Construction of a point cloud denoising model, point cloud denoising method and device

Abstract

The present invention relates to the technical field of three-dimensional data processing, and specifically, to the construction of a point cloud denoising model, a point cloud denoising method and a device. The construction method comprises: obtaining a sample point cloud of a target to be denoised; converting the sample point cloud into a spectral domain signal, and determining the high-frequency component in the spectral domain signal; and constructing a spectral domain point cloud denoising model of the target to be denoised based on the high-frequency component in the spectral domain signal by adopting a diffusion model construction method. The spectral domain point cloud denoising model can effectively separate the geometric details and noise information in the high-frequency components of the point cloud data, that is, it removes the noise in the high-frequency components and retains the important geometric details of the target to be denoised in the high-frequency components; the retention of geometric details in the point cloud data can restore the original geometric shape of the target to be denoised, thereby improving the reconstruction quality of the three-dimensional model.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional data processing, and in particular to the construction of a point cloud denoising model, a point cloud denoising method and a device. Background Art

[0002] Point cloud data, often generated by LiDAR, is an indispensable component of modern 3D geographic information systems. These data are widely used in the reconstruction of three-dimensional (3D) models in robotics, autonomous driving and other engineering fields.

[0003] 3D model reconstruction is an important topic in the fields of computer vision, photogrammetry and graphics. The goal of this field is to recover the geometric shape and topological relationship that conforms to the real surface of the object from the original point cloud. However, due to the limitations of the measurement equipment and complex environmental factors, the original point cloud often contains noise, which directly affects the quality of the data and the effect of subsequent processing.

[0004] High-quality point cloud denoising is crucial to improving the quality of 3D models and reducing modeling costs. Effective denoising methods can accurately extract the surface of objects from noisy original point clouds, retain important geometric details, and eliminate noise points, thereby providing a clean data source for subsequent surface reconstruction. Summary of the invention

[0005] The purpose of the present invention is to provide a point cloud denoising model construction, a point cloud denoising method and a device, so as to accurately extract the surface of the object from the noisy original point cloud, retain important geometric details, and eliminate noise points, so as to provide a clean data source for subsequent surface reconstruction.

[0006] In a first aspect, the present invention provides a method for constructing a point cloud denoising model, the method comprising:

[0007] Get the sample point cloud of the target to be denoised;

[0008] Converting the sample point cloud into a spectral domain signal, and determining a high-frequency component in the spectral domain signal;

[0009] According to the high-frequency components in the spectral domain signal, a spectral domain point cloud denoising model of the target to be denoised is constructed by adopting a diffusion model construction method.

[0010] Optionally, determining the high-frequency component in the spectral domain signal includes:

[0011] Obtaining the lowest frequency of the high-frequency component to be determined;

[0012] The lowest frequency is taken as the starting frequency, and the high frequency band signal of the spectrum domain signal is taken as the high frequency component.

[0013] Optionally, obtaining the lowest frequency of the high-frequency component to be determined includes:

[0014] In the spectrum domain signal, a plurality of low-frequency band signals are sequentially determined, the starting frequency of each of the low-frequency band signals is the lowest frequency of the spectrum domain signal, the frequency ranges of two adjacent low-frequency band signals are sequentially increased, and the increase amplitude is a predetermined amplitude, and the frequency range of the low-frequency band signal is not greater than half of the global frequency range of the spectrum domain signal;

[0015] By inverse Fourier transform calculation, each of the low-frequency band signals is converted into a graph signal s' corresponding to each of the low-frequency band signals;

[0016] Determine the difference between the image signal s corresponding to the sample point cloud and the image signal s' corresponding to each of the low-frequency band signals;

[0017] Comparing the difference values ​​corresponding to each of the low-frequency band signals;

[0018] When the difference corresponding to a continuous number of low-frequency band signals is greater than the difference corresponding to the preceding low-frequency band signal, the highest frequency of the low-frequency band signal with the smallest frequency range among the continuous number of low-frequency band signals is taken as the lowest frequency of the high-frequency component to be determined.

[0019] Optionally, the sample point clouds include several pairs, each pair of sample point clouds includes a clean point cloud and a noisy point cloud, the noisy point clouds in every two pairs of sample point clouds are different, and in each pair of sample point clouds, the clean point cloud is obtained based on the noisy point cloud in the same pair;

[0020] The method of constructing a spectral domain point cloud denoising model of the target to be denoised is carried out according to the high-frequency components in the spectral domain signal by adopting a diffusion model construction method, including:

[0021] In the diffusion process, based on the high-frequency components in the spectral domain signal, several groups of sample signals are determined; one group of sample signals corresponds to a pair of sample point clouds one by one, each group of sample signals includes a starting signal, a plurality of intermediate signals and an end signal, in each group of sample signals, the starting signal is a high-frequency component converted from the corresponding clean point cloud, the end signal is a high-frequency component converted from the corresponding noisy point cloud, the intermediate signal is a signal inserted between the starting signal and the end signal of the same group, and the noise level of each intermediate signal gradually increases in the order from the starting signal to the end signal;

[0022] In the reverse process, each group of sample signals is used to train the diffusion model according to the order from the end signal to the start signal in each group of sample signals to obtain a trained spectral domain point cloud denoising model.

[0023] Optionally, determining a plurality of groups of sample signals based on the high frequency components in the spectral domain signal includes:

[0024] After determining the start signal and the end signal of the current group of sample signals, inserting a predetermined number of intermediate signals into the start signal and the end signal of the current group by linear interpolation;

[0025] The linear interpolation method is as follows:

[0026]

[0027] x t represents the tth intermediate signal, x 0 represents the starting signal, x T represents the endpoint signal, and α represents the interpolation coefficient.

[0028] Optionally, the diffusion model is U-Net,

[0029] The step of training the diffusion model using each group of sample signals according to the sequence from the end signal to the start signal in each group of sample signals comprises:

[0030] In the current group of sample signals, in the order from the end signal to the start signal, each signal except the start signal is sequentially used to perform denoising training on the diffusion model,

[0031] The current training signal is x t-1 When the signal sampled by the diffusion model is x t-1 ’ , x t-1 ’ It is obtained by the following formula;

[0032]

[0033] x t is the signal x in the diffusion process t-1 The next signal, represents the first correction value, represents the second correction value, x T is the endpoint signal, f θ is the diffusion model obtained from the last training, θ is the parameter of the diffusion model, t' is the time step of the last training diffusion model, α t represents the signal x in the diffusion process t The corresponding interpolation coefficient, α t-1 represents the signal x in the diffusion process t-1 The corresponding interpolation coefficients.

