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CN-122023660-A - Gaussian spot parameter initialization method based on k nearest neighbor covariance estimation

CN122023660ACN 122023660 ACN122023660 ACN 122023660ACN-122023660-A

Abstract

The invention discloses a Gaussian spot parameter initialization method based on k nearest neighbor covariance estimation, and belongs to the fields of computer graphics and three-dimensional reconstruction. According to the invention, the covariance structure of the k adjacent point set of each point is analyzed, and the characteristic value and the characteristic vector of the covariance matrix are utilized to respectively generate the scale parameter and the rotation parameter of the Gaussian spot, so that the Gaussian spot has the anisotropic morphology of Fu Gedian cloud local surface geometric features in the initialization stage, the initialization quality is remarkably improved, a better starting point is provided for subsequent micro-optimization, and the continuous stability of the construction quality is effectively ensured in synchronous positioning, construction and rendering systems. The invention effectively solves the problem that the traditional method can form stable map representation only by repeated iterative optimization due to insufficient initial geometric expression capacity, shortens the transition stage of map quality improvement, and meets the requirements of high-quality three-dimensional reconstruction and synchronous positioning, map building and rendering system on the precision and efficiency of the initialization environment.

Inventors

  • ZHUANG YAN
  • LI FUZHE
  • YAN FEI

Assignees

  • 大连理工大学

Dates

Publication Date
20260512
Application Date
20260130

Claims (10)

  1. 1. The Gaussian spot parameter initialization method based on k-nearest neighbor covariance estimation is characterized by comprising the following steps of: s1, acquiring a three-dimensional point set for representing a scene structure and preprocessing point cloud data in the three-dimensional point set; S2, acquiring a local domain point set of each point in the three-dimensional point set by adopting a k neighbor query method, and calculating a local covariance matrix of each point based on the local domain point set; s3, carrying out eigenvalue decomposition on the local covariance matrix of each point to obtain a corresponding eigenvalue set and an eigenvector set, generating Gaussian spot scale parameters corresponding to the point based on the eigenvalue set, and generating Gaussian spot rotation parameters corresponding to the point based on the eigenvector set; S4, setting an opacity parameter, a position parameter and a color parameter of the Gaussian spot; and S5, integrating the scale parameter, the rotation parameter, the opacity parameter, the position parameter and the color parameter to form a Gaussian spot parameter of the three-dimensional reconstruction scene.
  2. 2. The method for initializing gaussian spot parameters based on k-nearest neighbor covariance estimation according to claim 1, wherein in step S2, the local domain point set and local covariance matrix calculation of each point specifically comprises: Each point in the point cloud K neighbor query is carried out, and a point is obtained Is a local neighborhood point set , wherein, For the index number of the point in the input point cloud, Is a preset positive integer, the preferable range is 8 to 32, and based on the local neighborhood point set, the points are calculated Is a local covariance matrix of (a): Wherein, the Is taken as a point Is the first of (2) Local adjacent points; for the center of the mean value of the local neighborhood point set, the formula is as follows: To ensure numerical stability, to the local covariance matrix Adding tiny regularization terms Wherein Is a positive number, and the number of the components is a positive number, Is an identity matrix.
  3. 3. The method for initializing gaussian spot parameters based on K-nearest neighbor covariance estimation according to claim 1, wherein in step S2, the point cloud performs K-nearest neighbor query by constructing a spatial index structure comprising a K-dimensional tree, a spherical tree, or an octree.
  4. 4. The method for initializing gaussian spot parameters based on k-nearest neighbor covariance estimation according to claim 1, wherein in step S3, a gaussian spot scale parameter and a rotation parameter corresponding to the point are generated based on the feature value set and the feature vector set, respectively, specifically: generating a Gaussian spot scale initial value based on the characteristic value set, applying L2 regularized smoothing to the Gaussian spot scale initial value, and scaling to obtain Gaussian spot scale parameters; And converting the initial rotation matrix into a quaternion form serving as a Gaussian spot rotation parameter based on the characteristic vector set serving as an initial rotation matrix of the Gaussian spot.
  5. 5. The method for initializing a gaussian spot parameter based on k-nearest neighbor covariance estimation according to claim 4, wherein in step S3, the local covariance matrix performs eigenvalue decomposition and gaussian spot scale parameter extraction, and the method comprises: for the local covariance matrix And (3) performing eigenvalue decomposition: Wherein, the In order to rotate the matrix is rotated, Reflecting three local principal directions for orthogonal feature vectors; For a diagonal matrix of eigenvalues, Corresponding to three feature values arranged in descending order, respectively representing discrete scales along corresponding local principal directions, and generating initial values of Gaussian spot scales according to the feature values Is marked as Wherein Is a size scaling factor; And respectively applying L2 regularized smoothing processing to the first two scale components: Wherein, the Is a smoothing coefficient; The formula is that the mean value of the first two components of the initial value of the Gaussian spot scale is: the initial value of the processed Gaussian spot scale is ; To prevent the partial Gaussian spot size from being oversized, a maximum allowable scale is set If (1) Any dimension in the three-dimensional component of (2) exceeds Scaling the three dimensions to obtain Gaussian spot scale parameters 。
  6. 6. The method for initializing gaussian spot parameters based on k-nearest neighbor covariance estimation according to claim 5, wherein in step S3, for two-dimensional gaussian sputtering, a gaussian spot scale initial value is generated by selecting a previous two-dimensional eigenvalue of the diagonal matrix, and an L2 regularized smoothing process is applied to two-dimensional components of the gaussian spot scale initial value and scaled to obtain gaussian spot scale parameters.
  7. 7. The method for initializing Gaussian spot parameters based on k-nearest neighbor covariance estimation according to claim 1, wherein in the step S4, opacity of the Gaussian spot is set to 0.5-0.9 in the initialization stage, the position parameters are directly given by positions of input point clouds, zero-order coefficients of color attributes are initialized to colors of the point clouds, and higher-order coefficients are initialized to 0.
  8. 8. The method according to claim 1, wherein in step S1, the point cloud data source comprises a motion restoration structure reconstruction point cloud, a depth image back projection point cloud, or a laser radar point cloud.
  9. 9. The method for initializing Gaussian spot parameters based on k-nearest neighbor covariance estimation according to claim 1, wherein the step S1 is based on the fact that the robot acquires color images and depth images of indoor environment through the built-in RGB-D camera for indoor scene, calculates the position of each pixel in the image according to the depth value, pixel coordinates and camera parameters of each pixel and gives the corresponding color value to the point by utilizing the known camera internal parameters and the camera pose of the frame image, and thus a dense three-dimensional point cloud with RGB colors is directly generated from a single frame RGB-D image.
  10. 10. The method for initializing Gaussian spot parameters based on k-nearest neighbor covariance estimation according to claim 9, wherein in the step S1, the preprocessing comprises projecting three-dimensional point clouds of an indoor scene to an image plane for three-dimensional point clouds with uneven density, calculating average distances from each projection point to three nearest neighbors, randomly downsampling the projection points with squares of the average distances as sampling probabilities to make the sampling points uniformly distributed in an image space, and wherein in the step S5, the Gaussian spot parameters of the three-dimensional reconstructed scene are used for representing an initial map model.

