Underwater plectropomus leopardus phenotype establishment method based on three-dimensional reconstruction

The method uses multi-resolution hash grids, SDF, and numerical gradients with coarse-to-fine optimization to address reconstruction challenges in leopard gill perch, achieving accurate and stable 3D modeling.

CN119206138APending Publication Date: 2024-12-27WUHAN UNIV OF TECH
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Patent Information

Application Number
CN202411247527.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-06
Publication Date
2024-12-27

AI Technical Summary

Technical Problem

Existing methods struggle to accurately recover the detailed structure of underwater leopard gill perch, particularly in areas with uniform color or repeated textures, leading to inaccurate reconstructions and noise in 3D representations.

Method used

A method combining multi-resolution three-dimensional hash grid encoding, signed distance function (SDF) for implicit surface modeling, numerical gradient calculation of surface normals, and coarse-to-fine optimization to enhance reconstruction accuracy and stability.

Benefits of technology

The method achieves more accurate and stable three-dimensional reconstruction of the leopard gill perch by ensuring smoothness and consistency in surface representation, capturing fine details through progressive refinement.

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Abstract

The invention relates to an underwater plectropomus leopardus phenotype establishment method based on three-dimensional reconstruction. The method comprises the following steps: S1, encoding and decoding scene information of plectropomus leopardus by using a multi-resolution three-dimensional Hash grid; s2, simulating the surface of the plectropomus leopardus by using a signed distance function SDF to realize implicit curved surface modeling; s3, calculating the surface normal of the plectropomus leopardus by using the numerical gradient; s4, performing coarse-to-fine optimization, and recovering structures of different detail levels of the plectropomus leopardus by adopting a coarse-to-fine optimization strategy; and S5, regularizing the curvature, smoothing the curved surface, and smoothing the reconstructed plectropomus leopardus curved surface by minimizing the curvature of the curved surface of a curvature regularization item. According to the method, the geometric structure of the target plectropomus leopardus is recovered from the sequence image of the reconstructed target plectropomus leopardus, manual participation is reduced through an automatic complex reconstruction method, so that the manual labor intensity is reduced, data required by the method can be acquired through a common digital camera, and the reconstruction cost is reduced.
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Description

Technical Field

[0001] The present invention relates to the field of computer vision, and more specifically to a method for establishing underwater leopard spiny bass phenotype based on three-dimensional reconstruction. Background Art

[0002] Leopard gill perch is a fish of the genus Gill perch of the family Serranidae. Its common names include spotted gill perch, leopard gill perch, and seven-star grouper. It is a warm-water coastal fish. It generally lives in coral reefs. It has been rated as near threatened by the IUCN. It has a smooth skin, a small head, and is covered with fine white spots.

[0003] Existing methods have difficulty in recovering the detailed structure of real scenes, especially in areas with uniform color or repeated textures. Classic multi-view stereo matching algorithms produce inaccurate reconstructions when dealing with areas with strong color changes, and density-based representation methods produce noise when extracting 3D. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for establishing the phenotype of an underwater leopard gill perch based on three-dimensional reconstruction, which has the advantage of being able to accurately provide the contour information of the leopard gill perch, especially having a better reconstruction effect for texture-free areas, and achieving more accurate and stable reconstruction.

[0005] The technical solution adopted by the present invention to solve the technical problem is: constructing a method for establishing the phenotype of underwater leopard gill perch based on three-dimensional reconstruction, comprising the following steps:

[0006] S1, using multi-resolution three-dimensional hash grid to encode and decode the leopard gill perch scene information;

[0007] S2, using signed distance function SDF to simulate the surface of leopard gill perch to achieve implicit surface modeling;

[0008] S3, using numerical gradient to calculate the surface normal of leopard gill bass;

[0009] S4, from coarse to fine optimization, using a coarse to fine optimization strategy to restore the structure of different detail levels of the leopard gill perch;

[0010] S5. Curvature regularization, smoothing the surface, smoothing the reconstructed leopard gill perch surface by minimizing the surface curvature of the curvature regularization term.

