Anisotropic noise generation method based on local tensor integral field feature modulation

Abstract

The invention discloses an anisotropic noise generation method based on local tensor integral field feature modulation, and is applied to the technical field of computer texture generation. The method comprises the following steps: step 1, constructing a global tensor field of spatial anisotropy intensity and direction; step 2, calculating local tensor integral features in a support domain based on the support domain of a Gabor noise kernel function, the local tensor integral features including principal direction features and anisotropic ratio features; step 3, calculating a curvature penalty factor based on the deviation between the local tensor integral feature and the center tensor of the seed point; step 4, based on the local tensor integral features, performing weighted correction on the frequency domain center frequency and Gaussian envelope parameters of the Gabor kernel function; and step 5, generating a final noise texture based on the corrected kernel function. The Gabor kernel function parameter is subjected to weighted correction through the local tensor integral feature and the curvature penalty factor, modulation of the kernel function direction under the high-curvature tensor field is achieved, spectrum leakage, texture fracture and artifacts caused by inconsistent direction changes in the kernel function can be reduced, and the robustness of the kernel function is improved. Therefore, the topological continuity and the simulation fidelity of the anisotropic noise texture at the complex structure are improved.

Description

Technical Field

[0001] This application relates to the fields of computer graphics and procedural texture generation, and in particular to an anisotropic noise generation method based on local tensor integral field feature modulation. Background Technology

[0002] With the rapid development of film and television special effects, digital entertainment, and virtual reality technologies, the demand for realistic simulation of complex textures in nature is increasing. Procedural texture generation technology, due to its advantages such as small storage space, unlimited resolution, and parameterizable control, has become a research hotspot in this field. In anisotropic texture generation, Gabor noise based on tensor fields is one of the mainstream methods.

[0003] Traditional tensor-guided Gabor noise generation methods typically employ point-sampling static mapping. When dealing with high-curvature tensor fields, the flow field direction changes drastically within a small, single range, causing the kernel function's edge direction to deviate significantly from the surrounding flow field direction. This geometric misalignment visually manifests as texture breaks, jagged edges, and high-frequency aliasing artifacts, severely impacting the realism of simulations of complex natural phenomena. Summary of the Invention

[0004] This invention provides an anisotropic noise generation method based on local tensor integral field feature modulation, aiming to solve the problems of spectral leakage and texture breakage caused by inconsistent internal orientation changes of kernel functions when processing high curvature tensor fields using existing static mapping-based Gabor noise, thereby improving the simulation realism of complex natural phenomena.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] Step 1, define any point in space tensor field at the location This is used to describe the anisotropic characteristics at that location. Tensor field The expression is:

[0007] (1)

[0008] In the formula, Represents the rotation matrix. This represents the transpose of a rotation matrix. Represents a diagonal matrix. The expression is:

[0009] (2)

[0010] and Diagonal matrices The maximum and minimum eigenvalues ​​are used to characterize the intensity of anisotropy.

[0011] Step 2, within the effective support region of the Gabor kernel function Integrating within the local area yields a local tensor integral that reflects the average geometric characteristics of the local region. Local tensor integral The expression is:

[0012] (3)

[0013] In the formula, This represents the Gaussian weighted window function. The expression is:

[0014] (4)

[0015] In the formula, Representing a spatial point To the center point distance, This represents the standard deviation of the Gaussian function.

[0016] right Perform eigenvalue decomposition to obtain its principal eigenvectors. and the ratio of local anisotropy . The expression is:

[0017] (5)

[0018] In the formula, and These are the largest and smallest eigenvalues ​​of the diagonal matrix in the local tensor integral, respectively.

[0019] Step 3, based on seed point The central tensor of the global tensor field at that location and the local tensor integral calculated in step 2 Extract the principal direction feature vectors of both. and Calculate the curvature penalty factor . The expression is:

[0020] (6)

[0021] , This represents the absolute value of the dot product of two unit vectors, reflecting the consistency of their directions. This is a hyperparameter used to adjust the sensitivity of the penalty factor to directional deviation; when the directions are consistent, Approaching 1, when the directional deviation is large, Decrease.

[0022] Step 4: Utilize the local tensor integral features calculated in Step 2. The parameters of the Gabor kernel function are reconstructed to ensure that the support shape of the kernel function is aligned with the local flow field geometry. The corrected Gabor kernel function. The expression is:

[0023] (7)

[0024] In the formula, Represented as a point The transpose of the local coordinate vector centered at the center. Indicates according to The inverse of the covariance matrix is ​​calculated. It is based on the ratio of local anisotropy The transpose of the adjusted frequency vector.

[0025] Step 5: Superimpose all kernel functions to obtain the final anisotropic noise texture. . The expression is:

[0026] (8)

[0027] In the formula, This indicates the number of seed points.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] By introducing local tensor integral features, the geometric changes within the kernel function's support domain can be reflected, ensuring that the generated texture has better directional consistency in high curvature regions.

[0030] Introducing curvature penalty factor It can automatically adjust the output intensity in regions where the tensor field changes drastically, thus avoiding texture breakage and artifacts.

