Accurate tracing method of three-dimensional fluorescence spectrum similarity based on Reeb graph and application thereof

Abstract

The invention belongs to the technical field of substance traceability, and particularly discloses a precise traceability method for three-dimensional fluorescence spectrum similarity based on a Reeb graph and application thereof, and the precise traceability method for the three-dimensional fluorescence spectrum similarity based on the Reeb graph comprises the following steps: obtaining a three-dimensional fluorescence spectrum of a preset wastewater sample library; carrying out data normalization processing on the three-dimensional fluorescence spectrum of the preset wastewater sample library, removing noise, and drawing an equal-gray-scale line graph; acquiring feature points on the equal-gray-scale line graph; based on the equal-gray-scale graph containing the feature points, judging a surrounding relation layer by layer, and constructing a Reeb graph of a preset wastewater sample library; acquiring a three-dimensional fluorescence spectrum of a to-be-detected water sample, and constructing a Reeb graph of the to-be-detected water sample according to the same method; and matching the Reeb graph of the to-be-detected water sample with the Reeb graph of a preset wastewater sample library, and calculating the similarity. According to the method, efficient and accurate map traceability matching can be realized, and reliable similarity evaluation can be provided in a complex multi-source pollution scene.

Description

Technical Field

[0001] This application belongs to the technical field of material traceability, and specifically relates to a precise traceability method for the similarity of three-dimensional fluorescence spectra based on Reeb graphs and its applications. Background Art

[0002] Three-dimensional fluorescence spectra (Excitation-Emission Matrix, EEM) form three-dimensional "fingerprint" spectral data by recording the fluorescence intensities of a sample at different excitation / emission wavelengths. A large amount of characteristic information is lost in traditional two-dimensional spectra or single-wavelength analysis, while three-dimensional data can more comprehensively reflect the optical properties of substances. However, the high-dimensionality, non-linearity, and noise interference of three-dimensional fluorescence spectra easily lead to the following problems: 1) overlapping peak interference: the spectra of multiple fluorescent substances in complex samples overlap and are difficult to separate; 2) dynamic changes: environmental factors (such as pH, temperature, etc.) or sample degradation will change the spectral pattern; 3) big data matching: an efficient traceability method is required to quickly and precisely match the source in a massive spectral library.

[0003] In the prior art, a multi-dimensional fluorescence data traceability method combining parallel factor analysis and random forest classification or an end-to-end similarity learning method based on a convolutional neural network (CNN) is often used for multi-source pollution traceability. However, both the multi-dimensional fluorescence data traceability method combining parallel factor analysis and random forest classification and the end-to-end similarity learning method based on a convolutional neural network (CNN) have certain limitations.

[0004] Specifically, the limitations of the multi-dimensional fluorescence data traceability method combining parallel factor analysis (PARAFAC) and random forest classification in practical applications are mainly reflected in three aspects: computational efficiency, generalization ability, and feature utilization. First, the PARAFAC decomposition process depends on artificially presetting the number of factors, which requires repeated iterative optimization and combined with core consistency analysis to determine the best components. This not only has a large computational overhead but is also sensitive to noise and it is difficult to ensure stability in large-scale data scenarios. Second, this method is limited by prior knowledge. If there are fluorescent components in actual samples that are not predefined (such as new pollutants or unknown coexisting substances), the decomposition results may deviate from the real situation and even cause the model to fail. In addition, the classification performance of the random forest model highly depends on the factor scores and fluorescence indices manually selected, which may cause some important but undecomposed local fluorescence features (such as weak peaks or peak shape details) to be ignored, thus losing key information. In small-sample scenarios, this method is prone to overfitting, resulting in a decline in generalization ability and difficulty in adapting to the dynamic expansion requirements of pollution source categories.

[0005] The limitations of the end-to-end similarity learning method based on convolutional neural network (CNN) in practical applications are mainly reflected in three aspects: data requirements, model interpretability, and hardware dependence. First, deep learning models require a large amount of high-quality labeled data (usually reaching the scale of thousands) for training. However, the cost of sample annotation in the environmental field is high, and it is difficult to obtain sufficient training data, which limits the practical application of the method. Second, the interpretability of this method is weak. Although Grad-CAM heatmaps can partially reveal the fluorescence regions that the model focuses on, it is still difficult to establish a clear correspondence between features and specific chemical components, thereby reducing the credibility of the tracing results. In addition, the computational complexity of the Siamese network is high, and it is strongly dependent on GPU hardware, making it difficult to achieve real-time analysis on portable devices. Although data augmentation strategies can alleviate the problem of data scarcity to a certain extent, the artificially simulated noise or wavelength shift cannot fully cover the complex variations in the real environment (such as instrument calibration errors, environmental interference, etc.), resulting in insufficient robustness of the model under different experimental conditions and affecting the stability of practical applications. Summary of the Invention

[0006] This application aims to solve at least one of the technical problems in the related art to some extent. To this end, the purpose of this application is to propose a precise tracing method and its application for the similarity of three-dimensional fluorescence spectra based on Reeb graphs. This method can achieve efficient and accurate spectrum tracing matching and can provide reliable similarity evaluation in complex multi-source pollution scenarios.