[0011] According to the above scheme, in step S1, the method of encoding and decoding the leopard gill perch scene information using a multi-resolution three-dimensional hash grid includes:

[0012] For input location:

[0013]

[0014] Among them, pi is the embedding vector of leopard gill perch image i

[0015] Calculate the resolution Rl and scale S of the current level 1 l :

[0016] R l =2 base_resolution+l·log2_per-level_scale (2)

[0017]

[0018] Among them, baseresolution is the initial coarsest resolution, the default value is 64, log2_per_level_scale is the scaling ratio, the default value is 1;

[0019] S represents the level of the grid to which an input should be processed;

[0020] Compute quantized grid positions

[0021] g d =floor(p d ·R1) (4)

[0022] Among them, p d is the vector of the dth dimension of the input position, and floor is the floor function;

[0023] Get the eigenvalue f by grid hash index grid :

[0024] f grid =grid[h(g)] (5)

[0025] Where h is the grid hash function. By default, a hash function based on prime numbers is used. The process is as follows: Initialize the hash value result to 0, traverse each dimension of the grid data g, and for each dimension: XOR the result with (the product of the dimension coordinate of g and the prime factor 1958374283);

[0026] Then, the weight W is calculated according to the linear interpolation method d

[0027] W d =P d —g d (6)

[0028] Interpolate the grid points to obtain the encoded features f encoded

[0029] f encoded =∑ i wi ·f grid [i] (7)

[0030] Where i is the index of all grid points;

[0031] Compute the gradient relative to the input position

[0032]

[0033] Update the grid feature gradient g grid :

[0034]

[0035] According to the above scheme, in step S2, the sampling position in the voxel grid is determined, and each 3D point x i By grid resolution V l Scaling is performed, expressed as:

[0036] x i,l =x i ·V l , (10)

[0037] The coefficient of linear interpolation is β = x i,l -[x i,l ], the obtained eigenvector is:

[0038] γ l (x i,l )=γ l ([x i,l ])·(1-β)+γ l ([x i,l ])·β (11)

[0039] Among them, the rounding position [x i,l ],[x i,l ] corresponds to the corner point of the local grid unit, and the derivative of the hash code relative to the position is expressed as:

[0040]

[0041] When x i When crossing the grid cell boundary, the corresponding hash key-value pairs are different, and the eikonal loss defined in equation (26) is back-propagated to the locally sampled hash entries, that is, and The calculation of these two hash entries is the hash coding process, which is the same as step S1. When a continuous surface spans multiple grid cells, the grid cells generate consistent surface normals and the grid cells are jointly optimized.

[0042] According to the above scheme, in step S3, the SDF surface normal is calculated using the analytical gradient When the step size of the numerical gradient is smaller than the hash-encoded grid size, the numerical gradient will be equivalent to the analytical gradient. Otherwise, the hash entries of multiple grid cells will participate in the surface normal calculation. Backpropagation through the surface normal allows the hash entries of multiple grids to receive optimization updates simultaneously. The numerical gradient of the selected step size is interpreted as a smoothing operation on the analytical gradient expression.

[0043] According to the above scheme, the method for calculating the surface normal by numerical gradient is: additional SDF sampling, given a sampling point x i =(x i ,y i , z i ), in x i Two additional points are sampled in the surrounding standard coordinate system in each axis within a proximity of step size ∈, and the x component of the surface normal is expressed as:

[0044]

[0045] Among them, ∈ x = [∈, 0, 0], collecting six additional SDF samples for numerical surface normal calculation.