[0034] In a second aspect, the present invention provides a point cloud denoising method, the point cloud denoising method comprising:

[0035] Converting the point cloud to be denoised into a spectral domain signal, and determining a high-frequency component in the spectral domain signal;

[0036] Determine a point cloud denoising model, wherein the point cloud denoising model is a point cloud denoising model constructed by the aforementioned point cloud denoising model construction method;

[0037] Using the point cloud denoising model to remove noise in the high-frequency component;

[0038] Based on the high-frequency components after noise removal, a spectral domain signal after noise removal is obtained;

[0039] The spectral domain signal after the noise is removed is converted into a point cloud to obtain a point cloud after the noise is removed.

[0040] In a third aspect, the present invention provides a device for constructing a point cloud denoising model, the device comprising:

[0041] A first acquisition unit, used to acquire a sample point cloud of a target to be denoised;

[0042] A first conversion unit, used to convert the sample point cloud into a spectral domain signal;

[0043] A first determining unit, configured to determine a high frequency component in the spectral domain signal;

[0044] The construction unit is used to construct a spectral domain point cloud denoising model of the target to be denoised based on the high-frequency components in the spectral domain signal by adopting a diffusion model construction method.

[0045] In a fourth aspect, the present invention provides a point cloud denoising device, the point cloud denoising device comprising:

[0046] A second conversion unit, used for converting the point cloud to be denoised into a spectral domain signal;

[0047] A second determination unit, used to determine the high-frequency component in the spectral domain signal;

[0048] The second determining unit is further used to determine a point cloud denoising model, where the point cloud denoising model is a point cloud denoising model constructed by the aforementioned point cloud denoising model construction device;

[0049] A removal unit, used to remove noise in the high-frequency component by using the point cloud denoising model;

[0050] A second acquisition unit is used to acquire a spectral domain signal after the noise is removed based on the high-frequency component after the noise is removed;

[0051] The second conversion unit is further used to convert the spectral domain signal after noise removal into a point cloud to obtain a point cloud after noise removal.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] By obtaining a sample point cloud of a target to be denoised; converting the sample point cloud into a spectral domain signal, and determining the high-frequency components in the spectral domain signal; constructing a spectral domain point cloud denoising model of the target to be denoised based on the high-frequency components in the spectral domain signal by adopting a diffusion model construction method; the spectral domain point cloud denoising model can be trained to remove noise in the high-frequency components of the spectral domain signal converted from the point cloud; in this way, the geometric details and noise information in the high-frequency components of the point cloud data are effectively separated, that is, the noise in the high-frequency components is removed, and the important geometric details of the target to be denoised in the high-frequency components are retained; the retention of geometric details in the point cloud data can restore the original geometric shape of the target to be denoised, thereby improving the reconstruction quality of the three-dimensional model. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of a method for constructing a point cloud denoising model provided by an embodiment of the present invention;

[0055] Figure 2 is a flowchart of another method for constructing a point cloud denoising model provided by an embodiment of the present invention;

[0056] Figure 3 is a schematic diagram of constructing a diffusion model for denoising tasks provided by an embodiment of the present invention;

[0057] Figure 4 Schematic diagram of the network architecture of U-Net provided by an embodiment of the present invention;

[0058] Figure 5 Schematic diagram of the working principle of the attention mechanism layer provided by an embodiment of the present invention;

[0059] Figure 6 is a flow chart of a point cloud denoising method provided by an embodiment of the present invention;

[0060] Figure 7 is a graph of experimental results of the point cloud denoising model provided by an embodiment of the present invention on a public point cloud dataset;

[0061] Figure 8 is a graph showing experimental results of the point cloud denoising model provided by an embodiment of the present invention on a point cloud of a power facility;

[0062] Fig. 9 is a schematic diagram of a device for constructing a point cloud denoising model provided by an embodiment of the present invention;

[0063] Fig.10is a schematic diagram of a point cloud denoising device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0066] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0067] First, the origin of the inventive concept of the present invention is briefly introduced.

[0068] In recent years, methods based on graph signal processing have attracted widespread attention, especially in the processing of high-frequency components. With the help of graph Fourier transform, the point cloud coordinates are mapped from the spatial domain to the frequency-based spectral domain, and its potential surface information is re-examined from the perspective of the spectral domain, providing a solution to "point cloud denoising".

[0069] The latest research on point cloud adversarial attacks shows that the noise and geometric details of the point cloud are encoded by high-frequency components in the spectral domain signal, while the basic shape is encoded by low-frequency components. This not only means that high-frequency components can achieve an interpretable global representation of point cloud noise, but also shows that low-frequency components do not need to participate in the point cloud denoising process, thereby achieving the purpose of maintaining geometric consistency.

[0070] However, there are drawbacks in the method of directly cutting off high-frequency components for denoising. Referring to the low-pass filter in two-dimensional image processing, although directly cutting off high-frequency components can obtain effective denoising results, the cost is the loss of sharp features in the point cloud. The reason is that high-frequency components are also a global representation of the geometric details of the point cloud.

[0071] Therefore, how to achieve the decoupling of noise and sharp features becomes the main problem currently faced.

[0072] Recently, generative neural networks represented by diffusion models have shown great potential in preserving texture details in the denoising task of two-dimensional images. Clean data is gradually separated from noisy data by fitting the posterior distribution of clean data to reconstruct high-fidelity texture details. However, this model has not yet been used in point cloud denoising tasks.

[0073] Inspired by this, the technical solution provided in the embodiment of the present invention utilizes a diffusion model to decouple the noise and geometric details in the high-frequency components, thereby achieving a refined denoising effect while retaining the geometric details.

[0074] The technical solution provided by the embodiment of the present invention is described in detail below.

[0075] Figure 1 is a flow chart of a method for constructing a point cloud denoising model provided by an embodiment of the present invention. Figure 1 ,The construction method includes the following steps.

[0076] S11. Obtain a sample point cloud of the target to be denoised.

[0077] S12. Convert the sample point cloud into a spectral domain signal, and determine the high-frequency component in the spectral domain signal.

[0078] S13. According to the high-frequency components in the spectral domain signal, a spectral domain point cloud denoising model of the target to be denoised is constructed by adopting a diffusion model construction method.

[0079] The spectral domain point cloud denoising model is used to remove noise in high-frequency components.

