Consistent Monte Carlo drawing noise reduction method and device based on neural network and kernel regression

Abstract

The invention discloses a consistent Monte Carlo drawing noise reduction method and device based on a neural network and kernel regression, and the method comprises the steps: carrying out the modeling of a kernel regression mathematical model for Monte Carlo drawing noise reduction, and deducing a theoretical kernel bandwidth expression based on a kernel regression consistency theory and a progressive integral mean square error, and finally, estimating the value of the kernel bandwidth by using a neural network, and iteratively optimizing the kernel bandwidth by using cross bilateral filtering and T test so as to calculate a noise-reduced image. According to the method, the distribution-independent kernel regression model and the kernel regression consistency theory are introduced into the field of Monte Carlo drawing noise reduction, and the kernel bandwidth selection strategy and the iterative optimization strategy are well designed, so that high-quality consistent Monte Carlo drawing noise reduction is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of rendering, and in particular relates to a consistent Monte Carlo rendering denoising method and device based on neural network and kernel regression. Background Art

[0002] High-realistic rendering technology has always been a core research field in computer graphics and is widely used in fields such as digital twins, virtual reality, and film and television special effects. Its main purpose is to generate high-quality images that are close to reality through three-dimensional modeling and light simulation calculations of the rendering scene. Although traditional high-realistic rendering methods, especially the path tracing algorithm based on Monte Carlo sampling, have reached an unprecedented level of realism in generating images, their computational complexity is extremely high and often requires a lot of time and computing resources. The path tracing algorithm calculates the color value of each pixel by simulating the process of light starting from the light source, passing through the reflection and refraction of objects in the scene, and finally reaching the camera. This process involves a large amount of random sampling and complex optical calculations, resulting in the generation of even a single frame of high-quality images. It may take minutes or even hours, which not only greatly increases the production cost, but also seriously limits the widespread application of high-realistic rendering technology in real-time applications or large-scale scene rendering.

[0003] Faced with this challenge, researchers began to explore new solutions. With the rapid development of neural networks in recent years, a series of Monte Carlo rendering denoising methods based on neural networks have emerged. These methods aim to use the powerful regression ability of neural networks to restore low-quality rendering images at low sampling rates (Sample per pixel, SPP for short) to high-quality images, thereby accelerating the high-realistic rendering process. Specifically, the neural network-based denoising method first generates a series of images at low sampling rates through a path tracing algorithm. These images often contain a lot of noise and artifacts due to insufficient sampling points. Subsequently, these low-quality images are input into a pre-trained neural network. The network uses its feature representation and mapping relationship learned on a large amount of data to denoise the input image and output a high-quality image. This method not only greatly shortens the rendering time, but also can maintain the realism and details of the image to a certain extent.

[0004] However, despite the significant progress made in neural network-based denoising methods, there are still some key issues, the most prominent of which is the unbiasedness of the denoising process. Unbiasedness means that the denoising result should reflect the actual lighting conditions of the original scene as accurately as possible, without introducing additional errors or deviations. Although existing neural network denoising methods can achieve satisfactory denoising effects visually, it is often difficult to guarantee unbiasedness mathematically, that is, when exceeding a certain rendering SPP, the denoising result will inevitably introduce additional errors, resulting in lower quality than the rendered image.

[0005] Therefore, how to further improve the unbiasedness of the neural network denoising method while ensuring the denoising efficiency is one of the key research directions at present, in order to achieve more accurate and unbiased high-realistic image generation while maintaining efficient rendering. Summary of the invention

[0006] In view of the above, the purpose of the present invention is to provide a consistent Monte Carlo rendering denoising method and device based on neural network and kernel regression, by introducing distribution-independent kernel regression model and kernel regression consistency theory into the field of Monte Carlo rendering denoising, as well as carefully designed kernel bandwidth selection strategy and iterative optimization strategy, to achieve high-quality consistent Monte Carlo rendering denoising.