[0046] According to the above scheme, in step S4, numerical gradients are used to calculate high-order derivatives to perform coarse-to-fine optimization from two perspectives: step size ∈ and hash grid resolution V, and the surface is reconstructed by gradually increasing the level of detail;

[0047] The step length ∈ Controls the resolution and amount of detail recovered; for numerical surface normal calculations, applies a larger ∈ Ensure that surface normals remain consistent at larger scales, producing a consistent and continuous surface, and apply smaller ∈ Affect less areas, avoid smoothing out details, and set the step size ∈ Initialized to the coarsest hash grid size and reduced exponentially with different hash grid sizes throughout the optimization process;

[0048] The hash grid resolution V: All hash grids are activated at the beginning of the optimization. To capture the geometric details of the leopard gill bass, the fine grid is first generated using a large step size. ∈ "Eliminate learning" in the coarse optimization, and then use smaller ∈ “Relearn”, enable=group an initial coarse hash grid, and progressively activate finer hash grids during optimization as the step size ∈ decreases to their spatial size, avoiding the relearning process and applying weight decay to all parameters to avoid single-resolution features dominating the final result.

[0049] According to the above scheme, in step S5, in order to promote the smoothness of the reconstructed surface, the average curvature of the SDF is regularized, and the average curvature is calculated from the discrete Laplace operator, and the curvature loss The definition is as follows:

[0050]

[0051] Samples for surface normal calculations Sufficient for curvature calculation, the total loss of leopard gill bass reconstruction is defined as the weighted sum of each loss:

[0052]

[0053]

[0054] The 3D position x of the i-th sample i The distance from the camera center is t i , the volume density σ of each sampling point i and color c i Using the coordinate MLP for prediction, the rendered color of a given pixel is approximated as the Riemann sum:

[0055]

[0056] Among them, α i =1-exp(-σ i δ i ) is the opacity of the i-th light segment, δ i =t i+1 -t i is the distance between adjacent sampling points, is the cumulative transmittance, which represents the proportion of light reaching the camera, For the input image c and the rendered image Color loss between.

[0057] The method for establishing the underwater leopard gill perch phenotype based on three-dimensional reconstruction of the present invention has the following beneficial effects:

[0058] 1. The present invention combines multi-resolution hash coding with SDF to solve the problem of lack of smoothness during back propagation of leopard gill perch hash coding;

[0059] 2. The present invention uses numerical gradient to calculate the SDF surface normal, combined with Eikonal regularization, to solve the local problem of the hash coding analytical gradient of the leopard gill perch;

[0060] 3. The present invention proposes a coarse-to-fine optimization scheme to gradually refine the three-dimensional surface details of the leopard gill perch to achieve more accurate and stable reconstruction.

[0061] 4. The present invention enhances the representation capability by combining multi-resolution 3D hash grid with neural surface rendering, improves the stability of optimization by using numerical gradient calculation of high-order derivatives, and can gradually restore the structure at different levels of detail through a coarse-to-fine optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0063] Figure 1 It is a flow chart of the method for establishing the phenotype of underwater leopard gill perch based on three-dimensional reconstruction of the present invention;

[0064] Figure 2 It is a result diagram of the phenotypic data of underwater leopard gill perch according to an example of the present invention;

[0065] Figure 3 Schematic diagram of using numerical gradient to calculate high-order derivatives according to an embodiment of the present invention. DETAILED DESCRIPTION

[0066] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0067] like Figure 1 As shown in FIG. 3 , the present invention reconstructs the dense structure of the scene from the multi-view image, samples the three-dimensional positions along the camera view direction, and encodes these positions using multi-resolution hashing. The encoded features are input into the SDF MLP and the color MLP to synthesize the image using the SDF. The method for establishing the underwater leopard gill perch phenotype based on three-dimensional reconstruction of the present invention comprises the following steps:

[0068] S1. Encode and decode the leopard gill perch scene information using a multi-resolution three-dimensional hash grid. The specific process is as follows:

[0069] The analytical gradient of the hash-coded position is affected by the local changes in the encoded features, and the optimization update is only propagated to the local hash grid, lacking smoothness. A method is proposed to solve this locality problem by using numerical gradients. For the input position:

[0070]

[0071] Calculate the resolution R of the current level 1 l and ratio S l :

[0072] R l =2 base_resolution+l·log2_per-level_scale (2)

[0073]

[0074] Compute quantized grid positions

[0075] g d =floor(p d ·R l ) (4)

