An Acoustic Boundary Element Method Combined with Neural Implicit 3D Reconstruction

Abstract

The present invention belongs to the technical fields of computer vision and acoustic boundary element technology, and particularly relates to an acoustic boundary element method combined with neural implicit three-dimensional reconstruction, comprising the following steps: acquiring a set of acoustic images based on a single-beam forward-looking sonar; obtaining the azimuth, elevation and range information corresponding to the image data, and calculating sampling points; constructing a neural implicit three-dimensional reconstruction model, including an SDF field and an intensity field for describing the geometric information of the target, and implicitly representing the three-dimensional shape of the target by the SDF field; taking the image data and the corresponding azimuth information as training data, and constructing an acoustic volume rendering equation; training the neural implicit three-dimensional reconstruction model; performing dense sampling on the trained neural implicit three-dimensional reconstruction model to obtain a discrete representation of the boundary; and calculating the structural surface sound pressure distribution based on the fast multipole boundary element method. The present invention can improve the processing efficiency and flexibility of complex geometric objects while maintaining high calculation accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical fields of computer vision and acoustic boundary element technology, and particularly relates to an acoustic boundary element method combined with neural implicit three-dimensional reconstruction. Background Art

[0002] The acoustic boundary element method is a classical numerical calculation method, which is widely used in solving problems such as acoustic propagation, scattering, and radiation. By restricting the solution region to the geometric boundary, the boundary element method greatly reduces the computational scale and is particularly suitable for acoustic problems in infinite domains. However, when dealing with complex geometric shapes, the geometric modeling and mesh generation processes in traditional boundary element methods are usually very cumbersome, which easily leads to a decrease in computational efficiency and an increase in errors. Especially in the case of complex three-dimensional geometric structures, the quality of mesh generation often directly affects the accuracy and stability of acoustic calculations. In recent years, with the development of deep learning technology, neural implicit reconstruction has received extensive attention in the field of three-dimensional geometric modeling. By learning the implicit function description of the geometric surface, neural implicit reconstruction can express complex three-dimensional geometric structures in a continuous form, avoiding the limitations of traditional explicit meshing methods. However, these methods are mainly applied in the fields of computer vision and three-dimensional reconstruction and have not been combined with the acoustic boundary element method, failing to fully exploit the potential of neural implicit modeling in solving acoustic problems. Therefore, how to combine neural implicit three-dimensional reconstruction with the acoustic boundary element method to achieve the purpose of improving the efficiency and accuracy of acoustic calculations while accurately representing complex geometric structures is a technical problem that urgently needs to be solved currently. Summary of the Invention

[0003] Aiming at the technical problem that in the above-mentioned traditional boundary element method when dealing with complex geometric shapes, the geometric modeling and mesh generation processes are usually very cumbersome, which easily leads to a decrease in computational efficiency and an increase in errors, the present invention provides an acoustic boundary element method combined with neural implicit three-dimensional reconstruction, aiming to map the two-dimensional information in the sonar image into an implicit field in three-dimensional space, optimize the network parameters by backpropagation, and gradually approximate the real surface of the object. By densely sampling the trained neural implicit three-dimensional reconstruction model, a discrete representation of the boundary is obtained and combined with the acoustic boundary element method to solve acoustic problems.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0005] An acoustic boundary element method combined with neural implicit three-dimensional reconstruction, comprising the following steps:

[0006] S1. Acquire a set of acoustic images based on a single-beam forward-looking sonar;

[0007] S2. Obtain the azimuth, elevation, and range information corresponding to the image data, and calculate the sampling points;

[0008] S3. Construct a neural implicit three-dimensional reconstruction model, including an SDF field and an intensity field for describing the geometric information of the target, and implicitly represent the three-dimensional shape of the target by the SDF field;

[0009] S4. Use the image data and the corresponding orientation information as training data to construct an acoustic volume rendering equation;

[0010] S5. Based on backpropagation, jointly optimize the SDF field and the intensity field through multiple constraints to train the neural implicit three-dimensional reconstruction model;

[0011] S6. Perform dense sampling on the trained neural implicit three-dimensional reconstruction model to obtain a discrete representation of the boundary;

[0012] S7. Calculate the structural surface sound pressure distribution based on the fast multipole boundary element method.

