image sequences. Based on the image sequences, the SfM algorithm is used to reconstruct sparse 3D point clouds.

[0140] The lotus model generates a depth map and a normal map for each frame. The bin format point cloud output by SfM is converted to ply format, and statistical filtering and radius filtering are performed through CloudCompare:

[0141] Statistical filtering: Calculate the average Euclidean distance between each point and its 10 neighboring points. If the distance exceeds the overall average distance + 2 times the standard deviation (for example, the threshold for indoor scenes is set to 0.15 meters), the point is considered an outlier and removed.

[0142] The specific calculation formula is:

[0143] removeifd i >μ global +λσ;

[0144] where ||X i -X j || represents point X i to X j The Euclidean distance between global represents the overall density level of the point cloud, and σ is the standard deviation of all points. i Greater than the overall average distance μ global Add a certain threshold λσ, then it is considered an outlier and removed;

[0145] Radius filtering: The preset radius is r = 0.2 meters. The number of neighboring points of each point is counted. If there are less than 10 points, they are removed. After filtering, the point cloud is re-encoded into a bin format, including coordinates, RGB color and normal information, which is adapted to the input specification of the 3D Gaussian rendering engine;

[0146] The specific calculation formula is:

[0147] Radius filtering: Count the number of neighboring points within the preset radius r for each point. The formula is:

[0148] removeif R i ≤R min ;

[0149] For each point X i , calculate its neighborhood point cloud R within radius r i If R i Less than the set threshold R min , then delete the point.

[0150] Gaussian initialization and structure screening:

[0151] Initialize 3D Gaussian based on the filtered point cloud:

[0152] Geometric initialization: The center of each Gaussian point corresponds to the point cloud coordinates, that is, the position center μ j : directly corresponds to the spatial point coordinate μ in the sparse point cloud j =X j ∈R 3 ;

[0153] Color c∈R k Extracted from the image pixel RGB value, the opacity α∈R is initialized to 0.5, and the covariance matrix is ​​initially a diagonal matrix:

[0154] Its probability density formula is:

[0155]

[0156] Normal alignment: Through the normal consistency regularization optimization, the loss function is:

[0157] Weight w i Adjust according to visibility and stability (such as V i ≥5 times is set to 1.2, V i <3 times is set to 0.8), n i is the Gaussian minor axis direction, N i It is the estimated normal direction and the minimum eigenvector N of the constrained Gaussian covariance matrix i (corresponding to the short axis direction) and the normal direction n i Alignment, where w i The weight is dynamically adjusted based on visibility.

[0158] Structural property analysis: Decompose the covariance matrix to extract eigenvalues ​​λ1≤λ2≤λ3, calculate the anisotropy index A = (λ3-λ1) / λ3 to reflect the directionality of the Gaussian shape (A>0.7 is determined as an edge area), local curvature C = λ1 / (λ1+λ2+λ3) (C>0.3 is determined as a high curvature area), characterize the degree of surface curvature, and count the number of visible times V i And the opacity variance Δα (Δα>0.1 is considered an unstable point). Count the number of visible times across frames V i : The higher the visibility, the stronger the stability; calculate the opacity change variance Δα: the smaller the fluctuation, the higher the credibility.

[0159] Comprehensive scoring screening: Construct a comprehensive scoring function to screen Gaussian points.

[0160] S(X i)=w1(1-C(X i ))+w2V i -w3Δα i +w4A(X i ); where w1-w4 are weight coefficients (e.g., w1=0.3, w2=0.2, w3=0.3, w4=0.2). Gaussian points with scores below a threshold (e.g., 0.5) are removed or downgraded; high-scoring regions (e.g., continuous surfaces, S≥0.7) are densified through interpolation, and boundary regions (A>0.7) are scale-limited to maintain edge clarity.

[0161] The Gaussian point screening mechanism is shown in Table 1 below:

[0162] Table 1. Gaussian point screening mechanism

[0163]

[0164] Step S8: Joint optimization using a Gaussian rendering training framework with multi-dimensional loss

[0165] Adopt a joint training framework with multiple losses:

[0166] Photometric loss: Calculate the mean square error between the rendered image and the real image. The formula is:

[0167] L1=∑|I render -I gt |;

[0168] Structural continuity loss: constrains the position and color consistency of adjacent Gaussian points. The formula is:

[0169]

[0170] Optimize color c i With opacity α i , the learning rate is set to 0.001, and training is performed for 200 rounds;

[0171] Total loss function:

[0172] L=L1+λ normal L normal +λ structure L structure ;

[0173] Among them, λ normal and λ structure The positions, scaling matrices, and opacity of Gaussian points are dynamically adjusted through gradient backpropagation for hyperparameters (e.g., set to 0.1 and 0.5, respectively), ultimately generating a high-quality 3D Gaussian scene model with clear geometry and consistent rendering.