[0076] Get the eigenvalue fgrid by grid hash index:

[0077] f grid =grid[h(g)] (5)

[0078] Where h is the grid hash function;

[0079] Then, the weight w is calculated according to the linear interpolation method

[0080] W d =p d —g d (6)

[0081] Interpolate the grid points to obtain the encoded features f encoded

[0082] f encoded =∑ i w i ·f grid [i] (7)

[0083] Among them, i is the index of all adjacent grid points;

[0084] Compute the gradient relative to the input position

[0085]

[0086] Update the grid feature gradient g grid :

[0087]

[0088] A special property of SDF is that it has a unit norm gradient that is differentiable. The gradient of SDF satisfies the eikonal equation To ensure that the optimized neural representation is a valid signed distance function (SDF), an eikonal loss is added to the SDF prediction:

[0089]

[0090] N is the total number of sampling points. In order to achieve end-to-end optimization, the SDF prediction f(x) needs to be back-propagated twice.

[0091] S2. Use signed distance function (SDF) to simulate the surface of leopard gill perch and realize implicit surface modeling. The specific process is as follows:

[0092] Compute SDF surface normals using analytical gradients Under trilinear interpolation, the hash-encoded analytical gradient with respect to position is not continuous in space. To find the sampling position in the voxel grid, for each 3D point x i First, the grid resolution V l Scaling, denoted by x i,l =x i ·V l The coefficients of linear interpolation are The resulting feature vector is:

[0093]

[0094] Among them, the rounding position [x i,l ],[x i,l ] corresponds to the corner points of the local grid cell. Note that the rounding operation [·] and is not differentiable. Therefore, the derivative of the hash code with respect to the position is expressed as

[0095]

[0096] The derivative of the hash code is local, that is, when x i When crossing grid cell boundaries, the corresponding hash key-value pairs will be different. Therefore, the eikonal loss defined in Equation (5) will only backpropagate to the locally sampled hash entries, i.e. and When a continuous surface spans multiple grid cells, these grid cells should generate consistent surface normals without abrupt changes. To ensure the consistency of the surface representation, these grid cells need to be jointly optimized. However, the analytical gradient is limited to local grid cells unless all corresponding grid cells happen to be sampled and optimized at the same time.

[0097] S3. Use numerical gradient to calculate the surface normal of the leopard gill perch. The specific process is as follows:

[0098] To overcome the locality of hash-encoded analytic gradients, we propose to use numerical gradients to compute surface normals. If the step size of the numerical gradient is smaller than the hash-encoded grid size, the numerical gradient will be equivalent to the analytical gradient; otherwise, hash entries of multiple grid cells will participate in the surface normal computation. Therefore, backpropagation through the surface normals allows hash entries of multiple grids to receive optimization updates simultaneously. Intuitively, the choice of the step size of the numerical gradient can be interpreted as a smoothing operation on the analytical gradient expression.

[0099] In order to use the numerical gradient to calculate the surface normal, additional SDF sampling is required. Given a sampling point x i =(x i ,y i , z i ), you also need to i Two additional points are sampled in the surrounding standard coordinate system in each axis with a step size ∈ in the neighborhood. For example, the x-component of the surface normal can be expressed as:

[0100]

[0101] Among them, ∈ x = [∈, 0, 0]. A total of six additional SDF samples are required for the numerical surface normal calculation.

[0102] S4, from coarse to fine optimization, a coarse to fine optimization strategy is used to restore the structure of different detail levels of the leopard gill perch. This strategy starts with a coarse approximation and gradually refines to capture complex details. The specific steps are as follows:

[0103] Coarse-to-fine optimization can better reduce the loss and avoid falling into the wrong local minimum. A coarse-to-fine optimization scheme is adopted to reconstruct the surface by gradually increasing the level of detail. Using numerical gradients to calculate high-order derivatives naturally allows this method to perform coarse-to-fine optimization from two perspectives.

