Hand motion modeling method based on 3D Gaussian

Abstract

The invention relates to the field of three-dimensional graphic processing and hand motion modeling, and discloses a 3D Gaussian distribution-based hand motion modeling method, which comprises the following steps of: initializing a hand skeleton and joints by using an MANO model, mapping a hand vertex to a normalized 3D Gaussian distribution space, and generating initial 3D Gaussian point distribution; the posture of the 3D Gaussian point is adjusted through a linear hybrid skin algorithm, and it is ensured that the posture change in the hand action process can be smoothly and accurately modeled; a K-nearest neighbor (KNN) algorithm is combined with KL divergence to carry out adaptive encryption and optimization on Gaussian points, Gaussian point distribution is optimized through splitting, cloning and cutting operations, and finally, a high-fidelity rendering image of hand actions is generated through a 3D Gaussian projection technology, and multi-view real-time rendering is supported. According to the method, the hand action can be quickly and efficiently modeled, and the training and rendering speed is greatly improved on the premise of ensuring the rendering quality.

Description

Technical Field

[0001] The present invention relates to the field of three-dimensional image processing and computer vision technology, in particular to a hand motion modeling method based on 3D Gaussian. Background Art

[0002] Hand motion modeling aims to accurately reconstruct and simulate the posture of human hands through computer vision technology. This technology has been widely used in fields such as virtual reality (VR), augmented reality (AR) and human-computer interaction, and can significantly improve user experience and system interaction performance. For example, in a virtual reality environment, accurate hand motion modeling can enhance the user's sense of immersion and enable users to interact with virtual objects naturally. In addition, in gesture recognition and human-computer interaction, high-quality hand motion modeling can improve the accuracy of the system's response to user commands.

[0003] Hand motion modeling is a long-standing research topic. Traditional methods mainly rely on explicit geometric models and complex capture equipment. These methods perform well in controlled environments, but in complex real-world environments, they are often difficult to achieve ideal results due to factors such as lighting changes, background interference, and fast movements. At the same time, the training process of traditional methods usually requires a lot of time and computing resources, making it difficult to achieve real-time applications.

[0004] In recent years, deep learning technology based on neural networks has provided a new solution for hand motion modeling. Such data-driven models demonstrate strong adaptability and generalization capabilities by learning patterns and features from large-scale datasets. Deep learning models can maintain high modeling accuracy in complex and dynamic scenes and effectively handle subtle changes in hand motions.

[0005] In particular, the use of 3D Gaussian distribution brings significant advantages to hand motion modeling. By representing hand motion as 3D Gaussian points, the model can simplify the representation of hand morphology, reduce computational complexity, and improve rendering efficiency. However, achieving fast and efficient hand motion modeling while maintaining high-quality rendering remains a challenge to be solved. Summary of the invention

[0006] The purpose of the present invention is to solve the above problems and to design a hand motion modeling method based on 3D Gaussian.

[0007] To achieve the above object, the technical solution of the present invention is that, further, in the above-mentioned 3D Gaussian-based hand motion modeling method, the hand motion modeling method comprises the following steps:

[0008] The captured images are obtained by using multiple cameras to perform multi-view image capture of different postures of the same hand;

[0009] Use the motion structure recovery SFM algorithm to calculate the camera's intrinsic and extrinsic parameters, including at least feature detection, feature matching, camera pose estimation, and 3D point cloud reconstruction;

[0010] Using the OpenPose algorithm to perform mask processing on the captured image, and calculating the rotation vector and translation coordinates of the hand joint in each posture;

[0011] Using the MANO model as a basis for the hand skeleton and joints, initializing and obtaining vertex data of the MANO model, wherein the MANO model includes at least 778 vertices;

[0012] Mapping the hand vertices of the MANO model to a normalized 3D Gaussian distribution space to generate an initial 3D Gaussian point distribution;

[0013] According to the hand posture parameters, the linear hybrid skeleton LBS conversion algorithm is used to adjust the posture of the 3D Gaussian point through the rotation matrix and transformation matrix of the joint;

[0014] Feedforward convolutional neural network is used to optimize LBS weights;

[0015] A K-nearest neighbor (KNN) algorithm is introduced to calculate the proximity relationship of the 3D Gaussian points, and the distribution and number of the Gaussian points are optimized according to the proximity relationship;

[0016] Use KL divergence to calculate the difference between adjacent Gaussian points;

[0017] Based on the optimized 3D Gaussian points, high-fidelity multi-view rendering images of hand movements are generated through Gaussian projection technology;

[0018] The resulting high-fidelity images are post-processed by applying image enhancement techniques such as sharpening and contrast adjustment.

