Field dyeing tracing and soil nutrient migration analysis method fused with spectral analysis

Abstract

The invention relates to the technical field of in-situ monitoring, in particular to a field dyeing tracing and soil nutrient migration analysis method fused with spectral analysis, in which a statistical analysis and threshold screening strategy of total gradient change of channels effectively focuses on key concentration evolution channels, avoids interference of redundant paths on overall analysis precision, and improves the accuracy of the analysis. A graph convolutional neural network is adopted to carry out topology propagation and embedded representation on an adjacency relationship constructed by concentration difference nodes, and through a combined judgment mode of a concentration change rate, an included angle cosine value and a distance, it is ensured that a graph structure has physical coherence when expressing nutrient migration spatial evolution characteristics; through the similarity measurement and high-frequency serial number clustering processing between node feature vectors, hot spot region extraction and structured expression of concentration migration are realized, and the dynamic evolution trend of a local high-risk region in soil is effectively restored in combination with a frequency chart generated by time and depth index statistics, so that the reliability of the system is improved. And the analysis precision and the expression level of the complex nutrient migration behavior are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of in-situ monitoring technology, and in particular to a field dye tracing and soil nutrient migration analysis method combined with spectral analysis. BACKGROUND

[0002] The field of in-situ monitoring technology aims to realize the on-site, non-destructive and real-time detection of target media in natural and artificial environments, independent of sample removal and laboratory analysis, and is mainly applied to the dynamic perception and data collection of soil moisture, pollutant concentration, nutrient changes and the like, and uses various optical, electrochemical or physical sensing mechanisms to realize on-site data acquisition.

[0003] A field dye tracing and soil nutrient migration analysis method combined with spectral analysis introduces a dye tracer with specific optical absorption characteristics into the soil, and uses a spectrometer to measure the concentration distribution of the dye at different positions, thereby inferring the rules of the movement of soluble nutrients in the soil with water, with the purpose of realizing dynamic quantitative analysis of nutrient migration behavior, evaluating the environmental impact of agricultural fertilization behavior, irrigation efficiency and soil erosion risk, and providing a data basis for precision agriculture management and soil conservation.

[0004] The prior art relies on fixed optical or electrochemical sensor units to collect local response signals, and the data structure is mainly based on static numerical values or single-time period images, lacking the ability to construct data structures with continuous time dimensions, resulting in limitations in modeling dynamic processes such as nutrient migration, which are confined to low-dimensional state inference, and unable to capture the time evolution process of concentration changes. The single-point comparison method of reflectance changes lacks sensitivity in detecting multi-path parallel migration or local mutation phenomena, and in high spatial complexity environments, often results in false positives or false negatives. There is a lack of comprehensive judgment basis for the directionality and adjacency strength of change trends, which can easily construct physically unreasonable graph structures, reducing the accuracy of subsequent analysis. The quantitative characterization of concentration changes lacks systematic extraction and statistical support for the aggregation behavior of hot spot distribution areas in the time and depth dimensions, making it difficult to meet the needs of high-density area identification for precision agricultural strategies and risk prediction. SUMMARY

[0005] The purpose of the present application is to solve the problems existing in the prior art and to provide a field dye tracing and soil nutrient migration analysis method combined with spectral analysis.

[0006] In order to achieve the above-mentioned purpose, the present application adopts the following technical solution: a field dye tracing and soil nutrient migration analysis method combined with spectral analysis, comprising the following steps:

[0007] S1: Based on the image profile sequence obtained by the field dye tracing monitoring unit, the reflectivity of the numbered area is extracted and the time sequence is divided, the difference of the numbered value among three time periods is calculated and the sign change is identified, the numbered group with change frequency exceeding the limit is screened out, the coordinate positioning and numbering are combined, and the change coordinate set is obtained;

[0008] S2: Based on the change coordinate set, the reflectivity of the numbered area is extracted and the time sequence is divided, the difference of the numbered value among three time periods is calculated and the sign change is identified, the numbered group with change frequency exceeding the limit is screened out, the coordinate positioning and numbering are combined, and the gradient annotation map is obtained;

[0009] S3: Based on the gradient annotation map, a long short-term memory network is used to construct a three-element sequence of concentration value, time and depth, and to combine fertilizer application amount, water value and lag time to integrate into an input tensor. The total gradient change of the channel is calculated and a threshold value is set to judge, select the effective channel and activate, and establish a migration sequence diagram.

[0010] S4: Based on the migration sequence diagram, a graph convolution network is used to extract concentration difference nodes and construct adjacency relationship, calculate the combined value of the included angle cosine and the distance to judge the connection condition, form the edge set of the graph structure, generate node representation and integrate, and generate a topological embedding graph.

[0011] S5: Based on the topological embedding graph, the similarity of node vectors is calculated and the numbered groups are clustered, the high-density groups are screened out, the time and depth indexes corresponding to the groups are extracted, the frequency statistics and distribution record are performed, and the hotspot distribution table is obtained.

[0012] As a further scheme of the present application, the specific steps for generating the change coordinate set are:

[0013] Based on the image profile sequence obtained by the field dye tracing monitoring unit, the pixel row and column index of the numbered area is analyzed and the boundary index is located, the image frames are divided in time label order and the reflectivity value sequence of the numbered area is extracted, three groups of time matrices are constructed through frame time order, and a time period sequence matrix is generated.

[0014] Based on the time period sequence matrix, the difference of the three groups of reflectivity values under each number is calculated and the positive and negative change states are marked, the number of sign changes is counted and the numbered groups with change frequency more than one are screened out, the numbered set is aggregated through numbered screening logic, and a mutation numbered set is generated.

[0015] Based on the mutation numbered set, the pixel position horizontal and vertical coordinates corresponding to the number are extracted and the time index is merged, the extracted coordinates are rearranged and integrated into positioning coordinate groups in grid space, and three-dimensional positioning information is constructed combined with the number, and the change coordinate set is obtained.

