Three-dimensional air pollution concentration mapping method based on high-field signed distance function

Abstract

The present invention discloses a three-dimensional air pollution concentration mapping method based on a high-field signed distance function, comprising the following steps: S1, lifting air pollution data to a three-dimensional space to obtain an air pollutant concentration estimation space; S2, introducing a high-field signed distance function, constructing a single-image high-field directed signed distance network for estimating a single-day concentration map and an encoded high-field directed signed distance network for estimating a concentration map of any region of interest, and performing self-supervised training; S3, inputting a three-dimensional representation of air pollution data observed within a single day into the single-image high-field directed signed distance network for encoding, and outputting a high-field signed distance function estimation value corresponding to the single-day pollution concentration; inputting a three-dimensional representation of air pollution data of an observed region of interest and its corresponding latent code into the encoded high-field directed signed distance network, and outputting a high-field signed distance function estimation value corresponding to the pollution concentration of the region of interest; S4, performing three-dimensional query reconstruction on the output of the single-image high-field directed signed distance network and the output of the encoded high-field directed signed distance network, respectively, to obtain a single-day concentration map and a region of interest concentration map accordingly.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence and air pollution monitoring technology, and in particular to a three-dimensional air pollution concentration mapping method based on a high-field signed distance function. Background Art

[0002] At present, the main methods for monitoring air pollution concentrations include ground monitoring stations, satellite measurement methods, traditional methods based on physical knowledge, and methods based on deep learning. However, these existing monitoring methods have limitations in terms of spatial adaptability, resolution, and coverage. Specifically, (1) Although the existing ground monitoring station method can provide accurate measurements, it is difficult to achieve wide spatial coverage due to the high construction cost and limited deployment, especially in suburban areas; (2) Although the satellite measurement method provides wide spatial coverage and cost-effectiveness, its spatial resolution is insufficient and is affected by clouds and other environmental factors, resulting in low data availability; (3) Traditional methods based on physical knowledge have difficulty in accurately capturing the complex nonlinear relationship of air pollution distribution; (4) Although the deep learning method has made some progress, it has the problems of strong data dependence and poor transferability. Usually, predictors can only be designed for specific areas to improve the accuracy and comprehensiveness of air pollution monitoring. Summary of the Invention

[0003] In view of this, the present invention proposes a three-dimensional air pollution concentration mapping method based on the high-field signed distance function, which aims to solve the problems existing in the above-mentioned prior art by introducing an innovative three-dimensional implicit representation method Height-Field SDF (Height-Field Signed Distance Function) to achieve wider spatial coverage, higher spatial resolution and stronger transferability for air pollution concentration monitoring.

[0004] According to one aspect of the present invention, a three-dimensional air pollution concentration mapping method based on a high-field signed distance function is proposed, comprising the following process steps: S1, lifting air pollution data to a three-dimensional space to obtain an air pollutant concentration estimation space; S2, introducing a high-field signed distance function, constructing a single-image high-field directed signed distance network for estimating a single-day concentration map and an encoded high-field directed signed distance network for estimating a concentration map of any region of interest, and performing self-supervised training; S3, inputting a three-dimensional representation of air pollution data observed within a single day into the single-image high-field directed signed distance network for encoding, and outputting a high-field signed distance function estimate corresponding to the single-day pollution concentration; inputting a three-dimensional representation of air pollution data of the observed region of interest and its corresponding latent code into the encoded high-field directed signed distance network, and outputting a high-field signed distance function estimate corresponding to the pollution concentration of the region of interest; S4, performing three-dimensional query reconstruction on the output of the single-image high-field directed signed distance network and the output of the encoded high-field directed signed distance network, respectively, to obtain a single-day concentration map and a region of interest concentration map.

[0005] Furthermore, in step S1, the air pollution data is elevated to a three-dimensional space, including: organizing the air pollution data into a set {(longitude, latitude, observation value)}, and parameterizing it in the form of a continuous field.

[0006] Furthermore, the high-field signed distance function calculates the directed signed distance relative to the concentration surface by measuring the height information of the point in the three-dimensional Euclidean space.