[0007] In one aspect of this application, this application proposes a precise tracing method for the similarity of three-dimensional fluorescence spectra based on Reeb graphs. According to the embodiments of this application, the method includes: (1) Obtain the three-dimensional fluorescence spectra of a preset wastewater sample library; (2) Perform data normalization processing on the three-dimensional fluorescence spectra of the preset wastewater sample library, remove noise, and draw an isogray scale map; (3) Obtain the feature points on the isogray scale map; (4) Based on the isogray scale map containing the feature points, judge the enclosure relationship layer by layer to construct the Reeb graph of the preset wastewater sample library; (5) Obtain the three-dimensional fluorescence spectra of the water sample to be tested, and construct the Reeb graph of the water sample to be tested according to the methods in steps (2) to (4); (6) Match the Reeb graph of the water sample to be tested with the Reeb graphs in the preset wastewater sample library and calculate the similarity. When the similarity between the Reeb graph of the water sample to be tested and a certain Reeb graph in the preset wastewater sample library is greater than or equal to 0.6, it is considered to have the possibility of homology and has a clear directivity; when the similarity between the Reeb graph of the water sample to be tested and all the Reeb graphs in the preset wastewater sample library is less than 0.6, it is considered not to have the possibility of homology and does not have a clear directivity.

[0008] According to the accurate tracing method based on the similarity of three-dimensional fluorescence spectra using Reeb graphs in the embodiments of the present application, the accuracy and robustness of complex water body pollution tracing are significantly improved. Compared with the traditional method that relies on the position and intensity of characteristic peaks for comparison, the Reeb graph of the present application captures the topological structure relationship between isogray lines in the spectrum, realizes the modeling and recognition of the global morphology of the fluorescence spectrum, and has strong anti-interference ability and pattern recognition ability. In practical applications, this method can effectively alleviate the problem of spectrum distortion caused by factors such as water sample dilution, mixing, or fluorescence intensity change, ensuring that stable recognition can still be achieved through the topological structure even when the fluorescence signal is partially distorted or shifted. Experimental results show that the similarity matching method combining Reeb graphs in the present application can increase the accuracy of pollution source identification to more than 85% in typical industrial pollution scenarios, which is about 20% higher than the existing methods.

[0009] Additionally, the method according to the above embodiments of the present application may further have the following additional technical features: In some embodiments of the present application, in step (2), the three-dimensional fluorescence spectrum data is normalized to an 8-bit grayscale image.

[0010] In some embodiments of the present application, standardization or min-max scaling method is used for the data normalization process.

[0011] In some embodiments of the present application, in step (2), Gaussian window filtering, median filtering, or Wiener filtering is used to remove noise.

[0012] In some embodiments of the present application, step (3) includes: extracting the closed isogray lines in the isogray line graph, calculating the concave points corresponding to the minimum curvature values on each closed isogray line, and calculating the pairwise distances of the points in the concave point set on the XOY plane; using a preset distance threshold to screen out adjacent concave points, defining the concave points with a distance lower than the preset threshold as adjacent to form several subsets of concave points; identifying and extracting the concave point pairs on the same closed isogray line as feature points.

[0013] In some embodiments of the present application, the pairwise distance is pairwise Euclidean distance, pairwise Huffman distance, or pairwise Manhattan distance.

[0014] In some embodiments of the present application, step (4) includes: calculating the average of the positions and heights of all points inside each isogray line containing at least one pair of the feature points as the spatial position and intensity attribute of the Reeb graph node.

[0015] In some embodiments of the present application, step (4) further includes: incorporating at least one of the shape features, symmetry, and change trend of the peaks in the three-dimensional fluorescence spectrum into the attributes of the Reeb graph node.

[0016] In some embodiments of the present application, step (6) includes: starting from the root node of the Reeb graph, layer by layer, matching the spatial positions and intensity attributes of the nodes in the same layer of the Reeb graph of the water sample to be tested and the Reeb graph of the preset wastewater sample library, calculating the similarity, and taking the maximum similarity value as the matching result of the current layer; iteratively calculating the similarity of the sub-nodes; and accumulating the matching results of all levels to obtain the global similarity between the Reeb graph of the water sample to be tested and the Reeb graph of the preset wastewater sample library.

