A multi-feature three-dimensional reconstruction 3D Gaussian method based on laser vision

Abstract

A kind of multi-feature three-dimensional reconstruction 3D Gaussian method based on laser vision, comprising: aligning laser radar point cloud and camera image by space-time calibration, establishing unified coordinate system;Geometric features are extracted using point cloud data obtained by Lidar point cloud, and Gaussian ellipsoid is initialized according to Lidar point cloud;The brightness, contrast and structural similarity of rendered image and real image are optimized in combination with mean absolute error L1 and structural similarity SSIM;The curvature of forced K nearest neighbor Gaussian ellipsoid is consistent, and the major and minor axes of aligned Gaussian ellipsoid are combined with line and surface features to reduce geometric distortion;The distribution density of 3D Gaussian is dynamically adjusted through line / surface features and visual structure information extracted by Lidar, to realize the balance between geometric detail enhancement and calculation efficiency.The position, scale and rotation parameters of Gaussian are uniformly optimized, the consistency of model structure is improved, and the details and calculation efficiency of model are balanced.

Description

Technical Field

[0001] This invention relates to a multi-feature 3D reconstruction 3D Gaussian method based on laser vision, belonging to the field of 3D modeling and real-time rendering technology. Background Technology

[0002] In recent years, 3D reconstruction techniques based on 3D Gaussian (3DGS) representation have attracted much attention in the fields of computer vision and graphics due to their efficient rendering capabilities and high-quality detail recovery. This technique renders scenes by representing them as a large number of anisotropic Gaussian ellipsoids. However, the reconstruction of high-quality 3DGS models is highly dependent on the accuracy of initialization and the effectiveness of optimization strategies.

[0003] Currently, mainstream vision-based initialization methods heavily rely on sparse point clouds output by motion reconstruction algorithms such as Colmap. When dealing with low-texture regions or scenes with highly similar structures, these methods are prone to problems such as feature matching failure, geometric distortion, and point cloud holes, resulting in limited geometric accuracy of initialization and subsequent optimization, making it difficult to guarantee the consistency of the 3D structure. To address the inherent defects of vision initialization, multimodal methods that fuse LiDAR and visual images have become a research trend. For example, LOD-3DGS uses LiDAR point clouds to directly initialize the center position of the Gaussian ellipsoid, partially alleviating the dependence on Colmap point clouds. However, existing fusion methods still have the following limitations: (1) Insufficient geometric constraints: Existing methods fail to fully utilize the rich geometric structure information contained in LiDAR point clouds to finely constrain the scale and rotation parameters of the Gaussian ellipsoid, resulting in a loose reconstructed model structure and loss of geometric details; (2) Lack of adaptive optimization: The optimization of the 3DGS model depends on the dynamic splitting and merging operations of the Gaussian distribution to control the density. Most existing strategies use a globally uniform density adjustment threshold, which cannot perceive the local structural characteristics of the scene, resulting in excessive splitting of Gaussians in flat areas and causing computational redundancy; insufficient density at structural edges or in areas with complex textures, resulting in loss of geometric sharpness and details; (3) Weak multimodal feature synergy: Existing technologies have not explored in depth the effective synergistic optimization mechanism between laser-precise geometric features and visually rich gradient / texture features. This lack of feature fusion makes it difficult for the model to simultaneously meet the requirements of high-precision geometric structure and high-quality photometric consistency, and details are easily lost or artifacts are easily generated in the geometry-texture coupling area; (4) Computational efficiency challenge: Although the introduction of large-scale LiDAR point clouds has improved geometric potential, it has also put forward higher requirements for computing resources, and more efficient optimization strategies are urgently needed. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a multi-feature 3D reconstruction 3D Gaussian method based on laser vision. This method can uniformly optimize the position, scale, and rotation parameters of the Gaussian model, improving the consistency of the model structure while balancing the model's details and computational efficiency.

[0005] To achieve the above objectives, this invention provides a multi-feature 3D Gaussian reconstruction method based on laser vision, comprising the following steps:

[0006] S1, 3D Gaussian initialization: Align the LiDAR point cloud and camera image through spatiotemporal calibration to establish a unified coordinate system; extract geometric features using the point cloud data obtained from the LiDAR point cloud, and initialize the Gaussian ellipsoid based on the LiDAR point cloud.