[0016] As a further scheme of the present application, the specific steps for generating the gradient annotation map are:

[0017] Based on the change coordinate set, the image vertical direction spectrum sequence corresponding to the coordinates is extracted, the vertical change amount between adjacent pixel values is calculated and recorded as a continuous gradient value sequence, each channel gradient is assembled in the coordinate order, and a longitudinal gradient sequence is generated;

[0018] Based on the longitudinal gradient sequence, the corresponding number of infiltration path length values is obtained, and the ratio operation of each path and gradient value is performed, the numbers greater than the upper quartile and less than the lower quartile are screened out through the ratio range, an abnormal number sequence is assembled, and a gradient abnormal number set is generated;

[0019] Based on the gradient abnormal number set, the depth number is found and extracted in the number upper and lower pixel sequence according to the reflectivity value, the three-dimensional labeling data structure is established by combining the depth number and the horizontal and vertical coordinates, the gradient labeling map is obtained after mapping into the image index system after uniform labeling format.

[0020] As a further scheme of the present application, the specific steps for generating the migration sequence map are:

[0021] Based on the gradient labeling map, the pixel concentration value under each labeling number is extracted and matched with the corresponding time number and depth index, a three-element array is established in the number order, the fertilizer amount, water value and lag time are integrated in the order index mode, the field is aligned and the channel input structure is constructed, and a structure input sequence set is generated;

[0022] Based on the structure input sequence set, the numerical change amount of each channel along the time dimension is extracted and a summation operation is performed, the total value of the channel change amplitude is obtained and compared with the set threshold value, the channel index with the change amplitude greater than the threshold value is marked and the number sequence is output, and an active channel number set is generated;

[0023] Based on the active channel number set, a long short-term memory network is used to extract the corresponding sequence of the matching channel number in the original input structure and construct a three-dimensional array structure, the data path is rearranged so that the concentration time sequence is spliced in the order of channel number, a channel activation tensor structure is formed by combination, and a migration sequence map is obtained.

[0024] As a further scheme of the present application, the long short-term memory network is according to the formula:

[0025] h t =σ(W ih ·(x t ⊙γ c )+b ih +α t ·(W hh ·h t-1 )+λ s ·∈ t +b hh );

[0026] wherein: h t denotes the hidden state output at time t, and σ denotes a nonlinear activation function, W ih denotes the weight matrix input to the hidden state, x t denotes the dye spectral concentration time series extracted at the activation channel number at time t, and γ c denotes the channel number suppression factor, b ih denotes the bias vector at the input stage, h t-1 denotes the hidden state output at time t-1, and W hh denotes the weight matrix between the hidden layers, α t denotes the time sequence attention coefficient, ∈ t denotes the spectral concentration gradient change tensor between channels at time t, and λ s denotes the channel gradient suppression coefficient, b hh denotes the bias vector at the hidden state stage.

[0027] As a further scheme of the present application, the long short-term memory network first extracts the concentration values, time series and depth indexes corresponding to the activation channel number set in order of channel number, and constructs a three-dimensional array structure, each dimension corresponding to the channel, time step and feature quantity, respectively, then inputs the array to the long short-term memory network unit in turn, and sequentially performs the gating mechanism operation, including the state update of the input gate, the forgetting gate and the output gate, controls the information retention and discard process through the formula, and transmits the hidden state and the cell state in the time dimension, and outputs the complete concentration change sequence representation, and generates the channel activation tensor structure fused with the time sequence and spatial features in combination with the fertilizer amount, water value and lag time.

[0028] As a further scheme of the present application, the specific steps for generating the topological embedding graph are:

[0029] Based on the migration sequence graph, the concentration values are extracted according to the numbered positions and the difference sequence between adjacent time points is calculated, the channel positions with the absolute value of concentration difference greater than a set threshold are screened, the numbered positions satisfying the condition and the corresponding time indexes are extracted to form a sequence set, and a concentration mutation node set is generated;

[0030] Based on the concentration mutation node set, the Euclidean distance corresponding to the coordinates between nodes is calculated and the water vector direction value is extracted, the node pair vector angle structure is constructed and the cosine value is calculated, it is judged whether the cosine of the angle is greater than a set threshold and the distance is less than double the average value, the node pairs meeting the conditions are screened, and a connected node edge set is generated;

[0031] Based on the connection node edge set, a graph convolution network is used to splice the concentration sequence of each pair of nodes with the time index sequence to generate a double-channel input structure, the embedding vector matrix is constructed after rearranging and merging all nodes according to the number, the spatial mapping structure is organized in the matrix arrangement format, and the topological embedding graph is generated.

[0032] As a further scheme of the application, the graph convolution network is according to the formula:

[0033]

[0034] Wherein: H (l+1) represents the node embedding feature matrix of the l+1 layer graph convolution output, ζ represents the nonlinear activation function in the graph convolution network, ψ m represents the time hierarchical attention weight matrix, represents the degree matrix corresponding to the graph adjacency matrix after adding the self-loop, represents the node adjacency matrix after adding the self-loop, H (l) represents the node feature matrix input at the lth layer, ξ n represents the node channel screening vector, W (l) represents the learnable weight matrix at the lth layer, μ g represents the spatial disturbance adjustment coefficient, Δ s represents the spatial offset compensation matrix composed of the two-dimensional coordinate position difference of the node in the field deployment.

[0035] As a further scheme of the application, the graph convolution network splices the concentration value sequence corresponding to each node with the time index sequence to form a double-channel feature vector, then rearranges and merges all nodes in the order of the number to form an embedding vector matrix, and the features of each node and the features of the directly connected adjacent nodes are weighted and converged, the weight is determined by the defined connection edge structure in the graph, and after convergence, linear transformation and nonlinear activation function processing are performed, the graph structure information and node attribute information in a larger range are integrated layer by layer, and the node embedding vector reflecting the fusion relationship of spatial topology and time sequence concentration features is obtained.

[0036] As a further scheme of the application, the specific steps for generating the hotspot distribution table are:

[0037] Based on the topological embedding graph, all node numbers are extracted and matched with corresponding embedding vectors, a combination list of number pairs is constructed in order, the inner product calculation of each pair of embedding vectors is performed and the cosine similarity value is recorded, the similarity matrix corresponding to the number is summarized and indexed into the number index structure, and the node similarity structure set is generated;

[0038] Based on the node similar structure set, the similarity values in each column vector are sorted in descending order and the first fixed proportion of numbered indexes are screened out, the frequency of each number appearing in the high similarity pair is counted and is converted into a ratio with the total number of indexes, a number set with a ratio higher than a density threshold is extracted, and a high density number group is generated;

[0039] Based on the high density number group, the time index and depth position index of the corresponding node in the original graph structure are extracted, a number and index double key mapping table structure is established, the time and depth index fields in the mapping table are counted and the cumulative frequency values are recorded, the two field frequency structure tables are combined, and a hotspot distribution table is obtained.