[0007] Furthermore, the high-field signed distance function is defined as follows:

[0008] SDF * (x, y, z) = z-z', (x, y, z')∈S (1)

[0009] And the following mathematical constraints are satisfied:

[0010]

[0011] Where (x,y,z)∈R 3 is an arbitrary point in three-dimensional Euclidean space, representing the estimated value of air pollution concentration z corresponding to the geographic coordinates (x, y); (x, y, z') is the point obtained by projecting the point (x, y, z) onto the reference surface S. In the representation of air pollution concentration distribution, the reference surface is the concentration surface.

[0012] Furthermore, the single-image high-field directed signed distance network and the coded high-field directed signed distance network are implemented using PyTorch, and both share the same backbone network AutoDecoder.

[0013] Furthermore, the backbone network AutoDecoder includes 8 fully connected layers, and the (x, y, z) query is spliced ​​on the 5th fully connected layer.

[0014] Furthermore, the self-supervised training of step S2 includes: through the high-field signed distance function semantics implied in the three-dimensional representation and the mathematical constraints satisfied by the high-field signed distance function, the single-map high-field directed signed distance network and the encoded high-field directed signed distance network become high-field signed distance function field approximators of the single-day concentration map and the area of ​​interest concentration map, respectively.

[0015] Furthermore, for the training of the single-image high-field directed signed distance network, the loss function used is:

[0016] L(θ)=L I (θ)+λL' J (θ)

[0017] in, Represents the semantics of the high-field signed distance function implied by the three-dimensional representation, Represents the high-field signed distance function that satisfies mathematical constraints; f θ (x i ) represents the estimation of the single-image high-field directed signed distance network; I is a three-dimensional point cloud corresponding to a set of three-dimensional representations of air pollution observations; θ is a learnable parameter; x i is a point in the 3D point cloud I; J is another point cloud sampled near the 3D point cloud I; x j is a point in the 3D point cloud J; λ is a hyperparameter greater than 0, used to adjust the weight;

[0018] For the encoded high-field directed signed distance network, a learnable vector is introduced as a high-dimensional feature embedding to encode the features of the high-field signed distance function field corresponding to the air pollution observation map; assuming that the index of an air pollution observation map is M k , and its corresponding high-dimensional feature embedding is labeled Z k , Z k The spatial distribution characteristics of the corresponding air pollution observations are encoded; for the training of the encoded high-field directed signed distance network, the loss function used is:

[0019]

[0020] in:

[0021] L(θ,Z k )=L I (θ,Z k )+λL' J (θ,Z k )

[0022]

[0023]

[0024] Among them, f θ (x i ,Z k ) represents the estimation of the coded high-field directed signed distance network, B represents a batch, k represents the air pollution observation obtained by random sampling within a batch, α is an adjustable weight, α>0.

[0025] Furthermore, the three-dimensional query reconstruction in step S4 is achieved by densely querying the positions in the high-field signed distance function field, implicitly representing the concentration surface as the zero isosurface of the high-field signed distance function field, and identifying the three-dimensional concentration surface through the Marching Cube algorithm; then, the final concentration estimation map is obtained by projecting the determined surface points onto the two-dimensional image.

[0026] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the aforementioned three-dimensional air pollution concentration mapping method can be implemented.

[0027] Compared with the prior art, the beneficial effects of the technical solution of the present invention are embodied in:

[0028] 1) 3D Spatial Modeling: This paper introduces a novel 3D implicit representation method, the Height-Field Signed Distance Function (SDF). Compared to traditional methods, it fully combines deep learning networks and height-guided constraints to effectively capture the topological structure of air pollution distribution and achieve ultra-high-resolution estimation in the presence of noisy and locally incomplete satellite data.

[0029] 2) Superiority over traditional satellite and ground-based monitoring: The method of the present invention combines the advantages of traditional satellite and ground-based monitoring while addressing their shortcomings. Compared to traditional satellite monitoring, the present invention provides higher spatial resolution; compared to ground-based monitoring, the present invention has a wider monitoring coverage area and does not require a large number of monitoring stations;

[0030] 3) Strong adaptability to low-quality labeled data and transfer learning: By learning a continuous, generalizable 3D generative model, this method improves its transferability and generalization across different regions and pollution types. This makes the method far superior to previous methods in handling low-quality labeled data and effectively learning across different regions and pollution types, enabling its application in a wider range of scenarios.

