A method for predicting surface reflectance properties based on a microfacet model guided neural process

Abstract

A neural process prediction method for surface reflection characteristics based on micro-surface model guidance is proposed. Current BRDF representations based on analytical models or deterministic neural networks perform poorly in complex material modeling and sparse sampling scenarios. There is a lack of standardized and accurate probabilistic prediction methods for tasks related to quantifying prediction uncertainty and analyzing and controlling error propagation. This invention forms an initial model by training a network on a completed BRDF dataset and applying physical guidance constraints. Based on the initial model, a probabilistic model of the bidirectional reflection distribution function is formed to create a family of BRDF function probability distribution models. The prediction process for reflection characteristics in unobserved directions is then completed based on the established family of BRDF function probability distribution models.

Description

Technical Field

[0001] Specifically, this invention is a method for predicting neural processes of surface reflection characteristics based on a micro-surface model. Background Technology

[0002] Traditional analytical model-based BRDF representations describe surface reflection behavior through manually designed mathematical formulas with explicit physical meaning. The core idea is to decompose the material's reflection characteristics into diffuse and specular terms, and then model different reflection components using predefined functional forms. For example, Lambert and Oren-Nayar models are used to describe diffuse reflection, while Phong, Blinn-Phong, Cook-Torrance, and GGX models are used to characterize specular reflection. These methods have a fixed structure, a small number of parameters, and a degree of physical interpretability, allowing control over the reflection characteristics of ideal materials by adjusting a few parameters such as roughness, reflectivity, and normal distribution. However, analytical models rely on prior knowledge, and their functional forms and expressive power are strictly limited. They struggle to accurately characterize complex reflection phenomena in real materials, such as multi-scale microstructures, anisotropy, multilayer interference, and dispersion effects. Their fitting accuracy to measured BRDF data is limited, resulting in significant limitations in representing complex materials.

[0003] BRDF representation methods based on deterministic neural networks abandon the method of manually pre-setting formulas. Instead, they use structures such as multilayer perceptrons and convolutional networks as general function approximators, directly learning the nonlinear mapping relationship between incident direction, exit direction, material parameters, and reflectivity from a large amount of BRDF measurement or simulation data. Compared with analytical models, this type of method has stronger expressive power and can fit more complex and refined reflection distributions. However, since it is a purely data-driven black-box model, the network only uses data error as the optimization objective during training and does not explicitly embed physical constraints such as energy conservation, reciprocity, and optical path reversibility. Therefore, it is difficult to guarantee the physical consistency of the output results, and artifacts such as reflection energy overflow, abnormal angle distribution, and violation of optical laws are prone to occur. At the same time, the generalization ability of deterministic neural networks is highly dependent on the coverage of training data. Significant errors will occur in extrapolation scenarios such as sparse viewpoints, grazing angles, and unseen material types. Moreover, the model lacks an interpretable physical structure and cannot describe the optical behavior of materials at the mechanistic level. It still has obvious defects in stability, reliability, and cross-scene transferability. In summary, compared with BRDF representations based on analytical models or deterministic neural networks, there is currently a lack of standardized and accurate prediction methods for complex material modeling, sparse sampling scenarios, and uncertainty representation. Summary of the Invention

[0004] This invention provides a method for predicting the neural processes of surface reflection characteristics based on a micro-surface model, in order to solve the above-mentioned problems.

[0005] A neural process prediction method for surface reflectance properties based on a micro-surface model guides the prediction of surface reflectance properties. This method trains a network on a constructed BRDF dataset and applies physical guidance constraints to form an initial model. Based on this initial model, the method predicts the bidirectional reflectance distribution function. Probabilistic modeling is performed to form a family of BRDF function probability distribution models. Based on the established family of BRDF function probability distribution models, the prediction process of reflection characteristics in unobserved directions is completed.

[0006] As a preferred option: the BRDF dataset is a dataset used to characterize the reflection behavior of different materials under various combinations of incident and exit directions. The construction process of the BRDF dataset is as follows:

[0007] Data acquisition process: For each material to be modeled, the incident direction is measured within the unit hemispherical directional space. and the direction of launch Sampling is performed using uniform sampling, layered sampling, and / or importance-based directional sampling to ensure that the sampled data covers the reflection characteristics of the specular reflection area, highlight area, and diffuse reflection area. For each set of reflection characteristics, the directional pair... Record the corresponding BRDF values. This forms the basic sample pairs, and the corresponding calculation formula is:

[0008]

[0009] In the above formula, when using an analytical physical model to generate data, the reflection value is calculated based on the preset material parameters and the corresponding physical BRDF function, ensuring that the data meets the physical constraints of energy conservation, non-negativity, and directional symmetry. When using measured data, the original measurement data is interpolated, denoised, or normalized to ensure that the impact of measurement errors on model training is reduced and the consistency of the data on the numerical scale is guaranteed.

[0010] Data organization process: The collected data is processed and organized. The complete BRDF sampling set corresponding to each material is regarded as a function instance, and several samples are randomly selected from each function instance to form a context subset. The remaining samples are used as the target prediction set. The context subset is used to provide known observation conditions to the neural stochastic process network, and the target set is used to supervise the model's ability to predict reflection values ​​in unobserved directions. The formal representation of the construction method is as follows:

[0011]

[0012] In the above formula, This represents the complete BRDF dataset corresponding to a single material.

[0013] The number of context samples can be adjusted during training. Random variations are introduced to ensure the robustness of the model under different sampling densities, enabling the network to work stably under both few and many sample conditions. By transforming the directional input into a parameterized form using half-angle vectors and local coordinate system representations, the dataset is ensured to have the required expressive performance for directional changes. The BRDF dataset formed through data collection and organization is a dataset that fully covers the high-dimensional reflection characteristics of BRDF.