[0007] In order to achieve the above-mentioned invention object, the technical solution provided by the present invention is as follows:

[0008] The embodiment of the present invention provides a consistent Monte Carlo rendering denoising method based on neural network and kernel regression, comprising the following steps:

[0009] Modeling the kernel regression mathematical model for Monte Carlo plotting denoising;

[0010] Theoretical kernel bandwidth expression is derived based on kernel regression consistency theory and asymptotic integrated mean square error;

[0011] A neural network is used to estimate the value of the kernel bandwidth and cross-bilateral filtering and T-test are used to iteratively optimize the kernel bandwidth to calculate the denoised image.

[0012] Specifically, the kernel regression mathematical model for Monte Carlo drawing noise reduction is modeled, including:

[0013] The Monte Carlo rendering process is modeled as solving the mapping of scene features to pixel irradiance for each pixel. Based on the mapping, the denoising process is constructed as a kernel regression equation for estimating pixel color. The Nadaraya-Watson kernel regression model is used to model the Monte Carlo rendering process. The kernel regression equation is expressed as:

[0014]

[0015] in, represents the estimation of the color at the center pixel c, X c represents the feature vector at the center pixel c extracted by the neural network, X i represents the feature vector at pixel i extracted by the neural network, Ω c represents the window centered at pixel c, Y i represents the irradiance at pixel i, K h (·) represents kernel function;

[0016] Kernel function K h (·) Using Gaussian kernel function, it is expressed as:

[0017]

[0018] Among them, α c represents the non-negative weight coefficient of the center pixel c, h c represents the kernel bandwidth at the center pixel c, ∈ represents a very small positive number, ‖·‖ 2 represents the L2 norm.

[0019] Specifically, the kernel bandwidth expression based on kernel regression consistency theory and asymptotic integrated mean square error derivation theory includes:

[0020] Under the assumption that the pixel values ​​in the local slice of the drawn image satisfy the homoscedasticity, the asymptotic integrated mean square error It is expressed as:

[0021]

[0022] Among them, C 1 and C 2 are constants, with variance σ 2 =var(Y|X), var(·) represents the variance function, Y represents the pixel irradiance, X represents the scene feature of the pixel, i.e., the feature vector extracted by the neural network, n represents the number of pixels in the image slice, and h represents the kernel bandwidth;

[0023] Theoretical core bandwidth h AMISE The expression is expressed as:

[0024]

[0025] Where C is a constant.

[0026] Specifically, the method of estimating the value of the kernel bandwidth by using a neural network and iteratively optimizing the kernel bandwidth by using cross-bilateral filtering and T-test to calculate the denoised image includes:

[0027] Using neural networks to predict the feature vector of each pixel, the weight coefficient in the kernel function, the weight coefficient in the expression of theoretical kernel bandwidth, and the bandwidth optimization parameter of cross bilateral filtering;

[0028] The initial kernel bandwidth is calculated based on the weight coefficient in the expression of the predicted theoretical kernel bandwidth;

[0029] The bandwidth optimization parameters of the predicted cross-bilateral filter are used to optimize the initial kernel bandwidth to obtain the first optimized kernel bandwidth;

[0030] Based on the predicted feature vector of each pixel, the weight coefficient in the kernel function, and the first optimized kernel bandwidth, the initial denoising result is calculated through the kernel regression equation, a T test is performed based on the denoising result, and a kernel bandwidth correction function is constructed based on the T test to iteratively optimize the first optimized kernel bandwidth to obtain the optimized kernel bandwidth;

[0031] The optimized kernel bandwidth, the predicted feature vector of each pixel, and the weight coefficient of the kernel function are substituted into the kernel regression equation to calculate the pixel color to obtain the final denoised image.