[0007] S2. Establish photometric and geometric consistency constraints: Combine mean absolute error L1 and structural similarity SSIM to optimize the brightness, contrast and structural similarity between the rendered image and the real image; force the curvature of the Gaussian ellipsoid of the K nearest neighbors to be consistent and align the major and minor axes of the Gaussian ellipsoid with line and surface features to reduce geometric distortion;

[0008] S3. Adaptive density control by combining Gaussian ellipsoidal line and surface features: By using line / surface features extracted from LiDAR and visual structural information, the distribution density of 3D Gaussian is dynamically adjusted to achieve a balance between geometric detail enhancement and computational efficiency.

[0009] Furthermore, the specific process of S1 is as follows:

[0010] S1.1. Using a 3D Gaussian function to represent 3D points, the 3D Gaussian ellipsoid is parameterized by position μ, opacity α, anisotropy, and spherical harmonics to represent viewpoint-dependent color. The 3D Gaussian ellipsoid is defined as:

[0011]

[0012] Where x = [x, y, z] T , represents the position information of three-dimensional points, and ∑ is the covariance matrix;

[0013] The nonlinear formula for projecting a 3D Gaussian image onto a 2D image plane is:

[0014]

[0015] Where, x img ,y img f represents the pixel coordinates of the image. x ,f y It's the focal length, c x ,c y These are the optical center coordinates, where x, y, and z represent the three-dimensional coordinates of a point in the camera coordinate system.

[0016] To simplify the calculation, a first-order Taylor expansion is performed on the nonlinear projection, with the Gaussian center u. cam = (x0, y0, z0) is the expansion point, approximated by the perspective projection matrix P and the Jacobian matrix J:

[0017] ∑′=JP′P T J T ;

[0018] Where J is a local linear approximation of the projection transformation:

[0019] ;

[0020] By applying the covariance matrix, the standard 3D Gaussian ellipsoid is transformed to an arbitrary ellipsoid. To ensure the positive semidefiniteness of the covariance matrix during the optimization process, the covariance matrix is ​​calculated by the following formula:

[0021] ∑=RSS T R T ;

[0022] Where S is a parameterized three-dimensional vector and R is a normalized rotation quaternion;

[0023] S1.2, 3D Gaussian parameter initialization:

[0024] Let Lidar point p i ∈P{p1,p2,...p n}, calculate p i nearest neighbor distance:

[0025]

[0026] The initial scaling factor is calculated by the following formula:

[0027] Copy the scaling factor to all three axes: S i =[s i ,s i ,s i ];

[0028] Initialize rotation parameters using a unity quaternion:

[0029] q i =[1,0,0,0].

[0030] Furthermore, the specific process of S2 is as follows:

[0031] S2.1, 3D Gaussian is projected onto a 2D plane, sorted by depth, and then pixel color C is calculated using α-mixing. k :

[0032]

[0033] Among them, c i It is the color of the i-th Gaussian, α i Used to control transparency, G i (x) is the projected 2D Gaussian function, let C k For the output rendered image, C k gt For the visually acquired image, the photometric consistency constraint module optimizes the Gaussian parameters by minimizing the mean absolute error L1 and the structural similarity error SSIM. The L1 error is used to calculate the absolute difference between the rendered pixel and the real pixel, as shown in the following formula:

[0034]

[0035] Where N is the total number of pixels;

[0036] L1 error is robust to outliers but lacks constraints on structural consistency. By weighting structural similarity error, the brightness, contrast and structural information of local image regions can be compared, which can effectively enhance the fidelity of texture and geometric details.

[0037] The formula for the SSIM error is as follows:

[0038]

[0039] Where v is the mean, σ is the standard deviation, c1 and c2 are stability constants, and the loss of D-SSIM is defined as:

[0040]

[0041] Among them, I render ,I gt Representing the 3D Gaussian-rendered image and the real image from a specific viewpoint, respectively, defined as:

[0042]

[0043] in, κ is a hyperparameter used to measure the difference between an image rendered by a 3D Gaussian model and a real reference image. It is typically set to κ = 0.2.