[0014] As a preferred approach, the process of training the network and applying physical guidance constraints to form the network architecture after constructing the BRDF dataset is as follows:

[0015] After forming a BRDF dataset from the observed finite BRDF sampling data, context set processing is performed, and the corresponding calculation formula is as follows:

[0016] ;

[0017] In the above formula, For direction-oriented input, The above formula represents the corresponding reflection value; it indicates that the target is within a given set of contexts. Predict arbitrary target input under the given conditions The probability distribution of the BRDF at that location;

[0018] The network architecture employs a composite structure of encoder, aggregator, and decoder, and utilizes a context encoder network. Each context sample is mapped to a latent space representation, calculated using the following formula:

[0019]

[0020] In the above formula, It consists of a multi-layer fully connected neural network, whose inputs include half-angle vectors, spherical coordinates, or directional parameterizations of the local tangent space;

[0021] At the level of stochastic process modeling, latent random variables are introduced. The uncertainty at the BRDF function level is characterized by its conditional distribution, which is parameterized by the context. The processing formula is as follows:

[0022]

[0023] In the above formula, and All are outputs from neural networks. and Let Z and Z represent the two distribution parameters of the latent variable z under the assumption of normal distribution.

[0024] Arbitrary target input via decoder network In conditional random variables and context representation Under the combined effect of these factors, the predicted distribution parameters of the BRDF are output. These parameters are used to quantitatively assess the mean prediction and uncertainty of the BRDF values. The corresponding calculation formula is as follows:

[0025]

[0026] In the above formula, Let represent the conditional probability of y given x and z, where z represents the latent variable that locates the current mapping position in the global function space;

[0027] After determining the predicted distribution parameters of the BRDF, physical prior information is explicitly embedded in the network output layer or loss function. By normalizing or integrating the predicted BRDF, the predicted distribution parameters of the BRDF are ensured to satisfy the energy conservation condition. The calculation formula is as follows:

[0028]

[0029] For isotropic or anisotropic materials, symmetry constraints are introduced into the network input parameterization or weight sharing structure. After calculating the predicted distribution parameters of BRDF to satisfy the energy conservation condition, an initial model is obtained. That is, while maintaining the high expressive performance of the neural network, the network architecture is formed by modeling the stochastic process of the uncertainty of the BRDF function. The network architecture is an initial model that improves the reconstruction accuracy and physical consistency under finite sampling conditions, thus completing the initial process of network architecture modeling.

[0030] As a preferred option: Based on the initial model, the bidirectional reflection distribution function... The process of performing probabilistic modeling to form the BRDF function family probability distribution model is a BRDF neural compact processing process based on the physical guidance of the micro-surface model. The specific process is as follows:

[0031] The BRDF function family probability distribution model is a model that uses a physical reflection model to constrain the function space and describe the probability distribution of the BRDF function family. The BRDF function family probability distribution model combines compactness with accurate reflection of the physical laws of real materials, using the surface bidirectional reflection distribution function as an example. , middle and These represent the incident light direction and the observation direction, respectively; for isotropic surfaces, BRDF is parameterized by angles as follows: ,exist In , These are the incident polar angle, the observed polar angle, and the azimuth difference, respectively; the training data consists of a set of BRDF samples, namely... ,in ;

[0032] Within the neural process framework, the BRDF of each material is considered as a function instance sampled from a certain function distribution; therefore, the model learns the conditional distribution. ,in For a small number of observation samples contextset, The target set is the set of observations to be predicted. The encoder first extracts features from each observation pair, obtains the mean and covariance of the latent variables through a parametric network, and thus constructs the latent variable distribution process. The calculation formula is as follows:

[0033] ;

[0034] In the above formula, These are low-dimensional latent variables describing the microstructural characteristics of materials. During training, they are sampled from the aforementioned distribution through reparameterization. This ensures that the model accurately represents the relationship between the reflection functions of different materials in the latent space. The reflection process is physically modeled using a micro-surface model, and the expression for BRDF is:

[0035]

[0036] In the above formula, Let be the normal distribution function of the micro-surface. For Fresnel items, For geometric occlusion items, It is a half-angle vector.

[0037] As a preferred approach: In the process of combining neural representations and physical models, the decoder does not directly output the BRDF value, but instead determines it based on the input direction. With latent variables Key parameters for predicting microsurface models That is, combined roughness With Fresnel reflectivity The calculation is performed using the following formula:

[0038]

[0039] The predicted parameters are then substituted into the micro-surface model to calculate the corresponding BRDF value. The calculation formula is as follows:

[0040]

[0041] The above formula quantitatively calculates the relationship between material parameters and angles, while the overall shape of the reflection function is guaranteed by the physical model, thus completing the process of narrowing the function search space through calculation.

[0042] As a preferred approach: during the prediction of uncertainty, the decoder also outputs the observation noise variance. Thus, the conditional probability model is obtained, and the corresponding calculation formula for the conditional probability model is:

[0043]

[0044] During the training phase, based on latent variables The existence of is solved through variational inference. Specifically, a posterior approximation is introduced. The maximum change is determined by the lower bound, and the corresponding calculation formula is:

[0045]

[0046] In the above formula, the first term The first term is the reconstruction term, used to measure the difference between the model's predicted BRDF and the actual observations; the second term is the KL divergence, used to constrain the distance between the posterior and prior distributions of the latent variables, ensuring that the latent space maintains a good structure; when the observed noise follows a Gaussian distribution, the corresponding reconstruction term is:

[0047]

[0048] In the above formula, in addition to statistical modeling, several physical consistency constraints are introduced during the training process to further ensure the rationality of BRDF. Among them, to satisfy the energy conservation condition and ensure that the reflected energy on the incident hemisphere does not exceed the incident energy, the calculation formula is as follows:

[0049]

[0050] During training, numerical integration can be performed over the random sampling direction, and a penalty term can be added for violations of constraints. Furthermore, according to the reciprocity principle, the BRDF should satisfy the following formula:

[0051]

[0052] In the above formula, the constraint is further implemented by calculating the error by exchanging the incident and observation directions and adding a loss function; based on the statistical reconstruction error, the latent variable regularization term, and the physical constraint term, the final formula for calculating the training objective is as follows:

[0053]

[0054] In the above formula, For physical consistency constraints, and As the weighting coefficients, during training, a material sample is randomly selected from the BRDF dataset, and the observation set and target set are randomly divided from its sample set; the observation set is used to estimate the latent variable distribution. The target set is used to calculate the prediction error and update the model parameters. By repeatedly performing the above process, the model gradually learns the statistical structure between different materials in the latent variable space, ensuring that the BRDF function of each material is derived from a low-dimensional latent variable. Simply provide a description.