[0013] The method for calculating the sampling points in S2 is as follows:

[0014] S21. Obtain the azimuth angle θ i ∈[θmax min , elevation angle φ i ∈[φmax min , and range information r i ∈[rmax min ;

[0015] S22. Construct a pixel sample set While randomly selecting pixels from the image, select pixels with pixel intensity higher than the threshold; let the set of these pixels be

[0016] S23. Construct a sampling point set A on the arc p : For each pixel Use hierarchical sampling to sample on the arc corresponding to the pixel; Divide the elevation angle range [φmax min into angles equally, and the difference between two adjacent angles is Add random noise ~Uniform(0,1)Δφ to these angles to obtain the sampling point set on the arc

[0017] S24. Construct a sampling point set on the sonar ray For each sampling point P p on the arc, construct a sonar ray starting from the sonar acoustic center and terminating at P p ; Uniformly sample on each ray Points are used to obtain the sampling point set on the sonar ray

[0018] S25. The final sampling point set consists of constitute.

[0019] The method for constructing the neural implicit three-dimensional reconstruction model in S3 is as follows:

[0020] S31. Construct the SDF field: Map the spatial position x ∈ R of any sampling point in the three-dimensional space 3 to its corresponding SDF value sdf ∈ R 1 , intermediate feature f ∈ R 256 , where γ is the positional encoding, is a multi-layer fully connected neural network, is the learnable parameter of the network;

[0021] S'32. Construct the target density σ: where Φ s (x) = (1 + e ―sx ) ―1 is the sigmoid function, is the gradient information of the SDF field, and s is the learnable standard deviation;

[0022] S33. Construct the intensity field: Map the spatial position x of any sampling point in the three-dimensional space and the observation direction d ∈ R from the camera to this point 3 to its corresponding intensity value c ∈ R 3 , F ω is a multi-layer fully connected neural network, and ω is the learnable parameter of the network.

[0023] The method for constructing the acoustic volume rendering equation in S4 is as follows:

[0024] S41. After converting the point set to Cartesian coordinates, multiply it by the transformation matrix from sonar to the world coordinate system

[0025]

[0026] to convert the point set from the sonar local coordinate system to the world coordinate system;

[0027] S42. Define the direction of each ray as the unit vector D(P p ):

[0028]

[0029] S43. Obtain the intensity and SDF value: The intensity and SDF value of the target corresponding to each sampling point predicted and output by the neural implicit three-dimensional reconstruction model.

[0030] S44. Construct the target rendering item

[0031]

[0032] Where is the arc located at (r,θ), is the perturbed point P on the arc p The distance of, M(P p ) is the predicted intensity of the intensity field at point P p At, T[P p is the discrete transmittance, defined as follows:

[0033]

[0034] Where α[P i is defined as:

[0035]

[0036] Represents the discrete opacity.

[0037] The method for training the neural implicit three-dimensional reconstruction model in S5 is as follows:

[0038] S51. Construct the SDF regularization loss function L eikonal :

[0039]

[0040] Where Represents the gradient of the SDF field, and x is any point in three-dimensional space;

[0041] S52. Construct the squared error photometric loss function L intensity :

[0042]

[0043] Where Is the rendering intensity, and I is the true intensity;

[0044] S53. Construct the total loss function L:

[0045] L = L intensity + λ·L eikonal

[0046] Where λ is a hyperparameter, set to 0.1.

[0047] The method for obtaining the discrete representation of the boundary in S6 is as follows: After optimization, densely sample the SDF field to obtain the SDF value of each sampling point, extract the isosurface through the Marching Cubes algorithm, generate the three-dimensional surface model of the target using the extracted isosurface, and obtain the discrete representation of the boundary.