[0019] Furthermore, in the above-mentioned 3D Gaussian-based hand motion modeling method, the use of the motion structure recovery SFM algorithm to calculate the intrinsic and extrinsic parameters of the camera includes at least feature detection, feature matching, camera posture estimation, and 3D point cloud reconstruction, including:

[0020] Feature detection and matching: extract stable feature points from the image sequence and find the correspondence between these feature points in different images. The detectors include at least SIFT and SURF.

[0021] Camera calibration matrix calculation: Assume that the camera calibration matrix is ​​in the form of:

[0022]

[0023] Among them, f x and f y is the focal length, c xand c y is the position of the center point of the image in pixel coordinates;

[0024] Camera pose estimation: The position and orientation of the camera are estimated by solving the PnP problem. The core is to calculate the basic matrix and the essential matrix.

[0025] Triangulation and 3D reconstruction: Using the camera’s pose, the 3D point cloud is restored through triangulation.

[0026] Bundle adjustment optimization: Further optimize the estimated results of camera pose and 3D points by minimizing the reprojection error of all observation points.

[0027] Furthermore, in the above-mentioned 3D Gaussian-based hand motion modeling method, mapping the hand vertices of the MANO model to a normalized 3D Gaussian distribution space to generate an initial 3D Gaussian point distribution includes:

[0028] The hand vertices of the MANO model are mapped to the normalized 3D Gaussian distribution space to generate the initial 3D Gaussian point distribution. Through the multivariate normal distribution, an ellipsoid of any shape and posture in the space is covered. The formula of the ellipsoid is:

[0029]

[0030] Among them, x represents the three-dimensional space coordinate, μ is the center of the ellipsoid, and the covariance matrix Σ controls the expansion and rotation of the ellipsoid.

[0031] Furthermore, in the above-mentioned 3D Gaussian-based hand motion modeling method, the linear mixed skeleton LBS conversion algorithm is used according to the hand posture parameters to adjust the posture of the 3D Gaussian point through the rotation matrix and transformation matrix of the joint, including:

[0032] According to the hand posture parameters, the linear blended skeleton (LBS) conversion algorithm is used to adjust the posture of the 3D Gaussian points through the rotation matrix and transformation matrix of the joint. The conversion formula of the mean vector and covariance matrix is:

[0033] v p =R(θ p ,J p )·v t +T(θ p ,β p ,J p )

[0034] Σ p =R(θ p ,J p )·Σ t ·R(θ p ,J p ) T.

[0035] Furthermore, in the above-mentioned 3D Gaussian-based hand motion modeling method, the optimization of LBS weights by using a feedforward convolutional neural network includes:

[0036] Since the optimization of Gaussian distribution points will lead to an increase in the number of vertices, the initial LBS weight matrix has deviations. A feedforward convolutional neural network is used to optimize the LBS weights. The formula is:

[0037]

[0038] Furthermore, in the above-mentioned 3D Gaussian-based hand motion modeling method, the use of KL divergence to calculate the difference between adjacent Gaussian points includes:

[0039] Use KL divergence to calculate the difference between adjacent Gaussian points and optimize their distribution. The calculation formula of KL divergence is:

[0040]