[0104] Step size ∈. As mentioned before, the numerical gradient can be interpreted as a smoothing operation, where the step size ∈ controls the resolution and the amount of detail recovered. For numerical surface normal computation, applying a larger ∈ ensures that the surface normals remain consistent over larger scales, resulting in a consistent and continuous surface. On the other hand, applying a smaller ∈ affects smaller regions and avoids smoothing out details. In practice, the step size ∈ is initialized to the coarsest hash grid size and is reduced exponentially with different hash grid sizes throughout the optimization process.

[0105] Hash grid resolution V. If all hash grids are activated at the beginning of the optimization, in order to capture the geometric details of the leopard gill bass, the fine grids must first be "unlearned" from the coarse optimization using a large step size ∈, and then "relearned" with a smaller ∈. If this process is unsuccessful due to optimization convergence, the geometric details will be lost. Therefore, only an initial set of coarse hash grids are enabled, and finer hash grids are progressively activated as ∈ decreases to their spatial size during the optimization process. This avoids the re-learning process and allows better capture of details. In practice, weight decay is also applied to all parameters to avoid single-resolution features dominating the final result.

[0106] S5, curvature regularization, smoothing the surface, smoothing the reconstructed leopard gill perch surface by minimizing the surface curvature of the curvature regularization term. The specific steps are as follows:

[0107] To further promote the smoothness of the reconstructed surface, a prior is introduced by regularizing the mean curvature of the SDF. The mean curvature is computed from the discrete Laplacian operator, otherwise the hash-encoded second-order analytical gradient is zero everywhere when using trilinear interpolation. Curvature Loss The definition is as follows:

[0108]

[0109] Samples for surface normal calculations is sufficient for curvature calculation. The total loss of the leopard gill perch reconstruction is defined as the weighted sum of the individual losses:

[0110]

[0111]

[0112] The 3D position x of the i-th sample i The distance from the camera center is t i The volume density σ of each sampling point i and color c i Prediction is done using coordinate MLP. The rendered color of a given pixel is approximated by the Riemann sum:

[0113]

[0114] Here, α i =1-exp(-σ i δ i ) is the opacity of the i-th ray segment, δ i =t i+1 -t i is the distance between adjacent sampling points, is the cumulative transmittance, which represents the fraction of light that reaches the camera. is the input image c and the rendered image Color loss between.

[0115] Example

[0116] The experimental platform of this embodiment is set to AMD Ryzen 5 3.5GHz CPU and 16GB RAM multi-core processing platform. The code environment is Python 3.8.16.

[0117] Dataset: Experiments are conducted on 30 scenes centered on the Leopard Gillfish dataset. Each scene has 49 or 64 images captured by a robot-held monocular RGB camera. The ground truth is obtained using a structured light scanner.

[0118] Implementation details: Hash encoding resolution spans 2 5 To 2 11 , a total of 16 levels. The channel size of each hash key-value pair is 8. The maximum number of hash key-value pairs per resolution is 2 22 Due to the difference in scene scale, 4 hash resolutions are activated for the leopard gillfish dataset at the beginning of optimization. A new hash resolution is enabled every 5000 iterations when the step size ∈ is equal to its grid cell size. For all experiments, no auxiliary data such as depth are used during optimization.

[0119] like Figure 1 As shown, a method for establishing the phenotype of underwater leopard gill perch based on three-dimensional reconstruction comprises the following steps:

[0120] Step 1: Encode and decode the leopard gill perch scene information using a multi-resolution three-dimensional hash grid, specifically including the following steps:

[0121] (1) Read the leopard gill perch image sequence Ii(x) in Python 3.8.16 language environment;

[0122] (2) Using image EXIF ​​information, calculate the camera focal length, optical center, and radial distortion parameters;

[0123] (3) Extract local feature points and their descriptors from each image using scale-invariant feature transform;

[0124] (4) Use the matched feature points to triangulate the leopard gill perch, estimate the camera's pose, including position and orientation, and generate a preliminary three-dimensional point cloud;

[0125] (5) The input 3D points are converted into high-dimensional features using hash grid coding. Hash grid coding first divides the 3D space into multiple hash grids of different resolutions, and then performs feature encoding on the 3D points in each grid.