[0080] In this embodiment, a sample point cloud of a target to be denoised is obtained; the sample point cloud is converted into a spectral domain signal, and the high-frequency components in the spectral domain signal are determined; according to the high-frequency components in the spectral domain signal, a spectral domain point cloud denoising model of the target to be denoised is constructed by constructing a diffusion model; the spectral domain point cloud denoising model can be trained to remove noise in the high-frequency components of the spectral domain signal converted from the point cloud; in this way, the geometric details and noise information in the high-frequency components of the point cloud data are effectively separated, that is, the noise in the high-frequency components is removed, and the important geometric details of the target to be denoised in the high-frequency components are retained; the retention of geometric details in the point cloud data can restore the original geometric shape of the target to be denoised, thereby improving the reconstruction quality of the three-dimensional model.

[0081] Figure 2 is a flow chart of another method for constructing a point cloud denoising model provided by an embodiment of the present invention. Figure 2 ,The method of constructing the point cloud denoising model includes the ,following steps.

[0082] S21. Obtain a sample point cloud of the target to be denoised.

[0083] Exemplarily, there are several pairs of sample point clouds.

[0084] Each pair of sample point clouds includes a clean point cloud and a noisy point cloud. The noisy point clouds in every two pairs of sample point clouds are different. In each pair of sample point clouds, the clean point cloud is obtained based on the noisy point cloud in the same pair.

[0085] S21 may include: collecting point cloud data of the target to be denoised; processing the collected point cloud data to obtain a clean point cloud from the noisy point cloud, and obtaining a plurality of pairs of sample point clouds.

[0086] The collection method may be to directly use a laser radar system to scan the target to be denoised.

[0087] The processing method may be to manually denoise the noisy point cloud.

[0088] Optionally, the target to be denoised may be an electric power facility.

[0089] S22, converting the sample point cloud into a spectral domain signal.

[0090] S22 may include: converting the clean point cloud and the noisy point cloud in each pair of sample point clouds into spectral domain signals respectively.

[0091] Specifically, the sample point cloud is subjected to a graph Fourier transform calculation to obtain a graph spectrum domain signal corresponding to the sample point cloud. The graph Fourier transform calculation may include the following steps.

[0092] The first step is to construct an undirected graph 𝒢 of the sample point cloud.

[0093] The graph variation operator is closely related to the graph Fourier transform, and the graph variation operator is the basis of the graph Fourier transform. In the process of graph variation operator processing, the point cloud 𝑃 = { 𝑝 𝑖 | = 1, … , 𝑛} ∈ ℝ 𝑛×3 , constructed as an undirected graph 𝒢 = { 𝒱, ℰ, 𝐴} containing 𝑛 nodes.

[0094] Among them, 𝒱 represents the set of vertices, ℰ represents the set of edges connecting vertices, and 𝐴 represents the adjacency matrix. Each element 𝑎 in the adjacency matrix 𝐴 𝑖𝑗 The value of represents the corresponding vertex 𝑣 𝑖 and 𝑣 𝑗 Between, that is, the point cloud 𝑝 𝑖 and 𝑝 𝑗 The weight of the connecting edge is a way to measure the similarity between two vertices.

[0095] The graph variation operator processing process is a technology well known to those skilled in the art and will not be described in detail here.

[0096] The second step is to determine the graph Laplacian matrix L based on the undirected graph 𝒢.

[0097] In the variational operators for graph signal processing for point clouds, considering that the point clouds are piecewise smooth, the focus is on the graph Laplacian matrix 𝐿 directly defined by the adjacency matrix 𝐴 and the degree matrix 𝐷.

[0098] The degree matrix D is determined by placing the sum of the elements of each row of the adjacency matrix 𝐴 in the diagonal position and clearing all other elements to zero, thereby obtaining the degree matrix 𝐷 as a diagonal matrix, that is, d 𝑖𝑖 =∑ 𝑛 𝑗=1 𝑎 𝑖𝑗 .

[0099] The graph Laplacian matrix L is calculated according to formula (1);

[0100]

[0101] The third step is to obtain the spectral domain signal corresponding to the sample point cloud according to the graph Laplacian matrix L and the graph signal s corresponding to the sample point cloud .

[0102] First, according to the graph Laplacian matrix L, the standard orthogonal matrix U containing the eigenvectors is calculated.

[0103] Since the adjacency matrix 𝐴 is a non-negative real symmetric matrix, the graph Laplacian matrix 𝐿 is also a real symmetric matrix and has a semi-positive definite property, so the eigendecomposition can be performed according to formula (2);

[0104]

[0105] Where, 𝑈 = [𝒖 1 , 𝒖 2 , … , 𝒖 𝑛 ], 𝒖 𝑖 is the feature vector.

[0106] Λ is a diagonal matrix, Λ = diag(𝜆 1 , 𝜆 2 , … , 𝜆 𝑛 ), 𝜆 i is the eigenvalue, 1 = 0 ≤ 𝜆 2 ≤⋯ ≤ 𝜆 𝑛 .

[0107] In graph signal processing, the eigenvalue provides a concept similar to the frequency in traditional Fourier signal analysis, called graph frequency or graph spectrum. A smaller eigenvalue corresponds to a lower graph spectrum.

[0108] The eigendecomposition of the graph Laplacian matrix 𝐿 is a well-known technical means for those skilled in the art and will not be described in detail here.

[0109] Secondly, based on the standard orthogonal matrix U and the graph signal s, the spectral domain signal corresponding to the sample point cloud is obtained .

[0110] Among them, the graph signal s corresponding to the sample point cloud is the vertex 𝑣 of the undirected graph 𝒢, that is, the coordinates of the midpoint of the point cloud.

[0111] In the graph Fourier transform, any vertex 𝑣 of the graph 𝒢 𝑖 Related graph signals , for point cloud, 𝑛 = 3, and its Graph Fourier Transform (GFT) process is defined as equation (3);

[0112]

[0113] In formula (3), T represents the transpose operation of U.

[0114] By constructing an appropriate graph structure on the point cloud and using the point cloud coordinates as the graph signal, its global representation in the graph domain can be achieved through GFT.

[0115] S23. Obtain the lowest frequency of the high-frequency component to be determined.

[0116] Optionally, S23 may include the following steps.

[0117] S231. In the spectrum domain signal, sequentially determine a plurality of low-frequency band signals.

[0118] The starting frequency of each low-frequency band signal is the lowest frequency of the spectrum domain signal. The frequency ranges of two adjacent low-frequency band signals increase in sequence, and the increase amplitude is a predetermined amplitude. The frequency range of the low-frequency band signal is not greater than half of the global frequency range of the spectrum domain signal.

[0119] The predetermined amplitude may be 1% of the global frequency range of the spectrum domain signal.