[0044] S2.2 Establishing Geometric Consistency Constraints: This involves forcibly aligning the major and minor axes of the Gaussian ellipsoid with the curvature of its nearest neighbors to improve the geometric distribution of the Gaussian ellipsoid. The specific process is as follows:

[0045] S2.2-1. Establishing Planar and Linear Constraints: The process for constructing planar feature constraints is as follows:

[0046] Let Lidar point p i The neighborhood point set is P near ={p1,p2,...p n} Calculate the centroid of the neighborhood points:

[0047]

[0048] Construct the covariance matrix C:

[0049]

[0050] Perform eigenvalue decomposition on the covariance matrix C and solve the equation:

[0051] det(C-λI) = 0;

[0052] Where λ is the eigenvector and I is the identity matrix, the eigenvalues ​​are obtained as follows: λ1≥λ2≥λ3. If λ3 / λ1<ε and λ2 / λ1>ζ, then the point cloud to which the neighboring point belongs is considered to be a plane. Here, ε and ζ are hyperparameters that are adjusted according to the actual scene.

[0053] The process of constructing linear feature constraints is as follows: the method of constructing planar feature constraints is also applied to LiDAR points p. i Construct the covariance matrix and perform eigenvalue decomposition to obtain eigenvalues: λ1≥λ2≥λ3. If λ3 / λ1<ε and λ2 / λ1<γ, then the point cloud of the neighboring points is considered to be a line. Here, ε and γ are hyperparameters that are adjusted according to the actual scene.

[0054] Let Lidar point p i The normal vector is Define the minor axis of the Gaussian ellipsoid Let be the normal vector of the Gaussian ellipsoid. For a planar Gaussian ellipsoid, minimize Normal vector of Gaussian ellipsoid The differences between the aligned point cloud surfaces are as follows:

[0055] For a LiDAR point p i As a surface feature, its covariance matrix is ​​calculated from its neighboring points. The eigenvalue decomposition of the covariance matrix is ​​expressed as:

[0056]

[0057] Among them, R i It is a rotation matrix, and its column vectors are eigenvectors, representing the principal directions of the ellipsoid. Let Λ be the smallest direction vector among them. iThis is a diagonal matrix, where the diagonal elements are eigenvalues ​​representing the variance of the Gaussian ellipsoid's scaling along the three axes. The plane loss achieves geometric optimization of the Gaussian ellipsoid by aligning the Lidar point normal vectors with the Gaussian ellipsoid normal vector. The plane loss is defined as follows:

[0058]

[0059] Where ∈ is a local minimum value used to ensure that the denominator is not zero, ||n g ||,||n p || represents the norm of the Gaussian ellipsoid normal vector and the plane normal vector, respectively, and their calculation formulas are as follows:

[0060]

[0061] Where, n g,x n g,y n g,z Let n represent the components of the Gaussian ellipsoid normal vector on the x, y, and z axes, respectively. p,x n p,y n p,z These represent the components of the plane normal vector on the x, y, and z axes, respectively.

[0062] For a point that belongs to the characteristics of a line, let the line point direction vector be... Its covariance matrix is ​​calculated from its neighborhood points, and the eigenvalue decomposition of the covariance matrix is ​​expressed as:

[0063]

[0064] Among them, R i It is a rotation matrix, and its column vectors are eigenvectors, representing the principal directions of the ellipsoid. The direction vector of the major axis of the Gaussian ellipsoid is defined as the largest of these direction vectors. Λ i As a diagonal matrix, the linear loss optimizes the Gaussian ellipsoid by aligning the principal axis of the stretched ellipsoid with the direction of the line point cloud, thereby reducing geometric distortion. The linear loss is defined as follows:

[0065]

[0066] Where ∈ is a local minimum value used to ensure that the denominator is not zero;

[0067] S2.2-2. Constructing curvature consistency constraints through a constrained Gaussian ellipsoid curvature smoothing model: For LiDAR point clouds that are neither planar nor linear points, a smoothing model minimizing the curvature differences of k Gaussian ellipsoids is adopted to reduce ambiguity, specifically:

[0068] For a LiDAR point p that is neither a planar point nor a linei , with p i The three principal axes of a Gaussian ellipsoid centered at its geometry are obtained by decomposing its covariance C. Similarly, the eigenvalue decomposition of the covariance matrix is ​​expressed as:

[0069]

[0070] Among them, Λ i Let κ1≥κ2≥κ3 be a diagonal matrix Λ i The three eigenvalues ​​on the ∑ = RSS T R T and Solve for: Λ i =SS T ,Right now The lengths of the three principal axes of the Gaussian ellipsoid are make For curvature consistency, only the curvature of the Gaussian ellipsoid along the shortest axis is constrained. The formula for calculating curvature is:

[0071]