[0126] Step 2: Use signed distance function (SDF) to implement implicit surface modeling, including the following steps:

[0127] (1) For each pixel encoded in the hash grid, convert the camera coordinates into world space coordinates to obtain the light direction;

[0128] (2) When the ray does not exceed the maximum distance and the number of steps does not reach the maximum number of steps, continue to trace the ray. According to the starting point and direction of the ray, calculate the signed distance from point p at a specific distance on the ray to the nearest object surface. If the distance from point p to the nearest object surface is less than ε = 0.01, it is considered that the point is very close to the object surface and can be regarded as a point on the surface.

[0129] Step 3: Use numerical gradient to calculate the surface normal of the leopard gill perch, including the following steps:

[0130] (1) For the three components x, y, and z, calculate the infimum p_minus[i] and supremum p_plus[i] of the normal component of each pixel, and use step 2 to calculate their signed distances dist_minus and dist_plus relative to the object surface;

[0131] (2) Get the surface normal.

[0132] Step 4: Use a coarse-to-fine optimization strategy to restore the structure of the leopard gill perch at different levels of detail, including the following steps:

[0133] (1) Initialization: Initialize the step size parameter ∈ to the coarsest hash grid size, taking the value of 0.01, and initialize the hash grid resolution V to 128 3 ;

[0134] (2) Calculate the normal using the method in step 3;

[0135] (3) Adjust the step size ∈, which is reduced exponentially with different hash grid sizes during the entire optimization process. ∈ ;

[0136] Step 5: Smooth the reconstructed surface by minimizing the surface curvature of the curvature regularization term, including the following steps:

[0137] (1) Calculate the initial average curvature of each vertex of the object and Gaussian curvature Among them, A v is the area around vertex v, n is the number of adjacent vertices, k i1 , k i2 is the principal curvature of the i-th adjacent vertex.

[0138] (2) For each round: For each vertex in the grid, calculate the Laplace-Beltrami operator of vertex v where α i is the angle between vertex v and its ith adjacent vertex, v i is the position of the ith adjacent vertex, and v is the position of vertex v. Update vertex position: vnew =v-λΔv;

[0139] (3) Update the mean curvature and Gaussian curvature of each vertex according to the new vertex position;

[0140] (4) Update the normal of each vertex.

[0141] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A method for establishing the phenotype of underwater leopard gill perch based on three-dimensional reconstruction, characterized in that: The following steps are involved: S1, using multi-resolution three-dimensional hash grid to encode and decode the leopard gill perch scene information; S2, using signed distance function SDF to simulate the surface of leopard gill perch to achieve implicit surface modeling; S3, using numerical gradient to calculate the surface normal of leopard gill bass; S4, from coarse to fine optimization, using a coarse to fine optimization strategy to restore the structure of different detail levels of the leopard gill perch; S5. Curvature regularization, smoothing the surface, smoothing the reconstructed leopard gill perch surface by minimizing the surface curvature of the curvature regularization term.

2. The method for establishing the underwater leopard gill perch phenotype based on three-dimensional reconstruction according to claim 1, characterized in that: In the step S1, the method for encoding and decoding the leopard gill perch scene information using a multi-resolution three-dimensional hash grid includes: For input location: Calculate the resolution R of the current level l l and ratio S l : R l =2 base_resolution+l·log2_per_level_scale (2) Compute quantized grid positions g d =floor(p d ·R l ) (4) Get the eigenvalue f by grid hash index grid : f grid =grid[h(g)] (5) Where h is the grid hash function; Then, the weight w is calculated according to the linear interpolation method d w d =p d -g d (6) Interpolate the grid points to obtain the encoded features f encoded f encoded =∑ i w i ·f grid [i] (7) Among them, i is the index of all adjacent grid points; Compute the gradient relative to the input position Update the grid feature gradient g grid :