[0120] The low frequency signal can be determined by using the Fourier transform coefficient and the transformed amplitude energy of the image, and then entering the transform coefficient energy square sum formula for calculation. The specific calculation process is well known to those skilled in the art and will not be repeated here.

[0121] S232. Convert each low-frequency band signal into a graph signal s' corresponding to each low-frequency band signal by inverse graph Fourier transform calculation.

[0122] The inverse Fourier transform is calculated as the inverse transform of GFT (Inverse GFT, IGFT), which is defined as equation (4);

[0123]

[0124] Since 𝑈 is an orthogonal matrix, GFT and IGFT are information lossless.

[0125] S233 , determining the difference between the image signal s corresponding to the sample point cloud and the image signal s′ corresponding to each low-frequency band signal.

[0126] S234: Compare the difference values ​​corresponding to each low-frequency band signal.

[0127] When the difference corresponding to a continuous number of low-frequency band signals is greater than the difference corresponding to the preceding low-frequency band signal, the highest frequency of the low-frequency band signal with the smallest frequency range among the continuous number of low-frequency band signals is taken as the lowest frequency of the high-frequency component to be determined.

[0128] Among them, the continuous number can be 5.

[0129] S24, taking the lowest frequency as the starting frequency, and taking the high frequency band signal of the spectrum domain signal as the high frequency component.

[0130] S23 and S24 realize the determination of high-frequency components in the spectrum domain signal by using an adaptive frequency selection method.

[0131] Specifically, the spectral domain signals of the clean point cloud and the noisy point cloud are truncated from a certain low-frequency frequency 𝜆', and the truncated spectral domain signals are restored to the point cloud (graph signal) through the inverse graph Fourier transform (IGFT), and the difference measure between the two is calculated. Since noise and outliers do not affect the consistency of the low-frequency and medium-frequency components, the difference measure at this time will be small. Subsequently, the value of 𝜆' is increased with a step size of 1% of the global frequency range and the above process is repeated until 50% of the global frequency range. When the noisy point cloud shows noise, the difference measure will show a mutation. In order to ensure that the mutation is a global property rather than a local property, a simple linear fit is performed on the difference measure curve with a step size of 5% of the global frequency range. Only when the frequency 𝜆' before fitting falls into the mutation interval after fitting can 𝜆' be considered as the starting frequency of the high-frequency component of the current point cloud.

[0132] S25. In the diffusion process, a plurality of groups of sample signals are determined based on high-frequency components in the spectral domain signal.

[0133] Figure 3 Schematic diagram of constructing a diffusion model for denoising tasks provided by an embodiment of the present invention. Figure 3 ,The construction of the diffusion model is divided into the diffusion process and the reverse process.

[0134] According to the traditional practice, in the diffusion process, a noise-free signal is used as the starting signal, and random Gaussian noise is fixedly added to the starting signal in each time step to obtain several intermediate signals until a complete Gaussian noise is obtained as the end signal; the added noise level gradually increases according to the time step. In the reverse process, starting from the end signal, the diffusion model is trained in the reverse order of the diffusion process to predict and eliminate the noise in the signal obtained by the diffusion process.

[0135] The embodiments of the present invention improve both the traditional diffusion process and the reverse process.

[0136] Exemplarily, S25 may include: a group of sample signals corresponds to a pair of sample point clouds one by one. Each group of sample signals includes a start signal, a plurality of intermediate signals and an end signal. In each group of sample signals, the start signal is a high-frequency component converted from the corresponding clean point cloud, the end signal is a high-frequency component converted from the corresponding noisy point cloud, and the intermediate signal is a signal inserted between the start signal and the end signal of the same group. The noise level of each intermediate signal gradually increases in the order from the start signal to the end signal.

[0137] Correspondingly, after determining the start signal and the end signal of the current group of sample signals, a predetermined number of intermediate signals are inserted into the start signal and the end signal of the current group by linear interpolation.

[0138] The linear interpolation method is shown in formula (5);

[0139]

[0140] In formula (5), x t represents the tth intermediate signal, x 0 Indicates the start signal, x T represents the endpoint signal, and α represents the interpolation coefficient.

[0141] Optionally, α=X / T, X is the serial number of the current interpolation signal, and T is the serial number of the end signal. For example, assuming that the serial number of the start signal is 0, and 1000 intermediate signals are inserted, the serial number of the end signal is 1001, and the serial numbers of the intermediate signals are 1, 2, ..., 999, 1000.

[0142] S25 implements a noise adding mechanism based on linear interpolation. This noise adding mechanism is different from the traditional diffusion process that adds random Gaussian noise in each time step until the complete Gaussian noise is obtained. The diffusion process used for the denoising task ends with the noisy data. If Gaussian noise is still used, it cannot be guaranteed that the diffusion result is consistent with the noisy data. Therefore, the embodiment of the present invention introduces a noise adding mechanism based on linear interpolation, which controls the added noise with the help of the high-frequency components of the clean point cloud and the noisy point cloud and the interpolation coefficient 𝛼. If 𝑥 𝑇 Corresponding to the noisy data in the real world, the noise added according to this formula is also more consistent with the complex characteristics of real noise.

[0143] S26. In the reverse process, each group of sample signals is used to train the diffusion model in the order from the end signal to the start signal in each group of sample signals to obtain a trained spectral domain point cloud denoising model.

[0144] During the training process, the diffusion model is used to predict and eliminate the noise in each signal except the starting signal in each group of sample signals.

[0145] Exemplarily, the diffusion model may be U-Net.

[0146] S26 can be the same as the reverse process of the original diffusion model U-Net.

[0147] The performance of the original diffusion model depends largely on the sampling strategy of the inverse process, that is, iterative sampling according to the time step in the inverse process. Specifically, according to the time step 𝑡 in the diffusion process and the intermediate signal 𝑥 𝑡 To train the model 𝑓 𝜃 So that it can estimate the high-frequency component 𝑥 of the clean point cloud according to different noise levels 0 ; Then in the reverse process, use 𝑓 𝜃 Gradually denoise the high-frequency components of the noisy point cloud.

[0148] The sampling strategy in the reverse process of the original diffusion model is shown in the pseudo code of Algorithm 1 in Table 1.

[0149] Table 1

[0150]

[0151] Algorithm 1 can be expressed as formula (6);

[0152]

[0153] x t-1 ’ The diffusion model f θ The current sampled signal is different from the signal x in the diffusion process t-1 Corresponding; θ is the parameter of the diffusion model, α t-1 represents the signal x in the diffusion process t-1 The interpolation coefficient, x T The endpoint signal.

