Difference detection device, difference detection method, and program

Abstract

To provide a difference detection device, a difference detection method, and a program capable of more efficiently grasping the overall picture of distortion or deformation of a shape.SOLUTION: A differential detection device comprises a data generation unit that obtains a union of a first point cloud, which is a collection of points representing three-dimensional positions on a surface of an object, and a second point cloud, which is a collection of points different from the first point cloud; an analysis unit that calculates persistent homology for the union and extracts a partial point cloud representing a hole shape; and a determination unit that determines whether the points that make up the partial point cloud include points from both the first point cloud and the second point cloud, and identifies the partial point cloud that includes both points as a difference point cloud that indicates the range of differences occurring between the first point cloud and the second point cloud.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a difference detection device, a difference detection method, and a program. [Background technology]

[0002] In recent years, research has been conducted into the use of three-dimensional point clouds to evaluate the surface shapes and deformations of structures and landforms. For example, in the inspection of river levees, it is required to evaluate whether there is any deformation such as overhanging of the river levees, and if there is any deformation, the extent of the deformation. In civil engineering works, for example, it is required to evaluate the amount of error of the completed form from the design. For this purpose, the completed form evaluation system for civil engineering works described in Patent Document 1 easily judges the suitability of the surface shape of the completed form by an evaluation value indicating whether or not an element of the completed form point cloud is within the range of the offset amount in a specified direction from a certain design surface. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2018-40181 A Summary of the Invention [Problem to be solved by the invention]

[0004] However, conventional technology only evaluates in a specified direction, so when the surface shape of a structure or terrain, and its distortions and deformations, are complex, it becomes difficult to efficiently grasp the overall shape and deformation.

[0005] An object of the present invention is to provide a difference detection device, a difference detection method, and a program that can more efficiently grasp the overall picture of distortion or deformation of a shape. [Means for solving the problem]

[0006] In order to achieve the above object, the present disclosure provides: a data generation unit that obtains a union of a first point cloud, which is a set of points that represent three-dimensional positions on a surface of an object, and a second point cloud, which is a set of points different from the first point cloud; an analysis unit that calculates persistent homology for the union and extracts a partial point group that represents a hole shape; a determination unit that determines whether the points constituting the partial point cloud include both the first point cloud and the second point cloud, and identifies the partial point cloud that includes both points as a difference point cloud that indicates the range of difference occurring between the first point cloud and the second point cloud; The differential detection device includes: Effect of the Invention

[0007] According to the present disclosure, it is possible to obtain an effect of more efficiently grasping the overall picture of distortion and deformation of a shape. [Brief description of the drawings]

[0008] [Figure 1] FIG. 2 is a block diagram showing a functional configuration of the information processing device. [Diagram 2] FIG. 1 is a diagram for explaining the use of persistent homology in this embodiment. [Diagram 3] This is an example of the appearance / disappearance periods obtained from point cloud data sorted in descending order. [Figure 4] 4 shows an example of setting a distance calculation range. [Diagram 5] 13 is a flowchart showing a control procedure for a differential region detection process. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing the functional configuration of an information processing device 1 which is a difference detection device according to this embodiment.

[0010] The information processing device 1 includes a control unit 11, a storage unit 12, an input / output interface (I / F) 13, a display unit 14, an operation reception unit 15, and the like.

[0011] The control unit 11 performs overall control of the operation of the information processing device 1. The control unit 11 has a processor that performs arithmetic processing. The processor may be a single general-purpose CPU (Central Processing Unit), or multiple CPUs that perform arithmetic processing in parallel or independently depending on the application. The processor may include a processor specialized for a specific arithmetic processing or image processing. The control unit 11 performs various control processing by reading and executing a program 121 from the storage unit 12.

[0012] The storage unit 12 has a RAM (Random Access Memory) and a non-volatile memory, and stores various data. The RAM provides a working memory space for the control unit 11 and stores temporary data. The non-volatile memory stores and holds the program 121, setting data, and the like. The non-volatile memory is, for example, a flash memory or an HDD (Hard Disk Drive), but is not limited to these. The storage unit 12 may have a ROM (Read Only Memory). An initial control program and the like can be stored in the ROM. The program 121 includes a control program related to a differential area detection process described below.

[0013] The input / output interface 13 inputs and outputs data between the information processing device 1 and the outside (including peripheral devices). The input / output interface 13 has a connection terminal 131 and a communication unit 132. The connection terminal 131 includes, for example, a Universal Serial Bus (USB) terminal and a Local Area Network (LAN) connector. The communication unit 132 controls communication in accordance with a communication rule (protocol) related to the LAN, such as TCP / IP.