[0072] Let the lengths of the three principal axes of the current Gaussian ellipsoid be... The scale parameters of the k nearest neighbor Gaussian ellipsoids are: Among them, s i,j =(s i,j,1 ,s i,j,2 ,s i,j,3 );

[0073] Current point s i The curvature is: Neighboring point s i,j The curvature is: The curvature difference is: Δκ i,j =κ i -κ i,j ;

[0074] To reduce the impact of outliers, a Huber loss form is adopted to robustly penalize curvature differences, as shown in the following expression:

[0075]

[0076] By adaptively weighting the curvature differences in different regions, the smaller the neighborhood scale (i.e., the more geometrically sensitive), the larger the weight. The specific process is as follows:

[0077] Filtering invalid criteria:

[0078] in, is an indicator function, ∧ is the logical AND operator, s i,j,2 ,s i,j,3Let represent the second and third principal axes of the j-th neighbor ellipsoid of the i-th Gaussian ellipsoid;

[0079] Weight allocation is based on neighborhood scale stability:

[0080] Weighted loss for curvature differences:

[0081] The final curvature consistency loss, averaged over all points and their neighborhoods, is:

[0082] The final geometric loss, through weighted plane constraints, line constraints, and curvature consistency constraints, is defined as:

[0083]

[0084] Where ω, β, and χ are hyperparameters that are adjusted according to the actual situation;

[0085] The final total loss function is defined as the sum of the photometric consistency loss and the geometric consistency loss, that is:

[0086]

[0087] Furthermore, the specific process of S3 is as follows:

[0088] S3.1. For line feature regions, the Gaussian ellipsoid density is increased to preserve sharp geometry, while for surface feature regions, the Gaussian density is reduced to avoid redundant calculations. Specifically:

[0089] For each Gaussian ellipsoid p i Assign density weights w based on feature type i :

[0090]

[0091] in, It is the visual gradient magnitude. It is a local curvature estimation, w max ,w min θ and ψ are the baseline weights for line / surface features; θ and ψ are the mixing coefficients for other regions and satisfy θ + ψ = 1. This is a classification function that determines the geometric type of a Gaussian point through eigenvalue decomposition.

[0092] S3.2, Perform adaptive density control for line / surface features, specifically as follows:

[0093] For Gaussian lines: if w i >w high And det(∑ i )>δsplit It splits into two sub-ellipsoids along the visual gradient direction, as expressed by:

[0094]

[0095] For Gaussian surfaces: if or w i <w low And ||μ i -μ j ||2<r merge The expression for merging coplanar ellipsoids is:

[0096]

[0097] Among them, w high ,w low These are the minimum and maximum weight values ​​that trigger the splitting and merging of the Gaussian ellipsoid, respectively, det(∑ i ) represents the determinant value of the covariance of the i-th Gaussian ellipsoid, u new The new Gaussian ellipsoid represents its spatial position, ι is a step size coefficient used to adjust the distance the new Gaussian ellipsoid moves, and τ is the step size coefficient. img δ is the image gradient threshold. split r is the splitting scale threshold. merge To determine the merging distance threshold, n gradient It is the unit vector of the gradient direction.

[0098] By using geometric consistency constraints and multi-feature adaptive density, the accuracy of 3D Gaussian modeling can be effectively improved, geometric distortion can be reduced, and the level of detail can be enriched.

[0099] This invention combines the core mechanisms of geometric loss and photometric consistency loss, and introduces multi-feature-guided adaptive density control. The geometric loss mechanism utilizes local curvature information from LiDAR point clouds to regularize the shape parameters of the 3D Gaussian ellipsoid, significantly improving model structural consistency. Line and surface features extracted from LiDAR are used to optimize the principal axis direction of the Gaussian ellipsoid, reducing geometric distortion. The photometric loss mechanism optimizes the color and transparency parameters of the 3D Gaussian ellipsoid by combining pixel-level and structural information from visual images, resulting in high-fidelity rendering. The multi-feature-guided adaptive density control dynamically adjusts the distribution density of the 3D Gaussian ellipsoid using line / surface features extracted from LiDAR and visual structural information, improving computational efficiency while preserving scene details, achieving a balance between geometric detail enhancement and computational efficiency. This invention significantly improves the reconstruction accuracy and robustness of 3D Gaussian ellipsoids by fusing LiDAR and visual data, combining geometric feature constraints and photometric consistency optimization. Attached Figure Description

[0100] Figure 1This is a flowchart of the method of the present invention;

[0101] Figure 2 This is a diagram showing the feature extraction effect of the method of the present invention;

[0102] Figure 3 This is a comparison diagram of the overall effect of reconstructing an underground parking garage using the method of this invention and other methods. Detailed Implementation

[0103] The invention will now be further described with reference to the accompanying drawings.