[0041] The beneficial effect is that a plurality of cameras are used to perform multi-view image acquisition of different postures of the same hand to obtain an acquired image; a motion structure recovery SFM algorithm is used to calculate the intrinsic and extrinsic parameters of the camera, including at least feature detection, feature matching, camera posture estimation and three-dimensional point cloud reconstruction; an OpenPose algorithm is used to perform mask processing on the acquired image to calculate the rotation vector and translation coordinate of the hand joint in each posture; a MANO model is used as the basis of the hand skeleton and joints, and the vertex data of the MANO model is initialized and obtained, and the MANO model contains at least 778 vertices; the hand vertices of the MANO model are mapped to a normalized 3D Gaussian distribution space, generate the initial 3D Gaussian point distribution; according to the hand posture parameters, use the linear mixed skeleton LBS conversion algorithm, adjust the posture of the 3D Gaussian points through the rotation matrix and transformation matrix of the joint; use the feedforward convolutional neural network to optimize the LBS weight; introduce the K-nearest neighbor KNN algorithm to calculate the neighbor relationship of the 3D Gaussian points, and optimize the distribution and number of Gaussian points according to the neighbor relationship; use the KL divergence to calculate the difference between adjacent Gaussian points; based on the optimized 3D Gaussian points, use the Gaussian projection technology to generate high-fidelity multi-view rendering images of hand movements; post-process the generated high-fidelity images, and apply image enhancement techniques such as sharpening and contrast adjustment. 1. A hand reconstruction method based on multi-view and Gaussian distribution is proposed, which can accurately capture the hand posture and generate a high-quality three-dimensional model. 2. The technology combining multivariate normal distribution and LBS is adopted to improve the posture conversion and rendering effect of the model. 3. Introduce a neural network to optimize the LBS weight to ensure that the model still has high fidelity under complex postures. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the following detailed description of the preferred embodiment.The drawings are only for the purpose of illustrating the preferred embodiments and are not to be construed as limiting the invention.

[0043] Figure 1 Schematic diagram of an embodiment of a 3D Gaussian-based hand motion modeling method in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a", "an", "said" and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0046] The present invention will be described in detail below in conjunction with the accompanying drawings. Figure 1 As shown, a hand motion modeling method based on 3D Gaussian includes the following steps:

[0047] Step 101, using multiple cameras to perform multi-view image acquisition of different postures of the same hand to obtain an acquired image;

[0048] Step 102: Use the motion structure recovery SFM algorithm to calculate the camera's intrinsic parameters and extrinsic parameters, including at least feature detection, feature matching, camera pose estimation, and 3D point cloud reconstruction;

[0049] Specifically, in this embodiment, feature detection and matching: extracting stable feature points from an image sequence and finding the corresponding relationship between these feature points in different images, the detector includes at least SIFT and SURF;

[0050] Camera calibration matrix calculation: Assume that the camera calibration matrix is ​​in the form of:

[0051]

[0052] Among them, f x and f y is the focal length, c x and c yis the position of the center point of the image in pixel coordinates;

[0053] Camera pose estimation: The position and orientation of the camera are estimated by solving the PnP problem. The core is to calculate the basic matrix and the essential matrix.

[0054] Triangulation and 3D reconstruction: Using the camera’s pose, the 3D point cloud is restored through triangulation.

[0055] Bundle adjustment optimization: Further optimize the estimated results of camera pose and 3D points by minimizing the reprojection error of all observation points.

[0056] Step 103: Use the OpenPose algorithm to perform mask processing on the collected image, and calculate the rotation vector and translation coordinates of the hand joint in each posture;

[0057] Step 104: using the MANO model as a basis for the hand skeleton and joints, initializing and acquiring vertex data of the MANO model, wherein the MANO model includes at least 778 vertices;

[0058] Step 105: Map the hand vertices of the MANO model to a normalized 3D Gaussian distribution space to generate an initial 3D Gaussian point distribution;

[0059] Specifically, in this embodiment

[0060] The hand vertices of the MANO model are mapped to the normalized 3D Gaussian distribution space to generate the initial 3D Gaussian point distribution. Through the multivariate normal distribution, an ellipsoid of any shape and posture in the space is covered. The formula of the ellipsoid is:

[0061]

[0062] Among them, x represents the three-dimensional space coordinate, μ is the center of the ellipsoid, and the covariance matrix Σ controls the expansion and rotation of the ellipsoid.

