Data processing method, data processing device, and program

Abstract

The present invention addresses the problem of providing a method for processing observation data that enables an understanding of local features of observational data in the field of earth science, such as topographic data. The above problem can be resolved by providing a data processing method including: an acquisition step for acquiring observational data including, in association with each other, position coordinates and observed values of an observed object at the position coordinates; a model generation step for applying a machine learning algorithm using the observational data as learning data to generate a regression model, in response to input of the position coordinates, that outputs estimated values of the observed object at the input position coordinates; and an output step for comparing the observed values of the observation object at the position coordinates with the estimated values of the observed object at position coordinates corresponding to the position coordinates output from the regression model, for each of the position coordinates included in the observational data, and outputting output data including information enabling identification of the position coordinates where both match.

Description

Data processing method, data processing device, and program

[0001] This disclosure primarily relates to data processing methods, data processing devices, and programs for processing observational data in the field of earth science.

[0002] Observational data in the field of earth science is obtained from sampling, observation, and analysis at a limited number of measurement points. Due to geographical constraints such as inaccessibility to measurement points, time constraints such as excessive time required, and cost constraints such as excessive expense, it is not easy to acquire data evenly across the entire area of ​​interest. Typically, measurement points are selected from locations where measurements are possible or from characteristic locations. In other words, observational data in the field of earth science is discrete and is a collection of point data irregularly distributed within the area of ​​interest.

[0003] To estimate the true distribution of values ​​behind a set of point data for measurement points with limited quantities and distributions, or the distribution of values ​​outside the target area, and to understand their characteristics, modeling is performed by spatially interpolating the acquired observation data. Representative spatial interpolation methods include, for example, the TIN (Triangulated Irregular Network) method, the IDW (Inverse Distance Weighted) method, and the Kriging method.

[0004] The TIN method, also known as the irregular triangulation method, is a technique that creates a plane by forming triangles with three adjacent measurement points as vertices, and then estimates values ​​at interpolation points within that plane. The values ​​at the interpolation points are estimated, for example, by linear interpolation using two vectors that point from a reference vertex to the other two vertices. The TIN method is described, for example, in Non-Patent Document 1.

[0005] On the other hand, the IDW method, also known as the inverse distance weighted average method, is a method for estimating values ​​at interpolation points by using a weighted average with weights based on the reciprocal of the distance from the measurement point to the interpolation point (inverse distance). By using a weighted average with weights based on the reciprocal of the distance from the measurement point to the interpolation point, the contribution of observed values ​​at measurement points close to the interpolation point is given greater weight. The IDW method is described, for example, in Non-Patent Document 2.

[0006] On the other hand, the kriging method is an interpolation technique that uses a variogram, which represents the relationship between the vectors between measurement points and the variance of the observed data. The variogram allows us to understand the spatial continuity of the data in the target region. In the kriging method, based on the spatial continuity understood from the variogram, the weights of the values ​​at each measurement point are determined, and the value at the interpolation point is estimated as a weighted average of the values ​​at each measurement point. The kriging method is described, for example, in Non-Patent Documents 3 and 4.

[0007] However, it is difficult to grasp the characteristics of observational data based on the models generated in the manner described above. In particular, conventional spatial interpolation methods such as the TIN method, IDW method, and kriging method all generate models that pass through all data points at each measurement point, and therefore basically produce models that smooth the obtained observational data, making them unsuitable for grasping local characteristics. For example, observational values ​​that deviate from the average or normal distribution may suggest underlying anomalous topography, abnormal weather, erosion, etc., but it is not easy to grasp such local characteristics based on models generated using conventional spatial interpolation methods, i.e., models that smooth the obtained observational data.

[0008] For example, in recent years, due to factors such as increased short-term rainfall, landslides and other slope failures have been occurring frequently throughout Japan, and the Ministry of Land, Infrastructure, Transport and Tourism has published a report recommending that dangerous areas should be detected by making advanced use of digital topographic data provided by the Geospatial Information Authority of Japan. One known method for interpreting topography using digital topographic data is the CS stereoscopic map (see, for example, Non-Patent Document 5). The CS stereoscopic map is a topographic map that visualizes valleys and ridges along with their slopes by determining the curvature (second derivative) and slope (first derivative) based on digital topographic data and coloring the topographic map. For example, it is used to identify areas with a high risk of slope failure, such as valley heads and zero-order valleys. However, slope failures are also occurring in areas that have not been identified as dangerous by local governments, such as municipalities, and human and material damage is expanding. Appropriately identifying areas at risk of slope failure based on observational data such as digital topographic data is an urgent task in order to minimize damage from rainfall, such as landslides.

[0009] Hiroshi Akima, A Method of Bivariate Interpolation and Smooth Surface Fitting for Values ​​Given at Irregularly Distributed Points, ACM Transactions on Mathematical Software, vol. 4, no. 2, pp. 148-159 (1978). Akiko Takahashi, Takashi Oguchi, Hiroaki Sugimori, Resolution and Topographic Representation of Raster-Type DEMs - A Case Study of the Tama Region -, Geographical Review of Japan, Vol. 76, No. 11 (2003), pp. 800-818. Tetsuya Shoji, Katsuaki Koike, Lecture Series "Geostatistics" Kriging: Interpolation of Spatial Data Considering Errors, Journal of the Geothermal Society of Japan, Vol. 29, No. 4 (2007), pp. 183-194. Tetsuya Shoji, Katsuaki Koike, Lecture Series "Geostatistics" Variogram - Analysis of Spatial Continuity of Data, Journal of the Geothermal Society of Japan, Vol. 29, No. 3 (2007), pp. 125-140. "Manual for Interpreting Topography Using CS Stereoscopic Maps," created by the Japan Forest Technology Association, published by the Forestry Agency in March 2023.

[0010] This invention was made to solve the problems of the prior art described above, and in one aspect, it aims to provide a method for processing observational data that enables the understanding of local characteristics of observational data in the field of earth science, such as topographic data.

[0011] In one aspect, the present invention solves the above problem by providing a data processing method that includes: an acquisition step of acquiring observation data that includes a correspondence between position coordinates and observed values ​​of an object to be observed at the position coordinates; a model generation step of generating a regression model that outputs estimated values ​​of the object to be observed at the input position coordinates by applying a machine learning algorithm to the observation data as training data and taking the position coordinates as input; and an output step of outputting output data that includes information that can identify a position coordinate where the observed values ​​of the object to be observed at the position coordinates and the estimated values ​​of the object to be observed at the position coordinates corresponding to the position coordinates output from the regression model are matched.

[0012] Furthermore, in another aspect, the present invention solves the above problem by providing a data processing device comprising: an acquisition unit that acquires observation data including a correspondence between position coordinates and observed values ​​of an object to be observed at the position coordinates; a model generation unit that generates a regression model that outputs estimated values ​​of the object to be observed at the input position coordinates by inputting the position coordinates, by applying a machine learning algorithm to the observation data as training data; and an output unit that outputs output data for each of the position coordinates included in the observation data, based on the observed value of the object to be observed at the position coordinate and the estimated value of the object to be observed at the position coordinate corresponding to the position coordinate output from the regression model, and / or a computer program for causing a computer to function as such a data processing device.

[0013] As described above, the method and apparatus relating to one aspect of the present invention are characterized in that, for each position coordinate included in the observation data, output data containing information that can identify a position coordinate that matches, based on the observed value included in the observation data and the estimated value at the position coordinate corresponding to that position coordinate output from a regression model generated by applying a machine learning algorithm to the observation data as training data. The regression model generated by applying a machine learning algorithm to the observation data as training data extracts features from the original observation data and infers an estimated value of the observation target that is considered standard at each point. The inventors have found that when comparing this inference result with the observation data used as training data, the set of position coordinates that match is extremely useful as a criterion for detecting local distortions or unnaturalness in the data included in the observation data. For example, as shown in the experimental example described later, when this method is applied to digital terrain data, the baseline generated by connecting the set of position coordinates that match the inferred value of the generated regression model and the observed data makes it easy to grasp the existence of unstable terrain that is abnormally bulging (i.e., has a high elevation) or abnormally concave (i.e., has a low elevation) compared to what it should be. By utilizing this method, the presence of embankments and cuts, valleys including early-stage valleys, and unstable terrain such as slopes at risk of landslides can be efficiently identified.

[0014] According to one aspect of the present invention, a method, apparatus, or computer program may enable the identification of local characteristics of observational data in the field of earth science, such as topographic data.