[0174] The present invention first captures a video of the target scene and extracts keyframe images at a fixed frame rate to construct an image sequence as the input dataset. A Lotus monocular depth estimation model is used to predict the normal map for each frame. The SfM algorithm is also used to estimate the camera pose and reconstruct a sparse point cloud. The sparse point cloud is then initially filtered to remove outliers. Based on this, a Gaussian position distribution is initialized, and properties such as the position, scaling rotation matrix, and opacity of the Gaussian sphere are set. Using the normal map direction as a reference for the Gaussian principal axis, a normal consistency regularization term is introduced to align the Gaussian covariance with the normal direction, thereby improving structural consistency. Furthermore, structural attribute analysis is performed on each Gaussian point, extracting metrics such as anisotropy, curvature, and visibility to assess its stability and reliability. Based on a comprehensive scoring function, the Gaussian point distribution is screened and adjusted to remove stray points, enhance surface details, and maintain clear boundaries. Finally, based on the screened Gaussian points, a Gaussian rendering training framework is used for joint optimization, guiding the Gaussian points to converge toward the true structure, generating a high-quality 3D Gaussian scene model with clear geometry and consistent rendering.

[0175] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A three-dimensional Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian, characterized in that: The following steps are involved: S1: Collect video data of the target scene, extract key frame images at a fixed frame rate, and generate image sequences; S2: Based on the image sequence, a sparse 3D point cloud is reconstructed using the SfM algorithm, and a depth map and normal map for each frame are simultaneously generated using the Lotus monocular depth estimation model. S3: performing statistical filtering and radius filtering on the sparse three-dimensional point cloud in sequence; S4: Based on the filtered sparse 3D point cloud, initialize the 3D Gaussian distribution and assign the position center, scaling rotation matrix, color and opacity attributes to each Gaussian point; S5: Using the normal direction in the normal map as a constraint condition, adjusting the direction of the minimum eigenvector of the Gaussian covariance matrix through the normal consistency regularization term so that the Gaussian minor axis direction is aligned with the normal direction; wherein the scaling rotation matrix is ​​used to construct the initial parameters of the covariance matrix, and the position center is used to determine the spatial distribution position of the Gaussian point; S6: Perform structural attribute analysis on each Gaussian point: decompose the covariance matrix to obtain eigenvalues, calculate the ratio of the maximum eigenvalue to the minimum eigenvalue as an anisotropy index; calculate the local curvature based on the eigenvalues; count the number of times the Gaussian point is visible in multiple frames of images, and calculate the opacity change variance; the opacity attribute is used to count the opacity change variance; S7: Based on the anisotropy index, local curvature, visibility times, and opacity change variance, a comprehensive scoring function is constructed to filter and remove Gaussian points with scores below the set threshold; s8: A joint training framework that includes photometric loss, normal consistency loss, and structural continuity loss is used to optimize the selected Gaussian points. The color attribute is used to calculate the photometric loss, the scaling rotation matrix and position center are dynamically adjusted through gradient backpropagation, and the opacity attribute is involved in the structural continuity loss calculation. Finally, a 3D Gaussian scene model is generated.

2. The three-dimensional Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian according to claim 1 is characterized in that: In step S2, the sparse point cloud generated by the SfM algorithm is converted from bin format to ply format. Statistical filtering and radius filtering are performed on the ply format point cloud using general point cloud processing tools to remove outliers and points with abnormal density distribution. After filtering, the optimized point cloud is re-encoded into bin format to adapt to the input specifications of the 3D Gaussian splatter rendering engine. The format conversion ensures that the filtered point cloud data is Compatible with the initialization requirements of three-dimensional Gaussian sputtering to avoid input errors caused by data format differences; the re The encoded bin format contains point cloud coordinates, color and normal information, and directly supports the position center of three-dimensional Gaussian points, Parameterized initialization of covariance matrix and opacity attributes to improve geometric consistency and rendering of scene reconstruction efficiency.

3. The three-dimensional Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian according to claim 1, characterized in that: Statistical filtering calculates the average Euclidean distance between each point and its neighboring points. If the threshold range of the sum of the mean distance and the standard deviation is exceeded, it is determined to be an outlier and removed; The calculation method of statistical filtering is: where ||X i -X j || represents point X i to X j The Euclidean distance between global Represents the overall density level of the point cloud, σ is the standard deviation of all points, if the average distance d of a point i Greater than the overall average distance μ global Add a certain threshold λσ, then it is considered an outlier and is removed.