[0031] 4) Comprehensive Pollution Coverage: This method can comprehensively reconstruct the distribution of multiple air pollutants, not just a single pollutant. Compared with existing methods, this method provides a more comprehensive pollutant coverage monitoring method;

[0032] 5) Combining Data-Driven Methods with Domain Knowledge: This paper combines data-driven methods with domain knowledge, capturing shared characteristics across different regions and pollution types through an encoded high-field signed distance function. This combination enables the present invention to demonstrate greater flexibility and adaptability in processing diverse forms of local observation data.

[0033] 6) Innovative Application Potential: The high spatial adaptability, fine resolution, and comprehensive coverage of the method make it ideal for building a Digital Twin of Earth, providing new opportunities for comprehensive monitoring and analysis of various environmental factors, going beyond the monitoring of specific pollutants. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of a three-dimensional air pollution concentration mapping method based on a high-field signed distance function according to an embodiment of the present invention.

[0035] Figure 2 3 is a conceptual diagram of a high-field signed distance function (Height-Field SDF) according to an embodiment of the present invention.

[0036] Figure 3-1 and Figure 3-2 They are schematic diagrams of a single-graph high-field directed signed distance network and a coded high-field directed signed distance network according to embodiments of the present invention.

[0037] Figure 4 The three-dimensional air pollution concentration mapping method of an embodiment of the present invention is applied to the reconstruction of the PM2.5 map of air pollutants in central China.

[0038] Figure 5 The three-dimensional air pollution concentration mapping method of an embodiment of the present invention is applied to high-resolution reconstruction of downsampling results at different scales.

[0039] Figure 6 The three-dimensional air pollution concentration mapping method of the embodiment of the present invention is generalized to high-resolution reconstruction of concentration maps of multiple pollutants.

[0040] Figure 7 The three-dimensional air pollution concentration mapping method of an embodiment of the present invention is applied to high-resolution reconstruction of TROPOMI satellite observation data. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings and specific implementation methods and examples. It should be understood that the examples are provided for illustration only and are not intended to limit the scope of protection and application scenarios of the present invention.

[0042] Implicit representations are a class of neural network methods whose core idea is to learn to represent complex, high-dimensional functions without explicit parameterization. Compared to explicit representations, implicit representations excel at shape reconstruction by extending the objective to a high-dimensional space and parameterizing it in the form of a continuous field, while using less memory. A key advantage of implicit representations is their ability to reconstruct shapes with arbitrary topology.

[0043] The present invention introduces a new implicit representation method - Height-Field Signed Distance Function (hereinafter referred to as Height-Field SDF). The purpose of this method is to elevate the two-dimensional concentration map of air pollution to three-dimensional space and reconstruct the concentration surface in a continuous manner, thereby efficiently achieving the reconstruction of the air pollution concentration map. Compared with existing methods, Height-Field SDF has advantages in efficiency, expressiveness and complete continuity. Existing implementation solutions usually lack a dedicated design for air pollution concentration maps. The present invention, through the introduction of Height-Field SDF, provides a more efficient, richly expressive and fully continuous method for generating map estimation, which is particularly suitable for the reconstruction of air pollution concentration maps. Height-Field SDF can better adapt to spatial changes and improve the accuracy of air pollution monitoring by continuously modeling in three-dimensional space. At the same time, by elevating the two-dimensional concentration map to three-dimensional space, the continuity of the distribution of pollutants at the spatial scale is utilized to provide higher-resolution observations to more detailed depictions of air pollution distribution. Through this innovative method, the present invention can effectively overcome the limitations of existing technologies and improve the comprehensiveness and accuracy of air pollution monitoring.

[0044] Please refer to Figure 1 The three-dimensional air pollution concentration mapping method based on the high-field signed distance function provided by the embodiment of the present invention mainly includes: dimensionality enhancement, network processing, and three-dimensional query reconstruction. The detailed process is described below.

[0045] The specific steps of dimensionality enhancement include: organizing air pollution data into a set {(longitude, latitude, observation value)}, parameterizing it in the form of a continuous field, and using this parameterization method to enhance the air pollution data to a three-dimensional space. The physical meaning given to this three-dimensional space is the concentration estimation space of air pollutants. Each point (x, y, z) in the space represents the estimated value of the air pollution concentration corresponding to the geographic coordinates (x, y) as z.