[0015] This figure was created using the procedure described in the example, based on a digital elevation model of the area around Handayama, located in Kita-ku, Okayama City, Okayama Prefecture. The white line segments are lines (topographic equilibrium lines) connecting sets of position coordinates identified by the method according to one embodiment of the present invention (i.e., sets of position coordinates where the observed elevation values ​​included in the digital elevation model coincide with the estimated values ​​estimated by the regression model); long arrows indicate locations where valleys were determined to exist by the method described in the example; and short arrows indicate locations where there was a risk of slope collapse by the method described in the example. In addition, a CS stereoscopic map of the same area is superimposed in the background. This figure was created using the procedure described in the example, based on a digital elevation model of the area around Handayama, located in Kita-ku, Okayama City, Okayama Prefecture. In the figure, the white line segments represent lines (topographic equilibrium lines) connecting sets of position coordinates identified by the method according to one embodiment of the present invention (i.e., sets of position coordinates where the observed elevation values ​​included in the numerical elevation model coincide with the estimated values ​​estimated by the regression model); long arrows indicate locations where valleys were determined to exist by the method described in the embodiment; and short arrows indicate locations where there was a risk of slope collapse by the method described in the embodiment. In addition, a surface image of the same area is shown superimposed in the background. This figure was created using the procedure described in the embodiment, based on a numerical elevation model of the area around Okayama University Tsushima Campus (Tsushima-naka, Kita-ku, Okayama City, Okayama Prefecture). The white line segments represent lines (topographic equilibrium lines) connecting sets of position coordinates identified by the method according to one embodiment of the present invention (i.e., sets of position coordinates where the observed elevation values ​​included in the numerical elevation model coincide with the estimated values ​​estimated by the regression model). On the other hand, the black and white arrows indicate areas that were determined to be at risk of slope collapse according to the method described in the examples. The black arrows indicate areas within the zones that are identified as being at risk of slope collapse in the hazard map, while the white arrows indicate areas outside of those zones. The black and white arrows indicate areas that were not determined to be at risk of slope collapse according to the method described in the examples, but are identified as being at risk of slope collapse in the hazard map. In addition, a slope map of the same area is shown overlaid in the background. This is a diagram of the hazard map around Okayama University's Tsushima Campus. In the diagram, areas identified as being at risk of slope collapse are indicated by light hatching for warning zones and dark hatching for special warning zones.This figure was created using the procedure described in the example, based on a numerical elevation model of the area around Takuwa, Mitoya-cho, Unnan City, Shimane Prefecture. The white line segments represent lines (topographic equilibrium lines) connecting sets of position coordinates identified by the method according to one embodiment of the present invention (i.e., sets of position coordinates where the observed elevation values ​​included in the numerical elevation model coincide with the estimated values ​​estimated by the regression model). On the other hand, the short arrows represent areas determined to be at risk of slope collapse by the method described in the example, with black arrows representing those within the slope disaster warning area designated by the municipality, and white arrows representing those outside that area. Furthermore, the long arrows represent areas determined to be valleys by the method described in the example, with plain arrows representing areas determined to have a primary valley, and dashed arrows representing areas determined to have a zero-order valley. In addition, a heatmap corresponding to the difference data of the same area is shown overlaid in the background. The thick dotted line represents the route of the field survey. This is the figure shown in Figure 5 with the arrows and numbers removed. This is a ground surface image of the area shown in Figure 5. Figure 5 is a photograph of the field survey results at the location indicated by "1". Figure 5 is a photograph of the field survey results at the location indicated by "2". Figure 5 is a photograph of the field survey results at the location indicated by "3". Figure 5 is a photograph of the field survey results at the location indicated by "4". Figure 5 is a photograph of the field survey results at the location indicated by "5". This figure was created using the procedure described in the example, based on a numerical elevation model of the area around Mt. Bizan in Tokushima City, Tokushima Prefecture. The white line segments represent lines (topographic equilibrium lines) connecting sets of position coordinates identified by the method according to one embodiment of the present invention (i.e., sets of position coordinates where the observed elevation values ​​included in the numerical elevation model and the estimated values ​​estimated by the regression model coincide). Short arrows represent locations determined to be at risk of slope collapse using the method described in the example. Long arrows represent locations determined to be in valleys using the method described in the example. In addition, a heat map corresponding to the difference data of the same area is superimposed in the background. The thick dotted line represents the route of the field survey. This is the same figure as shown in Figure 13, but with the arrows removed. This is a surface image of the area shown in Figure 13. The image shown is a field photograph of the location indicated by "1" in Figure 13, showing the results of the on-site survey.This is a photograph of the field survey results at the location indicated by "2" in Figure 13. This is a photograph of the field survey results at the location indicated by "3" in Figure 13. This is a photograph of the field survey results at the location indicated by "4" in Figure 13. This is a photograph of the field survey results at the location indicated by "5" in Figure 13. This is a photograph of the field survey results at the location indicated by "6" in Figure 13. This is a photograph of the field survey results at the location indicated by "7" in Figure 13. This is a photograph of the field survey results at the location indicated by "8" in Figure 13.

[0016] The observation data processed by the method and / or apparatus according to one aspect of the present invention includes position coordinates and observed values ​​of the object being observed at those position coordinates, in association with each other. In other words, the observation data may be a set of point data including position coordinates and observed values ​​of the object being observed at those position coordinates, or a set of point data consisting of position coordinates and observed values ​​of the object being observed at those position coordinates.

[0017] Position coordinates are information that specifies a position in any coordinate system. Typically, position coordinates can specify a position in a two-dimensional coordinate system defined by two elements, or in a three-dimensional coordinate system defined by three elements, but they can also specify a position in an n-dimensional coordinate system defined by n elements. For example, they could be a two-dimensional coordinate system where the planar position is defined by the X and Y coordinates, a three-dimensional coordinate system where the three-dimensional position is defined by the X, Y, and Z coordinates, or even a higher-dimensional coordinate system that takes time into account.

[0018] As an unrestricted example, two-dimensional coordinate systems may include, for example, geographic coordinate systems and projected coordinate systems. A geographic coordinate system is a coordinate system that defines a location on Earth using longitude and latitude, while a projected coordinate system is a coordinate system that projects the Earth onto a two-dimensional plane and represents the location on the projected plane using XY coordinates. More specifically, examples include, but are not limited to, the Japanese Geodetic System, Japanese Geodetic System 2000, Japanese Geodetic System 2011, WGS84, plane rectangular coordinate system, UTM coordinate system, and Web Mercator coordinate system. As an unrestricted example, three-dimensional coordinate systems may include, for example, the World Geodetic System and three-dimensional orthogonal coordinate systems. The World Geodetic System is a coordinate system that represents a location on Earth using longitude, latitude, and height above mean sea level, while a three-dimensional orthogonal coordinate system is a coordinate system with the Earth's center of mass as the origin. However, three-dimensional coordinate systems are not limited to these. For example, a coordinate system that uses the height from an arbitrary reference plane instead of the height from mean sea level may also be used.

[0019] Observed values ​​are values ​​obtained by observing, measuring, or testing a designated observation target using various surveys, positioning, or other methods. The observed values ​​are included in the observation data, associated with the positional coordinates that identify the measurement point.

[0020] There are no particular restrictions on the types of objects to be observed; for example, any object that is observed in the field of earth science. Examples include, but are not limited to, height from a predetermined reference point such as altitude or water depth; temperature; atmospheric pressure; humidity; precipitation; snowfall amount; snowfall depth; wind speed; wind rate; water temperature; sea surface temperature; concentration of a predetermined substance in the atmosphere, water, or soil (e.g., oxygen, ozone, sulfur, sulfur oxides, nitrogen oxides, dioxins, soot, dust, automobile exhaust gas, volatile organic compounds, microplastics, pollen, PM2.5 and other fine particles); quantity of a predetermined organism on land, in water, or in soil (plants, birds, fish, plankton, soil microorganisms, etc.); radiation dose; electromagnetic wave dose; microbial mass.

[0021] In one preferred embodiment, the observation data is preferably grid-like observation data, that is, observation data that includes a correspondence between position coordinates and the observed value of the object being observed at the position coordinates for each predetermined area (grid), and it is more preferable that the predetermined area is an area partitioned at a predetermined interval and in a predetermined shape. There are no particular restrictions on the predetermined shape, but for example it may be triangular, quadrilateral, equilateral triangle, or square, and it is particularly preferable that it be square. There are no particular restrictions on the predetermined interval, but for example it may be 1 mm, 5 mm, 1 cm, 10 cm, 50 cm, 1 m, 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, 11 m, 12 m, 13 m, 14 m, 15 m, 16 m, 17 m, 18 m, 19 m, 20 m, 25 m, 50 m, 100 m, 200 m, 500 m, 1 km, or longer intervals. The predetermined shape and spacing can be set as appropriate depending on the available observation data, the purpose and accuracy of the analysis, the computer's specifications, etc.

[0022] A more preferred example of observational data that can be processed by a method relating to one aspect of the present invention is data that includes location coordinates and observed elevation values ​​at those location coordinates, i.e., topographic data. A more specific example of topographic data is, for example, the Digital Elevation Model (DEM) provided by the Geospatial Information Authority of Japan of the Ministry of Land, Infrastructure, Transport and Tourism. The Digital Elevation Model is topographic data in which the ground surface is divided into a grid of equally spaced squares, for example, at intervals of 1 m, 5 m, 10 m, etc., and each grid has an elevation value at the center point of the square. The Digital Elevation Model can be downloaded from the website provided by the Geospatial Information Authority of Japan of the Ministry of Land, Infrastructure, Transport and Tourism.