3. The method for establishing the underwater leopard gill perch phenotype based on three-dimensional reconstruction according to claim 1, characterized in that: In step S2, the sampling position in the voxel grid is determined, and each 3D point x i By grid resolution V l Scaling is performed, expressed as: x i,l =x i ·V l , (10) The coefficients of linear interpolation are The resulting feature vector is: Among them, the rounding position The derivative of the hash code corresponding to the corner point of the local grid unit with respect to the position is expressed as: When x i When crossing the grid cell boundary, the corresponding hash key-value pairs are different, and the eikonal loss defined in equation (5) is back-propagated to the locally sampled hash entries, that is, and When a continuous surface spans multiple mesh cells, the mesh cells generate consistent surface normals and the mesh cells are jointly optimized.

4. The method for establishing the underwater leopard gill perch phenotype based on three-dimensional reconstruction according to claim 1, characterized in that: In step S3, the SDF surface normal is calculated using the analytical gradient When the step size of the numerical gradient is smaller than the hash-encoded grid size, the numerical gradient will be equivalent to the analytical gradient. Otherwise, the hash entries of multiple grid cells will participate in the surface normal calculation. Backpropagation through the surface normal allows the hash entries of multiple grids to receive optimization updates simultaneously. The numerical gradient of the selected step size is interpreted as a smoothing operation on the analytical gradient expression.

5. The method for establishing the underwater leopard gill perch phenotype based on three-dimensional reconstruction according to claim 4, characterized in that: The method for calculating the surface normal by numerical gradient is: additional SDF sampling, given a sampling point x i =(x i ,y i , z i ), in x i Two additional points are sampled in the surrounding standard coordinate system in each axis within a proximity of step size ∈, and the x component of the surface normal is expressed as: Among them, ∈ x = [∈, 0, 0], collecting six additional SDF samples for numerical surface normal calculation.

6. The method for establishing the underwater leopard gill perch phenotype based on three-dimensional reconstruction according to claim 1, characterized in that: In the step S4, numerical gradients are used to calculate high-order derivatives to perform coarse-to-fine optimization from two perspectives: step size ∈ and hash grid resolution V, and the surface is reconstructed by gradually increasing the level of detail; The step size ∈ controls the resolution and amount of detail recovered; for numerical surface normal calculations, applying a larger ∈ ensures that the surface normal remains consistent at larger scales, producing a consistent and continuous surface, and applying a smaller ∈ affects smaller areas and avoids smoothing out details. The step size ∈ is initialized to the coarsest hash grid size and decreases exponentially with different hash grid sizes throughout the optimization process; The hash grid resolution V: All hash grids are activated at the beginning of optimization. To capture the geometric details of the leopard gill bass, fine grids are first "eliminated" from the coarse optimization using a large step size ∈, and then "relearned" with a smaller ∈, enabling an initial set of coarse hash grids, and gradually activating finer hash grids as the step size ∈ decreases to their spatial size during the optimization process, avoiding the re-learning process, and applying weight decay to all parameters to avoid single-resolution features dominating the final result.

7. The method for establishing the phenotype of underwater leopard gill perch based on three-dimensional reconstruction according to claim 1, characterized in that: In step S5, in order to improve the smoothness of the reconstructed surface, the mean curvature of the SDF is regularized, and the mean curvature is calculated from the discrete Laplace operator, and the curvature loss The definition is as follows: Samples for surface normal calculations Sufficient for curvature calculation, the total loss of leopard gill perch reconstruction is defined as the weighted sum of each loss: The 3D position x of the i-th sample i The distance from the camera center is t i , the volume density σ of each sampling point i and color c i Using the coordinate MLP for prediction, the rendered color of a given pixel is approximated as the Riemann sum: Among them, α i =1=exp(-σ i δ i ) is the opacity of the i-th light segment, δ i =t i+1 =t i is the distance between adjacent sampling points, is the cumulative transmittance, which represents the proportion of light reaching the camera, For the input image c and the rendered image Color loss between.

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