[0055] As a preferred approach: the prediction process for the reflection characteristics of unobserved directions is completed based on the established BRDF function family probability distribution model. For any unobserved direction... The probability distribution of the BRDF values ​​in the corresponding direction of the model output is as follows: The distribution is parameterized by mean and variance. When the number of sampling points in the context sample set is between 6 and 16, the variance of the model prediction ranges from 0.05 to 0.2, and the mean is dominated by the physical prior of the micro-surface model, exhibiting a smooth interpolation state that conforms to the physical laws of energy conservation and reciprocity. When the minimum number of sampling points in the context sample set is 32, the variance of the model prediction ranges from 0.005 to 0.03, and the mean is dominated by observation data, exhibiting an accurate fit to the complex reflection details of the real material, and the prediction error is lower than the preset threshold in densely sampled areas.

[0056] Compared with existing technologies, this invention provides a method for predicting the neural processes of surface reflection characteristics based on micro-surface models, which has the following advantages:

[0057] This invention trains the constructed BRDF dataset through network training and physical guidance constraint processing to form an initial model, and then applies the initial model to the bidirectional reflection distribution function. This invention employs probabilistic modeling to develop a BRDF function family probability distribution model that combines stability, reliability, and cross-scene transferability. Based on this model, it completes the corresponding prediction process for reflection characteristics in unobserved directions. By introducing a neural stochastic process framework, this invention treats the BRDF modeling problem as a conditional stochastic function modeling problem. It learns the mapping relationship from observed reflection samples to the complete BRDF function distribution, achieving probabilistic prediction of unobserved reflection directions. Furthermore, this invention incorporates physical reflection mechanisms to constrain and guide the model structure and learning process, thereby enhancing the model's physical rationality while ensuring expressive flexibility.

[0058] This invention utilizes neural networks to parameterize the mean function and covariance structure of stochastic processes. By introducing prior physical information such as energy conservation and isotropic or anisotropic reflection characteristics, the network output is constrained or regularized, ensuring that the resulting BRDF representation conforms to physical laws and possesses good data adaptability. This invention can effectively reconstruct high-dimensional BRDF functions under limited sampling data conditions and naturally characterize reflection uncertainty. It exhibits particularly accurate adaptation advantages in complex material modeling, sparse sampling scenes, and uncertainty representation, making it suitable for widespread application in realistic rendering, material editing, reverse rendering, visual simulation, and other related fields. Attached Figure Description

[0059] Figure 1 This is a flowchart of the present invention;

[0060] Figure 2 A block diagram of the BRDF neural process representation method guided by micro-surface models. Detailed Implementation

[0061] 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.

[0062] Specific implementation method one: Combining Figure 1 and Figure 2 This embodiment describes a micro-surface model-guided reflection characteristic prediction method. The method primarily involves training a network and applying physical guidance constraints to the constructed BRDF dataset to form an initial model. Based on this initial model, the bidirectional reflection distribution function is then analyzed. Probabilistic modeling is performed to form a family of BRDF function probability distribution models. Based on the established family of BRDF function probability distribution models, the prediction process of reflection characteristics in unobserved directions is completed.

[0063] Furthermore, the BRDF dataset is a dataset used to characterize the reflection behavior of different materials under various combinations of incident and exit directions. The construction process of the BRDF dataset is as follows:

[0064] Data acquisition process: For each material to be modeled, the incident direction is measured within the unit hemispherical directional space. and the direction of launch Sampling is performed using uniform sampling, layered sampling, and / or importance-based directional sampling to ensure that the sampled data covers the reflection characteristics of the specular reflection area, highlight area, and diffuse reflection area. For each set of reflection characteristics, the directional pair... Record the corresponding BRDF values. This forms the basic sample pairs, and the corresponding calculation formula is:

[0065]

[0066] In the above formula, when using an analytical physical model to generate data, the reflection value is calculated based on the preset material parameters and the corresponding physical BRDF function, ensuring that the data meets the physical constraints of energy conservation, non-negativity, and directional symmetry. When using measured data, the original measurement data is interpolated, denoised, or normalized to ensure that the impact of measurement errors on model training is reduced and the consistency of the data on the numerical scale is guaranteed.

[0067] Data organization process: The collected data is processed and organized. The complete BRDF sampling set corresponding to each material is regarded as a function instance. Several samples are randomly selected from each function instance to form a context subset. The remaining samples are used as the target prediction set. The context subset is used to provide known observation conditions to the neural stochastic process network, and the target set is used to supervise the model's ability to predict reflection values ​​in unobserved directions. The formal representation of the construction method is as follows:

[0068]

[0069] In the above formula, This represents the complete BRDF dataset corresponding to a single material.

[0070] The number of context samples can be adjusted during training. Random variations are introduced to ensure the robustness of the model under different sampling densities, enabling the network to work stably under both few and many sample conditions. By transforming the directional input into a parameterized form using half-angle vectors and local coordinate system representations, the dataset is ensured to have the required expressive performance for directional changes. The BRDF dataset formed through data collection and organization is a dataset that fully covers the high-dimensional reflection characteristics of BRDF.