[0017] In the second aspect of the present application, the present application proposes an application of the accurate traceability method for the similarity of three-dimensional fluorescence spectra based on the Reeb graph as described in the above embodiments in environmental monitoring, biomedicine, food safety, or criminal investigation and cultural relic identification. Thus, the accurate traceability method for the similarity of three-dimensional fluorescence spectra based on the Reeb graph of the present application can achieve efficient and accurate spectrum traceability matching in the above application scenarios and can provide reliable similarity evaluation in the above application scenarios.

[0018] The additional aspects and advantages of the present application will be partially given in the following description, partially become apparent from the following description, or be understood through the practice of the present application. Description of the Drawings

[0019] The above and / or additional aspects and advantages of the present application will become apparent and be easily understood from the description of the embodiments in conjunction with the following drawings, where: Figure 1 is a schematic flowchart of the accurate traceability method for the similarity of three-dimensional fluorescence spectra based on the Reeb graph in some embodiments of the present application; Figure 2 is a schematic flowchart of the accurate traceability method for the similarity of three-dimensional fluorescence spectra based on the Reeb graph in still some other embodiments of the present application; Figure 3 is a schematic diagram of the matching between the Reeb graph (left) of DJ1Z25.csv and the Reeb graph (right) of DJGYTM101.csv in Embodiment 1 of the present application; Figure 4 is a partial matching result of Embodiment 1. Detailed implementation manners

[0020] The embodiments of the present application will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals indicate the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present application, but should not be construed as limiting the present application.

[0021] In one aspect of the present application, the present application proposes a precise traceability method for the similarity of three-dimensional fluorescence spectra based on the Reeb graph. According to the embodiments of the present application, with reference to the attached Figure 1 drawings, the method includes: S100: Obtain the three-dimensional fluorescence spectra of a preset wastewater sample library; S200: Perform data normalization processing on the three-dimensional fluorescence spectra of the preset wastewater sample library, remove noise, and draw an isogray scale map; S300: Obtain the feature points on the isogray scale map; S400: Based on the isogray scale map containing the feature points, judge the enclosure relationship layer by layer, and construct the Reeb graph of the preset wastewater sample library; S500: Obtain the three-dimensional fluorescence spectra of the water sample to be tested, and construct the Reeb graph of the water sample to be tested according to the method of steps S200 to S400; S600: Match the Reeb graph of the water sample to be tested with the Reeb graph of the preset wastewater sample library and calculate the similarity. When the similarity between the Reeb graph of the water sample to be tested and a certain Reeb graph in the preset wastewater sample library is greater than or equal to 0.6, it is considered to have the possibility of homology and has a clear directivity; when the similarity between the Reeb graph of the water sample to be tested and all the Reeb graphs of the preset wastewater sample library is less than 0.6, it is considered not to have the possibility of homology and does not have a clear directivity.

[0022] The precise traceability method for the similarity of three-dimensional fluorescence spectra based on the Reeb graph according to the embodiments of the present application significantly improves the accuracy and robustness of complex water body pollution traceability. Compared with the traditional method that relies on the comparison of the positions and intensities of characteristic peaks, the Reeb graph of the present application realizes the modeling and recognition of the global morphology of the fluorescence spectrum by capturing the topological structure relationship between the isogray scales in the spectrum, and has strong anti-interference ability and pattern recognition ability. In practical applications, this method can effectively alleviate the problem of spectrum distortion caused by factors such as water sample dilution, mixing, or fluorescence intensity change, and ensure that stable recognition can still be performed through the topological structure in the case of partial distortion or deviation of the fluorescence signal. Experimental results show that the similarity matching method combined with the Reeb graph of the present application can improve the accuracy of pollution source identification to more than 85% in typical industrial pollution scenarios, which is about 20% higher than the existing methods.

[0023] This application uses Reeb graphs to describe the topological structure features of three-dimensional fluorescence spectra. By extracting isogreyscale lines containing feature points and judging the enclosure relationship between isogreyscale lines layer by layer, a Reeb graph is generated. For each isogreyscale line, the average value of the positions (XY coordinates) and heights (Z coordinates) of its internal points is calculated as the spatial position and intensity attribute of the Reeb graph node. At the same time, based on the inclusion relationship of isogreyscale lines, the parent-child hierarchical structure of the nodes is determined to achieve multi-scale topological characterization of the fluorescence spectrum, thereby enhancing the spatial structure expression ability of the spectrum.