Description

Gaussian spot parameter initialization method based on k nearest neighbor covariance estimation Technical Field The invention belongs to the technical field of computer graphics and three-dimensional reconstruction, and particularly relates to a geometric parameter initialization method for Gaussian sputtering (GaussianSplatting) representation. Background Three-dimensional Gaussian sputtering is a novel explicit scene representation method which is rapidly developed in the fields of computer graphics and three-dimensional reconstruction in recent years. The method discretely characterizes a scene through millions of gauss ellipsoids (called gauss spots) with shapes, colors and opacity, and realizes high-quality real-time new view angle synthesis and three-dimensional reconstruction by means of a micro-renderers. Gaussian spot initialization is a key element in the gaussian sputtering process, and aims to assign initial geometric properties (scale, rotation, position) and appearance properties (color, opacity) to each gaussian spot, thereby providing a reasonable starting point for subsequent micromanipulation. In the existing three-dimensional Gaussian sputtering technology, a general Gaussian spot initialization method is generally adopted. According to the method, a sparse three-dimensional point cloud of a scene is firstly obtained through a motion recovery structure (StructurefromMotion, sfM), and then each point in the point cloud is mapped into a Gaussian spot. For the scale parameters, the average distance from each point in the point cloud to its three nearest neighbors is calculated and taken as the initial scale of the gaussian spot in the three principal axis directions. For rotation parameters, the method initializes the quaternion toCorresponding to the unit rotation matrix. Thus, each Gaussian spot is initialized to a spherical structure with undefined orientation and isotropy. In the existing two-dimensional gaussian sputtering technology, although the three-dimensional gaussian ellipsoids are degenerated into two-dimensional gaussian ellipsoids, the initialization logic still uses a similar naive strategy in terms of geometric parameters. Specifically, the scale is also calculated based on the neighbor distance, thereby obtaining an isotropic circular initial shape. For two-dimensional rotation parameters, random angle initialization is typically used instead of fixed rotation values in order to avoid optimization difficulties that may result from consistent initial direction. However, the existing initialization method has the obvious defect that the existing initialization method completely ignores local geometric structure information contained in the input point cloud, only generates an isotropic sphere based on the neighbor distance, and cannot describe anisotropic geometric features such as a plane, a prism or a curved surface presented by a local surface in a real scene. The lack of geometric representation capability results in slow convergence of the optimization process, and a large amount of iteration is needed to correct the initial shape deviation, so that the calculation cost is high, artifacts or blurring is easily introduced in the early stage of optimization, and the reconstruction precision and visual quality are restricted. The above problems are particularly pronounced in synchronous positioning, mapping and rendering systems based on gaussian sputtering. The system needs to process data frame by frame and update map and pose incrementally in a resource constrained environment. If the newly inserted gaussian spot is a geometrically distorted sphere due to improper initialization, a longer time to optimize is required to provide the effective geometric constraint. In the 'convergence empty window period', the low-quality map rendering directly influences the positioning precision, and pose drift is caused. The positioning error further worsens the subsequent map, and forms a negative feedback loop of map construction inaccuracy, positioning drift and map construction worsening, and the system can be disabled when serious. In addition, in order to meet the requirements of instantaneity and multi-view consistency, a real-time positioning, mapping and rendering system based on Gaussian sputtering is used for greatly simplifying color representation, and state estimation is performed by depending on geometric attributes, so that the initialized geometric prior is particularly critical. The low-quality initialization not only drags slow convergence, but also fundamentally weakens the stability and the robustness of the system. Disclosure of Invention Aiming at the problems of insufficient geometric representation capability, slow optimization convergence, poor map-building-positioning coupling stability caused by poor initialization quality in a synchronous positioning, map-building and rendering system and the like in the Gaussian spot initialization method in the existing Ga