[0048] The method for calculating the structural surface sound pressure distribution in S7 is as follows:

[0049] S71. Set the boundary conditions and establish the CBIE equation in the underwater acoustic scattering environment using the Helmholtz equation;

[0050] S72. Couple the CBIE equation and the HBIE equation to solve the non-uniqueness problem;

[0051] S73. Adopt regularization techniques to avoid singular integral problems;

[0052] S74. Establish a discrete system equation through the collocation method and use the broadband fast multipole algorithm to accelerate the solution of the structural surface radiation and scattering fields.

[0053] Compared with the prior art, the beneficial effects of the present invention are:

[0054] The present invention uses the compact representation of the implicit function network to reduce the time overhead of geometric modeling and mesh generation, and combines the fast multipole method with an efficient solution algorithm to reduce the time complexity of sound field calculation. Moreover, the present invention combines the neural implicit reconstruction method with the acoustic boundary element method for the first time, innovatively solves the efficient coupling problem between geometric modeling and acoustic solution, and provides a new solution for acoustic problems under complex geometric shapes. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only exemplary, and those of ordinary skill in the art can also obtain other implementation drawings according to the provided drawings without creative efforts.

[0056] The structures, ratios, sizes, etc. depicted in this specification are only used to cooperate with the content disclosed in the specification for those familiar with this technology to understand and read, and are not used to limit the limited conditions under which the present invention can be implemented. Therefore, they do not have technical substance. Any modification of the structure, change in the proportional relationship, or adjustment of the size should still fall within the scope covered by the technical content disclosed in the present invention without affecting the efficacy and purpose that the present invention can achieve.

[0057] Figure 1It is the process flow chart of the present invention;

[0058] Figure 2 It is the schematic diagram of the network framework of the present invention. Specific embodiments

[0059] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Apparently, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. These descriptions are only for further explaining the features and advantages of the present invention, rather than limiting the claims of the present invention; based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0060] The following will further describe in detail the specific embodiments of the present invention with reference to the drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0061] Refer to Figure 1 , the embodiments of the present invention provide an acoustic boundary element method combined with neural implicit three-dimensional reconstruction, including the following steps:

[0062] S1. Acquire a set of acoustic images based on a single-beam forward-looking sonar.

[0063] S2. Obtain the azimuth, elevation, and range information corresponding to the image data, and calculate the sampling points. The specific steps include:

[0064] S21. Obtain the azimuth θ i ∈[θmax min , elevation φ i ∈[φmax min and range information r i ∈[rmax min .

[0065] S22. Construct a pixel sample set while randomly selecting pixels from the image and selecting pixels with pixel intensity higher than the threshold. Let the set of these pixels be

[0066] S23. Construct a sampling point set A on the arc p : For each pixel sample on the arc corresponding to the pixel using stratified sampling. Divide the elevation range [φmax min into angles equally, and the difference between two adjacent angles is Add random noise~Uniform(0,1)Δφ to these angles to obtain a set of sampling points on the arc

[0067] S24. Construct a set of sampling points on the sonar ray For each sampling point P on the arc p , construct a sonar ray starting from the sonar acoustic center and ending at P p Uniformly sample points on each ray to obtain a set of sampling points on the sonar ray

[0068] S25. The final set of sampling points consists of .

[0069] S3. Construct a neural implicit three-dimensional reconstruction model, including an SDF field and an intensity field for describing the geometric information of the target. The three-dimensional shape of the target is implicitly represented by the SDF field, as Figure 2 shown. The specific steps include:

[0070] S31. Construct the SDF field: Map the spatial position x∈R of any sampling point in three-dimensional space 3 to its corresponding SDF value sdf∈R 1 , intermediate feature f∈R 256 , γ is the positional encoding, is a multi-layer fully connected neural network, are the learnable parameters of the network.

[0071] S32. Construct the target density σ: where Φ s (x)=(1 + e ―sx ) ―1 is the sigmoid function, is the gradient information of the SDF field, and s is the learnable standard deviation.

[0072] S33. Construct the intensity field: Map the spatial position x of any sampling point in three-dimensional space and the viewing direction d∈R from the camera to this point 3 to its corresponding intensity value c∈R 3 , F ω is a multi-layer fully connected neural network, and ω are the learnable parameters of the network.