[0046] In an embodiment of the present invention, the target is elevated to a higher one-dimensional space, namely the Level Set space of the Height-Field SDF, through the Height-Field SDF, thereby realizing the estimation of the continuous concentration surface. Height-Field SDF is a special signed distance function, which calculates the directed signed distance relative to the reference surface by measuring the height information of the point in the three-dimensional Euclidean space. In the representation of air pollution concentration of the present invention, the reference surface is the concentration surface, and the three-dimensional Euclidean space is the concentration estimation space. This continuous function can not only effectively represent the geometric structure of the concentration map, but also impose key constraints on the search space of the algorithm through its specific mathematical properties. In essence, the Height-Field SDF divides the entire space through the definition of the continuous function in the three-dimensional space, and then estimates the geometric structure of the concentration surface. The characteristic of this function is that it can effectively capture the distribution of air pollution.

[0047] like Figure 2 As shown, in the application of air pollution concentration distribution reconstruction in the embodiment of the present invention, we assume that there is a reference surface S in three-dimensional space that is consistent with the three-dimensional representation (the point cloud obtained by parameterizing the measured values). Figure 2 , where (a) represents the air pollution concentration estimation space, (b) is a longitudinal section of the space shown in (a), and (c) is a local display of the section shown in (b). The physical meaning given to the three-dimensional space is the concentration estimation space of air pollutants, and the physical meaning of the coordinate value of each point (x, y, z) in the space is the air pollution concentration value z corresponding to the geographic coordinate (x, y). The role of the Height-Field SDF field defined in this three-dimensional space is to train a classifier using a deep network. In this three-dimensional space, the physical meaning of the Height-Field SDF value corresponding to each point (x, y, z) can be interpreted as the estimated deviation between the estimated value z at the geographic location (x, y) and the true concentration value at the position (x, y). Therefore, the Height-Field SDF value of all points contained in the reference surface S is defined as 0, and it is considered that the z value corresponding to the point (x, y) in the set S is unbiased (= the true pollutant concentration value). Taking the reference surface S as the boundary, the points above S in the space ( Figure 2 The Height-Field SDF value is greater than 0, indicating that the estimated value z corresponding to the geographical location (x, y) of these points is greater than the actual pollutant concentration value at (x, y). Figure 2The Height-Field SDF value is <0, which means that the estimated value z corresponding to the geographical location (x, y) of these points is smaller than the actual pollutant concentration value at (x, y).

[0048] In the embodiment of the present invention, the mathematical definition of Height-Field SDF is as follows:

[0049] SDF * (x, y, z) = z-z', (x, y, z')∈S (1)

[0050] Furthermore, the Height-Field SDF satisfies the following mathematical constraints:

[0051]

[0052] Please refer to Figure 2 , where (x,y,z)∈R 3 is any point in three-dimensional Euclidean space, (x, y, z') is the point obtained by projecting the point (x, y, z) onto the reference surface S. In the representation of air pollution concentration distribution, the reference surface is the concentration surface.

[0053] The specific steps of network processing include:

[0054] First, a single-image high-field directed signed distance network for estimating the concentration map of a single day and an encoded high-field directed signed distance network for estimating the concentration map of any region of interest are constructed and self-supervised training is performed; then, the three-dimensional representation of the air pollution data observed within a single day is input into the single-image high-field directed signed distance network for encoding, and the high-field signed distance function estimate corresponding to the single-day pollution concentration is output; the three-dimensional representation of the observed air pollution data of the region of interest and its corresponding latent code are input into the encoded high-field directed signed distance network, and the high-field signed distance function estimate corresponding to the pollution concentration of the region of interest is output.

[0055] Air pollution observations are characterized by uneven spatial distribution and inherent biases. To reconstruct air pollution concentration maps that reflect these characteristics, after parameterizing the observations into a three-dimensional representation (point cloud) through dimensionality lifting, they are processed using two networks: a single-image high-field directed signed distance network and an encoded high-field directed signed distance network.