[0032] Specifically, the method of using a neural network to predict the feature vector of each pixel, the weight coefficient in the kernel function, the weight coefficient in the expression of the theoretical kernel bandwidth, and the bandwidth optimization parameter of the cross bilateral filter includes:

[0033] Input G-buffer auxiliary features into the feature extraction neural network NN θ In the above formula, these auxiliary features include noisy irradiance Y, albedo A, normal N, diffuse irradiance D, specular irradiance S, and the variance σ of Y, A, N, D, S features. 2 , expressed as:

[0034] X,α,ω σ ,β A ,β N ,β D ,β S =NN θ (Y,A,N,D,S,σ 2 )

[0035] Among them, X represents the feature vector extracted by the neural network, and α represents the weight coefficient α in the kernel function c ,ω σ The weight coefficient in the expression representing the theoretical kernel bandwidth, β A , β N , β D , β S Represents the bandwidth optimization parameter in cross-bilateral filtering.

[0036] Specifically, the initial kernel bandwidth is calculated based on the weight coefficient in the expression of the predicted theoretical kernel bandwidth, including:

[0037] Under the assumption that the pixel values ​​in the local slice of the drawn image meet the homoscedasticity, the initial kernel bandwidth h AMISE It is expressed as:

[0038]

[0039] Where C is a constant, n represents the number of pixels in the image slice, is the local estimated variance, expressed as:

[0040]

[0041] in, represents the variance at pixel i, Represents the weight coefficient at pixel i.

[0042] Specifically, the bandwidth optimization parameter of the cross bilateral filtering based on prediction uses the cross bilateral filtering to optimize the initial kernel bandwidth to obtain the first optimized kernel bandwidth, including:

[0043] Use cross bilateral filtering to filter the initial kernel bandwidth h AMISE Optimize to get the first optimized kernel bandwidth h aux The formula is expressed as:

[0044]

[0045] in,‖·‖ 2 represents the L2 norm, Respectively represent the weighted estimates of the pixel feature slices corresponding to the A, N, d, and S features, and the calculation formula is as follows:

[0046]

[0047] Among them, F represents the feature, F i represents the feature at pixel i, represents the estimated feature at the center pixel c.

[0048] Specifically, the formula for the T test is expressed as:

[0049]

[0050] Where T represents the value of the T test, Y represents the image drawn by unbiased path tracing, represents the initial denoising result calculated by the kernel regression equation, Represents the standard deviation of the local estimate, ∈ represents a very small positive number.

[0051] Specifically, the kernel bandwidth correction function constructed based on the T test is expressed as:

[0052] h′ aux =h aux *0.5*(1.0-erf(ξ*(T-γ))), where

[0053] Among them, h′ aux represents the optimized kernel bandwidth, h aux represents the first optimization kernel bandwidth, erf(·) represents the error function, and ξ and γ represent the parameters predicted by the bandwidth optimization neural network built based on MLP.

[0054] To achieve the above-mentioned purpose of the invention, the embodiment of the present invention further provides a consistent Monte Carlo rendering denoising device based on neural network and kernel regression, which is implemented by the consistent Monte Carlo rendering denoising method based on neural network and kernel regression, and includes: a kernel regression modeling module, a kernel bandwidth derivation module, and a kernel bandwidth optimization denoising module;

[0055] The kernel regression modeling module is used to model the kernel regression mathematical model of Monte Carlo drawing noise reduction;

[0056] The kernel bandwidth derivation module is used to derive a theoretical kernel bandwidth expression based on kernel regression consistency theory and asymptotic integrated mean square error;

[0057] The kernel bandwidth optimization denoising module is used to estimate the value of the kernel bandwidth by using a neural network and iteratively optimize the kernel bandwidth by using cross-bilateral filtering and T-test to calculate a denoised image.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] (1) The present invention introduces the kernel regression consistency theory and applies it to Monte Carlo rendering noise reduction, providing a theoretical basis for consistency noise reduction.

[0060] (2) The present invention effectively enhances the denoising capability and robustness through the designed kernel bandwidth selection and optimization strategy. The denoising results can restore more details in various scenarios without producing obvious artifacts, thereby achieving more accurate and unbiased high-realistic image generation.