[0073] S4. Use the image data and the corresponding azimuth information as training data to construct an acoustic volume rendering equation.

[0074] The specific steps include: ​

[0075] S41. Multiply the point set by the transformation matrix from sonar to the world coordinate system after converting it to Cartesian coordinates

[0076]

[0077] to convert the point set from the sonar local coordinate system to the world coordinate system.

[0078] S42. Define the direction of each ray as the unit vector D(P p ):

[0079]

[0080] S43. Obtain the intensity and SDF value: The intensity and SDF value of the target corresponding to each sampling point predicted and output by the neural implicit three-dimensional reconstruction model.

[0081] S44. Construct the target rendering item

[0082]

[0083] where is the arc located at (r,θ), is the distance of the perturbed point P p on the arc, M(P p ) is the predicted intensity of the intensity field at the point P p , T[P p is the discrete transmittance, defined as follows:

[0084]

[0085] where α[P i is defined as:

[0086]

[0087] represents the discrete opacity.

[0088] S5. Jointly optimize the SDF field and the intensity field through multiple constraints based on backpropagation to train the neural implicit three-dimensional reconstruction model. The specific steps include:

[0089] S51. Construct the SDF regularization loss function L eikonal :

[0090]

[0091] where represents the gradient of the SDF field, and x is any point in the three-dimensional space.

[0092] S52. Construct the squared - error photometric loss function \(L\) intensity :

[0093]

[0094] where, is the rendering intensity, and \(I\) is the true intensity.

[0095] S53. Construct the total loss function \(L\):

[0096] \(L = L\) intensity +\(\lambda\cdot L\) eikonal

[0097] where \(\lambda\) is a hyper - parameter, set to \(0.1\).

[0098] S6. Perform dense sampling on the trained neural implicit three - dimensional reconstruction model to obtain a discrete representation of the boundary. Its specific form is: after optimization, perform dense sampling on the SDF field to obtain the SDF value of each sampling point, extract the isosurface through the Marching Cubes algorithm, and generate a three - dimensional surface model of the target using the extracted isosurface to obtain a discrete representation of the boundary.

[0099] S7. Calculate the structural surface sound pressure distribution based on the fast multipole boundary element method. The specific steps include:

[0100] S71. Set the boundary conditions and establish the CBIE equation in the underwater acoustic scattering environment using the Helmholtz equation.

[0101] S72. Couple the CBIE equation and the HBIE equation to solve the non - unique solution problem.

[0102] S73. Adopt regularization techniques to avoid singular integral problems.

[0103] S74. Establish a discrete system equation through the collocation method and use the broadband fast multipole algorithm to accelerate the solution of the structural surface radiation and scattering fields.

[0104] The above only elaborates on the preferred embodiments of the present invention in detail. However, the present invention is not limited to the above - mentioned embodiments. Within the scope of knowledge possessed by those of ordinary skill in the art, various changes can be made without departing from the gist of the present invention, and all such changes should be included within the protection scope of the present invention.