[0154] Since the diffusion process signal corresponding to the current sampled signal of the diffusion model is x t-1 , whose serial number is t-1, so α=t-1 / T, T is the serial number of the endpoint signal. Substituting α into equation (6), we get equation (7);

[0155]

[0156] By changing equation (7), we get equation (8);

[0157]

[0158] According to formula (8), when 𝑓 𝜃 (𝑥 𝑡 ’ , 𝑡') is equivalent to 𝑥 0 When , the above sampling strategy can achieve good denoising effect, which means that for 𝑥 0The more accurate the estimate of , the better the denoising performance of the reverse process. However, due to the limitations of its own architecture and data size, the U-Net-based network will have 𝑥 0 In the case of inaccurate prediction, the prediction error will gradually accumulate in the reverse process of the linear process, making it difficult to obtain an accurate denoising effect. To address this problem, the embodiment of the present invention combines the noise addition mechanism based on linear interpolation in the diffusion process and proposes a similar distribution sampling strategy, namely, Algorithm 2 shown in Table 2, which can be used in 𝑓 𝜃 We cannot accurately estimate 𝑥 0 It can still produce good denoising results.

[0159] Table 2

[0160]

[0161] Algorithm 2 can be expressed as formula (9);

[0162]

[0163] x t-1 ’ The diffusion model f θ The currently sampled signal, x t is the signal x in the diffusion process t-1 The next signal, represents the first correction value, Indicates the second correction value.

[0164] and It can be calculated using formula (10) and formula (11) respectively;

[0165]

[0166] x T is the endpoint signal, f θ is the diffusion model obtained from the last training, θ is the parameter of the diffusion model, x t ' is the signal sampled by the last diffusion model, t' is the time step when the diffusion model was last trained, α t represents the signal x in the diffusion process t The corresponding interpolation coefficient, α t-1 represents the signal x in the diffusion process t-1 The corresponding interpolation coefficient. t-1 represents the signal x in the diffusion process t-1 , T is the sequence number of the endpoint signal.

[0167] Substitute α into formula (9) respectively. t and α t-1The value of , equation (10) and equation (11) give equation (12);

[0168]

[0169] By changing formula (12), we get formula (13);

[0170]

[0171] Comparing the above two strategies, it is not difficult to find that for all 𝑡 < 𝑇 and 𝑓 𝜃 (𝑥 𝑡 ’ , 𝑡') = 𝑥 0 In the case of , both strategies can accurately perform signal denoising, but there is a difference in their stability. From formula (8), it can be seen that algorithm 1 is more dependent on 𝑓 𝜃 (𝑥 𝑡 ’ , 𝑡') results, the first and second terms of the derivation results are consistent with 𝑓 𝜃 (𝑥 𝑡 ’ , 𝑡') and 𝑥 𝑇 − 𝑓 𝜃 (𝑥 𝑡 ’ , 𝑡') is 𝑡 − 1 times that of formula (13). Even if 𝑓 𝜃 (𝑥 𝑡 ’ , 𝑡') has a small error in the result. After several iterations, the error will gradually accumulate and affect the final effect. According to formula (13), Algorithm 2 has a small error in 𝑓 𝜃 (𝑥 𝑡 ’ , 𝑡') has a smaller dependence, 𝑥 𝑡 Only related to the current noisy signal, 𝑓 can be processed more effectively 𝜃 (𝑥 𝑡 ’ , 𝑡') estimation error.

[0172] The above algorithm 2 can be summarized as follows: In the current group of sample signals, in the order from the end signal to the start signal, each signal except the start signal is used to perform denoising training on the diffusion model. t-1 When the diffusion model samples the signal x t-1 ’ , x t-1 ’ It is obtained using formulas (9)-(11).

[0173] In addition to improving the sampling strategy of the reverse process, the embodiment of the present invention also improves the network architecture of the reverse process.

[0174] Preferably, the diffusion model may be a U-Net with an attention mechanism added, namely, Wave-U-Net.

[0175] Figure 4 is a schematic diagram of the network architecture of U-Net provided by an embodiment of the present invention, Figure 4 In the figure, (a) is a schematic diagram of the network architecture of U-Net without adding the attention mechanism, and (b) is a schematic diagram of the network architecture of Wave-U-Net.

[0176] See also Figure 4 ,The diffusion model includes an encoding module, a decoding module, and an attention mechanism module.

[0177] The encoding module includes n downsampling layers, the decoding module includes n upsampling layers, and the attention mechanism module includes n attention mechanism layers.

[0178] The encoding module and the decoding module have a symmetrical structure. According to the diffusion model from input to output, the downsampling layer is arranged in the forward direction, and the upsampling layer and the attention mechanism layer are arranged in the reverse direction.

[0179] The i-th downsampling layer is used to downsample the output of the i-1-th downsampling layer.

[0180] The i-th upsampling layer is used to upsample the output of the i+1-th upsampling layer and the output of the i-th attention mechanism layer.

[0181] Figure 5 Schematic diagram of the working principle of the attention mechanism layer provided by an embodiment of the present invention. Figure 5 The i-th attention mechanism layer is used to perform convolution calculations on the output of the i-th downsampling layer and the output of the 𝑖+1-th upsampling layer, respectively, and then perform addition operations on the convolution results; the ReLU activation function is used to perform nonlinear processing on the sum of the addition operations, and then a one-dimensional convolution is performed on the output of the ReLU activation function to generate an attention mask, and the attention mask is normalized by the Sigmoid activation function.

[0182] 𝑖 is an integer index starting from 0.

[0183] The ReLU activation function and the Sigmoid activation function are functions well known to those skilled in the art, and their contents will not be described in detail here.

[0184] The attention mechanism layer is used to enable the neural network of the diffusion model to focus on local information.

[0185] By adding the attention mechanism module, the Wave-U-Net network structure is specifically used to fit the posterior distribution of high-frequency components of long sequences. Through its unique encoding-decoding structure, it can better capture and restore the high-frequency features of point cloud data. The introduction of this network structure significantly improves the effect of the model in the reverse denoising process.

[0186] The working mechanism of the attention mechanism module is well known to those skilled in the art and will not be described in detail here.

[0187] In order to let Wave-U-Net know the current position in the reverse process, see Figure 4 (b) and formula (14), the time step t' of each downsampling layer and upsampling layer embedding is implemented based on the formula of sine and cosine functions. Here, the time step t' is a number. If you want to expand it to a vector that Wave-U-Net can learn, you must rely on formula (14);

[0188]

[0189] d is the dimension of the vector input to the downsampling layer or upsampling layer, that is, the total number of rows in the vector. Here, the value of d should be consistent with the shape and size of the Wave-U-Net network input data so that vector concatenation can be performed later. k represents the current k-th row of the vector, and 𝑓(⋅,⋅) is the value of the time step 𝑡' on the k-th row of the vector dimension.