[0023] The following describes each step that constitutes a method relating to one aspect of the present invention. Typically, each of the following steps is performed by an information processing device such as a personal computer terminal, tablet terminal, server, or smartphone terminal.

[0024] <Acquisition Step for Observation Data> This step involves acquiring observation data to be processed. This step can be achieved, for example, by reading observation data to be processed stored in any storage device or memory unit such as cloud storage, online storage, hard disk, SSD, or flash memory; by receiving observation data to be processed from another information processing device that has observation data; or by accepting input of observation data to be processed.

[0025] <Model generation step for generating a regression model> In one aspect of the present invention, a regression model is generated by applying a machine learning algorithm to observation data as training data. The generated regression model may be a regression model that outputs an estimated value of the observed object at the input location coordinates when location coordinates are input. In other words, the generated regression model may be a regression model in which location coordinates are the explanatory variable and the estimated value of the observed object is the dependent variable.

[0026] Regression models can be generated by using observed data as training data and applying a machine learning algorithm to it. The machine learning algorithms that can be used to generate regression models are not particularly limited, as long as they are capable of regression, preferably nonlinear regression. Examples include support vector machines, decision trees, k-nearest neighbors, neural networks, and ridge regression. In this disclosure, "decision tree" may include decision tree-based machine learning algorithms such as random forests and gradient boosting, unless otherwise specified. Furthermore, "k-nearest neighbors" may include k-nearest neighbors-based machine learning algorithms such as weighted k-nearest neighbors and kernel k-nearest neighbors, which use inverse distance weighting or weighting based on kernel functions. Also, "neural network" may include neural network-based machine learning algorithms such as multilayer perceptron (MLP) networks and radial basis function (RBF) networks, unless otherwise specified. Finally, "ridge regression" may include kernel ridge regression using kernel functions.

[0027] In one preferred embodiment, the machine learning algorithm is preferably a support vector machine, a decision tree, or k-nearest neighbors, more preferably a support vector machine, a random forest, or k-nearest neighbors, and even more preferably a support vector machine. In particular, a support vector machine using a kernel function (kernel SVM) is preferably used. By using a kernel function, which is a function equivalent to the inner product of nonlinear functions, margin calculations by the support vector machine can be performed without actually mapping the observed data to a high-dimensional feature space, thus enabling efficient nonlinear regression.

[0028] There are no particular restrictions on the type of kernel function, but non-restrictive examples include, for example, a linear kernel (equation (I) below), a polynomial kernel (equation (II) below), a Gaussian kernel (RBF kernel) (equation (III) below), a Laplacian kernel (equation (IV) below), and a sigmoid kernel (equation (V) below). A kernel function may be used alone, or multiple kernel functions may be combined by adding or multiplying them.

[0029]

[0030] The parameters of a support vector machine (e.g., kernel function parameters, regularization parameters, noise parameters, etc.) can be tuned using appropriate methods depending on the observed data to be processed. For example, tuning may be done by referring to an interpolation model generated by applying a spatial interpolation method to the observed data. There are no particular restrictions on the spatial interpolation method; for example, any of the TIN method, IDW method, or Kriging method may be used. For example, as shown in the experimental example described later, a variogram may be generated based on the observed data, and an interpolation model may be generated by applying a spatial interpolation method based on the generated variogram and the Kriging method.

[0031] <Output step for outputting output data> This step outputs output data that includes information that allows for the identification of position coordinates where the observed values ​​included in the observation data and the estimated values ​​output by the regression model coincide. More specifically, for each position coordinate included in the observation data, the step may involve comparing the observed value of the object at that position coordinate with the estimated value of the object at the corresponding position coordinate output by the regression model, and outputting output data that includes information that allows for the identification of position coordinates where the two coincide.

[0032] As described above, in this step, the generation of estimated values ​​of the observed object by the regression model is performed for position coordinates corresponding to the position coordinates included in the observation data, and the generated estimated values ​​are compared with the observed values ​​included in the observation data. In the field of earth science, the generation of estimated values ​​by the generated model is usually performed for position coordinates not included in the observation data. In contrast, in the method according to one aspect of the present invention, estimated values ​​are generated for position coordinates corresponding to the position coordinates included in the observation data based on the generated regression model, and the estimated values ​​generated by the regression model are compared with the observed values ​​included in the observation data. In this respect, the method according to one aspect of the present invention is fundamentally different from the prior art.

[0033] Here, the position coordinates corresponding to the position coordinates included in the observation data are preferably the same as the position coordinates included in the observation data, but they may be substantially the same. A position coordinate that is substantially the same as the position coordinates included in the observation data may, for example, be a position coordinate whose distance from the said position coordinate in the observation data is 30% or less, 25% or less, 20% or less, 15% or less, 10% or less, 7.5% or less, 5% or less, 2.5% or less, 2% or less, 1.5% or less, 1% or less, or 0.5% or less of the distance between grids in the observation data, but is not limited to these. If the distance between two position coordinates is within the above predetermined range, the two coordinates can be considered substantially the same in the grid-like observation data. Hereinafter, when referring to the estimated value of the observed object at a certain position coordinate, unless it is particularly unnatural, it may be interpreted to include the estimated value output by inputting a position coordinate substantially the same as the said position coordinate into a regression model.

[0034] There is no particular limitation on the specific method for comparing the observed values included in observation data with the estimated values output by a regression model. For example, based on the generated regression model described above, estimated data that includes (or consists of) a position coordinate associated with an estimated value of an observation target that is output when said position coordinate or a position coordinate substantially the same as said position coordinate is input to the regression model may be generated, and the observation data may be compared with the generated estimated data. The comparison between the observation data and the estimated data may be performed, for example, by determining whether the observed value included in the observation data matches the estimated value included in the estimated data for each position coordinate, or by calculating the difference between the observation data and the estimated data. More specifically, calculating the difference between the observation data and the estimated data refers to, for each position coordinate, calculating the difference between the observed value included in the observation data and the estimated value included in the estimated data, thereby generating difference data between the observation data and the estimated data that includes (or consists of) a position coordinate associated with the difference between the observed value and the estimated value of the observation target corresponding to said position coordinate, and said comparison may be performed based on the difference data. For example, in the difference data, if the value of the difference between the observed value and the estimated value of the observation target at a certain position coordinate is zero or equal to or less than a predetermined threshold, it may be determined that the observed value matches the estimated value at said position coordinate. There is no particular limitation on the predetermined threshold, and an appropriate threshold may be set according to factors such as the accuracy of observed values, required accuracy, specifications of available computers, and the amount of computation that can be executed by the computer; for example, the threshold may be 1% or less, 0.5% or less, 0.2% or less, 0.1% or less, 0.05% or less, 0.02% or less, 0.01% or less, 0.005% or less, 0.002% or less, or 0.001% or less of the observed value.

[0035] In a method relating to one aspect of the present invention, for example, as described above, for each position coordinate included in the observation data, the observed value included in the observation data and the estimated value output by the regression model are compared, and the position coordinates that match between the two are identified. Thus, a method relating to one aspect of the present invention may include the step of comparing, for each position coordinate included in the observation data, the observed value of the object at that position coordinate with the estimated value of the object at the position coordinate corresponding to that position coordinate output by the regression model, and / or the step of identifying the position coordinates that match as a result.

[0036] The output data can be basically any insofar as it includes information that allows for the identification of a location coordinate where the observed value of the observed object included in the observation data matches the estimated value of the observed object generated by the regression model. In one preferred embodiment, for example, it may be difference data between the observation data and the estimated data, which includes (or consists of) a location coordinate and the difference between the observed value and the estimated value of the observed object at that location coordinate. As mentioned above, if the difference value between the observed value and the estimated value of the observed object included in the difference data in association with a certain location coordinate is zero or less than or equal to a predetermined threshold, it can be determined that the observed value of the observed object included in the observation data matches the estimated value of the observed object generated by the regression model at that location coordinate. Furthermore, by using difference data that includes the sign and magnitude of the difference between the observed value and the estimated value of the observed object, it is possible to grasp not only the location coordinates where the observed value and the estimated value of the observed object match, but also the sign and magnitude of the difference between the observed value and the estimated value of the observed object at each location coordinate. Therefore, it is possible to grasp the magnitude of the deviation from a value considered standard and its direction for the observed value at each location coordinate. As will be described later, when applied to topographic data, for example, the sign and magnitude of the difference between the observed and estimated values ​​of the observed object are extremely useful for understanding unstable terrain such as cuts and fills. However, the format of the output data is not limited to this. For example, the data may include (or consist of) position coordinates and the agreement and / or disagreement between the observed and estimated values ​​of the observed object at those position coordinates, or it may be data in which position coordinates where the observed and estimated values ​​of the observed object coincide are extracted.