[0071] This invention comprehensively covers the high-dimensional reflection characteristics of BRDF by sequentially collecting and organizing data to form a BRDF dataset, which meets the modeling requirements of natural adaptive neural stochastic processes for functions, conditions, and uncertainties, and provides a reliable data foundation for subsequent network training and the introduction of physical guidance constraints.

[0072] Furthermore, the process of training the network and applying physical guidance constraints to the constructed BRDF dataset to form the network architecture is as follows:

[0073] After forming a BRDF dataset from the observed finite BRDF sampling data, context set processing is performed, and the corresponding calculation formula is as follows:

[0074] ;

[0075] In the above formula, For direction-oriented input, The above formula represents the corresponding reflection value; it indicates that the target is within a given set of contexts. Predict arbitrary target input under the given conditions The probability distribution of the BRDF at that location;

[0076] The network architecture employs a composite structure of encoder, aggregator, and decoder, and utilizes a context encoder network. Each context sample is mapped to a latent space representation, calculated using the following formula:

[0077]

[0078] In the above formula, It consists of a multi-layer fully connected neural network, whose inputs include half-angle vectors, spherical coordinates, or directional parameterizations of the local tangent space;

[0079] At the level of stochastic process modeling, latent random variables are introduced. The uncertainty at the BRDF function level is characterized by its conditional distribution, which is parameterized by the context. The processing formula is as follows:

[0080]

[0081] In the above formula, and All are outputs from neural networks. and Let Z and Z represent the two distribution parameters of the latent variable z under the assumption of normal distribution.

[0082] Arbitrary target input via decoder network In conditional random variables and context representation Under the combined effect of these factors, the predicted distribution parameters of the BRDF are output. These parameters are used to quantitatively assess the mean prediction and uncertainty of the BRDF values. The corresponding calculation formula is as follows:

[0083]

[0084] In the above formula, Let represent the conditional probability of y given x and z, where z represents the latent variable that locates the current mapping position in the global function space.

[0085] After determining the predicted distribution parameters of the BRDF, physical prior information is explicitly embedded in the network output layer or loss function. By normalizing or integrating the predicted BRDF, the predicted distribution parameters of the BRDF are ensured to satisfy the energy conservation condition. The calculation formula is as follows:

[0086]

[0087] For isotropic or anisotropic materials, symmetry constraints are introduced into the network input parameterization or weight sharing structure. After calculating the predicted distribution parameters of BRDF to satisfy the energy conservation condition, an initial model is obtained. That is, while maintaining the high expressive performance of the neural network, the network architecture is formed by modeling the stochastic process of the uncertainty of the BRDF function. The network architecture is an initial model that improves the reconstruction accuracy and physical consistency under finite sampling conditions, thus completing the initial process of network architecture modeling.

[0088] Furthermore, based on the initial model, the bidirectional reflection distribution function... The process of performing probabilistic modeling to form the BRDF function family probability distribution model is a BRDF neural compact processing process based on the physical guidance of the micro-surface model. The specific process is as follows:

[0089] The BRDF function family probability distribution model is a model that uses a physical reflection model to constrain the function space and describe the probability distribution of the BRDF function family. The BRDF function family probability distribution model combines compactness with accurate reflection of the physical laws of real materials, using the surface bidirectional reflection distribution function as an example. , middle and These represent the incident light direction and the observation direction, respectively; for isotropic surfaces, BRDF is parameterized by angles as follows: ,exist In , These are the incident polar angle, the observed polar angle, and the azimuth difference, respectively; the training data consists of a set of BRDF samples, namely... ,in ;

[0090] Within the neural process framework, the BRDF of each material is considered as a function instance sampled from a certain function distribution; therefore, the model learns the conditional distribution. ,in For a small number of observation samples (contextset). The target set to be predicted; given the set of observations. The encoder first extracts features from each observation pair, obtains the mean and covariance of the latent variables through a parametric network, and thus constructs the latent variable distribution process. The calculation formula is as follows:

[0091]

[0092] In the above formula, These are low-dimensional latent variables describing the microstructural characteristics of materials. During training, they are sampled from the aforementioned distribution using reparameterization techniques. This ensures that the model accurately represents the relationship between the reflection functions of different materials in the latent space. The reflection process is physically modeled using a micro-surface model, and the expression for BRDF is:

[0093]

[0094] In the above formula, Let be the normal distribution function of the micro-surface. For Fresnel items, For geometric occlusion items, It is a half-angle vector.

[0095] In the process of combining neural representations with physical models, the decoder does not directly output BRDF values, but rather determines them based on the input direction. With latent variables Key parameters for predicting microsurface models That is, combined roughness With Fresnel reflectivity The calculation is performed using the following formula:

[0096]

[0097] The predicted parameters are then substituted into the micro-surface model to calculate the corresponding BRDF value. The calculation formula is as follows:

[0098]

[0099] The above formula quantitatively calculates the relationship between material parameters and angles, while the overall shape of the reflection function is guaranteed by the physical model, thus completing the process of narrowing the function search space through calculation.