[0190] As shown in equation (14), each time step 𝑡′ corresponds to a set of sine and cosine values, which change as 𝑡 increases, providing time step information for the inverse process.

[0191] Optionally, in the design for the constrained diffusion model 𝑓 𝜃 When we use the loss function of the training process, we choose the loss function that is consistent with the original diffusion model because the posterior distribution of clean data is estimated from noisy data. , as shown in formula (15);

[0192]

[0193] Among them, 𝑞 data is the current group sample signal, 𝑥 0 is data The starting signal (the high-frequency component of the clean point cloud sampled by the diffusion model), 𝑥 𝑇 is data The middle endpoint signal (the high-frequency component of the noisy cloud sampled by the diffusion model), 𝑥 𝑡 is data The intermediate signal in Indicates the calculation of expected value.

[0194] Through S25 and S26, a spectral domain point cloud denoising model of the target to be denoised is constructed by adopting a diffusion model construction method based on the high-frequency components in the spectral domain signal.

[0195] The beneficial effects of the present invention are:

[0196] 1) In a variety of models and scenes, the point cloud denoising effect is good and the geometric details are well preserved.

[0197] The spectral domain denoising method based on the diffusion model proposed in this invention performs well in a variety of models and scenarios, can effectively remove noise from point cloud data, and has significant advantages in retaining geometric details. Traditional denoising methods often cause loss of geometric details of point cloud data when processing noise, affecting subsequent three-dimensional reconstruction and analysis. This method introduces high-frequency component encoding technology in the spectral domain, which can retain the geometric details of the point cloud to the greatest extent while removing noise.

[0198] Specifically, the high-frequency component encoding technology in the spectral domain enables the denoising process to deal with high-frequency noise in a targeted manner while retaining important geometric details. In the high-frequency components of the point cloud data, the geometric details and noise information are effectively separated, so that the original geometric shape of the point cloud is retained as much as possible while removing the noise. The introduction of this technology enables this method to achieve better denoising effects and geometric detail retention when processing point cloud data in complex scenes.

[0199] 2) The denoising model itself is more robust.

[0200] Another significant advantage of the present invention is that the denoising model itself is more robust. Traditional denoising methods often show instability and inconsistent denoising effects when facing different levels and types of noise. The present invention improves the robustness of the model through the following improvements.

[0201] First, adaptive frequency range selection: Through the adaptive frequency range selection method, this method can flexibly adjust the selection range of high-frequency components according to the characteristics of different point clouds. This adaptability enables the model to better cope with different types and degrees of noise, ensuring stability and consistency in the denoising process.

[0202] The second is the noise addition mechanism of linear interpolation: In the diffusion process, a noise addition mechanism based on linear interpolation is used to accurately control the amount of noise added in each step. This mechanism ensures that the end point of the diffusion process is consistent with the high-frequency component of the noisy point cloud, thereby improving the accuracy and robustness of the denoising process.

[0203] The third is the introduction of the Wave-U-Net network: The Wave-U-Net network structure is specifically used to fit the posterior distribution of high-frequency components of long sequences. Through its unique encoding-decoding structure, it can better capture and restore the high-frequency features of point cloud data. The introduction of this network structure significantly improves the effect of the model in the reverse denoising process.

[0204] Fourth, a new sampling strategy is designed: This sampling strategy can effectively prevent the error accumulation problem in the inverse denoising process. This strategy ensures that the denoising results at each time step are more accurate, thereby improving the robustness of the entire denoising process.

[0205] Figure 6 is a flow chart of a point cloud denoising method provided by an embodiment of the present invention, see Figure 6 ,The point cloud denoising method includes the following steps.

[0206] S31, converting the point cloud to be denoised into a spectral domain signal, and determining the high-frequency components in the spectral domain signal.

[0207] The specific process of S31 can refer to the aforementioned S22-S24, which will not be described in detail here.

[0208] S32. Determine a point cloud denoising model.

[0209] The point cloud denoising model is: Figure 1 or Figure 2 The point cloud denoising model constructed by the method for constructing the point cloud denoising model is shown.

[0210] S33. Use the point cloud denoising model to remove noise in high-frequency components.

[0211] The high-frequency component is used as the sampling signal of the point cloud denoising model, so that the point cloud denoising model removes the noise in the high-frequency component. The signal output by the point cloud denoising model is the high-frequency component after the noise is removed.

[0212] S34. Determine the spectral domain signal after noise removal based on the high-frequency component after noise removal.

[0213] S34 may include: replacing the noisy high-frequency component in the spectral domain signal converted from the original point cloud with the high-frequency component after the noise is removed, so as to obtain the spectral domain signal after the noise is removed.

[0214] The replacement method is well known to those skilled in the art and will not be described in detail here.

[0215] S35, converting the spectral domain signal after noise removal into a point cloud to obtain a point cloud after noise removal.

[0216] S35 may include: performing inverse Fourier transform calculation on the spectral domain signal after noise removal to obtain a graph signal corresponding to the point cloud, thereby obtaining the point cloud.

[0217] Specifically, S35 may refer to S232, which will not be described in detail here.

[0218] Figure 7 is a graph showing the experimental results of the point cloud denoising model provided by an embodiment of the present invention on a public point cloud dataset. Figure 8 This is a graph of experimental results of the point cloud denoising model provided by an embodiment of the present invention on a point cloud of power facilities.

[0219] See also Figure 7 In the upper row of images, the left image is the 3D model corresponding to the point cloud to be denoised, and the middle image and the right image are the 3D models corresponding to the denoised point cloud after denoising using the PCN and PDFlow denoising methods respectively; in the lower row of images, from left to right, they are the 3D models corresponding to the denoised point cloud after denoising using ScoreDenoise, Pointfilter and the denoising method provided by the embodiment of the present invention. By comparison, it can be seen that the denoising method provided by the embodiment of the present invention can retain the geometric details in the point cloud data and can restore the original geometric shape of the target to be denoised.

[0220] See also Figure 8 The left picture is a clean point cloud of an electric tower, the middle picture is a noisy point cloud of an electric tower, and the right picture is a point cloud after the noisy point cloud of an electric tower is denoised using the denoising method provided in an embodiment of the present invention, which is closer to the clean point cloud of the electric tower shown in the left picture.