Claims

1. An acoustic boundary element method combined with neural implicit three-dimensional reconstruction, characterized in that, It includes the following steps: S1. Acquire a set of acoustic images based on a single-beam forward-looking sonar; S2. Obtain the azimuth, elevation, and range information corresponding to the image data, and calculate the sampling points; The method for calculating the sampling points in S2 is as follows: S21. Obtain the azimuth angle θ corresponding to the image data i ∈ [θmax min , elevation angle φ i ∈ [φmax min , and range information r i ∈ [rmax min ; S22. Construct a pixel sample set While randomly selecting pixels from the image, select pixels with pixel intensity higher than the threshold; Let the set of these pixels be S23. Construct the sampling point set A on the arc p : For each pixel Use stratified sampling to sample on the arc corresponding to the pixel; Divide the elevation angle range [φmax min into angles, and the difference between two adjacent angles is Add random noise ~ Uniform(0,1)Δφ to these angles to obtain the sampling point set on the arc S24. Construct a set of sampling points on the sonar ray For the sampling point P on each arc p , construct a sonar ray starting from the sonar acoustic center and ending at P p Uniformly sample points on each ray to obtain a set of sampling points on the sonar ray ​ S25. The final sampling point set consists of and is formed; S3. Construct a neural implicit three-dimensional reconstruction model, including an SDF field and an intensity field for describing the geometric information of the target, and implicitly represent the three-dimensional shape of the target by the SDF field; The method for constructing the neural implicit three-dimensional reconstruction model in S3 is as follows: S31. Construct the SDF field: Map the spatial position x ∈ R of any sampling point in the three-dimensional space 3 to its corresponding SDF value sdf ∈ R 1 , intermediate feature f ∈ R 256 , where γ is the positional encoding, is a multi-layer fully connected neural network, and are the learnable parameters of the network; S32. Construct the target density σ: where φ s (x) = (1 + e -sx ) -1 is the sigmoid function, is the gradient information of the SDF field, and s is the learnable standard deviation; S33. Construct the intensity field: Map the spatial position x of any sampling point in the three-dimensional space and the observation direction d ∈ R from the camera to this point 3 to its corresponding intensity value c ∈ R 3 , F ω is a multi-layer fully connected neural network, and ω is the learnable parameter of the network; S4. Use the image data and the corresponding azimuth information as training data to construct an acoustic volume rendering equation; S5. Based on backpropagation, jointly optimize the SDF field and the intensity field through multiple constraints to train the neural implicit three-dimensional reconstruction model; S6. Densely sample the trained neural implicit three-dimensional reconstruction model to obtain a discrete representation of the boundary; S7. Calculate the structural surface sound pressure distribution based on the fast multipole boundary element method.

2. The acoustic boundary element method combined with neural implicit three-dimensional reconstruction according to claim 1, characterized in that The method for constructing the acoustic volume rendering equation in S4 is as follows: S41. Convert the point set after converting it to Cartesian coordinates and multiply it by the transformation matrix from sonar to the world coordinate system To convert the point set from the sonar local coordinate system to the world coordinate system; S42. Define the direction of each ray as the unit vector D(P p ): S43. Obtain the intensity and SDF values: the intensity and SDF values of the target corresponding to each sampling point predicted and output by the neural implicit three-dimensional reconstruction model; S44. Construct the target rendering item Among them, is the arc located at (r, θ), is the disturbed point P on the arc p 's distance, M(P p ) is the predicted intensity of the intensity field at point P p . T[P p is the discrete transmittance, defined as follows: where α[P i is defined as: Represent the discrete opacity.

3. The acoustic boundary element method combined with neural implicit three-dimensional reconstruction according to claim 1, wherein The method for training the neural implicit three-dimensional reconstruction model in S5 is as follows: S51. Construct the SDF regularization loss function L eikonal : Among them, represents the gradient of the SDF field, and x is an arbitrary point in three-dimensional space; S52. Construct the squared error photometric loss function L intensity : Among them, is the rendering intensity, and I is the true intensity; S53. Construct the total loss function L: L = L intensity + λ·L eikonal Among them, λ is a hyperparameter, set to 0.

1.

4. An acoustic boundary element method combined with neural implicit three-dimensional reconstruction according to claim 1, characterized in that, The method for obtaining the discrete representation of the boundary in S6 is as follows: After the optimization is completed, densely sample the SDF field to obtain the SDF value of each sampling point, extract the isosurface through the Marching Cubes algorithm, and generate a three-dimensional surface model of the target using the extracted isosurface to obtain the discrete representation of the boundary.

5. An acoustic boundary element method combined with neural implicit three-dimensional reconstruction according to claim 1, characterized in that The method for calculating the structural surface sound pressure distribution in S7 is as follows: S71. Set the boundary conditions and establish the CBIE equation in the underwater acoustic scattering environment using the Helmholtz equation; S72. Couple the CBIE equation and the HBIE equation to solve the non-uniqueness problem; S73. Adopt regularization techniques to avoid the singular integral problem; S74. Establish a discrete system equation through the collocation method, and use the wideband fast multipole algorithm to accelerate the solution of the structural surface radiation and scattering fields.

Images