[0040] Compared with the prior art, the application has the advantages and positive effects that:

[0041] In the application, the ratio of the spectral gradient change in the vertical direction to the path length is combined with the screening method, which improves the recognition sensitivity of the abnormal infiltration path, the concentration value, time and depth are combined to construct a ternary sequence structure, and multiple factor elements such as fertilizer amount, water value and lag time are fused to form a multi-dimensional input tensor, which is calculated by a long short-term memory neural network with a time memory mechanism, so that the model has state retention ability and long-distance dependence modeling ability in processing time series concentration change, and the depth of expression of causal relationship in the migration process is enhanced;

[0042] In the application, the statistical analysis and threshold screening strategy of the total gradient change of the channel effectively focus on the key concentration evolution channel, and avoid the interference of redundant paths on the overall analysis accuracy, the graph convolutional neural network is used to construct the adjacency relationship of the concentration difference nodes, and the combination judgment method of concentration change rate, angle cosine value and distance is used to ensure that the graph structure has physical coherence when expressing the spatial evolution characteristics of nutrient migration.

[0043] In the application, the similarity measurement between node feature vectors and high-frequency number clustering processing realize the extraction and structured expression of the hot spot area of concentration migration, and the frequency chart generated by combining the time and depth index statistics effectively restores the dynamic evolution trend of the local high-risk area in the soil, and improves the analysis accuracy and expression level of the complex nutrient migration behavior. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 The figure is a schematic diagram of the main steps of the application. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical scheme and advantages of the application more clear and explicit, the application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application and do not limit the application.

[0046] In the description of the present application, it should be understood that the terms "length", "width", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, which is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, in the description of the present application, the meaning of "a plurality of" is two or more, unless otherwise specifically limited.

[0047] Embodiment one

[0048] Please refer to Figure 1 The present application provides a technical solution: a field dye tracing and soil nutrient migration analysis method based on spectral analysis, comprising the following steps:

[0049] S1: Based on the image profile sequence obtained by the field dye tracing monitoring unit, the reflectivity of the numbered area is extracted and divided into time series, the difference between the numbered values in three time periods is calculated and the sign change is identified, the numbered groups with change frequency exceeding the limit are screened, the coordinate positioning and numbering are combined, and the change coordinate set is obtained;

[0050] S2: Based on the change coordinate set, the reflectivity of the numbered area is extracted and divided into time series, the difference between the numbered values in three time periods is calculated and the sign change is identified, the numbered groups with change frequency exceeding the limit are screened, the coordinate positioning and numbering are combined, and the gradient annotation map is obtained;

[0051] S3: Based on the gradient annotation map, a long short-term memory network is used to construct a three-element sequence of concentration value, time and depth, and to combine fertilizer amount, water value and lag time to integrate into an input tensor. The total gradient change of the channel is calculated and a threshold value is set to judge, screen the effective channel and activate it, and establish the migration sequence map;

[0052] S4: Based on the migration sequence map, a graph convolution network is used to extract concentration difference nodes and construct adjacency relationship, calculate the combination value of the included angle cosine and the distance to judge the connection condition, form the edge set of the graph structure, generate node representation and integration, and generate the topological embedding graph;

[0053] S5: Based on the topological embedding graph, the similarity of node vectors is calculated and the numbered groups are clustered, the high-density groups are screened, the time and depth indexes corresponding to the groups are extracted, the frequency statistics and distribution record are performed, and the hotspot distribution table is obtained.

[0054] The specific steps for generating the change coordinate set are:

[0055] Based on the image profile sequence obtained by the field dye tracing monitoring unit, the pixel row and column index analysis of the numbered area is performed and the boundary index is located, the image frames are divided in time label order and the reflectivity value sequence of the numbered area is extracted, three groups of time matrices are constructed through frame time sequence, and the time period sequence matrix is generated;

[0056] Based on the time period sequence matrix, the difference value of each numbered three groups of reflectivity is calculated and the positive and negative change state is marked, the number of symbol changes is counted and the numbered area with more than one change is screened out, the numbered set is aggregated through the numbered screening logic, and the mutation numbered set is generated;

[0057] Based on the mutation numbered set, the pixel position horizontal and vertical coordinates corresponding to the numbered are extracted and merged with the time index, the extracted coordinates are rearranged and integrated into the positioning coordinate group according to the grid space, and the three-dimensional positioning information is constructed combined with the numbered, and the change coordinate set is obtained;

[0058] Based on the image profile sequence obtained by the field dye tracing monitoring unit, the pixel distribution of the dyeing area in each image frame is subjected to contour detection processing by using the image contour extraction method, the pixel block structure of each numbered area is analyzed by scanning the area with non-zero gray value in the image gray matrix, the pixel set corresponding to each numbered is extracted and the row and column index boundary is located, the left upper corner and right lower corner coordinates are obtained as the boundary index of the numbered area by using the difference value calculation method of the minimum value and the maximum value of the pixel matrix, then the label field containing time information in the image sequence is analyzed, the time alignment processing of the image frame is completed by performing the string format standardization operation on the time label and then performing the lexicographic sorting, the time period image frame group is divided and it is ensured that each group corresponds to different time segments, the pixel gray value in each numbered area is extracted and counted by using the numbered area mean value calculation method, the pixel value summation operation is performed and then divided by the number of area pixels to obtain the reflectivity mean value of the numbered area in the current frame, the reflectivity mean value is extracted frame by frame in time label order and the time sequence is constructed, the numbered area reflectivity matrix of three different time segments is generated after merging according to the numbered, and the three time sequence data structures on the unified numbered axis are constructed by splicing according to the numbered alignment, and the time period sequence matrix is generated;

[0059] Based on the time period sequence matrix, the reflectivity difference comparison method is used to perform difference processing on the numerical values of the numbered regions in the adjacent two time periods in the three time period matrix. Two difference value matrices are formed by the item-by-item subtraction operation of the corresponding positions of the adjacent time frames. Then, the difference direction marking method is executed to classify the difference value results according to their numerical positive and negative, and the direction of change is marked as rising for positive values, falling for negative values, and unchanged for zero values. Through this classification logic, the corresponding symbol marking matrix is generated. The two symbol marking matrices are combined, and the symbol change sequence corresponding to each number is compared. The symbol variation count method is used to judge whether the adjacent markers change and count. Finally, the symbol change count table formed by all numbered regions is statistically processed. The numbered index list with a symbol change count greater than one is extracted. The numbered aggregation method is used to merge the selected numbers into a unified number set structure through the number field, and the mutation number set is integrated and generated.