[0063] Step 106: According to the hand posture parameters, the linear hybrid skeleton LBS conversion algorithm is used to adjust the posture of the 3D Gaussian point through the rotation matrix and transformation matrix of the joint;

[0064] Specifically, in this embodiment

[0065] According to the hand posture parameters, the linear blended skeleton (LBS) conversion algorithm is used to adjust the posture of the 3D Gaussian points through the rotation matrix and transformation matrix of the joint. The conversion formula of the mean vector and covariance matrix is:

[0066] v p =R(θ p ,J p )·v t +T(θp ,β p ,J p )

[0067] Σ p =R(θ p ,J p )·Σ t ·R(θ p ,J p ) T .

[0068] Step 107: Optimize the LBS weights using a feed-forward convolutional neural network;

[0069] Specifically, in this embodiment

[0070] Since the optimization of Gaussian distribution points will lead to an increase in the number of vertices, the initial LBS weight matrix has deviations. A feedforward convolutional neural network is used to optimize the LBS weights. The formula is:

[0071]

[0072] Step 108: Introduce a K-nearest neighbor (KNN) algorithm to calculate the neighbor relationship of the 3D Gaussian points, and optimize the distribution and number of Gaussian points according to the neighbor relationship;

[0073] Step 109, using KL divergence to calculate the difference between adjacent Gaussian points;

[0074] Specifically, in this embodiment

[0075] Use KL divergence to calculate the difference between adjacent Gaussian points and optimize their distribution. The calculation formula of KL divergence is:

[0076]

[0077] Step 1010: Generate a high-fidelity multi-view rendering image of the hand movement through Gaussian projection technology based on the optimized 3D Gaussian points;

[0078] Step 1011: post-process the generated high-fidelity image by applying image enhancement techniques such as sharpening and contrast adjustment.

[0079] The beneficial effect is that a plurality of cameras are used to perform multi-view image acquisition of different postures of the same hand to obtain an acquired image; a motion structure recovery SFM algorithm is used to calculate the intrinsic and extrinsic parameters of the camera, including at least feature detection, feature matching, camera posture estimation and three-dimensional point cloud reconstruction; an OpenPose algorithm is used to perform mask processing on the acquired image to calculate the rotation vector and translation coordinate of the hand joint in each posture; a MANO model is used as the basis of the hand skeleton and joints, and the vertex data of the MANO model is initialized and obtained, and the MANO model contains at least 778 vertices; the hand vertices of the MANO model are mapped to a normalized 3D Gaussian distribution space, generate the initial 3D Gaussian point distribution; according to the hand posture parameters, use the linear mixed skeleton LBS conversion algorithm, adjust the posture of the 3D Gaussian points through the rotation matrix and transformation matrix of the joint; use the feedforward convolutional neural network to optimize the LBS weight; introduce the K-nearest neighbor KNN algorithm to calculate the neighbor relationship of the 3D Gaussian points, and optimize the distribution and number of Gaussian points according to the neighbor relationship; use the KL divergence to calculate the difference between adjacent Gaussian points; based on the optimized 3D Gaussian points, use the Gaussian projection technology to generate high-fidelity multi-view rendering images of hand movements; post-process the generated high-fidelity images, and apply image enhancement techniques such as sharpening and contrast adjustment. 1. A hand reconstruction method based on multi-view and Gaussian distribution is proposed, which can accurately capture the hand posture and generate a high-quality three-dimensional model. 2. The technology combining multivariate normal distribution and LBS is adopted to improve the posture conversion and rendering effect of the model. 3. Introduce a neural network to optimize the LBS weight to ensure that the model still has high fidelity under complex postures.

[0080] Specifically, the technical solution to implement the present invention also includes:

[0081] Step S1: Multi-view image acquisition

[0082] By using multiple cameras to capture multi-view images of the same hand in different postures, the multi-view images provide basic data for subsequent 3D reconstruction.

[0083] Step S2: Camera parameter estimation

[0084] The camera's intrinsic and extrinsic parameters are calculated using the Structure from Motion (SFM) algorithm. SFM technology reconstructs a 3D scene from a 2D image sequence. The main steps include feature detection, feature matching, camera pose estimation, and 3D point cloud reconstruction. The specific implementation steps are as follows:

[0085] 1. Feature detection and matching: Extract stable feature points from the image sequence and find the correspondence between these feature points in different images. Commonly used detectors include SIFT and SURF.