[0221] In this embodiment, the point cloud to be denoised is converted into a spectral domain signal, and the high-frequency component in the spectral domain signal is determined; a point cloud denoising model is determined; the point cloud denoising model is used to remove the noise in the high-frequency component; based on the high-frequency component after the noise is removed, the spectral domain signal after the noise is removed is obtained; the spectral domain signal after the noise is removed is converted into a point cloud to obtain the point cloud after the noise is removed; the point cloud denoising model is trained to remove the noise in the high-frequency component of the spectral domain signal converted from the point cloud; in this way, the geometric details and noise information in the high-frequency component of the point cloud data are effectively separated, that is, the noise in the high-frequency component is removed, and the important geometric details of the target to be denoised in the high-frequency component are retained; the retention of geometric details in the point cloud data can restore the original geometric shape of the target to be denoised, thereby improving the reconstruction quality of the three-dimensional model.

[0222] Fig. 9 is a schematic diagram of a device for constructing a point cloud denoising model provided by an embodiment of the present invention. Fig. 9 The construction device includes: a first acquisition unit 91, a first conversion unit 92, a first determination unit 93 and a construction unit 94.

[0223] The first acquisition unit 91 is used to acquire a sample point cloud of a target to be denoised.

[0224] The first conversion unit 92 is used to convert the sample point cloud into a spectrum domain signal.

[0225] The first determination unit 93 is used to determine the high frequency component in the spectrum domain signal.

[0226] The construction unit 94 is used to construct a spectral domain point cloud denoising model of the target to be denoised based on the high-frequency components in the spectral domain signal by adopting a diffusion model construction method.

[0227] In this embodiment, a sample point cloud of a target to be denoised is obtained; the sample point cloud is converted into a spectral domain signal, and the high-frequency components in the spectral domain signal are determined; according to the high-frequency components in the spectral domain signal, a spectral domain point cloud denoising model of the target to be denoised is constructed by constructing a diffusion model; the spectral domain point cloud denoising model can be trained to remove noise in the high-frequency components of the spectral domain signal converted from the point cloud; in this way, the geometric details and noise information in the high-frequency components of the point cloud data are effectively separated, that is, the noise in the high-frequency components is removed, and the important geometric details of the target to be denoised in the high-frequency components are retained; the retention of geometric details in the point cloud data can restore the original geometric shape of the target to be denoised, thereby improving the reconstruction quality of the three-dimensional model.

[0228] Fig.10 is a schematic diagram of a point cloud denoising device provided by an embodiment of the present invention. Fig.10 The point cloud denoising device includes: a second conversion unit 101, a second determination unit 102, a removal unit 103 and a second acquisition unit 104.

[0229] The second conversion unit 101 is used to convert the point cloud to be denoised into a spectral domain signal.

[0230] The second determining unit 102 is used to determine the high frequency component in the spectral domain signal.

[0231] The second determining unit 102 is further used to determine a point cloud denoising model. The point cloud denoising model is Fig. 9 The point cloud denoising model constructed by the point cloud denoising model construction device shown.

[0232] The removal unit 103 is used to remove noise in high-frequency components by using a point cloud denoising model.

[0233] The second acquisition unit 104 is used to acquire the spectral domain signal after the noise is removed based on the high-frequency component after the noise is removed.

[0234] The second conversion unit 101 is further used to convert the spectral domain signal after noise removal into a point cloud to obtain the point cloud after noise removal.

[0235] In this embodiment, the point cloud to be denoised is converted into a spectral domain signal, and the high-frequency component in the spectral domain signal is determined; a point cloud denoising model is determined; the point cloud denoising model is used to remove the noise in the high-frequency component; based on the high-frequency component after the noise is removed, the spectral domain signal after the noise is removed is obtained; the spectral domain signal after the noise is removed is converted into a point cloud to obtain the point cloud after the noise is removed; the point cloud denoising model is trained to remove the noise in the high-frequency component of the spectral domain signal converted from the point cloud; in this way, the geometric details and noise information in the high-frequency component of the point cloud data are effectively separated, that is, the noise in the high-frequency component is removed, and the important geometric details of the target to be denoised in the high-frequency component are retained; the retention of geometric details in the point cloud data can restore the original geometric shape of the target to be denoised, thereby improving the reconstruction quality of the three-dimensional model.

[0236] An embodiment of the present invention further provides an electronic device, which includes: a processor and a memory, wherein the processor and the memory are interconnected and communicate with each other via a communication bus and / or other forms of connection mechanisms, and the memory stores a computer program executable by the processor.

[0237] The electronic device can be a device for constructing a point cloud denoising model. When the electronic device is running, the processor executes the computer program to execute the method for constructing a point cloud denoising model in any optional implementation of the above-mentioned embodiment to achieve the following functions: obtaining a sample point cloud of a target to be denoised; converting the sample point cloud into a spectral domain signal, and determining the high-frequency component in the spectral domain signal; and constructing a spectral domain point cloud denoising model of the target to be denoised based on the high-frequency component in the spectral domain signal by adopting a diffusion model construction method.

[0238] Alternatively, the electronic device may be a point cloud denoising device. When the electronic device is running, the processor executes the computer program to execute the point cloud denoising method in any optional implementation of the above-mentioned embodiment to achieve the following functions: converting the point cloud to be denoised into a spectral domain signal, and determining the high-frequency component in the spectral domain signal; determining a point cloud denoising model, which is a point cloud denoising model constructed by the aforementioned point cloud denoising model construction method; using the point cloud denoising model to remove noise in the high-frequency component; based on the high-frequency component after de-noising, obtaining the spectral domain signal after de-noising; converting the spectral domain signal after de-noising into a point cloud to obtain the point cloud after de-noising.

[0239] An embodiment of the present application also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for constructing a point cloud denoising model in any optional implementation of the above embodiment is executed; or the point cloud denoising method in any optional implementation of the above embodiment is executed.

[0240] Among them, the computer-readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory, electrically erasable programmable read-only memory, erasable programmable read-only memory, programmable read-only memory, read-only memory, magnetic memory, flash memory, and magnetic disk or optical disk.