[0104] like Figure 1 As shown, a multi-feature 3D reconstruction 3D Gaussian method based on laser vision includes the following steps:

[0105] S1, 3D Gaussian initialization: Align the LiDAR point cloud and camera image through spatiotemporal calibration to establish a unified coordinate system; extract geometric features using the point cloud data obtained from the LiDAR point cloud, and initialize the Gaussian ellipsoid based on the LiDAR point cloud.

[0106] S2. Establish photometric and geometric consistency constraints: Combine mean absolute error L1 and structural similarity SSIM to optimize the brightness, contrast and structural similarity between the rendered image and the real image; force the curvature of the Gaussian ellipsoid of the K nearest neighbors to be consistent and align the major and minor axes of the Gaussian ellipsoid with line and surface features to reduce geometric distortion;

[0107] S3. Adaptive density control by combining Gaussian ellipsoidal line and surface features: By using line / surface features extracted from LiDAR and visual structural information, the distribution density of 3D Gaussian is dynamically adjusted to achieve a balance between geometric detail enhancement and computational efficiency.

[0108] To verify the effectiveness of the method of the present invention, such as Figure 2 The image shows the surface point cloud and line point cloud extracted according to the method of the present invention, wherein, Figure 2 (a) The red dot cloud is a surface dot cloud. Figure 2 (b) The green point cloud is a line point cloud. As can be seen from the effect diagram of the adaptive density control of the line / surface feature, the present invention effectively reduces the number of point clouds and reduces floating artifacts through the adaptive density control of the line / surface feature.

[0109] like Figure 3 Images (a), (b), and (c) show a comparison of the overall reconstruction results of an underground parking garage using this method and other methods. Figure 3 (a) shows the reconstruction result from 3DGS. Figure 3 (b) shows the reconstruction results of LOD-3DGS. Figure 3 (c) shows the reconstruction result of this method; as can be seen from the figure, the floating artifacts on the periphery are significantly reduced compared to other methods.

[0110] Meanwhile, Table 1 shows a comparison of the geometric accuracy of the method of the present invention with other methods:

[0111] Table 1. Comparison of geometric accuracy between the method of this invention and other methods.

[0112]

[0113] As can be seen from the data comparison in Table 1, the geometric accuracy indicators reconstructed by this method are significantly better than those of other methods.

[0114] Table 2 shows a comparison of rendering metrics and final point counts between the method of this invention and other methods:

[0115] Table 2 Comparison of rendering metrics and final point counts between the method of this invention and other methods

[0116] LOSS Point cloud number L1↓ PSNR↑ RGB↓ LPIPS↓ 3DGS 627376 0.011 34.796 0.017 0.178 LOD-3DGS 727150 0.011 34.692 0.017 0.174 This invention 310110 0.013 32.087 0.021 0.211

[0117] As can be seen from the data comparison in Table 2, this method significantly reduces the number of Gaussian ellipsoids used while slightly lowering the rendering metrics, which is beneficial for the lightweight representation of the model.