[0024] The following details the accurate traceability method for the similarity of three-dimensional fluorescence spectra based on Reeb graphs proposed in this application: Specifically, referring to Appendix Figure 1 and Appendix Figure 2 the accurate traceability method for the similarity of three-dimensional fluorescence spectra based on Reeb graphs includes the following steps: S100: Obtain the three-dimensional fluorescence spectra of a preset wastewater sample library; In this step, typical polluting industries and key polluting emission enterprises can be selected as research objects, and their representative wastewater samples are collected and scanned and analyzed using a three-dimensional fluorescence spectrometer to obtain the three-dimensional fluorescence spectra (Excitation-Emission Matrix, EEM) of the preset wastewater sample library.

[0025] S200: Perform data normalization processing on the three-dimensional fluorescence spectra of the preset wastewater sample library, remove noise, and draw an isogreyscale line graph; In this step, the three-dimensional fluorescence spectrum data of the preset wastewater sample library can be normalized to an 8-bit grayscale image, and Gaussian window filtering is applied to smooth the noise. Subsequently, an isogreyscale line graph is drawn to extract the topological features of the fluorescence signal.

[0026] In the embodiments of this application, the data preprocessing step can be flexibly replaced by any technical combination including data normalization and noise removal. For example, other methods can be used for data normalization, such as standardization, min-max scaling, etc., and noise removal can be achieved through different filters, such as median filtering, Wiener filtering, etc. The specific selection depends on the data characteristics and application requirements.

[0027] S300: Obtain the feature points on the isogreyscale line graph; In this step, by processing the filtered grayscale image, closed isograys are extracted, and the points with minimum curvature are calculated as concave points. Adjacent concave points are selected using a preset distance threshold to form a subset of concave points. On this basis, concave point pairs from the same closed isogray are identified and extracted as feature points, and a key feature set representing the shape and distribution of the fluorescence peak is constructed. These feature sets can effectively capture the spatial features and morphological information of the fluorescence peak and are the basis for fluorescence spectrum similarity matching.

[0028] According to some specific embodiments of the present application, step S300 includes the following steps: S310: Extract the closed isograys in the isogray map, calculate the concave points corresponding to the minimum curvature on each closed isogray, and calculate the pairwise distances of the points in the concave point set in the XOY plane; S320: Use the preset distance threshold to select adjacent concave points, define the concave points with a distance lower than the preset threshold as adjacent, and form several subsets of concave points; S330: Identify and extract the concave point pairs on the same closed isogray as feature points for subsequent structural analysis.

[0029] In the embodiments of the present application, for the extraction of the feature point set, other quantization metrics can be used for selection. For example, concave points can be defined by setting different curvature thresholds, or important point sets can be determined based on other geometric features (such as curvature radius, inflection point, etc.). Different definitions of feature points help capture different detailed features of the data and further improve the adaptability of the model.

[0030] In the embodiments of the present application, in terms of the definition of the distance and height between nodes, in addition to the Euclidean distance, other similarity metrics can also be used, such as the Huffman distance or the Manhattan distance. The most suitable distance metric is selected according to the spatial and feature distribution characteristics in the actual application to improve the accuracy and reliability of the similarity calculation.

[0031] In some embodiments of the present application, to achieve accurate extraction of feature points, in step S300, first, each closed isogray is resampled with discrete points to ensure uniform point spacing. Subsequently, the curvature of each point on the isogray is calculated based on the differential geometry method, and the curvature can be estimated using the following formula:

[0032] where is the coordinate of the 𝑖-th sampling point on the closed isogray. The point corresponding to the minimum curvature is defined as a local concave point, which is used to characterize the concave feature region of the isogray and further used to construct the feature point set.

[0033] To improve the robustness of structural matching, a dynamic distance threshold selection mechanism is adopted during the construction of the concave point subset. The threshold range is adaptively set according to the overall size of the current atlas, avoiding matching failures caused by scale differences. The concave point pairs are composed of points located on the same closed isogray line and satisfying the angle constraint (for example, the included angle between the normal vectors of the concave points is within a preset range), thus better reflecting the regional fluorescence structure characteristics.

[0034] S400: Based on the isogray line map containing feature points, judge the enclosure relationship layer by layer to construct the Reeb graph of the preset wastewater sample library; In this step, for each isogray line containing at least one pair of feature points, calculate the average value of the positions (XY coordinates) and heights (Z coordinates) of all points inside the line, and use it as the spatial position and height attribute (i.e., intensity attribute) of the Reeb graph node. The parent-child relationship of the Reeb graph is determined by the hierarchical enclosure relationship of the isogray lines.