[0061] (3) The denoising consistency provided by the present invention does not rely on other pre-denoising methods, and can maintain efficient rendering without trying multiple pre-denoising methods to obtain the best denoising effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0063] Figure 1 It is a flow chart of a consistent Monte Carlo rendering denoising method based on neural network and kernel regression provided by an embodiment of the present invention;

[0064] Figure 2 is a schematic diagram of the structure of a feature extraction neural network provided by an embodiment of the present invention;

[0065] Figure 3 It is a structural schematic diagram of a consistent Monte Carlo rendering denoising device based on neural network and kernel regression provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0066] To make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation methods described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0067] The inventive concept of the present invention is: in view of the bias problem of the denoising process faced by the denoising method based on neural network in the prior art, the embodiment of the present invention provides a consistent Monte Carlo rendering denoising method and device based on neural network and kernel regression, by modeling the kernel regression mathematical model of Monte Carlo rendering denoising, and deriving the theoretical kernel bandwidth expression based on kernel regression consistency theory and asymptotic integrated mean square error, finally using neural network to estimate the value of kernel bandwidth and using cross bilateral filtering and T test to iteratively optimize the kernel bandwidth to calculate the denoised image, thereby achieving high-quality consistent Monte Carlo rendering denoising.

[0068] Figure 1 FIG. 1 is a flow chart of a consistent Monte Carlo rendering denoising method based on neural network and kernel regression provided by an embodiment of the present invention. Figure 1 As shown, the embodiment provides a consistent Monte Carlo rendering denoising method based on neural network and kernel regression, comprising the following steps:

[0069] S01, Nadaraya-Watson kernel regression model building.

[0070] The path tracing process based on Monte Carlo sampling can be expressed as solving the mapping equation from the scene feature X of the pixel to the pixel irradiance Y. Therefore, the denoising process can be regarded as an estimation of m(X) = E(Y|X). The Nadaraya-Watson kernel regression model is used to model the Monte Carlo rendering process to estimate the color at pixel c and record it as The kernel regression equation is expressed as:

[0071]

[0072] in, represents the color of the center pixel c, X c represents the feature vector at the center pixel c extracted by the neural network, X i represents the feature vector at pixel i extracted by the neural network, Ω c represents the window centered at pixel c, Y i represents the irradiance at pixel i, K h (·) represents the kernel function.

[0073] Kernel function K h (·) Using Gaussian kernel function, it is expressed as:

[0074]

[0075] Among them, α c represents the non-negative weight coefficient of the center pixel c, h c represents the kernel bandwidth at the center pixel c, ∈ represents a very small positive number, ‖·‖ 2 represents the L2 norm.

[0076] S02, derivation of theoretical kernel bandwidth expression.

[0077] The kernel regression consistency theory is defined as: if lim n→∞ h→0 and lim n→∞ nh→∞ is a consistency estimate.

[0078] Under the assumption of homoscedasticity, the asymptotic integrated mean square error It is expressed as:

[0079]

[0080] Among them, C 1 and C 2 are constants, with variance σ 2 =var(Y|X), var(·) represents the variance function, Y represents the pixel irradiance, X represents the scene feature of the pixel, i.e., the feature vector extracted by the neural network, n represents the number of pixels in the image slice, and h represents the kernel bandwidth.

[0081] Theoretical core bandwidth h AMISE The expression is expressed as:

[0082]

[0083] Wherein, C is a constant, and its value in the embodiment is 1.06.

[0084] It can be proved that h AMISE It satisfies the conditions of kernel regression consistency theory, so h AMISE The consistency of kernel regression is ensured.

[0085] S03, pixel-by-pixel feature extraction and parameter prediction.