[0086] 2. Camera calibration matrix calculation: Assume that the camera calibration matrix is ​​in the form of:

[0087]

[0088] Among them, f x and f y is the focal length, c x and c y is the position of the center point of the image in pixel coordinates.

[0089] 3. Camera pose estimation: The position and direction of the camera are estimated by solving the PnP (Perspective-n-Point) problem. The core is to calculate the basic matrix and the essential matrix.

[0090] 4. Triangulation and 3D reconstruction: Using the camera’s posture, the 3D point cloud is restored through triangulation.

[0091] 5. Bundle adjustment optimization: Further optimize the camera pose and 3D point estimation results by minimizing the reprojection error of all observation points.

[0092] Step S3: Hand pose joint calculation

[0093] The collected images are masked using the OpenPose algorithm to calculate the rotation vectors and translation coordinates of the hand joints in each pose.

[0094] Step S4: Hand model initialization

[0095] Use the MANO model as the basis for the hand skeleton and joints, initialize and obtain the vertex data of the model. The model contains 778 vertices, representing the three-dimensional structure of the hand.

[0096] Step S5: 3D Gaussian point generation

[0097] The hand vertices of the MANO model are mapped to the normalized 3D Gaussian distribution space to generate the initial 3D Gaussian point distribution. Through the multivariate normal distribution, an ellipsoid of any shape and posture in space can be covered. The formula of the ellipsoid is:

[0098]

[0099] Among them, x represents the three-dimensional space coordinate, μ is the center of the ellipsoid, and the covariance matrix Σ controls the expansion and rotation of the ellipsoid.

[0100] Step S6: Posture adjustment and conversion

[0101] According to the hand posture parameters, the linear blended skeleton (LBS) conversion algorithm is used to adjust the posture of the 3D Gaussian points through the rotation matrix and transformation matrix of the joint. The conversion formula of the mean vector and covariance matrix is:

[0102] v p =R(θ p ,J p )·v t +T(θ p ,β p ,J p )

[0103] Σ p =R(θ p ,J p )·Σ t ·R(θ p ,J p ) T

[0104] Step S7: Optimization of LBS weights

[0105] Since the optimization of Gaussian distribution points will increase the number of vertices, the initial LBS weight matrix may be biased. A feedforward convolutional neural network is used to optimize the LBS weights, and the formula is:

[0106]

[0107] Step S8: Neighborhood optimization of Gaussian points

[0108] The K-nearest neighbor (KNN) algorithm is introduced to calculate the proximity relationship of 3D Gaussian points, and the distribution and number of Gaussian points are optimized according to the proximity relationship to avoid redundancy or sparse distribution.

[0109] Step S9: KL divergence optimization

[0110] Use KL divergence to calculate the difference between adjacent Gaussian points and optimize their distribution. The calculation formula of KL divergence is:

[0111]

[0112] Step S10: Multi-view rendering

[0113] Based on the optimized 3D Gaussian points, high-fidelity multi-view rendering images of hand movements are generated through Gaussian projection technology.

[0114] Step S11: Post-processing and quality improvement

[0115] Post-process the generated high-fidelity images and apply image enhancement techniques such as sharpening and contrast adjustment to further improve the quality of the rendered images.

[0116] Compared with the prior art, the present invention has the following advantages:

[0117] 1. A hand reconstruction method based on multi-view and Gaussian distribution is proposed, which can accurately capture hand posture and generate high-quality 3D models.

[0118] 2. The technology combining multivariate normal distribution and LBS is adopted to improve the posture conversion and rendering effects of the model.

[0119] 3. Introduce neural network to optimize LBS weights to ensure that the model still has high fidelity in complex postures.