[0035] In this step, construct the Reeb graph based on the above feature points. Each isogray line is regarded as an initial node, and its position and intensity attribute in three-dimensional space are determined by calculating the weighted center of gravity and average gray value of the feature points it contains. The connection relationship between nodes is automatically generated according to the nested or adjacent relationship of the isogray lines in space to form a complete Reeb topological structure.

[0036] In the embodiments of the present application, in addition to the spatial position and intensity attributes in the above embodiments, the nodes of the Reeb graph may further include data describing the topological features of the fluorescence atlas. For example, other spectral features such as the shape features, symmetry, or change trends of the peaks in the three-dimensional fluorescence atlas can be further incorporated into the attributes of the nodes, so as to achieve richer information expression and similarity analysis.

[0037] The Reeb graph of the present application has: 1) Structural sensitivity: It can capture the geometric morphology of the atlas and the relationship of key peak positions, reducing noise interference; 2) Interpretability: It can quantify the similarity through topological features (such as persistent barcodes) to support the traceability decision-making; 3) Cross-scale analysis: It adapts to data with different resolutions or local distortions, improving the robustness. The accurate traceability method for the similarity of three-dimensional fluorescence spectra based on the Reeb graph can break through the limitations of existing spectral matching technologies (such as parallel factor analysis PARAFAC, cosine similarity) in complex scenarios, providing core technical support for accurately identifying the source of pollutants, optimizing environmental governance, and ensuring the reliability of biomedical detection.

[0038] S500: Obtain the three-dimensional fluorescence spectrum of the water sample to be tested, and construct the Reeb graph of the water sample to be tested according to the methods in steps S200~S400; In this step, a three-dimensional fluorescence spectrometer can be used for scanning and analysis to obtain the three-dimensional fluorescence spectrum of the water sample to be tested, and then the Reeb graph of the water sample to be tested is constructed according to the methods in steps S200 to S400. Specifically, data normalization processing is performed on the three-dimensional fluorescence spectrum of the water sample to be tested to remove noise, an isogray scale map is drawn, characteristic points on the isogray scale map are obtained, and based on the isogray scale map containing the characteristic points, the enclosure relationship is judged layer by layer to construct the Reeb graph of the water sample to be tested. The specific process and details of constructing the Reeb graph of the water sample to be tested are the same as those of constructing the Reeb graph of the preset wastewater sample library, and will not be elaborated here.

[0039] S600: Match the Reeb graph of the water sample to be tested with the Reeb graph of the preset wastewater sample library and calculate the similarity.

[0040] In this step, the Reeb graph of the water sample to be tested is matched with the Reeb graph of the preset wastewater sample library and the similarity is calculated. When the similarity between the Reeb graph of the water sample to be tested and a certain Reeb graph in the preset wastewater sample library is greater than or equal to 0.6, it is regarded as having the possibility of homology and having a clear directivity; when the similarity between the Reeb graph of the water sample to be tested and all the Reeb graphs of the preset wastewater sample library is less than 0.6, it is regarded as not having the possibility of homology and not having a clear directivity.

[0041] Considering that pollutants in the actual water body may be mixed, diluted, degraded, etc. during the transport process, resulting in intensity offset or feature weakening of the fluorescence signal, a similarity threshold (SimilarityThreshold) of 0.6 is set during the matching process. That is, when the similarity between the water sample to be tested and the database spectrum is greater than or equal to 0.6, it is regarded as having a high possibility of homology and having a clear directivity, providing a technical basis for locking the pollution source.

[0042] In this step, the calculation of the similarity of the fluorescence spectrum is transformed into a Reeb graph matching problem. During the matching process, starting from the root node of the Reeb graph, the spatial positions and intensity attributes of the same-layer nodes of the Reeb graph of the water sample to be tested and the Reeb graph of the preset wastewater sample library are matched layer by layer, and the maximum similarity value is taken as the matching result of the current layer. Then, the child nodes are iteratively matched to gradually optimize the matching accuracy. Finally, the matching results of all levels are accumulated to obtain the global similarity between the Reeb graph of the water sample to be tested and the Reeb graph of the preset wastewater sample library. This method realizes efficient and accurate spectrum traceability matching and can provide reliable similarity evaluation in complex multi-source pollution scenarios.