4. The three-dimensional Gaussian sputtering scene reconstruction method based on structure-aware refined Gaussian according to claim 1, characterized in that: Radius filtering counts the number of neighboring points within a preset radius of each point. If the number is lower than the set threshold, it is considered an outlier and removed. The calculation method of radius filtering is: For each point X i , calculate its neighborhood point cloud R within radius r i If R i Less than the set threshold R min , then delete the point.

5. The method for reconstructing a three-dimensional Gaussian sputtering scene based on structure-aware refined Gaussian according to claim 1, characterized in that: In step S4, an initialized three-dimensional Gaussian is constructed based on each spatial point in the sparse point cloud, and initial geometric and appearance attributes are assigned to each Gaussian point; Among them, the position center of the Gaussian point is: μ j =X j ∈R 3 ; Color c∈R k ;Opacity α∈R; Covariance matrix ∑ N for: Its probability density formula is: μ j : The position center of the j-th Gaussian point, which is the spatial point X in the sparse point cloud j OK, X j ∈R 3 Indicates that it is in three-dimensional real space; c: the color of the Gaussian point, c∈R k Indicates that color is a k-dimensional vector; α: opacity of the Gaussian point, α∈R indicates that it is a real number; σ x 2 is the variance in the x direction, σ xy is the covariance between x and y directions, σ yx is the covariance between the y and x directions; x: Any point in space, used to calculate the probability density under Gaussian distribution; μ: the position center of the Gaussian point; ∑: inverse matrix of covariance matrix ∑N; g(x): probability density of point x under the Gaussian distribution; The initial parameters of the scaling rotation matrix are associated with the density distribution of the point cloud after statistical filtering; The initialization process ensures that the spatial distribution and anisotropic scale of the Gaussian points strictly correspond to the geometric characteristics of the filtered point cloud, providing a geometrically consistent Gaussian sputtering scene initial model for subsequent normal consistency alignment, comprehensive score screening and joint optimization.

6. The method for reconstructing a three-dimensional Gaussian sputtering scene based on structure-aware refined Gaussian according to claim 1, characterized in that: In step S5, based on the covariance matrix of the initialized three-dimensional Gaussian sputtering scene, the The line consistency regularization term dynamically adjusts the direction of the minimum eigenvector of the Gaussian distribution to align it with the normal direction; the normal The loss function of the consistency regularization term is: L normal : The loss function of the normal consistency regularization term, which obtains the overall loss by summing the individual losses of all Gaussian points; w i : The weight of Gaussian point i is dynamically adjusted according to the visibility and stability of the point; N i : The minimum eigenvector of the Gaussian point covariance matrix, corresponding to the minor axis direction of the Gaussian sphere; n i : The normal direction of the point extracted from the normal map estimated by the Lotus model; The regularization term forces Ni and n to be i Direction alignment makes the short axis of the Gaussian distribution in the edge area of ​​the Gaussian sputtering scene fit the surface normal, suppressing the edge blurring phenomenon of the sparse area retained by the radius filter; at the same time, the dynamic weight w i Based on the adjustment of visibility and stability indicators, the interference of low-confidence Gaussian points on normal alignment is reduced, ensuring that the geometric structure of the 3D Gaussian sputtering scene is consistent with the real surface topology.

7. The method for reconstructing a three-dimensional Gaussian sputtering scene based on structure-aware refined Gaussian according to claim 1, characterized in that: In step S6, the covariance matrix of each Gaussian point is subjected to eigenvalue decomposition to extract three eigenvalues ​​λ1, λ2, and λ3, where λ1≤λ2≤λ3. The anisotropy A is calculated based on the eigenvalues ​​using the following formula: A=(λ3-λ1) / λ3; The anisotropy index is used to quantify the directional distribution of Gaussian points. High anisotropy corresponds to edge areas where the normal consistency regularization term needs to be strongly constrained, and low anisotropy corresponds to curved or flat areas. Based on the eigenvalue estimation, the local curvature and dimensional characteristics are calculated by combining the eigenvalues ​​of the covariance matrix. The calculation formula is: C(X i ) is the local curvature index of the i-th Gaussian point; The local curvature is used to identify the geometric complexity of the area where the Gaussian point is located. Combined with the normal direction alignment result, the density of Gaussian points is increased in the curvature mutation area to suppress structural artifacts. At the same time, the number of visible times V and the opacity change variance Δα of the Gaussian point in multiple frames are counted. The visible times V is used to calculate the dynamic weight w. i The weight of high-visibility points is increased to strengthen the normal alignment constraint, and the weight of low-visibility points is decreased to reduce noise interference; the opacity change variance Δα is linked with the structural continuity loss to suppress the negative impact of unstable Gaussian points on the joint optimization.