Claims

1. A method for constructing a point cloud denoising model, characterized in that: The construction method comprises: Get the sample point cloud of the target to be denoised; Converting the sample point cloud into a spectral domain signal, and determining a high-frequency component in the spectral domain signal; According to the high-frequency components in the spectral domain signal, a spectral domain point cloud denoising model of the target to be denoised is constructed by adopting a diffusion model construction method; There are several pairs of sample point clouds, each pair of sample point clouds includes a clean point cloud and a noisy point cloud, the noisy point clouds in every two pairs of sample point clouds are different, and in each pair of sample point clouds, the clean point cloud is obtained based on the noisy point cloud in the same pair; The method of constructing a spectral domain point cloud denoising model of the target to be denoised is carried out according to the high-frequency components in the spectral domain signal by adopting a diffusion model construction method, including: In the diffusion process, based on the high-frequency components in the spectral domain signal, several groups of sample signals are determined; one group of sample signals corresponds to a pair of sample point clouds one by one, each group of sample signals includes a starting signal, a plurality of intermediate signals and an end signal, in each group of sample signals, the starting signal is a high-frequency component converted from the corresponding clean point cloud, the end signal is a high-frequency component converted from the corresponding noisy point cloud, the intermediate signal is a signal inserted between the starting signal and the end signal of the same group, and the noise level of each intermediate signal gradually increases in the order from the starting signal to the end signal; In the reverse process, each group of sample signals is used to train the diffusion model according to the order from the end signal to the start signal in each group of sample signals to obtain a trained spectral domain point cloud denoising model.

2. The construction method according to claim 1, characterized in that: The determining of the high frequency component in the spectral domain signal comprises: Obtaining the lowest frequency of the high-frequency component to be determined; The lowest frequency is taken as the starting frequency, and the high frequency band signal of the spectrum domain signal is taken as the high frequency component.

3. The construction method according to claim 2, characterized in that: The obtaining of the lowest frequency of the high-frequency component to be determined comprises: In the spectrum domain signal, a plurality of low-frequency band signals are sequentially determined, the starting frequency of each of the low-frequency band signals is the lowest frequency of the spectrum domain signal, the frequency ranges of two adjacent low-frequency band signals are sequentially increased, and the increase amplitude is a predetermined amplitude, and the frequency range of the low-frequency band signal is not greater than half of the global frequency range of the spectrum domain signal; By inverse Fourier transform calculation, each of the low-frequency band signals is converted into a graph signal s' corresponding to each of the low-frequency band signals; Determine the difference between the image signal s corresponding to the sample point cloud and the image signal s' corresponding to each of the low-frequency band signals; Comparing the difference values ​​corresponding to each of the low-frequency band signals; When the difference corresponding to a continuous number of low-frequency band signals is greater than the difference corresponding to the preceding low-frequency band signal, the highest frequency of the low-frequency band signal with the smallest frequency range among the continuous number of low-frequency band signals is taken as the lowest frequency of the high-frequency component to be determined.

4. The construction method according to claim 1, characterized in that: The step of determining a plurality of groups of sample signals based on the high frequency components in the spectral domain signal comprises: After determining the start signal and the end signal of the current group of sample signals, inserting a predetermined number of intermediate signals into the start signal and the end signal of the current group by linear interpolation; The linear interpolation method is as follows: ； x t represents the tth intermediate signal, x0 represents the starting signal, x T represents the endpoint signal, and α represents the interpolation coefficient.

5. The construction method according to claim 4, characterized in that: The diffusion model is U-Net, The step of training the diffusion model using each group of sample signals according to the sequence from the end signal to the start signal in each group of sample signals comprises: In the current group of sample signals, in the order from the end signal to the start signal, each signal except the start signal is sequentially used to perform denoising training on the diffusion model, The current training signal is x t-1 When the signal sampled by the diffusion model is x t-1 ’ , x t-1 ’ It is obtained by the following formula; ； x t is the signal x in the diffusion process t-1 The next signal, represents the first correction value, represents the second correction value, x T is the endpoint signal, f θ is the diffusion model obtained from the last training, θ is the parameter of the diffusion model, x t ' is the signal sampled by the last diffusion model, t' is the time step when the diffusion model was last trained, α t represents the signal x in the diffusion process t The corresponding interpolation coefficient, α t-1 represents the signal x in the diffusion process t-1 The corresponding interpolation coefficients.

6. A point cloud denoising method, characterized in that: The point cloud denoising method comprises: Converting the point cloud to be denoised into a spectral domain signal, and determining a high-frequency component in the spectral domain signal; Determine a point cloud denoising model, wherein the point cloud denoising model is a point cloud denoising model constructed by the method for constructing a point cloud denoising model according to any one of claims 1 to 5; Using the point cloud denoising model to remove noise in the high-frequency component; Based on the high-frequency components after noise removal, a spectral domain signal after noise removal is obtained; The spectral domain signal after the noise is removed is converted into a point cloud to obtain a point cloud after the noise is removed.

7. A device for constructing a point cloud denoising model, characterized in that: The construction device comprises: A first acquisition unit, used to acquire a sample point cloud of a target to be denoised; A first conversion unit, used to convert the sample point cloud into a spectral domain signal; A first determining unit, used to determine the high-frequency component in the spectral domain signal; A construction unit, configured to construct a spectral domain point cloud denoising model of the target to be denoised by adopting a diffusion model construction method according to the high-frequency components in the spectral domain signal; There are several pairs of sample point clouds, each pair of sample point clouds includes a clean point cloud and a noisy point cloud, the noisy point clouds in every two pairs of sample point clouds are different, and in each pair of sample point clouds, the clean point cloud is obtained based on the noisy point cloud in the same pair; The building block is used to In the diffusion process, based on the high-frequency components in the spectral domain signal, several groups of sample signals are determined; one group of sample signals corresponds to a pair of sample point clouds one by one, each group of sample signals includes a starting signal, a plurality of intermediate signals and an end signal, in each group of sample signals, the starting signal is a high-frequency component converted from the corresponding clean point cloud, the end signal is a high-frequency component converted from the corresponding noisy point cloud, the intermediate signal is a signal inserted between the starting signal and the end signal of the same group, and the noise level of each intermediate signal gradually increases in the order from the starting signal to the end signal; In the reverse process, each group of sample signals is used to train the diffusion model according to the order from the end signal to the start signal in each group of sample signals to obtain a trained spectral domain point cloud denoising model.

8. A point cloud denoising device, characterized in that: The point cloud denoising device comprises: A second conversion unit, used for converting the point cloud to be denoised into a spectral domain signal; A second determination unit, used to determine the high frequency component in the spectral domain signal; The second determination unit is further used to determine a point cloud denoising model, wherein the point cloud denoising model is a point cloud denoising model constructed by the point cloud denoising model construction device according to claim 7; A removal unit, used to remove noise in the high-frequency component by using the point cloud denoising model; A second acquisition unit is used to acquire a spectral domain signal after the noise is removed based on the high-frequency component after the noise is removed; The second conversion unit is further used to convert the spectral domain signal after noise removal into a point cloud to obtain a point cloud after noise removal.

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