[0086] Input the 20-dimensional G-buffer auxiliary features into the feature extraction neural network NN θ In (such as Figure 2 These auxiliary features include 3D irradiance Y with noise, 3D albedo A, 3D normal N, 3D diffuse irradiance D, 3D specular irradiance S, and 5D variance σ of Y, A, N, D, S features. 2 , expressed as:

[0087] X,α,ω σ ,β A ,β N ,β D ,β S =NN θ (Y,A,N,D,S,σ 2 )

[0088] Among them, X represents the feature vector extracted by the neural network, and α represents the weight coefficient α in the kernel function c , β A , β N , β D , β S represents the bandwidth optimization parameter in cross-bilateral filtering; ω σ The weight coefficient in the expression representing the theoretical kernel bandwidth is used to estimate h AMISE Local variance in expression and features of cross-bilateral filtering

[0089] S04, initial kernel bandwidth estimation.

[0090] Under the assumption that the pixel values ​​in the local slice of the drawn image meet the homoscedasticity, the initial kernel bandwidth h AMISE It is expressed as:

[0091]

[0092] Wherein, C is a constant, and its value in the embodiment is 1.06; n represents the number of pixels in the image slice, is the local estimated variance, expressed as:

[0093]

[0094] in, represents the variance at pixel i, Represents the weight coefficient at pixel i.

[0095] S05, cross-bilateral filtering optimizes kernel bandwidth.

[0096] Although the initial kernel bandwidth h AMISE The consistency of denoising can be satisfied, but since it only depends on the local variance, low-frequency artifacts will appear in the denoising results of low SPP. Therefore, cross-bilateral filtering is used to optimize the initial kernel bandwidth. AMISE Optimize to get the first optimized kernel bandwidth h aux The formula is expressed as:

[0097]

[0098] in,‖·‖ 2 represents the L2 norm, Respectively represent the weighted average of the pixel feature slices corresponding to the A, N, D, and S features, and the calculation formula is as follows:

[0099]

[0100] Among them, F represents the feature, F i represents the feature at pixel i, Represents the weighted average feature at the center pixel c.

[0101] S06, T-test to optimize kernel bandwidth.

[0102] Get the first optimized kernel bandwidth h after cross bilateral filtering optimization aux , and the features X and weights α generated by the feature extraction network, the Gaussian kernel function combined with kernel regression is used to estimate the initial denoising result Subsequently, a T test is performed on the denoising result and the image Y drawn by unbiased path tracing to obtain a T test value T for each pixel.

[0103] The formula for the T test is:

[0104]

[0105] Where T represents the value of the T test, Y represents the image drawn by unbiased path tracing, represents the initial denoising result calculated by the kernel regression equation, Represents the standard deviation of the local estimate, ∈ represents a very small positive number.

[0106] Finally, a pixel-by-pixel bandwidth correction function is constructed to scale the bandwidth, expressed as:

[0107] h′ aux =h aux *0.5*(1.0-erf(ξ*(T-γ))), where

[0108] Among them, h′ aux represents the optimized kernel bandwidth, h aux represents the first optimization kernel bandwidth, erf(·) represents the error function. ξ and γ represent the bandwidth optimization neural network NN constructed based on MLP. φ The predicted parameters are expressed as:

[0109]

[0110] S07, calculating the final noise reduction result.

[0111] The optimized kernel bandwidth h′ aux , the predicted feature vector X of each pixel and the weight coefficient α in the kernel function are substituted into the kernel regression equation, and a secondary kernel regression is performed to calculate the pixel color to obtain the final denoised image.

[0112] In order to train the neural network involved in the embodiment, it is necessary to obtain the true value of the Monte Carlo drawing result, and calculate the image difference between it and the denoising result as the loss function to jointly optimize all neural network parameters.

[0113] In summary, the consistent Monte Carlo rendering denoising method based on neural network and kernel regression provided by the embodiment of the present invention can achieve more accurate and unbiased high-realistic image generation while maintaining efficient rendering, and will show its great potential and value in more fields.

[0114] Based on the same inventive concept, Figure 3 As shown, the embodiment of the present invention also provides a consistent Monte Carlo rendering denoising device 300 based on neural network and kernel regression, including: a kernel regression modeling module 310, a kernel bandwidth derivation module 320, and a kernel bandwidth optimization denoising module 330.