8. The method for reconstructing a three-dimensional Gaussian sputtering scene based on structure-aware refined Gaussian according to claim 1, characterized in that: In step S7, the constructed comprehensive scoring function is: S(X i )=w1(1-C(X i ))+w2V i -w3Δα i +w4A(X i ); A(X i ) is an anisotropy index based on the eigenvalue decomposition of the covariance matrix, which is used to quantify the directional distribution of Gaussian points. The high anisotropy region corresponds to the edge structure in the three-dimensional Gaussian sputtering scene, and the edge clarity is maintained by limiting the scale change of Gaussian points; C(X i ) is the local curvature, which is used to identify surface details or flat areas. Combined with the density adaptive mechanism of three-dimensional Gaussian sputtering, Gaussian points are interpolated and added at the curvature mutation point to suppress artifacts; V i is the number of times the Gaussian point is visible, and the dynamic weight w i Linkage: High-visibility points are prioritized and normal alignment constraints are strengthened, while low-visibility points are treated as noise and removed; Δα i It is the opacity variation variance, which works together with the structural continuity loss to suppress the destruction of scene rendering consistency caused by Gaussian points with excessively high opacity fluctuations; w1~w4 are weight coefficients, which are dynamically adjusted according to the geometric characteristics of the three-dimensional Gaussian sputtering scene: In the edge area, w1 is increased to strictly limit the Gaussian point scale and prevent edge blurring; In curved areas, increase w2 to enhance detail density; In the stable region, increase w3 and w4 to retain high-quality Gaussian points.

9. The method for reconstructing a three-dimensional Gaussian sputtering scene based on structure-aware refined Gaussian according to claim 1, characterized in that: In step S8, the structural continuity loss L is calculated. structure When, for each Gaussian point i (i = 1, 2, ..., N) in the Gaussian point set, determine its neighborhood Gaussian point set N(i); for each neighborhood point j∈N(i), calculate the position difference ||x i -x j || and color difference || c i -c j ||, use Measure the weight of the impact of position distance on the loss, and then multiply it by the square of the color difference || c i -c j || 2 ; Finally, the above products of all i and its neighborhood j are accumulated, and the calculation function is: This loss function constrains the color and position consistency between adjacent Gaussian points to ensure the structural continuity of scene reconstruction. For each neighborhood point j∈N(i), calculate the position difference ||x i -x j || and color difference || c i -c j ||, use Measure the weight of the impact of position distance on the loss, and then multiply it by the square of the color difference || c i -c j || 2 ; Finally, the above products of all i and its neighborhood j are accumulated, and the calculation function is: The constraints of close-range neighborhood points are strengthened by Gaussian kernel function to ensure the geometric smoothness of dense areas in the three-dimensional Gaussian sputtering scene; Linked with the color attribute in the scoring function, it suppresses rendering color discontinuities caused by sudden changes in opacity.

10. The method for reconstructing a three-dimensional Gaussian sputtering scene based on structure-aware refined Gaussian according to claim 1, characterized in that: In step S8, the final loss function of the joint training framework is: L=L1+λ normal L normal +λ structure L structure ; Where L1 is the luminosity loss, which is used to measure the rendered image I render Compared with the real image I gt The difference is calculated as: L1=∑|I render -I gt |; Image I is generated by rasterization rendering of 3D Gaussian splattering render , and compared with the real image I gt In contrast, directly optimize the color attribute c of the Gaussian point i With opacity α i , ensuring that the scene appearance is consistent with the real data; For the interpolated Gaussian points, their color values ​​are dynamically adjusted through back propagation to ensure a smooth transition with the photometric characteristics of the neighboring high-scoring points. L normal Normal consistency loss is achieved by constraining the minor axis of the Gaussian covariance matrix to align with the normal to ensure the geometric directionality of the three-dimensional Gaussian sputtering scene; in the edge area, the hyperparameter λ is increased normal To strengthen normal alignment and suppress depth blur; in the surface area, through dynamic weight w i Adjust the normal constraint strength to avoid over-smoothing details; L structure To reduce the loss of structural continuity, the following optimization is achieved through dynamic neighborhood screening and stability constraints: for high-scoring areas, the neighborhood radius r is expanded and λ is reduced structure , promote the adaptive growth of Gaussian point density and enhance surface continuity; for low-scoring areas, increase λ structure To forcefully remove outliers and reduce their interference with joint optimization; through the hyperparameter λ structure In conjunction with the scoring weights w1 to w4, spatial consistency is prioritized in edge areas, while color smoothness is emphasized in stable areas.

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