[0056] Among them, the Single Map Height-Field Directed Signed Distance Network (Single Map Height-Field SDF Network) is used to estimate the air pollution concentration map for a single day. In this network, the network parameters are iteratively updated to encode the three-dimensional representation of the air pollution data observed within a single day, and then the corresponding Height-Field SDF value is output, effectively capturing the information of the concentration surface. The Coded Map Height-Field Directed Signed Distance Network (Coded Map Height-Field SDF Network) is used to estimate the air pollution concentration map for any region of interest. In this network, the concept of domain knowledge is introduced, and the corresponding Height-Field SDF value is predicted by inputting a learnable vector (latent code) and position information. The latent code is designed to encode the characteristics of the Height-Field SDF field corresponding to the three-dimensional representation of each air pollution observation. The two networks act as approximators of the Height-Field SDF field. By densely querying the approximate Height-Field SDF field, a fine estimate with extremely high resolution is obtained.

[0057] The main goal of the self-supervised training of the two networks is to make the single-image high-field directed signed distance network and the encoded high-field directed signed distance network become high-field signed distance function field approximators of the single-day concentration map and the area of ​​interest concentration map respectively through the high-field signed distance function semantics implied in the three-dimensional representation and the mathematical constraints satisfied by the high-field signed distance function.

[0058] In this embodiment, we use f θ (x) represents a single-graph high-field directed signed distance network, where θ is a learnable parameter and f θ (x) where x∈R 3 , represents the three-dimensional representation of air pollution observations. Since the training goal is to satisfy the mathematical constraints of Height-Field SDF through the semantics of Height-Field SDF implied by the three-dimensional representation, f θ (x) becomes the Height-Field SDF field approximator of the single-day concentration map. Therefore, during training, the loss function used includes two components, as follows:

[0059] L(θ)=L I (θ)+λL' J (θ)

[0060] Among them, the previous Represents the semantics of the high-field signed distance function implied by the three-dimensional representation, and the latter term Represents the high-field signed distance function that satisfies mathematical constraints; f θ (x i) represents the estimation of the single-image high-field directed signed distance network; I is a three-dimensional point cloud corresponding to a set of three-dimensional representations of air pollution observations; θ is a learnable parameter; x i is a point in the 3D point cloud I; J is another point cloud sampled near the 3D point cloud I; x j is a point in the three-dimensional point cloud J; λ is a hyperparameter greater than 0, used to adjust the weight.

[0061] For encoding high-field directed signed distance networks, a learnable vector is introduced as a high-dimensional feature embedding to encode the features of the high-field signed distance function field corresponding to the air pollution observation map; assuming that an air pollution observation map index is M k , and its corresponding high-dimensional feature embedding is labeled Z k , Z k The spatial distribution characteristics of the corresponding air pollution observations are encoded. In this embodiment, the encoded high-field directed signed distance network is represented as f θ (x,Z k ), where f θ (x,Z k ) in which x represents M k For the training of the high-field DSDN, the loss function used is:

[0062]

[0063] Among them, L(θ,Z k )=L I (θ,Z k )+λL' J (θ,Z k );

[0064] Similar to the single-graph high-field directed signed distance network,

[0065]

[0066]

[0067] Among them, f θ (x i ,Z k ) represents the estimation of the coded high-field directed signed distance network, B represents a batch, k represents the air pollution observation obtained by random sampling within a batch, α is an adjustable weight, α>0.

[0068] It is worth noting that during the training process, θ, Z kDuring the inference phase, the maximum a posteriori probability method is used to iterate for approximately 800 times to obtain a 256-dimensional high-dimensional feature embedding (latent code) representing the Height-Field SDF corresponding to the air pollution observation map.

[0069] In an embodiment of the present invention, the single-image high-field directed signed distance network and the coded high-field directed signed distance network can be implemented using PyTorch, and the two networks share the same backbone network AutoDecoder. Figure 3-1 and Figure 3-2 As shown, in an exemplary implementation, the backbone network AutoDecoder is implemented using multiple fully connected layers, for example, including 8 fully connected layers, each with 512 nodes, and the (x, y, z) query is spliced ​​on the 5th fully connected layer. The two networks use the same backbone network for feature extraction, where the input of the single-image high-field directed signed distance network is a three-dimensional representation of the air pollution data observed on a single day, and the output is the Height-Field SDF estimate corresponding to the air pollution data observed on a single day; the input of the coded high-field directed signed distance network includes not only the three-dimensional representation of the air pollution observation data of the region of interest, but also the latent code, and the output is the Height-Field SDF estimate corresponding to the air pollution observation data of the region of interest. Therefore, for the air pollution observation data sampled with finite precision, the embodiment of the present invention regresses a continuous Height-Field SDF function with the help of a decoder containing prior knowledge from the training set, thereby converting the finite precision observation data into an arbitrary precision query, achieving fine reconstruction. Under the AutoDecoder framework, the method of the embodiment of the present invention supports any number of sampling points for each input observation sample model.