[0037] <Additional Step> The output data can be used by any appropriate method. There are no particular restrictions on the specific method of use. For example, in one preferred embodiment, based on the output data, a diagram showing position coordinates where observed values of an observation target included in observation data match estimated values of the observation target generated by a regression model may be generated. That is, in one preferred embodiment, a method according to one aspect of the present invention may include a diagram generation step of generating a diagram that displays position coordinates where an observed value of an observation target included in observation data matches an estimated value of the observation target generated by a regression model. By generating a diagram that displays position coordinates where the observed value matches the estimated value and enabling visual recognition of the position coordinates, for example, comparison between the position coordinates and observation data, estimated data, and / or difference data is facilitated, and local features included in the observation data can be easily grasped.

[0038] The diagram displaying the position coordinates where the observed value and the estimated value of the observation target match may basically be any type of diagram, as long as the position coordinates can be visually recognized. For example, the diagram may be one that displays the position coordinates in a visually recognizable manner in a coordinate system corresponding to the position coordinates. The coordinate system corresponding to the position coordinates is, for example, a two-dimensional coordinate system when the position coordinates indicate a position in a two-dimensional coordinate system, and a three-dimensional coordinate system when the position coordinates indicate a position in a three-dimensional coordinate system. Such a coordinate system may be in the form of, but not limited to, for example, a map of a region corresponding to position coordinates included in observation data, a topographic map (e.g., contour map, CS stereogram, shaded relief map, slope gradient map, curvature map, shaded tint map, bird's-eye view, etc.), a ground surface image (e.g., aerial photograph, satellite photograph, etc.). That is, in one preferred embodiment, the above diagram may be a diagram in which the position coordinates where the observed value and the estimated value of the observation target match are superimposed and displayed on a map, a topographic map, a ground surface image or the like of a region corresponding to position coordinates included in observation data.

[0039] There are no particular restrictions on the specific method of displaying the above-mentioned position coordinates in the above-mentioned coordinate system. For example, the above-mentioned position coordinates may be plotted in the above-mentioned coordinate system, or a heat map color-coded according to the magnitude of the difference between the observed value and the estimated value of the observed target may be used to visually display the magnitude of the difference between the observed value and the estimated value, in addition to the above-mentioned position coordinates where the observed value and the estimated value coincide. Alternatively, each position coordinate where the observed value and the estimated value coincide may be connected by a line. When displaying each position coordinate by connecting it with a line, there are no particular restrictions on the method of drawing the line. For example, adjacent position coordinates may be connected by a line, or, if necessary, an appropriate spatial interpolation method may be applied to interpolate the position coordinates where the observed data and the regression model are estimated to coincide. There are no particular restrictions on the spatial interpolation method, but for example, linear interpolation, TIN method, IDW method, kriging method, etc. may be used. Furthermore, when drawing lines connecting each position coordinate, for example, difference data that includes (or consists of) the aforementioned position coordinates and the difference between the observed value and the estimated value of the observed target at that position coordinate may be used. The lines connecting each coordinate can be drawn using any software, such as the Contour plugin for the open-source GIS software (QGIS) (https: / / plugins.qgis.org / plugins / contour / ), as shown in the experimental example described later.

[0040] In one preferred embodiment, a diagram displaying the position coordinates that coincide with the observed and estimated values ​​of the object being observed may also display the observed data and / or the estimated data. Such a diagram may also display the observed and / or estimated values ​​of the object being observed corresponding to each position coordinate in the above coordinate system. For example, as shown in the experimental example described later, if the observed value is elevation (i.e., the observed data is topographic data), the diagram may also display the position coordinates that coincide with the observed and estimated values ​​of the object being observed in a topographic map (e.g., contour map, CS relief map, shaded relief map, slope map, curvature map, shaded relief map, bird's-eye view map, etc.) in a manner that appropriately displays the observed and / or estimated values ​​of elevation at each position coordinate on the map, so that the observed and / or estimated values ​​of the object being observed can be visually grasped.

[0041] Furthermore, in one preferred embodiment, the difference data may be displayed in a figure that shows the position coordinates where the observed and estimated values ​​of the observed object coincide. Such a figure may be a figure that displays the difference between the observed and estimated values ​​of the observed object at each position corresponding to the position coordinate in the above coordinate system (for example, a heat map color-coded according to the magnitude of the difference between the observed and estimated values ​​of the observed object), and in which the position coordinates where the observed and estimated values ​​of the observed object coincide can be visually grasped. The sign and / or magnitude of the difference between the observed and estimated values ​​represent the direction and magnitude of the deviation from the standard numerical value. By making this visually graspable, for example, it may become easier to grasp local features contained in the observation data.

[0042] In one embodiment, the figure generated based on the output data does not have to explicitly display the position coordinates where the observed value of the observed object included in the observation data coincides with the estimated value of the observed object generated by the regression model. For example, in one preferred embodiment, a figure (e.g., a heatmap) may be generated that displays the sign and / or magnitude of the difference value at each position coordinate in a way that can be understood, based on the output data which is difference data that includes the position coordinates and the difference between the observed value of the observed object at the position coordinate and the estimated value of the observed object at the position coordinate corresponding to the position coordinate. That is, in one preferred embodiment, a method according to one aspect of the present invention may include a figure generation step of generating a figure that displays the sign and / or magnitude of the difference between the position coordinates and the position coordinates where the difference value of the observed object at the position coordinate and the estimated value of the observed object at the position coordinate corresponding to the position coordinate in a way that can be understood, based on the difference data. If the sign and / or magnitude of the difference value at each position coordinate can be understood, then the position coordinates where the observed value and the estimated value coincide can be understood. It goes without saying that in the figures, the position coordinates where the observed value of the observed object included in the observation data coincides with the estimated value of the observed object generated by the regression model may be explicitly displayed. For example, auxiliary lines connecting position coordinates where the difference between the observed value and the estimated value is zero (i.e., the observed value and the estimated value coincide) may be included. The method for drawing these figures is as described above, so a detailed explanation will be omitted.

[0043] The figures generated based on the output data may be output in any format. For example, they may be output as an image file or as a printed document. Alternatively, they may be output in a format suitable for conversion into the above figures using an appropriate application (e.g., a Geographic Information System (GIS)). For example, when using a GIS, they may be output in formats such as shapefiles or geoTiff files. For example, if the data is output in these formats, including location coordinates and difference data that associates the observed value of the observed object at the given location coordinates with the estimated value of the observed object at the corresponding location coordinates, it will be possible to convert it into the above figures using a GIS.

[0044] <How to Use Output Data and Figures> The output data and / or figures generated in the above steps can be used for any appropriate purpose as needed. The following describes how to use the output data and / or figures generated by the method relating to one aspect of the present invention, but these uses are merely examples, and the uses of the output data and / or figures generated by the method relating to one aspect of the present invention are not limited to the following examples. In this disclosure, when the phrase "based on output data" is used, it also includes the use of the figures generated based on the output data, unless it is clear from the context that this is not to be the case, or unless it is specifically stated that this is not to be the case.

[0045] For example, in one preferred embodiment, if the observed value is elevation (i.e., if the observed data is topographic data), the stability of the topography may be evaluated based on the output data output in the above step and / or the figure generated in the above step. As shown in the experimental examples described later, the set of position coordinates where the observed value and estimated value of the observed object (elevation) identified by the output data output by the above method according to one aspect of the present invention coincide is useful as a criterion for judging local topographic changes. Evaluators of topographic stability can more efficiently grasp unstable topography, including erosional topography such as valleys, slopes, and landslides, sedimentary topography such as alluvial fans and deltas, depression topography such as old river channels, artificial topography such as cuts, fills, embankments, and reclaimed land, and subsidence topography and active fault displacement topography caused by ground movement, based on the output data output in the above step and / or the figure generated in the above step.

[0046] There are no particular restrictions on the types of unstable terrain that can be identified based on the output data and / or the diagrams generated in the above steps, and on the method of determining them. However, if we were to give an example, it could be as follows.

[0047] For example, in determining the presence of an embankment, an area where the difference between the observed value and the estimated value is positive (i.e., observed value > estimated value), preferably an area where the difference exceeds a predetermined threshold, may be estimated to be a topography formed by an embankment. An area where the difference between the observed value and the estimated value is positive (i.e., observed value > estimated value) is an area with a high elevation that deviates from the standard topographic distribution. Such an area may be a topography formed by an embankment, and in particular, if it overlaps with a residential area or urban area, it can be determined that there is a high probability that it is a topography formed by an embankment.

[0048] On the other hand, for example, when determining the presence of cuts, areas where the difference between the observed value and the estimated value is negative (i.e., observed value < estimated value), preferably areas where the difference is below a predetermined threshold, may be estimated to be topography formed by cuts. Areas where the difference between the observed value and the estimated value is negative (i.e., observed value < estimated value) are areas with low elevation that deviate from the standard topographic distribution. Such areas may be topography formed by cuts, and in particular, if they overlap with residential areas or urban areas, it can be determined that there is a high probability that they are topography formed by cuts.