[0100] In the process of predicting uncertainty, the decoder also outputs the observation noise variance. Thus, the conditional probability model is obtained, and the corresponding calculation formula for the conditional probability model is:

[0101]

[0102] During the training phase, based on latent variables The existence of is solved through variational inference. Specifically, a posterior approximation is introduced. The maximum change is determined by the lower bound, and the corresponding calculation formula is:

[0103]

[0104] In the above formula, the first term The first term is the reconstruction term, used to measure the difference between the model's predicted BRDF and the actual observations; the second term is the KL divergence, used to constrain the distance between the posterior and prior distributions of the latent variables, ensuring that the latent space maintains a good structure; when the observed noise follows a Gaussian distribution, the corresponding reconstruction term is:

[0105]

[0106] In the above formula, in addition to statistical modeling, several physical consistency constraints are introduced during the training process to further ensure the rationality of BRDF. Among them, to satisfy the energy conservation condition and ensure that the reflected energy on the incident hemisphere does not exceed the incident energy, the calculation formula is as follows:

[0107]

[0108] During training, numerical integration can be performed over the random sampling direction, and a penalty term can be added for violations of constraints. Furthermore, according to the reciprocity principle, the BRDF should satisfy the following formula:

[0109]

[0110] In the above formula, the constraint is further implemented by calculating the error by exchanging the incident and observation directions and adding a loss function; based on the statistical reconstruction error, the latent variable regularization term, and the physical constraint term, the final formula for calculating the training objective is as follows:

[0111]

[0112] In the above formula, For physical consistency constraints, and As the weighting coefficients, during training, a material sample is randomly selected from the BRDF dataset, and the observation set and target set are randomly divided from its sample set; the observation set is used to estimate the latent variable distribution. The target set is used to calculate the prediction error and update the model parameters. By repeatedly performing the above process, the model gradually learns the statistical structure between different materials in the latent variable space, ensuring that the BRDF function of each material is derived from a low-dimensional latent variable. Simply provide a description.

[0113] Based on the above, the process of predicting the reflection characteristics of unobserved directions using the established BRDF function family probability distribution model is as follows: For any or any unobserved direction... The probability distribution of the BRDF value output by the model in this direction is as follows: The distribution is parameterized by the mean and variance. When the number of sampling points in the context sample set is small, the variance of the model prediction is large, and the mean is mainly dominated by the physical prior of the micro-surface model, reflecting a smooth interpolation that conforms to physical laws such as energy conservation and reciprocity. When the number of sampling points in the context sample set is large, the variance of the model prediction is small, and the mean is driven by the observation data, which can accurately fit the complex reflection details of the real material, and the prediction error is lower than the preset threshold in densely sampled areas.

[0114] The optimal values ​​for the relevant data, as determined by calculations and statistics from the relevant system, are as follows:

[0115] The prediction process for the reflection characteristics of unobserved directions is completed based on the established BRDF function family probability distribution model. For any unobserved direction... The probability distribution of the BRDF values ​​in the corresponding direction of the model output is as follows: The distribution is parameterized by mean and variance. When the number of sampling points in the context sample set is between 6 and 16, the variance of the model prediction ranges from 0.05 to 0.2, and the mean is dominated by the physical prior of the micro-surface model, exhibiting a smooth interpolation state that conforms to the physical laws of energy conservation and reciprocity. When the minimum number of sampling points in the context sample set is 32, the variance of the model prediction ranges from 0.005 to 0.03, and the mean is dominated by observation data, exhibiting an accurate fit to the complex reflection details of the real material, and the prediction error is lower than the preset threshold in densely sampled areas.

[0116] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One, combined with... Figure 2 As shown, in this embodiment, the present invention employs a joint learning framework of probabilistic encoding aggregation and physical constraint decoding. The complete process is as follows:

[0117] First, the original sample features , Features of contrast / conditional samples Common input encoder The corresponding hidden state representation of the original sample is obtained through feature encoding. Compared with the corresponding sample The two sets of hidden states are then input into aggregator a, which outputs the Gaussian distribution parameters corresponding to the original samples. Gaussian distribution parameters corresponding to the comparison sample And by minimizing the KL divergence loss between the two sets of Gaussian distributions, combined with the formula The distribution regularization and contrast constraints of the latent space are completed to optimize the probabilistic modeling stage.

[0118] In the decoding and prediction phase, latent variables are sampled from the aggregated distribution. and combined with auxiliary features Input multi-branch decoder network: Decoder Output feature D, decoder Output feature F, decoder Output feature G; then substitute D, F, and G into the physical prior formula. The prediction results were calculated. Finally With real labels By comparison, the end-to-end optimization of the prediction task is achieved by minimizing the L2 loss, and the prediction process of combining probabilistic uncertainty modeling and physical optical prior constraints is realized as a whole.

[0119] Specific Implementation Method Three: This implementation method is a further limitation of Specific Implementation Method One or Two. In this implementation method, the BRDF neural stochastic process representation method based on physical guidance adopts a conditional neural stochastic process network structure for the bidirectional reflection distribution function. Probabilistic modeling is performed, where and These represent the incident and exit directions, respectively. This invention treats the BRDF as a random function defined in the direction space, and learns its conditional distribution to predict the reflection characteristics of unobserved directions. Specifically, the implementation includes the following:

[0120] First, the dataset creation process: To train and validate the physics-guided BRDF neural stochastic process representation method, a BRDF dataset for reflection characteristic modeling is first constructed. This dataset characterizes the reflection behavior of different materials under various combinations of incident and outgoing directions, and can be derived from physical measurement data, data generated by analyzing BRDF models, or a combination of both.

[0121] During the data acquisition phase, for each material to be modeled, the incident direction is defined within the unit hemispherical directional space. and the direction of launch Sampling is performed. Sampling methods can include uniform sampling, layered sampling, or importance-based directional sampling to cover key reflection features such as specular reflection areas, specular highlight areas, and diffuse reflection areas. For each pair of directions... Record the corresponding BRDF values. This forms the basic sample pairs:

[0122]

[0123] When using analytical physical models to generate data, reflection values ​​can be calculated using physically consistent BRDF functions based on preset material parameters to ensure that the data meets physical constraints such as energy conservation, non-negativity, and directional symmetry. When using measured data, interpolation, denoising, or normalization can be performed on the original measurement data to reduce the impact of measurement errors on model training and ensure data consistency across numerical scales.