[0070] Those skilled in the art should understand that in addition to the implementation methods listed above, the single-graph high-field directed signed distance network and the coded high-field directed signed distance network can also be implemented in other ways. The present invention is not limited to the specific network architecture. For example, a convolutional neural network can also be used for implementation.

[0071] The specific steps of 3D query reconstruction include performing 3D query reconstruction on the outputs of the single-image high-field directed signed distance network and the coded high-field directed signed distance network, respectively, to obtain a single-day concentration map and a concentration map for the area of ​​interest. The 3D query reconstruction stage demonstrates the process of deriving the final estimated map from the trained height-field SDF field. By densely querying locations in the height-field SDF field, the concentration surface is implicitly represented as the zero isosurface of the height-field SDF field. The 3D concentration surface is then identified using the Marching Cube algorithm. Finally, the final concentration estimate map is obtained by projecting the identified surface points onto a 2D image. Specifically, both the trained single-image high-field directed signed distance network and the coded high-field directed signed distance network possess information about the corresponding height-field SDF field of air pollution. For the single-image high-field directed signed distance network, this information is implicitly contained in the network parameters; for the coded high-field directed signed distance network, this information is implicitly contained in the corresponding latent code. Obtaining the desired concentration estimate map from the three-dimensional height-field SDF field requires a three-step process: first, obtaining the sampling values ​​of the three-dimensional height-field SDF field through dense position querying; second, based on the above sampling results, using the Marching Cube algorithm to identify the concentration surface; third, projecting the surface points identified in step 2 onto the two-dimensional image through inverse dimensionality lifting, thus obtaining the final concentration estimate map.

[0072] Compared with the prior art, the three-dimensional air pollution concentration mapping method based on the high-field signed distance function provided by the embodiment of the present invention has the following advantages:

[0073] 1) High-resolution map reconstruction: This paper adopts the implicit representation method of Height-Field SDF and, through deep network training, can achieve high-resolution and accurate reconstruction of air pollution maps, effectively restoring the concentration distribution in geographic space.

[0074] 2) Addressing Spatial Inhomogeneity: This paper takes into account the practical characteristics of air pollution observation, particularly the spatial inhomogeneity of concentration distribution and inherent measurement bias. By updating and training deep network parameters, it effectively addresses these characteristics and improves its adaptability to real-world environments.

[0075] 3) Flexibility and universality: This paper introduces a three-stage reconstruction process, including dimensionality enhancement, network processing, and 3D query reconstruction. This combined process makes the invention more flexible in different scenarios and can adapt to different types and qualities of observation data.

[0076] 4) Unique Height-Field SDF Design: The design of the Height-Field SDF in this invention is unique and innovative. By introducing this method, the concentration characterization of air pollution is successfully combined with the geometric structure, providing an effective means to achieve more accurate reconstruction.

[0077] In order to verify the effectiveness of the present invention, the embodiment of the present invention further provides evaluations on the analysis dataset TAP and the real observed satellite dataset TROPOMI.

[0078] First, the China Atmospheric Pollution Tracking Dataset (TAP) integrates multiple data sources such as ground observations, satellite remote sensing, and model simulations to provide a multi-scale, near-real-time reanalysis of the concentrations of aerosol and gaseous pollutants in China's atmosphere. The Height-Field SDF method uses only the TAP dataset for high-resolution reconstruction without introducing any additional information channels or factors. Figure 4 As shown, (b), (c), and (d) correspond to the Central China region, Hubei Province, and Wuhan City, respectively. In this experiment, we used the TAP 10km resolution pollution map (the three above) as the original input of the single-image high-field directed signed distance network for reconstruction. Figure 4 The fine-scale reconstruction capability of the Height-Field SDF method of the present invention is demonstrated in the "Central China - Hubei Province - Wuhan City" ladder. Experiments show that the reconstruction results of the Height-Field SDF method of the present invention exhibit extremely high correlation coefficients (R) and indices of consistency (IOA) compared to low-resolution inputs. In particular, in the case of a single-image high-field directed signed distance network, the Height-Field SDF performs well, with reported R and IOA values ​​exceeding 0.99, providing convincing evidence of its strong performance in fine-scale mapping.