[0049] Furthermore, for example, in identifying the presence of a valley, a region enclosed by a protruding shape with one end closed, defined by a set of position coordinates where the observed and estimated values ​​coincide, or by line segments connecting them, may be estimated as a valley if the length in the direction of the protrusion of the region is n and the width is m, and m / n < 1.0 (i.e., a region where width < length), and the difference between the observed and estimated values ​​is negative (i.e., observed value < estimated value). In this case, if the region is surrounded by steep slopes with a predetermined gradient or greater (e.g., 30 degrees or more, 35 degrees or more, or 40 degrees or more), it may be estimated as a primary or secondary valley, and if not, it may be estimated as a zero-order valley. Note that a valley is a landform where the depth of the contour lines is greater than the width, and they are called primary, secondary, and tertiary valleys from the uppermost valley. Valleys are landforms that are highly likely to be the starting point of slope failures.

[0050] Furthermore, the output data and / or figures produced in the above steps can be used to identify slopes at risk of landslides. There are no particular restrictions on the method for detecting slopes at risk of landslides, but for example, if the set of position coordinates identified by the output data produced in the above steps overlaps with a slope, the slope may be evaluated as having and / or a high risk of landslides. Here, the case where the set of position coordinates overlaps with a slope may refer to the case where the set of position coordinates and / or the line segments connecting the set (for example, the topographic equilibrium lines described later) overlap with the slope, and the slope may refer to a slope with a gradient of 20 degrees or more, preferably 25 degrees or more, and more preferably 30 degrees or more (steep slope). Depending on the surrounding topography, vegetation, geological conditions, and the state of erosion and weathering, areas where the set of position coordinates overlaps with such steep slopes are slopes accompanied by abrupt topographic changes that deviate from standard topographic analysis, and are presumed to have a high risk of landslides. Furthermore, in one preferred embodiment, if a valley exists above the area where the slope overlaps with the set of position coordinates where the observed and estimated values ​​coincide, and / or the line segments connecting such sets (i.e., the area with higher elevation), the slope may be assessed as having and / or a high risk of landslide. Valleys are a type of landform that frequently serves as the starting point for landslides. When such a landform is present above, the risk of landslide is judged to be higher. There are no particular restrictions on the method of calculating the slope's incline; for example, it may be appropriately extracted and calculated from a topographic map, or it may be calculated from observational data.

[0051] When evaluating the stability of the terrain, it is preferable to use other information in combination, not limited to the output data and figures described above, as needed. Such information may include, but is not limited to, the observation data, estimation data, and / or topographic maps such as CS stereoscopic maps, slope maps, and contour maps, as well as maps, aerial photographs, satellite photographs, and other ground images. The output data and figures obtained by the method according to one aspect of the present invention represent a baseline indicating an area that deviates from the standard terrain distribution, and, in a preferred embodiment, the degree of such deviation. Therefore, by using the output data and figures obtained by the method according to one aspect of the present invention in combination with, for example, topographic maps such as CS stereoscopic maps, slope maps, and contour maps, it is possible to gain insight into local terrain changes that would be difficult to grasp with these topographic maps alone.

[0052] <Embodiment> The present invention will be described in more detail below using as an example the case in which topographic data consisting of position coordinates and elevation at said position coordinates is processed as observation data, but this example does not limit the scope of the present invention in any way.

[0053] In this example, the processing of terrain data is performed by the data processing device 10. The data processing device is an information processing device, and may be, for example, a terminal device such as a personal computer, smartphone, or tablet terminal, a server device, or a cloud server. Functionally, the information processing device 10 comprises a control unit 101, a storage unit 102, an acquisition unit 103, a generation unit 104, an estimation unit 105, a comparison unit 106, and an output unit 107. Some or all of the acquisition unit 103, the generation unit 104, the estimation unit 105, the comparison unit 106, and the output unit 107 may be implemented as modules of a program executed by the control unit 101.

[0054] The control unit 101 is configured to include, for example, a CPU (Central Processing Unit). It reads various programs from the storage unit 102, executes the programs, and comprehensively controls the operation of the data processing device 10. This enables the various functions of the data processing device 10 to be realized.

[0055] The storage unit 102 is configured to include, for example, ROM (Read Only Memory), RAM (Random Access Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), etc. The storage unit 102 has a non-volatile area and a volatile area. The volatile area is configured to include, for example, RAM, etc., and provides a workspace for the CPU, etc. The non-volatile area is configured to include, for example, ROM, HDD, SSD, etc. ROM is a non-volatile memory and stores programs for starting the data processing device 10, etc. The HDD and SSD store programs for causing the data processing device 10 to perform various processes such as regression model generation, machine learning algorithms, generated regression models, observation data acquired by the acquisition unit 103, estimated data generated by the estimation unit 105, difference data generated by the comparison unit 106, etc.

[0056] The acquisition unit 103 acquires observation data (topographic data) to be processed. For example, the acquisition unit 103 acquires observation data to be processed from the storage unit 102 or from an external device. The external device may be, for example, a cloud server or cloud storage.

[0057] The generation unit 104 generates a regression model based on the observation data. Specifically, it uses observation data, which is a set of point data consisting of position coordinates and observed values ​​of the observed object at the position coordinates, as training data, and generates a regression model by applying a machine learning algorithm. The regression model generated in this way may be called a trained model.

[0058] The estimation unit 105 generates an estimated value of the observed object at the position coordinate corresponding to each of the position coordinates included in the observation data, based on the observation data and the regression model. In this example, the estimation unit 105 inputs each of the position coordinates included in the observation data into the regression model, so that the regression model outputs an estimated value of the observed object, thereby generating estimated data that includes the position coordinate and the estimated value of the observed object at that position coordinate in association.

[0059] The comparison unit 106 compares, for each position coordinate included in the observation data, the observed value of the observed object included in the observation data associated with that position coordinate, with the estimated value of the observed object at the position coordinate corresponding to that position coordinate, which is generated by the estimation unit 105, and identifies the position coordinates where the two values ​​match. In this example, the comparison unit 106 generates difference data that associates the position coordinate with the difference between the observed value and the estimated value at that position coordinate, based on the observation data and the estimated data generated by the estimation unit 105. In this difference data, the position coordinates where the corresponding value (i.e., the difference between the observed value and the estimated value) is zero are identified as the position coordinates where the observed value and the estimated value match.

[0060] The output unit 107 outputs output data that includes information that allows for the identification of position coordinates where the observed value and estimated value identified by the comparison unit 106 coincide. In this example, more specifically, the output data includes difference data generated by the comparison unit 106, that is, difference data that associates the position coordinates with the difference between the observed value and estimated value of the object being observed at those position coordinates. In other words, in this example, the difference data that associates the position coordinates with the difference between the observed value and estimated value of the object being observed at those position coordinates is the information that allows for the identification of position coordinates where the observed value and estimated value coincide. Furthermore, as mentioned above, among the position coordinates included in the difference data, position coordinates where the corresponding value is zero are considered to be position coordinates where the observed value and estimated value coincide.

[0061] Furthermore, the generation unit 104 generates a diagram based on the output data that displays the position coordinates where the observed value and estimated value of the observed object coincide. Specifically, the generation unit 104 extracts the position coordinates identified by the information contained in the output data and displays these position coordinates on a CS 3D diagram, map, and / or slope diagram of the area corresponding to those position coordinates. Here, the extracted position coordinates are displayed as lines connecting adjacent position coordinates (sometimes referred to as "topographic equilibrium lines" in this disclosure). The generation unit 104 also generates a diagram based on the output data that displays the sign and / or magnitude of the difference between the observed value and estimated value of the observed object at each position coordinate in a way that allows for understanding. This diagram includes lines (topographic equilibrium lines) connecting position coordinates where the difference value is zero.

[0062] The data processing performed by the data processing device 10 will be described below, step by step.

[0063] In this example, the observational data to be processed is topographic data that includes location coordinates and observed elevation values ​​at those location coordinates, specifically, base geological information (digital elevation model) provided by the Geospatial Information Authority of Japan of the Ministry of Land, Infrastructure, Transport and Tourism. The digital elevation model is mesh data that includes location coordinates and elevation values ​​at predetermined intervals, and in this example, a digital elevation model (DEM10B) with 10m intervals (10m mesh) was used.

[0064] <Step S1: Step to generate a regression model> The data processing device 10 generates a regression model (Step S1). This process is mainly performed by the acquisition unit 103 and the generation unit 104 of the data processing device 10. Step S1 is configured to include steps S11 to S13 in detail.

[0065] In step S11, the acquisition unit 103 acquires the observation data to be processed. In this example, the acquisition unit 103 stores the digital elevation model downloaded via the website provided by the Geospatial Information Authority of Japan in an external device (cloud storage) not shown in the diagram. The acquisition unit 103 acquires the digital elevation model from this external device.

[0066] In step S12, the observed data is converted into a suitable format that can be used in the regression model generation process. The observed data may be converted into a suitable format depending on the specific method used in the regression model generation process. In this example, the observed data is handled using the R language (hereinafter sometimes simply referred to as "R") and the regression model generation process is executed. The numerical elevation model, which is provided as XML data so that it can be handled in R, is converted into a format that can be handled in R using the software library sp.