[0124] In the data organization phase, this invention treats the complete BRDF sampling set corresponding to each material as a function instance, and further randomly selects several samples from it to form a context subset. The remaining samples are used as the target prediction set. The context subset provides known observation conditions to the neural stochastic process network, while the target set supervises the model's ability to predict reflection values ​​in unobserved directions. This construction method can be formally represented as:

[0125] in, This represents the complete BRDF dataset corresponding to a single material. To improve the robustness of the model under different sampling densities, the number of context samples can be adjusted during training. By introducing random variations, the network can operate stably under both few-sample and many-sample conditions. Furthermore, by transforming the directional input into different parameterization forms, such as half-angle vectors or local coordinate system representations, the dataset's ability to express directional changes can be enhanced.

[0126] Through the above-described dataset creation process, the data constructed by this invention can not only fully cover the high-dimensional reflection characteristics of BRDF, but also naturally adapt to the modeling requirements of neural stochastic processes for "function-condition-uncertainty", providing a reliable data foundation for subsequent network training and the introduction of physical guidance constraints.

[0127] Second: The implementation process of the network architecture. Specifically, let the observed finite BRDF sampling data be the context set.

[0128] in Indicates the direction relative to the input. This represents the corresponding reflection value. The goal is to achieve this within a given set of contexts. Predict arbitrary target input under the given conditions The probability distribution of the BRDF at that location.

[0129] The network as a whole adopts an encoder-aggregator-decoder structure. First, through the context encoder network... Map each context sample to a latent space representation:

[0130] in It consists of a multi-layer fully connected neural network, whose input can include orientation parameterization, such as half-angle vectors, spherical coordinates, or local tangent space representation, to enhance the expressive power of orientation-related features.

[0131] Subsequently, by pooling all contextual implicit representations using a permutation-invariant aggregation operator, the conditional representation of the global stochastic process is obtained:

[0132] Among them, aggregation operator The mean, weighted mean, or attention mechanism can be used to ensure that the model is insensitive to the order of context samples and can adapt to different amounts of observation data.

[0133] At the level of stochastic process modeling, latent random variables are introduced. Characterizing the uncertainty at the BRDF function level, its conditional distribution is parameterized by the context representation:

[0134] in and Outputted by a neural network, it is used to characterize the overall reflection changes caused by different materials or surface microstructures.

[0135] For any target input decoder network In conditional random variables With context representation Under the combined effect of these factors, the predicted distribution parameters of the BRDF are output:

[0136]

[0137] This enables the prediction of the mean and estimation of the uncertainty of BRDF values.

[0138] To introduce physical guidance constraints, this invention explicitly embeds physical prior information into the network output layer or loss function. For example, by normalizing or integrating the predicted BRDF, it ensures that energy conservation conditions are met.

[0139]

[0140] Simultaneously, for isotropic or anisotropic materials, symmetry constraints can be introduced into the network input parameterization or weight sharing structure to reduce non-physical understanding and improve the model's generalization performance.

[0141] Through the above network architecture, this invention achieves stochastic process modeling of BRDF function uncertainty while maintaining the high expressive power of neural networks, and significantly improves reconstruction accuracy and physical consistency under finite sampling conditions.

[0142] Third: The operational process of the training strategy:

[0143] In the compact representation method of BRDF neural processes based on micro-surface model physics guidance, the training objective is to learn a model that can describe the probability distribution of the BRDF function family. Simultaneously, a physical reflection model is used to constrain the function space, ensuring that the learned representation is both compact and satisfies the physical laws of reflection in real materials. Let the surface bidirectional reflection distribution function be... ,in and Let represent the incident light direction and the observation direction, respectively. For an isotropic surface, the BRDF can be parameterized by angles as follows: ,in This represents the incident polar angle, the observed polar angle, and the azimuth difference. The training data consists of a set of BRDF samples, i.e. ,in .

[0144] Within the neural process framework, the BRDF of each material is considered as a function instance sampled from a certain function distribution; therefore, the model learns the conditional distribution. ,in This represents a small number of observation samples (context set). This represents the target set to be predicted. Given the observation set... The encoder first extracts features from each observation pair, mapping the input angle and its corresponding BRDF value to a latent space representation, i.e.

[0145]

[0146] in The parameter is The neural network. To ensure invariance to the order of observation points, these representations are then aggregated through a symmetric aggregation operator to obtain the overall context representation.

[0147]

[0148] This representation is further mapped to a probability distribution of latent variables to describe the potential reflective properties of the current material. Specifically, the mean and covariance of the latent variables are obtained through a parametric network, thereby constructing the latent variable distribution.

[0149]

[0150] middle These are low-dimensional latent variables describing the microstructure characteristics of materials. During training, samples are taken from this distribution using reparameterization techniques. This allows the model to express the variations in reflection functions between different materials in the latent space. Unlike traditional neural processes that directly predict BRDF values, this method physically models the reflection process using a micro-surface model. Specifically, BRDF is represented as...

[0151]

[0152] in Represents the normal distribution function of the micro-surface. For the Fresnel item, For geometric occlusion items, This is a half-angle vector. To achieve the combination of neural representation and physical model, the decoder does not directly output the BRDF value, but instead outputs it based on the input direction. With latent variables Predicting key parameters of microsurface models For example, roughness With Fresnel reflectivity ,Right now

[0153]

[0154] The predicted parameters are then substituted into the microsurface model to calculate the corresponding BRDF values.

[0155]

[0156] This structure allows the neural network to learn only the relationship between material parameters and angles, while the overall shape of the reflection function is guaranteed by the physical model, thus significantly reducing the function search space.

[0157] To characterize the uncertainty of the prediction, the decoder also outputs the observation noise variance. Thus, the conditional probability model is obtained.

[0158]

[0159] During the training phase, it is necessary to maximize the conditional likelihood of the target set. This is due to the latent variables... The existence of this problem allows it to be solved through variational inference. Specifically, a posterior approximation is introduced. And the maximum change is divided into lower bounds.