[0060] Based on the mutation number set, the pixel position mapping method is used to extract the position index of each numbered image region. The horizontal coordinates and vertical coordinates of all pixels in the region covered by the number are retrieved, and the time label index in the current image frame is bound. The horizontal coordinates, vertical coordinates and time index are combined into a three-column record set in the field splicing manner, and the structured assembly operation is performed to form a three-field composite index structure. The spatial grid reconstruction method is used to rearrange the coordinates of the pixels in each numbered region in the two-dimensional image matrix according to the preset grid size. During the rearrangement process, the pixels are grouped based on the number as the primary key to ensure that each group of pixels corresponds to a unified number and a grid block. After sorting, a continuous coordinate set is obtained. Further, the time label index is merged into the rearranged coordinate structure, and the time-horizontal-vertical three-dimensional field combined information is constructed according to the number field. The output is a change coordinate set.

[0061] The specific steps for generating the gradient annotation map are as follows:

[0062] Based on the change coordinate set, the image vertical direction spectrum sequence corresponding to the coordinates is extracted and the pixel ordering structure is determined. The vertical change amount between adjacent pixel values is calculated and recorded as a continuous gradient value sequence. The channel gradients are assembled in the coordinate order to generate a longitudinal gradient sequence.

[0063] Based on the longitudinal gradient sequence, the corresponding number infiltration path length value is obtained and the ratio operation of each path and gradient value is performed. Through the ratio range, the numbers greater than the upper quartile and less than the lower quartile are selected, and an abnormal number sequence is assembled to generate a gradient abnormal number set.

[0064] Based on the gradient abnormal number set, the depth number is found and extracted according to the reflectivity value in the number upper and lower pixel sequence. The three-dimensional annotation data structure is assembled by combining the depth number with the horizontal and vertical coordinates. After uniform annotation format, it is mapped into the image index system to obtain the gradient annotation map.

[0065] Based on the changed coordinate set, the pixel sequence extraction method is adopted to group process the horizontal and vertical coordinate values in each set of three-dimensional coordinate positioning information, the continuous pixel rows in the vertical direction of the original image matrix are extracted according to the coordinate position index, the pixel positions corresponding to each numbered area are sequentially traversed according to the vertical coordinate by using the pixel-by-pixel row access method, and the gray values of the pixel rows in each channel are extracted as a one-dimensional sequence. The in-row sorting method is used to sort in ascending order based on the vertical coordinate, a unified pixel order structure is established, the difference value calculation operation is performed on each pixel sequence after sorting by using the row-by-row difference operation method, the current row and the next row of pixel values are subjected to subtraction operation and the original sign result is retained, the obtained difference value sequence is recorded in units of channels, and the gradient values of all channels of each set of coordinates are combined into an ordered array by using the channel data splicing method. Finally, the vertical gradient sequence is output.

[0066] Based on the vertical gradient sequence, the infiltration path estimation method is adopted to calculate the path length of each numbered pixel coordinate set. Specifically, the path length is calculated as the difference between the maximum vertical coordinate value and the minimum vertical coordinate value of the number in the vertical direction of the image, and the corresponding number is recorded. The ratio calculation method is used to pair the path length and its gradient value total one by one according to the number, and the ratio sequence is calculated by using the floating-point division operation. The quartile calculation method is used to calculate the upper quartile and lower quartile limits of the ratio sequence, and the logical filtering operation is used to construct the filtering conditions for the number indexes with a ratio greater than the upper quartile limit and a ratio less than the lower quartile limit. The numbers that meet the above two filtering conditions are merged to form an abnormal number list, and finally the gradient abnormal number set is output.

[0067] Based on the gradient abnormal number set, the local reflectivity search method is used to scan the reflectivity values of the upper and lower adjacent pixel rows in the vertical direction of each number. The scanning results are subjected to fixed window extraction operation to extract two rows of pixel data above and below the vertical coordinate as the key value, and the corresponding pixel reflectivity values are extracted to form a local pixel sequence. The local extreme point retrieval method is used to find the position indexes of the maximum and minimum values in the upper and lower pixel sequences, and the row number in the vertical direction of the index is extracted and set as the depth number value of the number. The three-column field joint index data structure is established by combining the depth number value and the original horizontal and vertical coordinates, and the structure assembly method is used to combine the three fields into a unified three-dimensional annotation array structure. The format of all numbers is standardized, the structured array is output, and the image matrix index mapping operation is performed. The structured annotation data is written into the corresponding pixel position in the image space, and finally the gradient annotation map is constructed and output.

[0068] The specific steps of generating the migration sequence diagram are as follows:

[0069] Based on the gradient labeled map, the pixel concentration value under each labeled number is extracted and matched with the corresponding time number and depth index. A three-element array is formed in the order of the number, and the fertilizer amount, water value and lag time are integrated by using the sequential index method. The field is aligned and the channel input structure is constructed to generate the structure input sequence set;

[0070] Based on the structure input sequence set, the numerical change of each channel along the time dimension is extracted and summed. The total value of the channel change amplitude is obtained and compared with the set threshold. The channel index with a change amplitude greater than the threshold is marked and the number sequence is output. The active channel number set is generated.

[0071] Based on the active channel number set, the long short-term memory network is used to extract the corresponding sequence of the matching channel number in the original input structure and construct a three-dimensional array structure. The data path is rearranged so that the concentration time sequence is spliced in the order of the channel number. The channel activation tensor structure is formed to obtain the migration sequence map.