[0079] In addition, the Tropospheric Monitoring Instrument (TROPOMI) is an advanced satellite sensor designed for high-resolution global observations. We apply the Height-Field SDF method to the TROPOMI dataset with partial data missing and irregular area sampling to perform continuous high-resolution reconstruction of the observation results. Figure 5As shown in this experiment, TAP 1km-resolution PM2.5 data was used as the raw data and manually downsampled to various scales, including 1km, 5km, 10km, 20km, 30km, and 40km. As shown in (a), the downsampled results were used as the raw input to a single-image high-field directed signed distance network (HSDN) for high-resolution reconstruction. The reconstruction result (b) demonstrates that the proposed Height-Field SDF method can still provide highly reliable high-resolution reconstruction results even when the input pollutant concentration map has very sparse valid monitoring values. (c) shows the visualization of the corresponding differences between the high-resolution reconstruction results and the low-resolution input; (d) shows the R and IOA changes between the reconstruction results and the original input in six control experiments. R and IOA are indicators that reflect image consistency; (e) provides the statistical characteristics of the corresponding differences between the reconstruction results and the original input in the six control experiments. The experimental results show that Height-Field SDF not only produces robust quantitative results (such as R and IOA) but also preserves fine details, generating continuous air pollution maps that are adaptable to any spatial resolution.

[0080] Furthermore, the present invention generalizes to high-resolution reconstruction of various pollutant concentration maps such as Figure 6 As shown in the figure, in this experiment, we use the PM2.5 pollution concentration map in the TAP dataset in 2021-2022 as the training data for the high-field DSDN. After the training is completed, the PM2.5 training dataset and the PM2.5 test dataset are used. High-resolution inference was performed on the test set. The results show that the present invention has strong generalization ability in the application of reconstructing concentration maps of different pollutants.

[0081] The present invention is applied to high-resolution reconstruction of TROPOMI satellite observation data. Figure 7 As shown in the figure, in this experiment, we use the real NO2 data observed by the TROPOMI satellite as the original input of the single-image high-field directed signed distance network for reconstruction. It should be noted that satellite observation data has the characteristics of local data missing and uneven distribution of observation locations. These characteristics make the reconstruction of satellite observation data more challenging than reanalysis datasets. Our method shows robustness to noise and sparse observations. (a.1) is the original input, and (a.2) to (a.5) show the reconstructed projections of our reconstructed continuous concentration surface (a.5) at 10km, 2km, and 1km, showing the strong spatial adaptability and accurate reconstruction efficiency of the continuous modeling method.

[0082] Another embodiment of the present invention further proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can implement the steps of the aforementioned three-dimensional air pollution concentration mapping method based on a high-field signed distance function. Based on this understanding, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, a USB flash drive, a mobile hard disk, etc.), including a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of various implementation scenarios of the present application.

[0083] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. Those skilled in the art will recognize that several equivalent substitutions or obvious variations can be made without departing from the scope of the present invention, and that any equivalent performance or application should be considered to fall within the scope of protection of the present invention.

Claims

1. A three-dimensional air pollution concentration mapping method based on high-field signed distance function, characterized in that: The process steps include: S1. Elevate air pollution data to three-dimensional space to obtain air pollutant concentration estimation space; S2. Introducing the high-field signed distance function, constructing a single-image high-field directed signed distance network for estimating the concentration map of a single day and an encoded high-field directed signed distance network for estimating the concentration map of any region of interest and performing self-supervised training; S3, inputting the three-dimensional representation of the air pollution data observed in a single day into the single-image high-field directed signed distance network for encoding, and outputting a high-field signed distance function estimate corresponding to the pollution concentration of the single day; inputting the three-dimensional representation of the air pollution data of the observed region of interest and its corresponding latent code into the encoded high-field directed signed distance network, and outputting a high-field signed distance function estimate corresponding to the pollution concentration of the region of interest; S4. Perform three-dimensional query reconstruction on the output of the single-image high-field directed signed distance network and the output of the coded high-field directed signed distance network, respectively, to obtain a single-day concentration map and a concentration map of an area of ​​interest.