[0043] According to some specific embodiments of the present application, step S600 includes: S610: Starting from the root node of the Reeb graph, layer by layer, match the spatial positions and intensity attributes of the nodes at the same layer of the Reeb graph of the water sample to be measured and the Reeb graph of the preset wastewater sample library. Pairwise compare the nodes at the same layer of different Reeb graphs, calculate the similarity, and take the maximum similarity value as the matching result of the current layer; Specifically, for the initial matching: starting from the root node, compare the top-layer nodes of the Reeb graph to be matched, calculate the spatial position distance (such as Euclidean distance) and intensity attribute distance between the nodes respectively, and calculate the node similarity in the following way :

[0044] where is the weight coefficient, is the Euclidean distance of the compared Reeb graph layer, is the magnitude of the intensity attribute of the compared Reeb graph layer.

[0045] S620: After the matching is completed, iteratively calculate the similarity of the child nodes; In this step, perform hierarchical recursive matching, iterate layer by layer for the child nodes, construct the matching path between the hierarchical structures, and calculate the cumulative similarity of each layer.

[0046] S630: Accumulate the matching results of all levels to obtain the global similarity between the Reeb graph of the water sample to be measured and the Reeb graph of the preset wastewater sample library.

[0047] In this step, use the path-weighted accumulation method to integrate the matching results of each layer to obtain the final global similarity , as the matching metric between the sample and the database graph.

[0048] In the embodiments of the present application, during the similarity calculation process, the matching method of the nodes also has flexibility. In addition to the layer-by-layer maximum similarity matching method used in the above embodiments, other matching strategies can also be selected, such as iterative deepening depth-first matching or global maximum similarity matching. These methods can be selected according to the complexity of the data and the topological structure of the graph to optimize the matching accuracy and algorithm performance.

[0049] According to the accurate tracing method of the three-dimensional fluorescence spectrum similarity based on the Reeb graph in the embodiments of the present application, the Reeb graph is used to analyze the data characteristics of the three-dimensional fluorescence spectrum, convert the fluorescence signal into topological structure information, and directly capture the spatial distribution and morphological characteristics of the fluorescence peaks (such as the position and shape symmetry of the peaks), rather than relying on the signal intensity or preset factors. Compared with the prior art, this method also has the following advantages: 1) Efficient analysis of non-linear mixed signals: Traditional methods (such as PARAFAC or PCA) rely on the assumption of linear decomposition and are difficult to handle complex non-linear mixed fluorescence signals. In contrast, the Reeb graph of the present application can characterize the nested relationship of multiple fluorescence peaks (such as the inclusion relationship between the main peak and the shoulder peak) through topological structure, analyze the spatial superposition pattern of mixed pollution sources, improve the analysis ability of non-linear data, and enhance the interpretability and robustness of the model.

[0050] 2) Topological structure enhances interpretability: The nodes of the Reeb graph of the present application directly correspond to the physical positions and intensities of the isogreyscales, enabling the matching results to be intuitively traced back to specific regions of the fluorescence spectrum (such as a certain excitation-emission peak). In contrast, deep learning models in the prior art usually operate as "black boxes" and are difficult to provide traceable decision-making bases. The structured information of the Reeb graph of the present application makes it more suitable for scientific research and engineering applications that require result interpretability.

[0051] 3) High computational efficiency and suitability for portable devices: The present application constructs a Reeb graph based on a grayscale image and only matches key feature points instead of performing global calculations on all isogreyscales, thereby reducing the computational complexity and the hardware computing power requirements. This makes it more suitable for deployment on portable devices and can be applied to scenarios such as rapid field detection. In contrast, traditional methods often involve a large amount of matrix operations and have high computational overhead, while deep learning models require high computing power for training and inference, which limits their application in resource-constrained environments.

[0052] 4) Wide application potential: Due to the high efficiency, interpretability, and computational economy of this method, it has significant technical advantages and application prospects in application scenarios that require rapid and high-precision analysis, such as environmental monitoring (such as multi-source pollution tracing) and food safety (such as adulteration detection).

[0053] In the second aspect of the present application, the present application proposes an application of the accurate tracing method based on the similarity of three-dimensional fluorescence spectra of the Reeb graph as described in the above embodiments in environmental monitoring, biomedicine, food safety, or criminal investigation and cultural relic identification. Thus, the accurate tracing method based on the similarity of three-dimensional fluorescence spectra of the Reeb graph of the present application can achieve efficient and accurate spectrum tracing matching in the above application scenarios and can provide reliable similarity evaluation in the above application scenarios.