[0072] Based on the gradient labeled map, the pixel index analysis of each numbered area in the labeled map is performed using the numbered pixel extraction method. The gray value of the corresponding pixel is extracted from the image matrix as the concentration value according to the number field. The time number field and the depth index field recorded in the labeled map are combined for field matching operation. The extracted concentration value, time number and depth index are combined to construct a three-field structure. The numbered sequence index is established by sorting according to the number field using the numbered order reconstruction method. The concentration-time-depth triplets corresponding to each numbered sequence are executed by structure combination. Then the sequence field binding method is used to introduce the fertilizer amount, water value and lag time. The field alignment operation is performed on each number to realize parameter insertion. The insertion method is fixed position interpolation matching and the field value is filled synchronously according to the number. The field order arrangement is six-field structure of concentration value, time number, depth index, fertilizer amount, water value and lag time. All numbered data are merged to build a unified data table using the multi-field splicing method. The output is the structure input sequence set.

[0073] Based on the structure input sequence set, the time series difference method is used to calculate the difference of each channel number in the time field. The channel division is based on the number field and the calculation is performed after sorting by the time field within the number. The time series difference value is obtained by subtracting the concentration value of two consecutive frames. Then the absolute value of all difference values of each channel number is summed using the difference sum method to obtain the total value of the concentration change amplitude of each number in the time dimension. The channel change amplitude total value is compared with the preset threshold value using the fixed threshold comparison logic. The threshold value is a constant value θ, and the value range is set to floating point 0.00 to 1.00. The channel numbers with a change amplitude greater than θ are selected by the greater than condition. The active channel number set is generated by extracting and outputting the channel number set that meets the condition.

[0074] Based on the activation channel number set, the long short-term memory network method is adopted to match the channel number field and the activation channel number set in the structure input sequence set. The corresponding sequence is filtered out through the number field and rearranged according to the time field to extract six field information such as concentration value, time number, depth index, fertilizer amount, moisture value and lag length as input data. A three-dimensional array structure is constructed, wherein the first dimension is the channel number index, the second dimension is the time step, and the third dimension is the six field channel data. Subsequently, the path rearrangement method is adopted to reorder the three-dimensional array according to the number dimension, so that the concentration sequences of different numbers are spliced in the order of the number to form a number continuous structure. Finally, a three-dimensional tensor is generated by combination, which is input into the long short-term memory network model to perform the tensor construction process. The network model structure includes input gate, forget gate, output gate and state transmission structure. The data time series modeling is performed in a multi-layer unit stacking manner, and the output is the channel activation tensor structure, which is used as the basic data input for subsequent generation of the migration sequence diagram.

[0075] The long short-term memory network is according to the formula:

[0076] h t =σ(W ih ·(x t ⊙γ c )+b ih +α t ·(W hh ·h t-1 )+λ s ·∈ t +b hh );

[0077] Wherein: h t represents the hidden state output at time t, σ represents a nonlinear activation function, W ih represents the weight matrix of input to hidden state, x t represents the dye spectrum concentration time sequence extracted under the activation channel number at time t, γ c represents the channel number inhibition factor, b ih represents the bias vector in the input stage, h t-1 represents the hidden state output at time t-1, W hh represents the weight matrix between hidden layers, α t represents the time series attention coefficient, ∈ t represents the spectrum concentration gradient change tensor between channels at time t, λ s represents the channel gradient inhibition coefficient, b hh represents the bias vector in the hidden state stage.

[0078] The Long Short-Term Memory (LSTM) network first extracts the concentration values, time series, and depth indices corresponding to the activation channel number set in channel number order and constructs a three-dimensional array structure, with each dimension corresponding to the channel, time step, and feature quantity, respectively. Then, the array is sequentially input into the LSM network unit, and the gating mechanism operation is executed sequentially, including the state updates of the input gate, forget gate, and output gate. The information retention and discarding process is controlled by formulas, and the hidden state and unit state are transmitted in the time dimension. The complete concentration change sequence representation is output, and combined with fertilizer amount, water value, and lag time, a channel activation tensor structure that integrates temporal and spatial features is generated.

[0079] Execution process: First, extract the spectral concentration time series x from the staining and tracing data collected in the field, after filtering by the set of activated channel numbers. t The sequence is related to the channel repressor γ c Element-wise multiplication is used to suppress the intensity of non-target channel inputs, highlighting channel responses directly related to soil nutrient migration. The suppressed input vector is then multiplied by the input weight matrix W. ih Multiply and then add to the bias vector b ih By summing the results, we obtain a preliminary mapping of the potential soil characteristic state at the current moment, and the hidden state h from the previous moment. t-1 via the hidden state weight matrix W hh After mapping, multiply by the temporal attention coefficient α t Based on the rate of change of the Euclidean distance between the current time and historical inputs, the algorithm calculates and normalizes the dynamic adjustment of the dependence of the current input on the historical migration process. Then, a channel concentration gradient term is introduced. t It is calculated from the concentration difference between each channel between the current and previous time points, characterizing the difference in soil nutrient migration rate between channels, and multiplied by the gradient inhibition coefficient λ. s This coefficient is normalized based on the standard deviation of all activated channels to avoid gradient perturbations interfering with the timing modeling process. Finally, the above results are summed and introduced into the bias term b. hh The entire system is mapped using the activation function σ to form the hidden state h at time t. t As a channel activation tensor representation under fusion spectral analysis, it is used to construct a time-series migration map of soil nutrients.

[0080] The specific steps for generating the topology embedding graph are as follows:

[0081] Based on the migration sequence map, concentration values ​​are extracted according to the number position and the difference sequence between adjacent time points is calculated. Channel positions with absolute concentration difference values ​​greater than a set threshold are selected, and sequence sets are formed by extracting the numbers that meet the conditions and their corresponding time indices to generate a concentration mutation node set.