[0160]

[0161] The first term is the reconstruction term, used to measure the difference between the model's predicted BRDF and the actual observations; the second term is the KL divergence, used to constrain the distance between the posterior and prior distributions of the latent variables, ensuring the latent space maintains a good structure. If we assume the observed noise follows a Gaussian distribution, the reconstruction term can be written as...

[0162]

[0163] In addition to statistical modeling, several physical consistency constraints are introduced during training to further ensure the rationality of the BRDF. For example, to satisfy the energy conservation condition, it is necessary to ensure that the reflected energy on the incident hemisphere does not exceed the incident energy, i.e.

[0164]

[0165] During training, numerical integration can be performed over the random sampling direction, and a penalty term can be added for violations of constraints. Furthermore, according to the reciprocity principle, the BRDF should satisfy...

[0166]

[0167] This constraint can also be achieved by swapping the incident and observed directions to calculate the error and adding it to the loss function. Taking into account the statistical reconstruction error, the latent variable regularization term, and the physical constraint term, the final training objective can be written as:

[0168] ,in Represents physical consistency constraints. and These are the weighting coefficients.

[0169] During training, a material sample is randomly selected from the BRDF dataset, and its sample set is randomly divided into an observation set and a target set. The observation set is used to estimate the latent variable distribution. The target set is used to calculate the prediction error and update the model parameters. By repeatedly performing this process, the model gradually learns the statistical structure between different materials in the latent variable space, so that the BRDF function of each material can be represented by a low-dimensional latent variable. The following description is provided. Since this latent variable typically only requires a few to a dozen dimensions to characterize material differences, compared to traditional representations that require dense sampling of the angular space, this demonstrates that the present invention can achieve a compact probabilistic representation of BRDF while retaining the ability to accurately express complex reflection characteristics.

Claims

1. A method for predicting neural processes of surface reflection characteristics based on microsurface models, characterized in that: The constructed BRDF dataset is subjected to network training and physical guidance constraint processing to form an initial model, and the initial model is used to predict the bidirectional reflectance distribution function The BRDF function family probability distribution model is formed by probabilistic modeling, and the prediction process of the reflection characteristics of unobserved directions is completed according to the established BRDF function family probability distribution model.

2. The method of claim 1, wherein the method is based on a microfacet model guided surface reflectance property neural process prediction. The BRDF dataset is used to characterize the reflection behavior of different materials under various combinations of incident and exit directions. The construction process of the BRDF dataset is as follows: Data collection process: for each kind of material to be modeled, the incident direction and the exit direction are sampled in the unit hemispherical direction space, using uniform sampling, stratified sampling and / or importance-based directional sampling methods, to ensure that the sampled data covers the reflection characteristics of the mirror reflection area, highlight area and diffuse reflection area. For each group of directions , the corresponding BRDF value is recorded, thereby forming a basic sample pair, and the corresponding calculation formula is: ； In the above formula, when using an analytical physical model to generate data, the reflection value is calculated based on the preset material parameters and the corresponding physical BRDF function, ensuring that the data meets the physical constraints of energy conservation, non-negativity, and directional symmetry; when using measured data, the original measurement data is interpolated, denoised, or normalized to ensure that the impact of measurement error on model training is reduced and the consistency of data on the numerical scale is guaranteed. Data organization process: after the data is collected, the data organization process is performed, a complete BRDF sample set corresponding to each material is regarded as a function instance, and a plurality of samples are randomly extracted from each function instance to form a context subset The remaining samples are used as a target prediction set The context subset is used to provide a known observation condition to the neural random process network, and the target set is used to supervise the prediction ability of the model to the unobserved direction reflection value, and the construction mode is formally represented by the following formula: ； In the above formula, represents a complete BRDF dataset corresponding to a single material; The number of context samples can be randomly changed during the training process, thereby ensuring robustness of the model under different sampling density conditions, and enabling the network to stably work under both few-sample and many-sample conditions. The parameterized form conversion of the semi-angle vector and the local coordinate system representation of the direction input ensures that the data set has a predetermined expression performance for direction changes. The BRDF data set formed through data collection and data organization is a data set that comprehensively covers the high-dimensional reflection characteristics of BRDF.

3. The method of claim 2, wherein the method is based on a microfacet model guided surface reflectance property neural process prediction. The process of forming the network architecture after training the network and applying physical guidance constraints to the constructed BRDF dataset is as follows: After forming a BRDF dataset from the observed finite BRDF sampling data, context set processing is performed, and the corresponding calculation formula is as follows: ； In the above formula, is the direction pair input, is the corresponding reflection value; The above equation represents the goal of predicting the probability distribution of the BRDF at an arbitrary target input given a set of context conditions. The network architecture adopts a composite structure of an encoder, an aggregator, and a decoder, and the network architecture calculates a context vector by using a context encoder network Each context sample is mapped to a latent space representation, calculated by the formula: ； In the above formula, consists of a multi-layer fully connected neural network whose inputs include a half-angle vector, a spherical coordinate, or a direction parameterization in a local tangent space; At the level of the stochastic process modeling, latent random variables are introduced The uncertainty at the level of the BRDF function is characterized, and its conditional distribution is parameterized by the context, with the processing formula: ； In the above formula, With Both are output by a neural network, And respectively represent two distribution parameters of the latent variable z based on the assumption of normal distribution. Any target input By the decoder network Under the joint action of the conditional random variable And the context representation The predicted distribution parameters of the BRDF are output, which are used to quantitatively evaluate the mean prediction and uncertainty of the BRDF values, and the corresponding calculation formula is: ； In the above formula, denotes the conditional probability of y given x and z, where z represents a latent variable that locates the current mapping in the overall function space. After determining the predicted distribution parameters of the BRDF, physical prior information is explicitly embedded in the network output layer or loss function. By normalizing or integrating the predicted BRDF, the predicted distribution parameters of the BRDF are ensured to satisfy the energy conservation condition. The calculation formula is as follows: ； For isotropic or anisotropic materials, symmetry constraints are introduced into the network input parameterization or weight sharing structure. After calculating the predicted distribution parameters of BRDF to satisfy the energy conservation condition, an initial model is obtained. That is, while maintaining the high expressive performance of the neural network, the network architecture is formed by modeling the stochastic process of the uncertainty of the BRDF function. The network architecture is an initial model that improves the reconstruction accuracy and physical consistency under finite sampling conditions, thus completing the initial process of network architecture modeling.