2. The three-dimensional air pollution concentration mapping method according to claim 1, characterized in that: In step S1, the air pollution data is elevated to a three-dimensional space, including: organizing the air pollution data into a set {(longitude, latitude, observation value)}, and parameterizing it in the form of a continuous field.

3. The three-dimensional air pollution concentration mapping method according to claim 1, wherein: The high-field signed distance function calculates the directed signed distance relative to the concentration surface by measuring the height information of the point in the three-dimensional Euclidean space.

4. The three-dimensional air pollution concentration mapping method according to claim 1 or 3, characterized in that: The high-field signed distance function is defined as follows: <h2 style=";text-align:left;direction:ltr">SDF<h2 style=";text-align:left;direction:ltr"> * <h2 style=";text-align:left;direction:ltr"> (x,y,z)=z-z',(x,y,z')∈S (1) And the following mathematical constraints are satisfied: Where (x,y,z)∈R 3 is an arbitrary point in three-dimensional Euclidean space, representing the estimated value of air pollution concentration z corresponding to the geographic coordinates (x, y); (x, y, z') is the point obtained by projecting the point (x, y, z) onto the reference surface S. In the representation of air pollution concentration distribution, the reference surface is the concentration surface.

5. The three-dimensional air pollution concentration mapping method according to claim 1, wherein: The single-image high-field directed signed distance network and the coded high-field directed signed distance network are implemented using PyTorch, and both share the same backbone network AutoDecoder.

6. The three-dimensional air pollution concentration mapping method according to claim 5, characterized in that: The backbone network AutoDecoder includes 8 fully connected layers, and the (x, y, z) query is spliced ​​on the 5th fully connected layer.

7. The three-dimensional air pollution concentration mapping method according to claim 5, characterized in that: The self-supervised training of step S2 includes: through the high-field signed distance function semantics implied in the three-dimensional representation and the mathematical constraints satisfied by the high-field signed distance function, the single-map high-field directed signed distance network and the encoded high-field directed signed distance network become high-field signed distance function field approximators of the single-day concentration map and the area of ​​interest concentration map, respectively.

8. The three-dimensional air pollution concentration mapping method according to claim 7, wherein: For the training of the single-image high-field directed signed distance network, the loss function used is: L(θ)=L I (θ)+λL' J (i) in, Represents the semantics of the high-field signed distance function implied by the three-dimensional representation, Represents the high-field signed distance function that satisfies mathematical constraints; f θ (x i ) represents the estimation of the single-image high-field directed signed distance network; I is a three-dimensional point cloud corresponding to a set of three-dimensional representations of air pollution observations; θ is a learnable parameter; x i is a point in the 3D point cloud I; J is another point cloud sampled near the 3D point cloud I; x j is a point in the 3D point cloud J; λ is a hyperparameter greater than 0, used to adjust the weight; For the encoded high-field directed signed distance network, a learnable vector is introduced as a high-dimensional feature embedding to encode the features of the high-field signed distance function field corresponding to the air pollution observation map; assuming that the index of an air pollution observation map is M k , and its corresponding high-dimensional feature embedding is marked as Z k , Z k The spatial distribution characteristics of the corresponding air pollution observations are encoded; for the training of the encoded high-field directed signed distance network, the loss function used is: in: L(θ,Z k )=L I (θ,Z k )+λL' J (θ,Z k ) Among them, f θ (x i ,Z k ) represents the estimation of the coded high-field directed signed distance network, B represents a batch, k represents the air pollution observation obtained by random sampling within a batch, α is an adjustable weight, α>0.

9. The three-dimensional air pollution concentration mapping method according to claim 1, wherein: The three-dimensional query reconstruction in step S4 is achieved by densely querying the positions in the high-field signed distance function field, implicitly representing the concentration surface as the zero isosurface of the high-field signed distance function field, and identifying the three-dimensional concentration surface through the Marching Cube algorithm; then, the final concentration estimation map is obtained by projecting the determined surface points onto the two-dimensional image.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it can implement the steps of the three-dimensional air pollution concentration mapping method described in any one of claims 1 to 9.

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