[0082] Based on the concentration mutation node set, the Euclidean distance corresponding to the coordinates between nodes is calculated, and the water vector direction value is extracted, the node pair vector angle structure is constructed, and the cosine value is calculated, to determine whether the angle cosine is greater than the set threshold value and the distance is less than double the average value, to screen the node pairs meeting the conditions, and to generate a connected node edge set;

[0083] Based on the connected node edge set, a graph convolution network is used to splice the concentration sequence of each node pair and the time index sequence to generate a double-channel input structure, to rearrange and combine all nodes to construct an embedding vector matrix, to organize a spatial mapping structure according to the matrix arrangement format, and to generate a topology embedding graph;

[0084] Based on the migration sequence graph, a number concentration extraction method is used to extract the concentration value data under each channel number in the three-dimensional tensor in the order of the number, the extraction method reads the concentration field value along the time axis dimension by fixing the channel axis index, then a time series difference calculation method is used to calculate the difference between the concentration values of adjacent time points in each number, the difference calculation generates a difference sequence by subtracting time step t from time step t+1, the absolute value of each item of the difference sequence is processed by using the difference absolute value judgment logic and compared with the set threshold value, the set threshold value is a constant θ, the value range is a floating point number between 0.00 and 1.00, the judgment result is the combination of the channel number and the corresponding time index whose absolute value of the difference is greater than the threshold value, a number and time index merging method is used to combine and splice all data items meeting the conditions to generate a two-dimensional data table structure, and the output is a concentration mutation node set;

[0085] Based on the concentration mutation node set, a node coordinate index acquisition method is used to extract the horizontal and vertical coordinate values of the corresponding pixels in the image space for each node number, and the coordinate pair is used as the position parameter to construct a coordinate set, then a Euclidean distance calculation method is used to calculate the difference sum of squares between the coordinate pairs of all nodes and take the square root to form a complete distance matrix, a water vector direction estimation method is used to extract the time index and water value field for each node, a two-dimensional direction vector sequence is constructed by the water value increment at consecutive time steps, then a vector angle calculation method is used to calculate the cosine value of the direction vector between each pair of nodes based on the cosine theorem, the cosine value calculation formula inputs the dot product of the node direction vector and the adjacent node direction vector divided by the product of its modulus, a threshold combination judgment method is used to set two judgment conditions for the cosine value and the Euclidean distance, wherein the angle cosine is greater than 0.7 and the Euclidean distance is less than double the average value of all Euclidean distances in the sample, the node pairs meeting the conditions are screened and the number index combination is recorded, and finally the connected node edge set is output;

[0086] Based on the connected node edge set, the corresponding concentration value sequence and time index sequence of each pair of node number are extracted by using the graph convolution network method, and are combined into a double-channel input structure by using the field splicing method. Channel one is the concentration sequence, and channel two is the time index sequence. The node rearrangement method is used to reorder all nodes according to the number field sequence. After uniformizing the input sequence, all double-channel structures are spliced into a two-dimensional tensor matrix, wherein the first dimension is the node index, and the second dimension is the spliced feature sequence. The two-dimensional tensor and the connected edge set are input into the graph convolution neural network model by using the tensor embedding construction method. The graph structure is represented in the form of an adjacency matrix. A single-layer convolution structure is used to construct the information propagation mechanism between nodes. The ReLU function is used as the activation function. The matrix multiplication method is to multiply the left input tensor by the adjacency matrix and multiply the right by the learnable weight matrix. Finally, the output is the node embedding representation tensor. The tensor dimension is rearranged according to the spatial structure mapping method, and the output is the topological embedding graph.

[0087] The graph convolution network is according to the formula:

[0088]

[0089] Wherein: H (l+1) represents the node embedding feature matrix of the l+1 layer graph convolution output, ζ represents the nonlinear activation function in the graph convolution network, ψ m represents the time hierarchical attention weight matrix, represents the degree matrix corresponding to the graph adjacency matrix after adding the self-loop, represents the node adjacency matrix after adding the self-loop, H (l) represents the node feature matrix input into the lth layer, ξ n represents the node channel screening vector, W (l) represents the learnable weight matrix of the lth layer, μ g represents the spatial disturbance adjustment coefficient, Δ s represents the spatial offset compensation matrix composed of the two-dimensional coordinate position difference of the nodes in the field layout;

[0090] The graph convolution network splices the concentration value sequence and the time index sequence corresponding to each node to form a double-channel feature vector. Then, all nodes are reordered according to the number sequence to form an embedding vector matrix. The features of each node and the features of the directly connected adjacent nodes are weighted and converged. The weight is determined by the defined connection edge structure in the graph. After convergence, linear transformation and nonlinear activation function processing are performed. The graph structure information and node attribute information in a larger range are integrated layer by layer to obtain the node embedding vector reflecting the fusion relationship of spatial topology and time sequence concentration features.

[0091] The execution process is as follows: first, the collected spectral concentration sequence corresponding to each pair of dyed nodes is spliced with the time index sequence to form a double-channel input feature matrix H with time sequence correlation (l) Then, the node channel screening vector ξ n The channel dimension of the input matrix is screened to retain the channel information related to the dye migration process, and then a self-loop is introduced in the constructed connection node edge set to form a normalized adjacency matrix And its corresponding degree matrix Through graph normalization operation The local node features are preliminarily propagated, and then multiplied by the learnable weight matrix W (l) To complete the feature transformation mapping, and introduce the time-level attention weight matrix ψ m To dynamically enhance the information connection between nodes with similar evolution patterns in the spectral time sequence dimension, the weight matrix is obtained by calculating the weighted cosine similarity between node time index vectors, and then the node spatial position difference matrix Δ s is introduced to calculate the spatial offset compensation between nodes based on two-dimensional field layout coordinates, and the adjustment coefficient μ g is used to limit its influence range, and the coefficient is set to a value range of 0.2 to 0.5 through node spatial variance normalization, which is used to prevent the spatial structure difference from dominating the feature propagation process too much, and finally the above results are input into the activation function ζ to generate node embedding representation H (l+1) under the graph structure, which is used to construct a topological embedding graph describing the spatio-temporal migration pattern of soil nutrients.