[0031] Improving the topological continuity of wood grain at the turning points of annual rings and enhancing the ability to retain details of the core of airflow vortex patterns can enhance the simulation realism of complex natural phenomena while ensuring structural controllability. Attached Figure Description

[0032] Figure 1 This is a diagram illustrating the overall framework of the anisotropic noise generation method based on local tensor integral field feature modulation in this invention.

[0033] Figure 2This is a flowchart of the Gabor kernel function parameter correction in this invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] To illustrate the technical solution described in this invention, specific embodiments are described below.

[0036] like Figure 1 The diagram shows the overall block diagram of an anisotropic noise generation method based on local tensor integral field feature modulation. It includes: S101 Constructing a global tensor field of spatial anisotropy intensity and direction; S102 Calculating local tensor integral features within the support domain of the Gabor noise kernel function, including principal direction features and anisotropic ratio features; S103 Calculating a curvature penalty factor based on the deviation between the local tensor integral features and the seed point center tensor; S104 Modulating the Gaussian envelope parameters of the Gabor kernel function based on the local tensor integral features, and using the curvature penalty factor to perform weighted correction on the kernel function; S105 Superimposing the corrected kernel functions to generate the final noise texture.

[0037] S101 is based on any spatial position within the defined domain. The global tensor field generated at the location is calculated . The expression is:

[0038] (1)

[0039] In the formula, Represents the rotation matrix. This represents the transpose of a rotation matrix. This represents a diagonal matrix. The expression is:

[0040] (2)

[0041] and Diagonal matrices The maximum and minimum eigenvalues ​​are used to characterize the intensity of anisotropy.

[0042] In step S102, for each seed point 𝑝, the effective support domain radius of its Gabor noise kernel function is determined, and within the effective support domain... Internally, use the Gaussian weighted window function. For global tensor fields By performing weighted integration, we obtain the local tensor integral. .

[0043] (3)

[0044] In the formula, This represents the spatial coordinate variables within the support domain. is the offset vector of the integration domain point relative to the center of the seed point. The expression is:

[0045] (4)

[0046] In the formula, This represents the offset vector of the integration domain point relative to the center of the seed point. This represents the standard deviation of the Gaussian function.

[0047] This integration process essentially smooths out the direction of drastic local changes, representing the average trend within the Gabor core support domain.

[0048] S103 is based on the local tensor integral feature With seed point center tensor Calculate the curvature penalty factor based on the deviation between them. . The expression is:

[0049] (5)

[0050] , This represents the absolute value of the dot product of two unit vectors, reflecting the consistency of their directions. This is a hyperparameter used to adjust the sensitivity of the penalty factor to directional deviation. When the directions are consistent, The value approaches 1, and when the directional deviation is large, The value will be less than 1, which has a suppressive effect and prevents textures from overlapping awkwardly in different directions.

[0051] In step S104, the Gaussian envelope parameters of the Gabor kernel function are corrected based on the local tensor integral features. The process steps are as follows: Figure 2 As shown.

[0052] S201: Input the calculated local tensor integral curvature penalty factor .

[0053] S202: Integral over local tensors Perform eigenvalue decomposition to extract local anisotropy ratios and principal direction eigenvectors .

[0054] S203: Construct a rotation matrix using the extracted eigenvectors The Gabor kernel function is oriented and rotated so that its major axis is aligned with the average flow direction; a diagonal matrix is ​​constructed using eigenvalues. Construct the inverse matrix of the corrected covariance matrix. To adjust the Gabor kernel function. Covariance matrix. The expression is:

[0055] (6)

[0056] , Represents the rotation matrix. Represents a diagonal matrix. This represents the transpose of a rotation matrix. Rotation matrix The expression is:

[0057] (7)

[0058] , This represents the eigenvector corresponding to the largest eigenvalue. This represents the eigenvector corresponding to the smallest eigenvalue.

[0059] diagonal matrix The expression is:

[0060] (8)

[0061] , Indicates the anisotropy ratio, The reference scale parameter determines the basic width of the isotropic Gaussian kernel when it is not stretched.

[0062] S204: The frequency of the Gabor kernel is scaled according to the anisotropy ratio φ to maintain visual consistency of the texture under different stretching degrees. The corrected frequency vector is shown below. The expression is:

[0063] = (9)

[0064] In the formula, Represents the rotation matrix. Represents the scaling matrix. Represents the reference frequency vector. Scaling matrix. The expression is:

[0065] (10)

[0066] In the formula, Represents the anisotropy ratio. Reference frequency vector. The expression is:

[0067] (11)

[0068] In the formula, This represents the initial spatial frequency.

[0069] Calculated using the above formula, when the anisotropy ratio As it increases, the frequency component along the flow direction This reduces the density of the generated ripples within the spatial area, ensuring that the density remains consistent with that before stretching, thus avoiding the loss or blurring of texture details caused by stretching.

[0070] S205: Obtain the corrected frequency vector The inverse of the covariance matrix Substitute into the Gabor kernel function formula and multiply by the curvature penalty factor. If the curvature penalty factor is small, the amplitude of the kernel function will be reduced as a whole in the high curvature region to reduce visual interference caused by inconsistency in direction.