Claims

1. A multi-feature 3D Gaussian reconstruction method based on laser vision, characterized in that, Includes the following steps: S1, 3D Gaussian initialization: Align the LiDAR point cloud and camera image through spatiotemporal calibration to establish a unified coordinate system; extract geometric features using the point cloud data obtained from the LiDAR point cloud, and initialize the Gaussian ellipsoid based on the LiDAR point cloud. S2. Establish photometric and geometric consistency constraints: Combine mean absolute error L1 and structural similarity SSIM to optimize the brightness, contrast and structural similarity between the rendered image and the real image; force the curvature of the Gaussian ellipsoid of the K nearest neighbors to be consistent and align the major and minor axes of the Gaussian ellipsoid with line and surface features to reduce geometric distortion; S3. Adaptive density control by combining Gaussian ellipsoidal line and surface features: Dynamically adjust the distribution density of 3D Gaussians by using line / surface features extracted from LiDAR and visual structural information to achieve a balance between geometric detail enhancement and computational efficiency. The specific process of S2 is as follows: S2.1, 3D Gaussian is transformed to a 2D plane through projection, and then sorted by depth. Mixed calculation of pixel color : ； in, It is the color of the i-th Gaussian. Used to control transparency. It is the projected 2D Gaussian function, let... For the output rendered image, For the visually acquired image, the photometric consistency constraint module optimizes the Gaussian parameters by minimizing the mean absolute error L1 and the structural similarity error SSIM. The L1 error is used to calculate the absolute difference between the rendered pixel and the real pixel, as shown in the following formula: ； Where N is the total number of pixels; The formula for the SSIM error is as follows: ； in, The mean, Standard deviation As a stability constant, the loss of D-SSIM is defined as: ； in, Representing the 3D Gaussian-rendered image and the real image from a specific viewpoint, respectively, defined as: ； in, Used to measure the difference between an image rendered by a 3D Gaussian model and a real reference image. For hyperparameters, take ; S2.2 Establishing Geometric Consistency Constraints: This involves forcibly aligning the major and minor axes of the Gaussian ellipsoid with the curvature of its nearest neighbors to improve the geometric distribution of the Gaussian ellipsoid. The specific process is as follows: S2.2-1. Establishing Planar and Linear Constraints: The process for constructing planar feature constraints is as follows: Set Lidar points The neighborhood point set is Calculate the centroid of the neighborhood points: ； Constructing the covariance matrix : ； Perform eigenvalue decomposition on the covariance matrix C and solve the equation: ； in, For feature vectors, For the identity matrix, the eigenvalues ​​are obtained: If satisfied ,and If the neighboring points belong to a point cloud, then the point cloud is considered to be a plane, where These are hyperparameters and should be adjusted according to the actual scenario. The process of constructing linear feature constraints is as follows: the method of constructing planar feature constraints is also applied to LiDAR points. Construct the covariance matrix and perform eigenvalue decomposition to obtain the eigenvalues: If satisfied ,and If the point cloud containing the nearest points is considered to be a line, then... These are hyperparameters and should be adjusted according to the actual scenario. Set Lidar points The normal vector is Define the minor axis of the Gaussian ellipsoid. Let be the normal vector of the Gaussian ellipsoid. For a planar Gaussian ellipsoid, minimize Normal vector of Gaussian ellipsoid The differences between the aligned point cloud surfaces are as follows: For a Lidar point As a surface feature, its covariance matrix is ​​calculated from its neighboring points. The eigenvalue decomposition of the covariance matrix is ​​expressed as: ； in, It is a rotation matrix, and its column vectors are eigenvectors, representing the principal directions of the ellipsoid. Let it be the smallest direction vector. This is a diagonal matrix, where the diagonal elements are eigenvalues ​​representing the variance of the Gaussian ellipsoid's scaling along the three axes. The plane loss achieves geometric optimization of the Gaussian ellipsoid by aligning the Lidar point normal vectors with the Gaussian ellipsoid normal vector. The plane loss is defined as follows: ； in, This is a local minimum value used to ensure that the denominator is not zero. , Let be the norms of the Gaussian ellipsoid normal vector and the plane normal vector, respectively, and their calculation formulas are as follows: ； in, , , These represent the normal vectors of the Gaussian ellipsoid at... Components on the three axes, , , These represent the plane normal vectors at... Components on the three axes; For a point that belongs to the characteristics of a line, let the line point direction vector be... Its covariance matrix is ​​calculated from its neighborhood points, and the eigenvalue decomposition of the covariance matrix is ​​expressed as: ； in, It is a rotation matrix, and its column vectors are eigenvectors, representing the principal directions of the ellipsoid. The direction vector of the major axis of the Gaussian ellipsoid is defined as the largest of these direction vectors. , As a diagonal matrix, the linear loss optimizes the Gaussian ellipsoid by aligning the principal axis of the stretched ellipsoid with the direction of the line point cloud, thereby reducing geometric distortion. The linear loss is defined as follows: ； in, It is a minimum value used to ensure that the denominator is not zero; S2.2-2. Constructing curvature consistency constraints through a constrained Gaussian ellipsoid curvature smoothing model: For LiDAR point clouds that are neither planar nor linear points, a smoothing model minimizing the curvature differences of k Gaussian ellipsoids is adopted to reduce ambiguity, specifically: For LiDAR points that are neither planar points nor lines ,by The three principal axes of a Gaussian ellipsoid centered at its geometry are obtained by decomposing its covariance C. Similarly, the eigenvalue decomposition of the covariance matrix is ​​expressed as: ； in, Let be a diagonal matrix. diagonal matrix The three eigenvalues ​​on the surface, combined and Please provide a solution: ,Right now The lengths of the three principal axes of the Gaussian ellipsoid are ,make For curvature consistency, only the curvature of the Gaussian ellipsoid along the shortest axis is constrained. The formula for calculating curvature is: ； Let the lengths of the three principal axes of the current Gaussian ellipsoid be... The scale parameters of the k nearest neighbor Gaussian ellipsoids are: ,in, ; Current point The curvature is: Neighborhood points The curvature is: The curvature difference is: ; To reduce the impact of outliers, a Huber loss form is adopted to robustly penalize curvature differences, as shown in the following expression: ； By adaptively weighting the curvature differences in different regions, the smaller the neighborhood scale (i.e., the more geometrically sensitive), the larger the weight. The specific process is as follows: Filtering invalid criteria: ; in, For indicator functions, For logical AND operator, Indicates the first The first Gaussian ellipsoid The second and third principal axes of the neighboring ellipsoids; Weight allocation is based on neighborhood scale stability: ; Weighted loss for curvature differences: ; The final curvature consistency loss, averaged over all points and their neighborhoods, is: ; The final geometric loss, through weighted plane constraints, line constraints, and curvature consistency constraints, is defined as: ； in, These are hyperparameters and should be adjusted according to actual conditions. The final total loss function is defined as the sum of the photometric consistency loss and the geometric consistency loss, that is: 。 2. The multi-feature 3D Gaussian reconstruction method based on laser vision according to claim 1, characterized in that, The specific process of S1 is as follows: S1.