[0092] The specific steps for generating the hotspot distribution table are as follows:

[0093] Based on the topological embedding graph, all node numbers are extracted and matched with the corresponding embedding vectors, the number pair combination list is constructed in order, the inner product of each pair of embedding vectors is calculated and the cosine similarity value is recorded, the similarity matrix corresponding to the number index structure is summarized and classified, and the node similarity structure set is generated;

[0094] Based on the node similarity structure set, the similarity values in each column vector are sorted in descending order and the first fixed proportion of number indexes are screened, the frequency of each number appearing in the high similarity pair is counted and converted into a ratio with the total number of numbers, and the number set with a ratio higher than the density threshold is extracted to generate a high-density number group;

[0095] Based on the high-density number group, the time index and depth position index of the corresponding node in the original graph structure are extracted, the number and index double-key mapping table structure is established, the time and depth index fields in the mapping table are counted and the cumulative frequency values are recorded, the two field frequency structure tables are merged, and the hotspot distribution table is obtained;

[0096] Based on the topology embedding graph, the node vector extraction method is used to perform the number traversal operation on each node number in the embedding graph and extract the corresponding embedding vector, the numbering order construction method is used to perform the number pair combination generation operation, the double nested loop is used to combine all node numbers in pairs and construct the number pair combination list, then the vector inner product operation method is used to extract the embedding vector corresponding to each pair of node combinations and perform the cosine similarity calculation, the numerical calculation is performed in the form of vector dot product divided by the product of the vector module length, the cosine similarity calculation accuracy is reserved to four decimal places, the number index merging method is used to store all the number pairs and their corresponding similarity values calculated into the similarity matrix structure, and each node number in the number pair is used as the primary key to construct the hash index mapping structure, to complete the fast retrieval binding operation of the node number to the similarity result, and finally generate the node similarity structure set;

[0097] Based on the node similarity structure set, the column vector sorting method is used to perform the descending order sorting operation on the similarity value column corresponding to each node number in the similarity structure set, the top p% of the sorting results are selected, the proportion parameter is set to p%, and p can be set to 5, 10, 15, etc. The position index method is used to extract the top p% of the number corresponding values from the top and construct the high similarity number index set, then the frequency statistics method is used to count the number of times each number appears in all high similarity number sets, the ratio conversion method is used to divide the frequency value by the number of appearances of the number in all combinations to obtain the density ratio, the density threshold parameter d is set, and the commonly used value is in the interval of 0.3 to 0.7, the logical judgment method is used to extract the number index whose ratio is greater than d, and the number set is formed by merging all numbers that meet the conditions, and the output is the high-density number group.

[0098] Based on the high-density number group, the number index mapping method is used to extract the time index value and the depth index value bound in the original graph structure for each number, the number is used as the primary key to quickly match the time and depth data corresponding to the number, then the key-value mapping structure construction method is used to establish a double-key mapping table structure, the primary key is set as the number, and the secondary key is set as the time index and the depth index two fields, the unique value statistics is performed on the time field and the frequency is recorded, the dictionary accumulator is used to record the cumulative count value of each time index, and the same operation is performed on the depth index field and the cumulative frequency is counted, finally the field structure table merging method is used to align the time frequency statistics table and the depth frequency statistics table in the number dimension and combine and splice them according to the field order to form a two-dimensional data structure, and the output is the hotspot distribution table.

[0099] The above merely describes the preferred embodiments of the present application, and is not intended to limit the present application in other forms. Any skilled person in the art can modify or change the disclosed technical content into equivalent embodiments with equivalent changes, and apply them to other fields. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, without departing from the technical solution content of the present application, still falls within the protection scope of the present application.

Claims

1. A method of field dye tracing with soil nutrient migration analysis integrated with fusion spectroscopy analysis, characterized in that, The method comprises the following steps: S1: Based on the image profile sequence obtained by the field dye tracing monitoring unit, the reflectivity of the numbered area is extracted and the time sequence is divided, the difference of the numbered value among three time periods is calculated and the sign change is identified, the numbered groups with change frequency exceeding the limit are screened out, the coordinate positioning and numbering are combined, and the change coordinate set is obtained; S2: Based on the change coordinate set, the reflectivity of the numbered area is extracted and the time sequence is divided, the difference of the numbered value among three time periods is calculated and the sign change is identified, the numbered groups with change frequency exceeding the limit are screened out, the coordinate positioning and numbering are combined, and the gradient annotation map is obtained; S3: Based on the gradient annotation map, a long short-term memory network is used to construct a three-element sequence of concentration value, time and depth, and to combine fertilizer application amount, water value and lag time to integrate into an input tensor, calculate the total gradient change of the channel and set a threshold value to judge, screen out effective channels and activate, and establish a migration sequence map; S4: Based on the migration sequence map, a graph convolution network is used to extract concentration difference nodes and build adjacency relationships, calculate the combined value of the included angle cosine and the distance to judge the connection condition, form a graph structure edge set, generate node representation and integration, and generate a topological embedding graph; S5: Based on the topological embedding graph, the similarity of node vectors is calculated and the numbered groups are clustered, the high-density groups are screened out, the time and depth indexes corresponding to the groups are extracted, the frequency statistics and distribution record are performed, and the hotspot distribution table is obtained.

2. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 1, characterized in that, The specific steps for generating the change coordinate set are as follows: Based on the image profile sequence obtained by the field dye tracing monitoring unit, the pixel row and column index of the numbered area is parsed and the boundary index is located, the image frames are divided in time label order and the reflectivity value sequence of the numbered area is extracted, three groups of time matrices are constructed through frame time order, and a time sequence matrix is generated; Based on the time sequence matrix, the difference of the reflectivity value of each numbered group is calculated and the positive and negative change states are marked, the number of sign changes is counted and the numbered groups with more than one change are screened out, the numbered groups are aggregated through numbered screening logic, and a mutation numbered group set is generated; Based on the mutation numbered group set, the horizontal and vertical coordinates of the numbered pixel position are extracted and the time index is combined, the extracted coordinates are rearranged and integrated into a positioning coordinate group according to the grid space, and three-dimensional positioning information is constructed combined with the numbering, and the change coordinate set is obtained.

3. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 1, characterized in that, The specific steps for generating the gradient annotation map are as follows: Based on the change coordinate set, the image vertical direction spectrum sequence corresponding to the coordinates is extracted and the pixel ordering structure is determined, the vertical change amount between adjacent pixel values is calculated and recorded as a continuous gradient value sequence, each channel gradient is assembled in coordinate order, and a longitudinal gradient sequence is generated; Based on the longitudinal gradient sequence, the corresponding numbered infiltration path length value is obtained and the ratio of each path to the gradient value is calculated, the numbered groups with a ratio greater than the upper quartile and less than the lower quartile are screened out through the ratio range, an abnormal numbered group sequence is assembled, and a gradient abnormal numbered group set is generated; Based on the gradient abnormal numbered group set, the depth number is found and extracted according to the reflectivity value in the pixel sequence above and below the numbered group, the depth number and the horizontal and vertical coordinates are combined to form a three-dimensional annotation data structure, the unified annotation format is mapped into the image index system, and the gradient annotation map is obtained.

4. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 1, characterized in that, The specific steps for generating the migration sequence diagram are: Based on the gradient annotation diagram, the pixel concentration value under each annotation number is extracted and matched with the corresponding time number and depth index, a three-element array is established in order of numbering, the fertilizer amount, water value and lag time are integrated in sequence index mode, the fields are aligned and the channel input structure is constructed, and a structure input sequence set is generated; Based on the structure input sequence set, the numerical change of each channel along the time dimension is extracted and a summation operation is performed, the total value of the channel change amplitude is obtained and compared with the set threshold, the channel index with a change amplitude greater than the threshold is marked and the number sequence is output, and an active channel number set is generated; Based on the active channel number set, a long short-term memory network is used to extract the corresponding sequence of the matching channel number in the original input structure and construct a three-dimensional array structure, rearrange the data path to splice the concentration time sequence in order of channel number, combine to form a channel activation tensor structure, and obtain a migration sequence diagram.

5. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 4, characterized in that, The long short-term memory network is according to the formula: h t = σ(W ih ·(x t ☉γ c )+b ih + α t ·(W hh ·h t-1 )+ λ s ·∈ t +b hh ); wherein: h t represents the hidden state output at the t time, σ represents a nonlinear activation function, W ih represents a weight matrix input to the hidden state, x t represents the dye spectrum concentration time series extracted under the activation channel number at the t time, γ c represents a channel number suppression factor, b ih represents a bias vector in the input stage, h t-1 represents the hidden state output at the t-1 time, W hh represents a weight matrix between hidden layers, α t represents a time series attention coefficient, ∈ t represents a spectral concentration gradient change tensor between channels at the t time, λ s represents a channel gradient suppression coefficient, b hh represents a bias vector in the hidden state stage.

6. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 4, characterized in that, The long short-term memory network first extracts the concentration value, time sequence and depth index corresponding to the active channel number set in order of channel number, and constructs a three-dimensional array structure, each dimension corresponds to a channel, a time step and a feature quantity, then the array is input into the long short-term memory network unit in turn, and the state updating of the input gate, the forgetting gate and the output gate is executed in turn, the information retention and discard process is controlled through the formula, the hidden state and the cell state are transmitted in the time dimension, the complete concentration change sequence representation is output, and the fertilizer amount, water value and lag time are combined to generate a channel activation tensor structure that integrates time sequence and spatial features.

7. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 1, wherein, The specific steps for generating the topology embedding diagram are: Based on the migration sequence diagram, the concentration value is extracted according to the number position and the difference sequence between adjacent time points is calculated, the channel position with an absolute value of concentration difference greater than a set threshold is screened, the number satisfying the condition and the corresponding time index are extracted to form a sequence set, and a concentration mutation node set is generated; Based on the concentration mutation node set, the Euclidean distance between the coordinates of each node is calculated and the water vector direction value is extracted, the node pair vector angle structure is constructed and the cosine value is calculated, it is judged whether the cosine of the angle is greater than a set threshold and the distance is less than double the average value, the node pairs meeting the conditions are screened, and a connected node edge set is generated; Based on the connected node edge set, a graph convolution network is used to splice the concentration sequence and the time index sequence of each pair of nodes to generate a two-channel input structure, merge and construct an embedding vector matrix after rearranging all nodes by number, organize a spatial mapping structure in matrix arrangement format, and generate a topology embedding diagram.

8. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 7, characterized in that, The graph convolution network is according to the formula: wherein: H (l+1) denotes the node embedding feature matrix of the (l+1)th layer graph convolution output, ζ denotes the nonlinear activation function in the graph convolution network, ψ m denotes the time hierarchical attention weight matrix, denotes the degree matrix corresponding to the graph adjacency matrix after adding the self-loop, denotes the node adjacency matrix after adding the self-loop, H (l) denotes the node feature matrix input of the lth layer, ξ n denotes the node channel screening vector, W (l) denotes the learnable weight matrix of the lth layer, μ g denotes the spatial disturbance adjustment coefficient, Δ s denotes the spatial offset compensation matrix composed of the two-dimensional coordinate position difference of the nodes in the field deployment.

9. The method of field dye tracer and soil nutrient transport analysis with fusion spectroscopy analysis according to claim 7, wherein, The graph convolution network splices the concentration value sequence corresponding to each node with the time index sequence to form a double-channel feature vector, then rearranges all nodes in numerical order, combines to form an embedding vector matrix, and performs weighted aggregation of the features of each node and the features of the directly connected adjacent nodes, with the weight determined by the defined connection edge structure in the graph, then performs linear transformation and nonlinear activation function processing after aggregation, integrates the graph structure information and node attribute information in a larger range layer by layer, and obtains the node embedding vector reflecting the fusion relationship of spatial topology and time series concentration characteristics.

10. The method of fusion of field dye tracer and soil nutrient transport analysis with spectroscopic analysis according to claim 1, wherein, The specific steps for generating the hotspot distribution table are as follows: Based on the topology embedding graph, extract all node numbers and match the corresponding embedding vectors, construct a number pair combination list in order, calculate the inner product of each pair of embedding vectors and record the cosine similarity value, summarize the similarity matrix corresponding to the number index structure and generate the node similarity structure set; Based on the node similarity structure set, perform descending order sorting on the similarity values in each column vector and select the front fixed proportion of number indexes, count the frequency of each number appearing in the high similarity pair and convert the ratio to the total number of numbers, extract the number set with a ratio higher than the density threshold, and generate a high-density number group; Based on the high-density number group, extract the time index and depth position index of the corresponding node in the original graph structure, establish a number and index double-key mapping table structure, count and record the cumulative frequency value of the time and depth index fields in the mapping table, and combine the two field frequency structure tables to obtain the hotspot distribution table.

Images