[0054] The above accurate tracing method based on the similarity of three-dimensional fluorescence spectra of the Reeb graph can be applied to fields such as environmental monitoring, biomedicine, chemical analysis, and materials science, especially in scenarios that require identifying the source or components of substances from complex mixtures or high-dimensional spectral data. For example: Environmental monitoring: Quickly trace the emission sources of organic pollutants (such as petroleum hydrocarbons, industrial dyes) in water bodies or the atmosphere; Biomedicine: Analyze the fluorescence markers in biological tissues or body fluids to assist in disease diagnosis or drug metabolism research; Food safety: Identify the sources of food additives or illegal additives; Criminal investigation and cultural relic identification: Support physical evidence comparison or authenticity identification of cultural relics through material composition traceability.

[0055] In particular, the above-mentioned precise traceability method based on the similarity of 3D fluorescence spectra of Reeb graphs can be applied to water environment monitoring and pollution traceability, including: Rapid location of pollution sources: Precisely identify the emission sources of industrial wastewater (such as petrochemical, pharmaceutical, printing and dyeing), agricultural non-point source pollution (pesticides / fertilizers), or domestic sewage.

[0056] Typical scenarios: Traceability of sudden oil spills in rivers (such as the distinction between petroleum hydrocarbons and marine fuel oil).

[0057] Analysis of pollutant components: Separate multi-component fluorescence signals such as dissolved organic matter (DOM) and pollutants adsorbed on the surface of microplastics from complex mixed water bodies.

[0058] Dynamic tracking of pollution incidents: Combine with a hydrological model to inversely infer the pollution diffusion path through the topological differences of Reeb graphs of multi-point sampling spectra.

[0059] The embodiments of the present application will be described in detail below. It should be noted that the embodiments described below are exemplary and are only used to explain the present application and should not be construed as a limitation of the present application. Additionally, if not explicitly stated, all reagents used in the following embodiments are commercially available or can be synthesized according to the methods described herein or known methods. For the reaction conditions not listed, they are also easily obtained by those skilled in the art.

[0060] Example 1 This example traces the 3D fluorescence data DJ1Z25.csv, including the following steps: (1) First, obtain the target abnormal surface water sample, and perform a full-band scan on the target abnormal surface water sample through a fluorescence spectrophotometer (model: F-7100, Hitachi). The excitation wavelength range is 200 nm - 500 nm, the emission wavelength range is 200 nm - 600 nm, the wavelength step size is 5 nm, and the integration time is set to 0.5 s to obtain its complete 3D fluorescence spectrum matrix. The obtained original data is saved as "DJ1Z25.csv".

[0061] Subsequently, preprocess the original EEM data, including: Normalization: Using the min - max normalization method, the intensity values are scaled to the range of [0, 255] and converted into an 8 - bit grayscale image for easy image processing and isogray line extraction; Noise removal: The image is smoothed using Gaussian window filtering (window size set to 5×5, σ = 1.0) to effectively reduce the random noise generated during instrument scanning.

[0062] (2)Isogray line map construction and feature point extraction Use the contour() function in Matplotlib to draw the isogray line map and extract the closed isogray lines in the map. For each isogray line, sample its coordinate points and calculate the curvature value of each point according to the discrete curvature estimation formula to identify the concave points at the minimum curvature.

[0063] Calculate the pairwise Euclidean distances of all concave points in the XOY plane. Set the distance threshold to 10 pixels, and those below this value are regarded as adjacent concave points. Divide all adjacent concave points into multiple subsets of concave points. In the same subset, if two concave points come from the same closed isogray line, then define this point pair as a feature point.

[0064] (3)Reeb graph construction Based on the above - mentioned feature points, construct the Reeb graph layer by layer according to the nested structure relationship of the isogray lines. For each closed isogray line containing at least one pair of feature points, calculate the spatial position mean gray - value mean of all the pixel points inside it, and use it as the coordinate attribute (x, y, intensity) of this node.

[0065] Directed edges are automatically generated between nodes according to the containment and nesting relationships to form a complete hierarchical structure. This graph structure preserves the global contour and local features of the map to a certain extent.

[0066] (4)Similarity matching and traceability analysis Load data of several other typical polluting enterprises in the three - dimensional fluorescence map database (such as DJGYTT101.csv, DJGYTM108.csv, etc., as shown in Table 1), and construct their Reeb graphs using the same process. Taking the Reeb graph of DJ1Z25.csv as the target graph, match it with the Reeb graphs of other graphs in the database one by one, and perform the following steps: Node matching: Starting from the root node, calculate the similarity between nodes in the same layer according to the spatial position and gray value: , where α = 0.5, β = 0.5; Hierarchical recursion: Recursively match the child nodes and record the matching scores of each layer; Global similarity calculation: The scores of each layer are weighted and accumulated to obtain the final global similarity , reflecting the structural similarity between the two graphs. Attached Figure 3 is a schematic diagram of the Reeb graph structure matching between DJ1Z25.csv and DJGYTM101.csv; Attached Figure 4 is a visualization diagram of partial matching results.