[0067] In step S13, the generation unit 104 uses the acquired observation data, or observation data converted to an appropriate format as needed, as training data, and generates a regression model by applying a machine learning algorithm to it. In this example, the machine learning algorithm is a support vector machine (kernel SVM) using kernel functions, and the process of generating the regression model using this machine learning algorithm is performed using the R software library kernlab.

[0068] When generating a regression model, the parameters of the machine learning algorithm are tuned. In this example, the parameters of the machine learning algorithm are tuned according to a standard method, based on the variogram generated from the numerical elevation model and the OK model obtained using the Ordinary Kriging (OK) method. The procedure for generating the OK model is described below.

[0069] Interpolation point x ｊ The estimated value of the observed object Z(x) ｊ ) are the n points x that exist around it. ｉ Observed value Z(x) ｉ It is expressed as a weighted average of ). Note that in the following equation (VI), λ ｊｉ is, point x ｉ These are the weights corresponding to [the specified value].

[0070]

[0071] A variogram represents the relationship between the vectors between measurement points and the variance of the observed data. Specifically, an experimental variogram defined by equation (VII) below is obtained based on a numerical elevation model, and then a logical variogram is generated by applying a function (sphere model) defined by equation (VIII) below to the obtained experimental variogram. In this example, the logical variogram generated in this way is usually used for kriging. When modeling the variogram, the least squares method or generalized least squares method is usually used, and the choice depends on the convergence of the solution.

[0072]

[0073] In the above formula (VII), h is the point x ｋ and the point x ｌ distance; N(h) is the point x ｋ and the point x ｌ the set of pairs of k and l whose distance is h; |N(h)| represents the number of elements in N(h).

[0074]

[0075] In the above formula (VIII), α is a range. As shown in the above formula (VIII), in this example, the nugget value is 0 and the sill value is 1.

[0076] A variogram can be generated by a person skilled in the art through an appropriate method, and the method is described in, for example, Non-Patent Document 4 and the like.

[0077] Next, based on the obtained experimental variogram and ordinary kriging, the weight λ ji is estimated. The estimation of the weight λ ji is performed by using the Lagrange multiplier method under the constraint of stationarity (sometimes also referred to as "constant nature") and solving the simultaneous equations represented by the following formula (IX).

[0078]

[0079] The weight λ obtained by solving the above formula (IX) ji is applied to the above formula (VI) to obtain the point x ｉ the estimated value at is obtained, whereby an OK model is obtained.

[0080] Estimation of the weight λ by ordinary kriging kl can be performed by a person skilled in the art through an appropriate method, and the method is described in, for example, Non-Patent Document 3 and the like.

[0081] <Step S2: Step to output output data> Based on the generated regression model, the data processing device 10 compares, for each of the position coordinates included in the observation data used as training data, the observed value of the observed object included in the observation data that is associated with the position coordinate, with the estimated value of the observed object output by inputting the position coordinate into the regression model, and outputs output data that includes information that can identify the position coordinates that match. Step S2 is composed of steps S21 to S23 in detail.

[0082] In step S21, based on the regression model, an estimated value of the observed object at each of the position coordinates included in the observation data is generated. In this example, for each of the position coordinates included in the numerical elevation model used as training data, estimated data is generated consisting of the position coordinate and the estimated elevation value output by inputting the position coordinate into the regression model.

[0083] In step S22, the estimated data generated in step S21 is compared with the observed data. In this example, by taking the difference between the observed data and the estimated data for the same position coordinates, difference data is generated that includes the position coordinate and the difference between the observed elevation value in the observed data and the estimated elevation value in the estimated data. In the generated difference data, if the corresponding value (i.e., the difference between the observed elevation value in the observed data and the estimated elevation value in the estimated data) for a certain position coordinate is zero, then that position coordinate is one in which the observed value of the observed object included in the observed data, associated with that position coordinate, matches the estimated value of the observed object output when that position coordinate is input into a regression model. On the other hand, if the corresponding value (i.e., the difference between the observed elevation value in the observed data and the estimated elevation value in the estimated data) for a certain position coordinate in the difference data is not zero, then that position coordinate is one in which the observed value of the observed object included in the observed data, associated with that position coordinate, does not match the estimated value of the observed object output when that position coordinate is input into a regression model. Thus, the difference data described above contains information that allows for the identification of position coordinates where the observed values ​​of the observed object included in the observation data coincide with the estimated values ​​of the observed object generated by the regression model.

[0084] Step S23 is a step in which the output data generated in step S22 is output. The output data is stored in the storage unit 102 and used in the figure generation process described later. Steps S21 to S23 described above realize a process that, for each position coordinate included in the observation data, compares the observed value of the observed object at that position coordinate with the estimated value of the observed object output by inputting that position coordinate into a regression model, and outputs output data that includes information that allows the identification of the position coordinate where the two match.

[0085] <Step S3: Figure Generation Step> The data processing device 10 generates a figure that extracts and displays a set of location coordinates identified in the output data based on the output data. Specifically, based on the location coordinates and the difference data (output data) which includes the difference between the observed elevation and the estimated elevation at those location coordinates, the device generates contour lines (hereinafter referred to as "topographic equilibrium lines") by using any software, such as the Contour plugin for the open-source GIS software (QGIS) (https: / / plugins.qgis.org / plugins / contour / ), to connect location coordinates where the difference between the observed elevation in the observation data and the estimated elevation in the estimation data is zero. This generates a figure that extracts and displays location coordinates where the observed elevation and the estimated elevation match. In this example, the generated topographic equilibrium lines are overlaid and displayed on a CS 3D map (Figure 1), a ground image (Figure 2), a slope map (Figure 3), and a heatmap (Figures 5 and 13) generated based on difference data for the region corresponding to the same position coordinates. It goes without saying that the generated figures may be output using an appropriate output method.

[0086] The following describes how to utilize the output data and figures generated by the above procedure according to one embodiment of the present invention, using as examples how the topographic analysis based on the numerical elevation model according to the above procedure was applied to the topographic analysis of Handayama in Okayama Prefecture (Example 1), the topographic analysis of the area around Okayama University (Example 2), the topographic analysis of Takuwa in Mitoya-cho, Unnan City, Shimane Prefecture (Example 3), and the topographic analysis of Mayuyama in Tokushima City, Tokushima Prefecture (Example 4).

[0087] <Example 1: Topographic analysis of Handayama, Okayama Prefecture> Figures 1 and 2 are diagrams created using the above procedure based on a digital elevation model of Handayama, located in Kita Ward, Okayama City, Okayama Prefecture.

[0088] In Figures 1 and 2, the line segments shown in white are topographic equilibrium lines connecting the position coordinates (i.e., position coordinates where the observed value and the estimated value coincide) that are specified in the output data output by the above procedure according to one embodiment of the present invention. Figure 1 shows these topographic equilibrium lines superimposed on a topographic map (CS stereoscopic map) of the same area. On the other hand, Figure 2 shows these topographic equilibrium lines superimposed on a ground surface image of the same area.

[0089] Furthermore, Figures 1 and 2 show that there are regions enclosed by topographic equilibrium lines that are closed at one end, where the length in the direction of the protrusion is n and the width is m, and m / n < 1.0 (i.e., regions where width < length). In this example, a region was determined to be a primary valley if it was surrounded by steep slopes with a gradient of 30 degrees or more, and the difference between the observed value and the estimated value was negative (i.e., observed value < estimated value). To indicate regions determined to be primary valleys, a long arrow pointing from a higher elevation to a lower elevation was shown. Here, if the arrow is located within an area designated as a warning area or special warning area in the hazard map of Okayama City, Okayama Prefecture, a black arrow is shown; if it is located outside such an area, a white arrow is shown.

[0090] As shown in Figure 1, the distribution of topographic equilibrium lines overlaps with the steep slope areas (areas shown in gray) in the CS stereoscopic map, indicating that topographic equilibrium lines are useful as a criterion for judging local topography, particularly local topographic changes that deviate from the standard topographic distribution.

[0091] Furthermore, as indicated by the long arrows in Figures 1 and 2, there were two locations in Figure 1 that were identified as primary valleys. When these locations were compared with the topography observed in satellite imagery, the presence of primary valleys was clearly confirmed at both locations (Figure 2). This result indicates that, according to the output data and / or figures output in the above procedure according to one embodiment of the present invention, more specifically the set of position coordinates identified in the output data, unstable terrain such as valleys can be detected based on the numerical elevation model. In particular, when comparing the CS stereoscopic map shown in the background of Figure 1 with the topographic equilibrium line, the presence of valley terrain can be identified in the CS stereoscopic map, but it is displayed as a broader area. This result indicates that, according to the output data and / or figures output in the above procedure according to one embodiment of the present invention, more specifically the set of position coordinates identified in the output data, valleys can be detected more sharply than in the CS stereoscopic map.