1. Represent 3D points using a 3D Gaussian function, and parameterize the 3D Gaussian ellipsoid into position parameters. Opacity α, anisotropy, and spherical harmonic functions represent viewpoint-dependent colors. A 3D Gaussian color is defined as: ； in, This represents the position information of a three-dimensional point. It is the covariance matrix; The nonlinear formula for projecting a 3D Gaussian image onto a 2D image plane is: ； in, Represents the pixel coordinates of the image. It's the focal length. These are the coordinates of the optical center. This represents the three-dimensional coordinates of a point in the camera coordinate system. To simplify the calculation, a first-order Taylor expansion is performed on the nonlinear projection, centered on the Gaussian center. Using the unfolding point, through the perspective projection matrix And Jacobi matrix approximate: ； in, It is a local linear approximation of the projection transformation: ； By applying the covariance matrix, the standard 3D Gaussian ellipsoid is transformed to an arbitrary ellipsoid. To ensure the positive semidefiniteness of the covariance matrix during the optimization process, the covariance matrix is ​​calculated by the following formula: ； Where S is a parameterized three-dimensional vector and R is a normalized rotation quaternion; S1.2, 3D Gaussian parameter initialization: Set Lidar points ,calculate nearest neighbor distance: ； The initial scaling factor is calculated by the following formula: Copy the scaling factor to all three axes: ; Initialize rotation parameters using a unity quaternion: 。 3. The multi-feature 3D Gaussian reconstruction method based on laser vision according to claim 1, characterized in that, The specific process of S3 is as follows: S3.

1. For line feature regions, the Gaussian ellipsoid density is increased to preserve sharp geometry, while for surface feature regions, the Gaussian density is reduced to avoid redundant calculations. Specifically: For each Gaussian ellipsoid Assign density weights based on feature type : ； in, It is the visual gradient magnitude. It is a local curvature estimation. It is the baseline weight of line / surface features; The mixing coefficients of other regions and satisfying , This is a classification function that determines the geometric type of a Gaussian point through eigenvalue decomposition. S3.2, Perform adaptive density control for line / surface features, specifically as follows: For Gaussian lines: if , and It splits into two sub-ellipsoids along the visual gradient direction, as expressed by: ； For Gaussian surfaces: if or and The expression for merging coplanar ellipsoids is: ； in, These are the minimum and maximum weight values ​​that trigger the splitting and merging of the Gaussian ellipsoid, respectively. Indicates the first The determinant value of the covariance of the Gaussian ellipsoids Indicates the spatial position of the newly split Gaussian ellipsoid. This is a step size coefficient used to adjust the movement distance of the new Gaussian ellipsoid. Image gradient threshold, The threshold for the split scale. To merge distance thresholds, It is the unit vector of the gradient direction.

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