[0120] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A hand motion modeling method based on 3D Gaussian, characterized in that: The hand motion modeling method comprises the following steps: The captured images are obtained by using multiple cameras to perform multi-view image capture of different postures of the same hand; Use the motion structure recovery SFM algorithm to calculate the camera's intrinsic and extrinsic parameters, including at least feature detection, feature matching, camera pose estimation, and 3D point cloud reconstruction; Using the OpenPose algorithm to perform mask processing on the captured image, and calculating the rotation vector and translation coordinates of the hand joint in each posture; Using the MANO model as a basis for the hand skeleton and joints, initializing and obtaining vertex data of the MANO model, wherein the MANO model includes at least 778 vertices; Mapping the hand vertices of the MANO model to a normalized 3D Gaussian distribution space to generate an initial 3D Gaussian point distribution; According to the hand posture parameters, the linear hybrid skeleton LBS conversion algorithm is used to adjust the posture of the 3D Gaussian point through the rotation matrix and transformation matrix of the joint; Feedforward convolutional neural network is used to optimize LBS weights; A K-nearest neighbor (KNN) algorithm is introduced to calculate the proximity relationship of the 3D Gaussian points, and the distribution and number of the Gaussian points are optimized according to the proximity relationship; Use KL divergence to calculate the difference between adjacent Gaussian points; Based on the optimized 3D Gaussian points, high-fidelity multi-view rendering images of hand movements are generated through Gaussian projection technology; The resulting high-fidelity images are post-processed by applying image enhancement techniques such as sharpening and contrast adjustment.

2. A 3D Gaussian hand motion modeling method as claimed in claim 1, characterized in that: The method of calculating the intrinsic and extrinsic parameters of the camera using the motion structure recovery SFM algorithm includes at least feature detection, feature matching, camera pose estimation, and 3D point cloud reconstruction, including: Feature detection and matching: extract stable feature points from the image sequence and find the correspondence between these feature points in different images. The detectors include at least SIFT and SURF. Camera calibration matrix calculation: Assume that the camera calibration matrix is ​​in the form of: Among them, f x and f y is the focal length, c x and c y is the position of the center point of the image in pixel coordinates; Camera pose estimation: The position and orientation of the camera are estimated by solving the PnP problem. The core is to calculate the basic matrix and the essential matrix. Triangulation and 3D reconstruction: Using the camera’s pose, the 3D point cloud is restored through triangulation. Bundle adjustment optimization: Further optimize the estimated results of camera pose and 3D points by minimizing the reprojection error of all observation points.

3. The 3D Gaussian hand motion modeling method according to claim 1, characterized in that: Mapping the hand vertices of the MANO model to a normalized 3D Gaussian distribution space to generate an initial 3D Gaussian point distribution includes: The hand vertices of the MANO model are mapped to the normalized 3D Gaussian distribution space to generate the initial 3D Gaussian point distribution. Through the multivariate normal distribution, an ellipsoid of any shape and posture in the space is covered. The formula of the ellipsoid is: Among them, x represents the three-dimensional space coordinate, μ is the center of the ellipsoid, and the covariance matrix Σ controls the expansion and rotation of the ellipsoid.

4. The 3D Gaussian hand motion modeling method according to claim 1, characterized in that: The method uses a linear hybrid skeleton LBS conversion algorithm according to the hand posture parameters to adjust the posture of the 3D Gaussian point through the rotation matrix and transformation matrix of the joint, including: According to the hand posture parameters, the linear blended skeleton (LBS) conversion algorithm is used to adjust the posture of the 3D Gaussian points through the rotation matrix and transformation matrix of the joint. The conversion formula of the mean vector and covariance matrix is: v p =R(θ p ,J p )·v t +T(θ p ,b p ,J p ) S p =R(θ p ,J p )·S t ·R(θ p ,J p ) T 。 5. The 3D Gaussian hand motion modeling method according to claim 1, characterized in that: The method of optimizing the LBS weight by using a feedforward convolutional neural network includes: Since the optimization of Gaussian distribution points will lead to an increase in the number of vertices, the initial LBS weight matrix has deviations. A feedforward convolutional neural network is used to optimize the LBS weights. The formula is:

6. The 3D Gaussian hand motion modeling method according to claim 1, characterized in that: The KL divergence is used to calculate the difference between adjacent Gaussian points, including: Use KL divergence to calculate the difference between adjacent Gaussian points and optimize their distribution. The calculation formula of KL divergence is:

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