[0115] The kernel regression modeling module 310 is used to model the kernel regression mathematical model of Monte Carlo drawing noise reduction.

[0116] The kernel bandwidth derivation module 320 is used to derive a theoretical kernel bandwidth expression based on kernel regression consistency theory and asymptotic integrated mean square error.

[0117] The kernel bandwidth derivation module 320 is used to estimate the value of the kernel bandwidth using a neural network and iteratively optimize the kernel bandwidth using cross-bilateral filtering and T-test to calculate the denoised image.

[0118] It should be noted that the consistent Monte Carlo rendering denoising device based on neural network and kernel regression provided in the above embodiment belongs to the same inventive concept as the consistent Monte Carlo rendering denoising method based on neural network and kernel regression. The specific implementation process is detailed in the embodiment of the consistent Monte Carlo rendering denoising method based on neural network and kernel regression, which will not be repeated here.

[0119] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A consistent Monte Carlo rendering denoising method based on neural network and kernel regression, characterized in that: The following steps are involved: Modeling the kernel regression mathematical model for Monte Carlo plotting denoising; Theoretical kernel bandwidth expression is derived based on kernel regression consistency theory and asymptotic integrated mean square error; A neural network is used to estimate the value of the kernel bandwidth and cross-bilateral filtering and T-test are used to iteratively optimize the kernel bandwidth to calculate the denoised image.

2. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 1 is characterized in that: The method of modeling the kernel regression mathematical model of Monte Carlo drawing noise reduction includes: The Monte Carlo rendering process is modeled as solving the mapping of scene features to pixel irradiance for each pixel. Based on the mapping, the denoising process is constructed as a kernel regression equation for estimating pixel color. The Nadaraya-Watson kernel regression model is used to model the Monte Carlo rendering process. The kernel regression equation is expressed as: in, represents the estimation of the color at the center pixel c, X c represents the feature vector at the center pixel c extracted by the neural network, X i represents the feature vector at pixel i extracted by the neural network, Ω c represents the window centered at pixel c, Y i represents the irradiance at pixel i, K h (·) represents kernel function; Kernel function K h (·) Using Gaussian kernel function, it is expressed as: Among them, α c represents the non-negative weight coefficient of the center pixel c, h c represents the kernel bandwidth at the center pixel c, ∈ represents a very small positive number, and ‖·‖2 represents the L2 norm.

3. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 1 is characterized in that: The kernel bandwidth expression based on kernel regression consistency theory and asymptotic integrated mean square error derivation theory includes: Under the assumption that the pixel values ​​in the local slice of the drawn image satisfy the homoscedasticity, the asymptotic integrated mean square error It is expressed as: Among them, C1 and C2 are constants, and the variance σ 2 =var(Y|X), var(·) represents the variance function, Y represents the pixel irradiance, X represents the scene feature of the pixel, i.e., the feature vector extracted by the neural network, n represents the number of pixels in the image slice, and h represents the kernel bandwidth; Theoretical core bandwidth h AMISE The expression is expressed as: Where C is a constant.

4. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 2 is characterized in that: The method of estimating the value of the kernel bandwidth by using a neural network and iteratively optimizing the kernel bandwidth by using cross-bilateral filtering and T-test to calculate the denoised image includes: Using neural networks to predict the feature vector of each pixel, the weight coefficient in the kernel function, the weight coefficient in the expression of theoretical kernel bandwidth, and the bandwidth optimization parameter of cross bilateral filtering; The initial kernel bandwidth is calculated based on the weight coefficient in the expression of the predicted theoretical kernel bandwidth; The bandwidth optimization parameters of the predicted cross-bilateral filter are used to optimize the initial kernel bandwidth to obtain the first optimized kernel bandwidth; Based on the predicted feature vector of each pixel, the weight coefficient in the kernel function, and the first optimized kernel bandwidth, the initial denoising result is calculated through the kernel regression equation, a T test is performed based on the denoising result, and a kernel bandwidth correction function is constructed based on the T test to iteratively optimize the first optimized kernel bandwidth to obtain the optimized kernel bandwidth; The optimized kernel bandwidth, the predicted feature vector of each pixel, and the weight coefficient in the kernel function are substituted into the kernel regression equation to calculate the pixel color to obtain the final denoised image.

5. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 4 is characterized in that: The method of using a neural network to predict the feature vector of each pixel, the weight coefficient in the kernel function, the weight coefficient in the expression of the theoretical kernel bandwidth, and the bandwidth optimization parameters of the cross bilateral filtering include: Input G-buffer auxiliary features into the feature extraction neural network NN θ In the above formula, these auxiliary features include noisy irradiance Y, albedo A, normal N, diffuse irradiance D, specular irradiance S, and the variance σ of Y, A, N, D, S features. 2 , expressed as: X,a,o σ ,b A ,b N ,b D ,b S =NN θ (Y,A,N,D,S,s 2 ) Among them, X represents the feature vector extracted by the neural network, and α represents the weight coefficient α in the kernel function c ,ω σ The weight coefficient in the expression representing the theoretical kernel bandwidth, β A , β N , β D , β S Represents the bandwidth optimization parameter in cross-bilateral filtering.

6. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 5 is characterized in that: The initial kernel bandwidth is calculated based on the weight coefficient in the expression of the predicted theoretical kernel bandwidth, including: Under the assumption that the pixel values ​​in the local slice of the drawn image meet the homoscedasticity, the initial kernel bandwidth h AMISE It is expressed as: Where C is a constant, n represents the number of pixels in the image slice, is the local estimated variance, expressed as: in, represents the variance at pixel i, Represents the weight coefficient at pixel i.

7. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 6 is characterized in that: The bandwidth optimization parameter of the predicted cross-bilateral filtering is used to optimize the initial kernel bandwidth using the cross-bilateral filtering to obtain the first optimized kernel bandwidth, including: Use cross bilateral filtering to filter the initial kernel bandwidth h AMISE Optimize to get the first optimized kernel bandwidth h aux The formula is expressed as: Among them, ‖·‖2 represents the L2 norm, Respectively represent the weighted estimates of the pixel feature slices corresponding to the A, N, D, and S features, and the calculation formula is as follows: Among them, F represents the feature, F i represents the feature at pixel i, represents the estimated feature at the center pixel c.

8. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 1 is characterized in that: The formula for the T test is: Where T represents the value of the T test, Y represents the image drawn by unbiased path tracing, represents the initial denoising result calculated by the kernel regression equation, Represents the standard deviation of the local estimate, ∈ represents a very small positive number.

9. The consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to claim 8 is characterized in that: The kernel bandwidth correction function constructed based on the T test is expressed as: h′ aux =h aux *0.5*(1.0-erf(ξ*(T-γ))), where Among them, h′ aux represents the optimized kernel bandwidth, h aux represents the first optimization kernel bandwidth, erf(·) represents the error function, and ξ and γ represent the parameters predicted by the bandwidth optimization neural network built based on MLP.

10. A consistent Monte Carlo rendering denoising device based on neural network and kernel regression, implemented by the consistent Monte Carlo rendering denoising method based on neural network and kernel regression according to any one of claims 1 to 9, characterized in that: include: Kernel regression modeling module, kernel bandwidth derivation module, kernel bandwidth optimization and denoising module; The kernel regression modeling module is used to model the kernel regression mathematical model of Monte Carlo drawing noise reduction; The kernel bandwidth derivation module is used to derive a theoretical kernel bandwidth expression based on kernel regression consistency theory and asymptotic integrated mean square error; The kernel bandwidth optimization denoising module is used to estimate the value of the kernel bandwidth by using a neural network and iteratively optimize the kernel bandwidth by using cross-bilateral filtering and T-test to calculate a denoised image.

Images