4. The method for predicting surface reflection characteristics based on a micro-surface model according to claim 3, characterized in that: Modeling the bidirectional reflectance distribution function (BRDF) of a material using a probabilistic approach The process of probabilistic modeling to form a BRDF function family probability distribution model is a physically guided BRDF neural compact processing process based on a micro-surface model, and the specific process is as follows: The BRDF function family probability distribution model is a model for constraining a function space by using a physical reflection model and describing a probability distribution of a BRDF function family, and the BRDF function family probability distribution model has compact performance and can accurately reflect a physical law of a real material. , In and are an incident light direction and an observation direction respectively; for an isotropic surface, the BRDF is parameterized by angles as , in , , are an incident polar angle, an observation polar angle and an azimuth angle difference respectively. The training data consists of a set of BRDF samples, i.e. where ; Under the neural process framework, each material's BRDF is treated as a function instance sampled from a function distribution, so the model learns the conditional distribution where is a small set of observed samples context set, is the target set that needs to be predicted; Given a set of observations The encoder first extracts features from each observation pair, obtaining the mean and covariance of the latent variables through a parameter network, thereby constructing the latent variable distribution process, and the calculation formula is: ； In the above formula, are low-dimensional latent variables that describe the microstructure features of materials, which are sampled from the above distribution by reparameterization during the training process , so as to ensure that the model accurately expresses the change relationship between different material reflection functions in the latent space, and the BRDF is expressed by physically modeling the reflection process by the micro-surface model. ； In the above formula, Let be the normal distribution function of the micro-surface. For Fresnel items, For geometric occlusion items, It is a half-angle vector.

5. The method for predicting surface reflection characteristics based on a micro-surface model according to claim 4, characterized in that: In the process of combining neural representations with physical models, the decoder does not directly output the BRDF value, but rather determines it based on the input direction. With latent variables Key parameters for predicting microsurface models That is, combined roughness With Fresnel reflectivity The calculation is performed using the following formula: ； The predicted parameters are then substituted into the micro-surface model to calculate the corresponding BRDF value. The calculation formula is as follows: ； The above formula quantitatively calculates the relationship between material parameters and angles, while the overall shape of the reflection function is guaranteed by the physical model, thus completing the process of narrowing the function search space through calculation.

6. The method for predicting surface reflectance characteristics based on a micro-surface model according to claim 5, characterized in that: In the process of predicting uncertainty, the decoder also outputs the observation noise variance. Thus, the conditional probability model is obtained, and the corresponding calculation formula for the conditional probability model is: During the training phase, based on latent variables The existence of is solved through variational inference; specifically, a posterior approximation is introduced. The maximum change is determined by the lower bound, and the corresponding calculation formula is: ； In the above formula, the first term The first term is the reconstruction term, used to measure the difference between the model's predicted BRDF and the actual observations; the second term is the KL divergence, used to constrain the distance between the posterior and prior distributions of the latent variables, ensuring that the latent space maintains a good structure; when the observed noise follows a Gaussian distribution, the corresponding reconstruction term is: ； In the above formula, in addition to statistical modeling, several physical consistency constraints are introduced during the training process to further ensure the rationality of BRDF. Among them, to satisfy the energy conservation condition and ensure that the reflected energy on the incident hemisphere does not exceed the incident energy, the calculation formula is as follows: ； During training, numerical integration can be performed over the random sampling direction, and a penalty term can be added for violations of constraints. Furthermore, according to the reciprocity principle, the BRDF should satisfy the following formula: ； In the above formula, the constraint is further implemented by calculating the error by exchanging the incident and observation directions and adding a loss function; based on the statistical reconstruction error, the latent variable regularization term, and the physical constraint term, the final formula for calculating the training objective is as follows: ； In the above formula, For physical consistency constraints, and As the weighting coefficients, during training, a material sample is randomly selected from the BRDF dataset, and the observation set and target set are randomly divided from its sample set; the observation set is used to estimate the latent variable distribution. The target set is used to calculate the prediction error and update the model parameters. By repeatedly performing the above process, the model gradually learns the statistical structure between different materials in the latent variable space, ensuring that the BRDF function of each material is derived from a low-dimensional latent variable. Simply provide a description.

7. A method for predicting surface reflectance characteristics based on a micro-surface model, as described in claim 1, 2, 3, 4, 5, or 6, characterized in that: The prediction process for the reflection characteristics of unobserved directions is completed based on the established BRDF function family probability distribution model. For any unobserved direction... The probability distribution of the BRDF values ​​in the corresponding direction of the model output is as follows: The distribution is parameterized by mean and variance. When the number of sampling points in the context sample set is between 6 and 16, the variance of the model prediction ranges from 0.05 to 0.

2. The mean is dominated by the physical prior of the micro-surface model and is a smooth interpolation state that conforms to the physical laws of energy conservation and reciprocity. When the minimum number of sampling points in the context sample set is 32, the variance of the model prediction ranges from 0.005 to 0.

03. The mean is mainly driven by the observed data, which shows that it accurately fits the complex reflection details of the real material, and the prediction error is lower than the preset threshold in the densely sampled area.

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