[0067] Table 1 lists the matching similarity results between DJ1Z25.csv and other typical pollution samples in the database. Attached Figure 3 is a schematic diagram of the matching between the Reeb graph (left) of DJ1Z25.csv and the Reeb graph (right) of DJGYTM101.csv. Attached Figure 4 is a partial matching result of Example 1.

[0068] Table 1

[0069] From Table 1 and Attached Figure 4 it can be seen that the global similarity between DJGYTT101.csv and DJ1Z25.csv is 22.9%, the similarity between DJGYTM108.csv and DJ1Z25.csv is 21.9%, and the similarities of the remaining data with DJ1Z25.csv are all lower than 20%. Based on this, it can be judged that DJGYTT101.csv is the most likely pollution source sample, but it does not have a clear directivity.

[0070] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic descriptions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0071] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present application. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. A precise tracing method for three-dimensional fluorescence spectrum similarity based on Reeb graph, characterized in that: include: (1) Obtaining a three-dimensional fluorescence spectrum of a preset wastewater sample library; (2) performing data normalization processing on the three-dimensional fluorescence spectrum of the preset wastewater sample library, removing noise, and drawing an isogray line diagram; (3) Obtaining feature points on the grayscale line map; (4) Based on the grayscale line map containing the feature points, the encirclement relationship is determined layer by layer to construct a Reeb map of the preset wastewater sample library; (5) obtaining a three-dimensional fluorescence spectrum of the water sample to be tested, and constructing a Reeb map of the water sample to be tested according to the method of steps (2) to (4); (6) The Reeb graph of the water sample to be tested is matched with the Reeb graph of the preset wastewater sample library and the similarity is calculated. When the similarity between the Reeb graph of the water sample to be tested and a certain Reeb graph in the preset wastewater sample library is greater than or equal to 0.6, it is considered that there is a possibility of homology and has a clear directionality; when the similarity between the Reeb graph of the water sample to be tested and all the Reeb graphs in the preset wastewater sample library is less than 0.6, it is considered that there is no possibility of homology and does not have a clear directionality.

2. The precise traceability method according to claim 1, characterized in that: In step (2), the three-dimensional fluorescence spectrum data is normalized to an 8-bit grayscale image.

3. The precise traceability method according to claim 2, characterized in that: The data were normalized using standardization or min-max scaling.

4. The precise traceability method according to claim 1, characterized in that: In step (2), Gaussian window filtering, median filtering or Wiener filtering is used to remove noise.

5. The precise traceability method according to claim 1, characterized in that: Step (3) includes: Extracting closed isogray lines in the isogray line map, calculating the concave points corresponding to the minimum curvature on each of the closed isogray lines, and calculating the pairwise distances of each point in the concave point set on the XOY plane; Adjacent concave points are screened out using a preset distance threshold, and concave points whose distance is lower than the preset threshold are defined as adjacent to form a number of concave point subsets; Identify and extract the concave point pairs on the same closed equal grayscale line as feature points.

6. The precise traceability method according to claim 5, characterized in that: The pairwise distances are pairwise Euclidean distances, pairwise Huffman distances, or pairwise Manhattan distances.

7. The precise traceability method according to any one of claims 1 to 6, characterized in that: Step (4) includes: The average values ​​of the positions and heights of all points inside each equal grayscale line containing at least one pair of the feature points are calculated as the spatial position and intensity attributes of the Reeb graph nodes.

8. The precise traceability method according to claim 7, characterized in that: Step (4) also includes: At least one of the shape characteristics, symmetry and change trend of the peaks in the three-dimensional fluorescence spectrum is incorporated into the attributes of the Reeb graph node.

9. The precise traceability method according to any one of claims 1 to 6, characterized in that: Step (6) includes: Starting from the root node of the Reeb graph, the spatial positions and intensity attributes of the nodes in the same layer of the Reeb graph of the water sample to be tested and the Reeb graph of the preset wastewater sample library are matched layer by layer, the similarity is calculated, and the maximum similarity value is taken as the matching result of the current layer; Iteratively calculate the similarity of child nodes; The matching results of all levels are accumulated to obtain the global similarity between the Reeb graph of the water sample to be tested and the Reeb graph of the preset wastewater sample library.

10. An application of a precise source tracing method based on the similarity of three-dimensional fluorescence spectra of Reeb graphs as claimed in any one of claims 1 to 9 in environmental monitoring, biomedicine, food safety or criminal investigation.

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