[0092] The region enclosed by the topographic equilibrium line has a topographic distribution that deviates from the standard topographic distribution estimated by the regression model, and is likely to be a region where unstable terrain exists. If the observed elevation in such a region is smaller than the estimate based on the regression model, it is estimated to be a region that is being eroded by some factor. By applying this idea, as shown in this example, it may be possible to sharply detect the presence of, for example, primary valleys.

[0093] <Example 2: Topographic analysis around Okayama University> Figure 3 is a diagram created using the above procedure based on a digital elevation model of the area around Tsushima-naka, Kita-ku, Okayama City, Okayama Prefecture.

[0094] In Figure 3, the line segments shown in white are topographic equilibrium lines connecting the position coordinates (i.e., position coordinates where the observed value and the estimated value coincide) that are identified by the output data output in the above procedure according to one embodiment of the present invention. Figure 3 shows these topographic equilibrium lines superimposed on a topographic map (slope map) of the same area.

[0095] In this example, a steep slope is defined as a section with a gradient of 30 degrees or more. A section that is a steep slope, passes through a topographic equilibrium line, and has a primary valley above it (i.e., at a higher elevation) is judged to have a particularly high risk of slope failure. Three types of arrows—black, white, and black and white—are shown centered on such a section, with the higher elevation side as the base and the lower elevation side as the tip. Note that a primary valley is a type of landform that can potentially be the starting point of a slope failure. The area through which the topographic equilibrium line passes is presumed to be an area where unstable topographic changes that deviate from the standard topographic distribution exist locally. In such an area, if the gradient is large and a primary valley exists above the steep slope area, the risk of slope failure is judged to be high.

[0096] In Figure 3, the arrows are color-coded according to whether or not they are designated as such in the hazard map. Specifically, in Figure 3, black arrows indicate areas within the hazard map that are designated as having a risk of slope failure on steep slopes through which the topographic equilibrium line passes and where a primary valley exists above, and where the hazard map indicates a risk of slope failure; white arrows indicate areas within the hazard map that are designated as having a risk of slope failure on steep slopes through which the topographic equilibrium line passes and where a primary valley exists above, and where the hazard map indicates a risk of slope failure; and black and white arrows indicate areas within the hazard map that are designated as having a risk of slope failure on steep slopes through which the topographic equilibrium line passes and where a primary valley does not exist above, but where the hazard map indicates a risk of slope failure.

[0097] For comparison, Figure 4 shows a hazard map of the area around Tsushima-naka, Kita-ku, Okayama City, Okayama Prefecture, obtained from the Okayama Prefecture Integrated GIS (http: / / www.gis.pref.okayama.jp / pref-okayama / Portal). In the hazard map shown in Figure 4, areas identified as being at risk of slope collapse are indicated as warning areas (light hatching) and special warning areas (dark hatching).

[0098] Comparing Figures 3 and 4, black arrows are displayed in most of the areas corresponding to those identified as being at risk of slope failure on the hazard map. This shows that the method used in this example can detect areas at risk of slope failure with a high accuracy of 96%. Furthermore, this method was able to detect 14 new hazardous areas not identified on the hazard map.

[0099] The results above demonstrate that the output data and figures obtained by the method relating to one aspect of the present invention can be useful for detecting unstable terrain at risk of landslides. The usefulness of this example method, which can detect unstable terrain at risk of landslides based on a digital elevation model (DEM) with greater precision and fewer omissions compared to hazard maps, and without requiring field surveys or the preparation of large amounts of training data, is considerable.

[0100] <Example 3: Topographic Analysis of Takuwa, Mitoya-cho, Unnan City, Shimane Prefecture> A topographic analysis was performed on the area around Kumomi Falls in Takuwa, Mitoya-cho, Unnan City, Shimane Prefecture. Figures 5 and 6 are diagrams created using the above procedure with a digital elevation model (DEM) of the area around Kumomi Falls. For reference, Figure 7 shows a ground image of the same area as in Figures 5 and 6.

[0101] In Figure 5, the white line segments represent topographic equilibrium lines connecting position coordinates where the difference between the observed elevation values ​​in the observation data and the estimated elevation values ​​in the estimation data is zero. Furthermore, in the background of Figure 5, a heatmap is displayed for the analyzed region, color-coded according to the difference between the observed elevation values ​​in the observation data and the estimated elevation values ​​in the estimation data for each mesh corresponding to the position coordinates. In the heatmap, areas (meshes) where the difference between the observed and estimated values ​​is positive are shown in white, and areas (meshes) where the difference is negative are shown in black, with gradations (shades) corresponding to the magnitude of the absolute value of the difference.

[0102] In this example, areas with a slope of 40 degrees or more were defined as steep slopes, and areas that were steep slopes and where the topographic equilibrium line passed through were determined to be areas at risk of slope failure. In Figure 5, among the areas determined to be at risk of slope failure, wide arrows are shown along the field survey route (the route shown by the dotted line in Figure 5), with the higher elevation side as the base and the lower elevation side as the tip, centered on the area in question.

[0103] In this example, a region surrounded by steep slopes and enclosed by a protruding shape with one end closed by a topographic equilibrium line, where the length in the direction of the protrusion is n and the width is m, is determined to be a primary valley if m / n < 1.0 (i.e., a region where width < length). Figure 5 shows thin arrows pointing from higher elevations to lower elevations in the regions determined to be primary valleys. On the other hand, regions where m / n < 1.0 does not have the highest steep slope in the region determined to be a primary valley are determined to be zero-order valleys and are shown with dashed arrows.

[0104] As a result, as shown in Figure 5, several locations were identified near the road on the west bank of the Iishigawa River where there was a risk of slope collapse or where a valley (primary or zero-order valley) existed. Therefore, a field survey was conducted at the identified locations (locations "1" to "6") along the route heading north from under the Iishigawa viaduct south of the Matsue Expressway Takaseyama Tunnel (the route shown by the dotted line in Figure 5). The results of the field survey are as follows: Location "1": A photograph of the site is shown in Figure 8. A clear valley topography was formed at the site. Location "2": A photograph of the site is shown in Figure 9. A clear valley topography was formed at the site. Many boulders and fallen trees were found at the bottom of the valley, and traces of past landslides were confirmed. It was judged that during rainfall, water flow would concentrate along the valley, causing a chain reaction of surface landslides. Location "3": A photograph of the site is shown in Figure 10. The formation of a valley topography was confirmed at the site. In addition, the site had already been marked by construction personnel as a location requiring caution regarding landslides. Location "4": A photograph of the site is shown in Figure 11. A landslide prevention fence was installed at the site, and it was confirmed that the determination result using the method of this embodiment was consistent with the perceptions of the local stakeholders. Location "5": A photograph of the site is shown in Figure 12. A large-scale landslide had already occurred at the site. Upon checking the heavy rain disaster information near Kumomi Falls, it was confirmed that this large-scale landslide occurred in July 2021 (https: / / www.city.izumo.shimane.jp / www / contents / 1627543778485 / files / houkoku3.pdf). On the other hand, the acquisition date of the elevation data included in the Digital Elevation Model (DEM) can be confirmed from the GSI Maps provided by the Geospatial Information Authority of Japan (https: / / maps.gsi.go.jp / ). Therefore, by referring to the Geographical Survey Institute map and checking the acquisition date of the elevation data for the digital elevation model near Kumomi Falls used in the analysis, it was confirmed that the work year was "H21 (Heisei 21 = 2009)" and the source material was "H21G0007-02," thus confirming that the digital elevation model is based on elevation data measured in 2009. In other words, the above determination result using the method of this embodiment is based on data from before the large-scale landslide near Kumomi Falls.Location "6": This location was determined to have a zero-order valley formed using the method described in this example. However, it is near the site of a large-scale landslide and access was not permitted, so on-site verification by visual inspection or other means was not possible.

[0105] As described above, based on the output data and figures obtained by the method according to one embodiment of the present invention, on-site investigations were conducted at locations determined to be at risk of slope collapse or to have valleys. At all locations, findings consistent with the determination were observed. This result indicates that, according to the method according to one embodiment of the present invention, locations at risk of slope collapse can be easily identified based on topographic data, such as a digital elevation model, which can be obtained relatively easily from remote locations, without the need for on-site investigations or the preparation of large amounts of training data. It is also possible to detect unstable terrain such as valleys. The output data and figures obtained by the method according to one embodiment of the present invention are extremely useful for improving the efficiency and prioritization of disaster countermeasures in the field of erosion control.

[0106] <Example 4: Topographic Analysis of Mount Bizan, Tokushima City, Tokushima Prefecture> A topographic analysis was performed on the area around Mount Bizan in Tokushima City, Tokushima Prefecture. Figures 13 and 14 are diagrams created using the above procedure with a digital elevation model (5m mesh) of the area around Tokushima Bizan Tenjin Shrine on Mount Bizan. For reference, Figure 15 shows a ground image of the same area as in Figures 13 and 14.

[0107] In Figure 13, the white line segments represent topographic equilibrium lines, which are lines connecting position coordinates where the difference between the observed elevation values ​​in the observation data and the estimated elevation values ​​in the estimation data is zero.