[0071] S206: Obtain the corrected Gabor kernel function This is used for the final noise superposition. Corrected Gabor kernel function. The expression is:

[0072] (12)

[0073] In the formula, Represented as a point The transpose of the local coordinate vector centered at the center. Indicates according to The inverse of the covariance matrix is ​​calculated. It is based on the ratio of local anisotropy The transpose of the adjusted frequency vector.

[0074] S105, Set of randomly distributed seed points For each seed point, calculate its corrected kernel function according to the steps described above. Then, all kernel functions are superimposed to obtain the final anisotropic noise texture. Final noise texture The expression is:

[0075] (13)

[0076] In the formula, Indicates the number of seed points. Represents any sampling point in space Relative to seed point position The relative vector.

[0077] The anisotropic noise generation method based on local tensor integral field feature modulation provided by this invention effectively overcomes the problems of kernel function direction misalignment with flow field geometry, easy fracture of texture structure, and generation of spectral artifacts in the prior art under high curvature flow field, and improves the topological continuity and overall simulation realism of anisotropic noise texture in complex flow field regions.

[0078] The above description is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, various improvements, substitutions or modifications can be made to the present invention without departing from the technical principles and core concepts of the present invention, and such improvements, substitutions or modifications should all fall within the protection scope of the present invention.

Claims

1. A method for generating anisotropic noise based on local tensor integral field feature modulation, characterized in that, Includes the following steps: Step 1: Using the eigenvalue decomposition method, at any spatial location within the domain... Generate a global tensor field ; Step 2: Support Domain Based on Gabor Noise Kernel Function Using Gaussian weighting functions to analyze the global tensor field Integral smoothing is performed to calculate the local tensor integral features. ,right Perform eigenvalue decomposition to obtain the eigenvectors of the local tensor integral. and the ratio of local anisotropy characteristics ; Step 3: Utilize the local tensor integral features With seed point center tensor The deviation is used to calculate the curvature penalty factor. ; Step 4: Features based on local tensor integrals The inverse of the covariance matrix reconstructed from eigenvalues and frequency vector Using the inverse of the covariance matrix and frequency vector The Gaussian envelope parameters of the Gabor kernel function are modulated using a curvature penalty factor. The kernel function is weighted and modified to obtain the modified kernel function: （1） in, For the transpose of a column vector, The inverse of the covariance matrix. This is the transpose of the frequency vector; Step 5: Modify the kernel function The final noise texture is generated by superposition. ; （2） in, Number of seed points For the position of the i-th seed point, the kernel function term It is a two-dimensional scalar function that takes a relative position variable as input. For any sampling point in space Relative to the seed point position The relative position vector.

2. The anisotropic noise generation method based on local tensor integral field feature modulation according to claim 1, characterized in that, global tensor field in step 1 The construction needs to be combined with the target anisotropic texture requirements, and precise control of anisotropic intensity and principal direction can be achieved through eigenvalue decomposition. The expression is: （3） In the formula, The rotation matrix is ​​composed of eigenvectors and is used to characterize the principal directions of anisotropy. This represents the transpose of a rotation matrix. Represents a diagonal matrix. The expression is: (4) and Diagonal matrices The maximum and minimum eigenvalues ​​are used to characterize the intensity of anisotropy.

3. The anisotropic noise generation method based on local tensor integral field feature modulation according to claim 1, characterized in that, In step 2, the core of calculating the local tensor integral features is to achieve smooth noise reduction and geometric feature aggregation of the tensor field within the supporting domain through Gaussian weighted integration. The feature vector of the local tensor integral... The expression is: In the formula, To support the spatial coordinate variables within the domain, Let be the offset vector of the integration domain point relative to the center of the seed point. The Gaussian weighted function is used, and the normalization operation of the denominator eliminates the influence of the size of the support domain on the integration result, ensuring that the local tensor integrals of seed points at different locations are comparable.

4. The anisotropic noise generation method based on local tensor integral field feature modulation according to claim 1, characterized in that, In step 3, the principal direction feature vector of the seed point center tensor From the global tensor field in step 1 Eigenvalue decomposition, principal direction eigenvectors of local tensor integrals From step 2 Both the eigenvalues ​​and the eigenvalues ​​need to be pre-normalized to unit vectors to ensure the effectiveness of the inner product calculation.

5. The anisotropic noise generation method based on local tensor integral field feature modulation according to claim 1, characterized in that, In step 4, the parameter correction of the Gabor kernel function needs to be achieved through the inverse of the covariance matrix. and frequency vector Constructing a rotation matrix using eigenvectors Construct a diagonal matrix D using eigenvalues, and the inverse of the covariance matrix. The covariance matrix is ​​derived from the two matrices and the diagonal matrix mentioned above. The expression is: （6） In the formula, Represents the rotation matrix. Represents a diagonal matrix. Represents the transpose of a rotation matrix, a diagonal matrix. The expression is: （7） , Indicates the anisotropy ratio, The reference scale parameter determines the basic width of the isotropic Gaussian kernel when it is not stretched.

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