[0108] Furthermore, in the background of Figure 13, a heatmap is displayed for the analyzed region, color-coded according to the difference between the observed elevation values ​​in the observation data and the estimated elevation values ​​in the estimation data for each mesh corresponding to the position coordinates. In the heatmap, areas (meshes) where the difference between the observed and estimated values ​​is positive are shown in white, and areas (meshes) where the difference is negative are shown in black, with gradations (shades) corresponding to the magnitude of the absolute value of the difference.

[0109] In this example, areas with a slope of 30 degrees or more are defined as steep slopes, and areas that are steep slopes and through which the topographic equilibrium line passes are determined to be areas at risk of slope collapse. These areas are indicated by a wide white arrow with the higher elevation side as the base and the lower elevation side as the tip, with the area as the center.

[0110] In this example, a region surrounded by steep slopes and enclosed by a protruding shape with one end closed by a topographic equilibrium line, where the length in the direction of the protrusion is n and the width is m, is determined to be a primary valley if m / n < 1.0 (i.e., a region where width < length). To indicate that a region is a primary valley, a thin white arrow pointing from a higher elevation to a lower elevation is shown.

[0111] As shown in Figure 13, several locations were identified along the walking trail near Tokushima Bizan Tenjin Shrine where primary valleys were determined to exist. Therefore, on July 8, 2025, and August 19, 2025, field surveys were conducted along the walking trail at the identified locations (locations "1" to "8"). The results of the field surveys are as follows: Location "1": A photograph of the site is shown in Figure 16. A clear valley topography was formed at the site. In addition, there was already a "Beware of Falling Rocks" sign and markings by Tokushima City Hall at the site, confirming the risk of slope collapse. Location "2": A photograph of the site is shown in Figure 17. A valley topography was formed at the site, although it was less clear than at locations "1" and "3". Location "3": A photograph of the site is shown in Figure 18. A clear valley topography was formed at the site, and the slope gradient reached nearly 30 degrees. Many boulders were scattered at the bottom of the valley, confirming the risk of slope collapse. Location "4": A photograph of the site is shown in Figure 19. At the site, a valley topography with traces of past landslides was confirmed, and many boulders and fallen trees were found at the bottom of the valley. These are traces of past landslides, and it was determined that there is still a risk of slope collapse. Location "5": A photograph of the site is shown in Figure 20. A clear valley topography was formed at the site. Location "6": A photograph of the site is shown in Figure 21. "Exposed tree roots" were prominently observed at the site. This suggests the erosion of surface soil and the progression of slow slope deformation, and is considered a sign of future instability. Location "7": A photograph of the site is shown in Figure 22. A valley topography extending to the edge of the mountain was confirmed at the site. This location overlaps with the warning area on the hazard map, and consistency with the administrative judgment was confirmed. Location "8": A photograph of the site is shown in Figure 23. Artificial structures such as shrines were installed at the site, making it difficult to judge the topography.

[0112] As described above, based on the output data and figures obtained by the method according to one embodiment of the present invention, field surveys were conducted at locations where valleys were determined to exist, and findings consistent with the determination were observed at all locations. This result indicates that, according to the method according to one embodiment of the present invention, unstable terrain such as valleys can be detected based on topographic data that can be obtained relatively easily from remote locations, such as a digital elevation model, without the need for field surveys or the preparation of large amounts of training data. Valley terrain is unstable terrain that has a high potential to develop into future disasters such as slope collapses. The output data and figures obtained by the method according to one embodiment of the present invention are extremely useful for improving the efficiency and prioritization of disaster countermeasures in the field of erosion control.

[0113] As shown in Examples 1 to 4 above, according to one embodiment of the present invention, it may be possible to detect unstable terrain such as steep slopes and valleys that are at risk of collapse, based on topographic data that can be obtained relatively easily from a distance, such as a digital elevation model, without the need to conduct field surveys or prepare a large amount of training data.

[0114] Conventionally, analysis and prediction systems using machine learning have faced challenges in that they require the preparation of large amounts of data related to the event being analyzed or predicted, such as past disaster occurrence history, and the prior preparation of ground truth labels assigned by experts, as well as annotation work, which is time-consuming and costly. Furthermore, because it is difficult to handle events that deviate from the learned known patterns, there is a drawback in that the inference accuracy is significantly reduced in unknown areas where past data has not been accumulated or in target areas with different environmental conditions. In contrast, the method of the present invention uses observational data acquired from the target area as training data, generates a regression model by applying a machine learning algorithm, and identifies localized anomalies or unnatural states in the area by extracting the difference between the estimated value of the observed target, which is considered standard, inferred by the regression model, and the actual observed value included in the observational data. The method of the present invention, which employs this approach, does not require ground truth data (training data) other than the observational data acquired from the target area, making it possible to reduce the costs required for preparing past historical data, preparing ground truth labels, and annotation work. As a result, this method can achieve a remarkable effect: it can rapidly and accurately detect local anomalies based on the difference between observed and estimated values, even in uncharted territories where historical data does not exist. This is a particularly useful feature in fields requiring rapid response, such as erosion control. It should also be noted that this method does not prevent the use of the output data (difference data, etc.) obtained by this method as training data or features in other machine learning models.

[0115] As described above, according to one aspect of the present invention, a method, apparatus, or computer program makes it possible to grasp local features from observational data in the field of earth science, which was difficult with conventional techniques. For example, when applied to topographic data, it becomes possible to more accurately grasp local topographic deformation, topographic stability, valleys, and slopes at risk of collapse. The analysis technology of observational data in the field of earth science is becoming increasingly important from the standpoint of understanding natural phenomena and preventing natural disasters, and the industrial applicability of the present invention is great.

Claims

1. A data processing method comprising: an acquisition step of acquiring observation data that includes a correspondence between position coordinates and observed values ​​of an observed object at the position coordinates; a model generation step of generating a regression model that outputs estimated values ​​of the observed object at the input position coordinates by applying a machine learning algorithm to the observation data as training data, and taking the position coordinates as input; and an output step of comparing the observed value of the observed object at each of the position coordinates included in the observation data with the estimated value of the observed object at the position coordinates corresponding to the position coordinates output from the regression model, and outputting output data that includes information that allows for the identification of the position coordinates where the two match.

2. The method according to claim 1, wherein the output data is difference data that includes a position coordinate and the difference between the observed value of the observed object at the position coordinate and the estimated value of the observed object at the position coordinate corresponding to the position coordinate.

3. The method according to claim 2, further comprising a figure generation step of generating a figure that displays, based on the output data, a figure that allows the sign and / or magnitude of the difference value at each position coordinate to be understood.

4. The method according to claim 3, wherein the figure includes auxiliary lines indicating position coordinates where the difference value is zero.

5. The method according to claim 1 or 2, further comprising a figure generation step of generating a figure that displays the position coordinates of the observed object where the observed value and the estimated value coincide, based on the output data.

6. The method according to any one of claims 1 to 5, wherein the observation data is terrain data that includes a correspondence between position coordinates and an observed value of the height from a predetermined reference point at the position coordinates.

7. A diagram generated by the method of claim 3, which displays the sign and / or magnitude of the difference value at each position coordinate in a manner that allows for understanding.

8. The figure according to claim 7, further including auxiliary lines that indicate position coordinates where the difference value is zero.

9. The figure according to claim 7 or 8, wherein the observation data is topographic data that includes a correspondence between position coordinates and an observed value of the height from a predetermined reference point at the position coordinates.

10. A data processing device comprising: an acquisition unit that acquires observation data including a correspondence between position coordinates and observed values ​​of an object at the position coordinates; a model generation unit that generates a regression model that outputs estimated values ​​of the object at the input position coordinates by applying a machine learning algorithm to the observation data as training data, and taking the position coordinates as input; and an output unit that, for each of the position coordinates included in the observation data, compares the observed value of the object at the said position coordinate with the estimated value of the object at the position coordinate corresponding to the position coordinate output from the regression model, and outputs output data that includes information that allows for the identification of a position coordinate where the two match.

11. The apparatus according to claim 10, wherein the output data includes a position coordinate and the difference between the observed value of the observed object at the position coordinate and the estimated value of the observed object at the position coordinate corresponding to the position coordinate.

12. The apparatus according to claim 11, further comprising a diagram generation unit that generates a diagram that displays the sign and / or magnitude of the difference value at each position coordinate based on the output data.

13. The apparatus according to claim 12, wherein the figure includes auxiliary lines indicating position coordinates where the difference value is zero.

14. The apparatus according to claim 10 or 11, further comprising a diagram generation unit that generates a diagram showing the position coordinates of the observed target where the observed value and the estimated value coincide, based on the output data.

15. The apparatus according to any one of claims 10 to 14, wherein the observation data is terrain data that includes a correspondence between position coordinates and an observed value of the height from a predetermined reference point at the position coordinates.

16. A computer program for causing a computer to function as the device described in any one of claims 10 to 15.

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