[0014] The peripheral devices may include a database device 21, which is an auxiliary storage device, and an optical reader 22 that reads portable storage media (optical disks) such as CD-ROM, DVD, and Blu-ray (registered trademark). The portable storage media may include a magnetic tape, and the peripheral devices may include a reader that reads the magnetic tape.

[0015] Data that the information processing device 1 can acquire from the outside via the input / output interface 13 includes point cloud data 201. The point cloud data 201 is data that represents a three-dimensional shape of the surface of an object, and is data that indicates the three-dimensional positions of a plurality of points on the surface of the object. Each point of the three-dimensional point cloud data 201 has information on a three-dimensional position in an orthogonal coordinate system represented by, for example, an X-axis and a Y-axis that are mutually orthogonal in the horizontal direction, and a Z-axis along the vertical direction. The information on the three-dimensional position is obtained based on laser measurement from the sky, that is, the time it takes for a laser light irradiated from an unmanned aerial vehicle (UAV) or the like to be reflected and returned. The laser light is irradiated at appropriate intervals. In response to this, each point is obtained as a set of discrete data (point cloud data) of points from which the laser light is reflected. The irradiation interval of the laser light does not need to be uniform, and may be different from one another for each measurement.

[0016] The point cloud data 201 includes first point cloud data 2011 and second point cloud data 2012 obtained at different measurement times (different days, different months, different years, etc.) with different coordinate distributions (mainly positions in a horizontal plane are not the same at the time of measurement). Both the first point cloud data 2011 and the second point cloud data 2012 include points in the coordinate ranges to be compared. Alternatively, one of the first point cloud data 2011 and the second point cloud data 2012 may be design data of a structure, etc. In this case, the point cloud data may be, for example, data in which the three-dimensional positions of points on a design line are appropriately set discretely. Furthermore, even if the point cloud data is the same, data points obtained at different times within a range in which identity is assumed may be mixed. The structures are not particularly limited, but may be river structures such as river levees, revetments, culverts, culverts, dams, ground sills, sluice gates, locks, pumping stations, and drainage stations. Structures may also include associated handrails, fences, etc.

[0017] The display unit 14 performs display on the display screen based on the control of the control unit 11. The display screen is, for example, a liquid crystal display or an organic EL (Electro-Luminescent) display, but is not limited to these.

[0018] The operation reception unit 15 receives an input operation from the outside, and outputs an operation signal corresponding to the input operation to the control unit 11. The operation reception unit 15 includes, for example, a keyboard and a pointing device. The pointing device may be a mouse. The display unit 14 and / or the operation reception unit 15 may be peripheral devices of the information processing device 1, and may be attached to the main body (computer) of the information processing device 1 including the control unit 11, the storage unit 12, and the input / output interface 13.

[0019] Next, difference detection using the point cloud data 201 will be described. As described above, the point cloud data 201 includes the first point cloud data 2011 and the second point cloud data 2012. The difference between the surfaces represented by these point cloud data represents the deviation between the designed structure and the actual structure, the change in the actual structure, etc. When the actual structure is a river structure, the change (deformation) in the structure includes, for example, a bulge, a slope, a crack, a subsidence, etc.

[0020] When such deformation occurs, the strength of the structure is reduced, making it more susceptible to breakage. Therefore, by inspecting the three-dimensional shapes of these structures periodically and in the event of a disaster, deformation can be quickly detected. The information processing device 1 of this embodiment compares the first point cloud data 2011 and the second point cloud data 2012 to detect the occurrence of deformation and its range and scale.

[0021] In different point cloud data obtained by aerial measurements, etc., the positions of each point are usually different, making it difficult to directly compare points. On the other hand, when the point cloud data is converted to mesh data, the original point cloud data and the mesh data must be prepared, processed, and compared in parallel, which increases the amount of work. The information processing device 1 quantitatively evaluates the extent and amount of deformation by utilizing persistent homology with the point cloud data as it is.

[0022] Persistent homology is a topological data analysis that is used in techniques to evaluate geometric structures such as the connections and biases between points in point cloud data. In the analysis of three-dimensional structures using persistent homology (second-order persistent homology), when the radius of a sphere centered on each point is expanded, the spheres come into contact and overlap in order of the distance between their centers. Areas that are far from any sphere (point) become gap areas (hole-shaped) that do not easily come into contact with the sphere. In other words, in persistent homology, voids that are far from any surrounding points in point cloud data (spatial distribution of points) are evaluated using the radius (or diameter) of the sphere as a parameter. The farther the space is from the surrounding points, the more it remains as a gap area even if the radius of the sphere becomes larger. In the analysis of two-dimensional structures (first-order persistent homology), persistent homology can be calculated in the same way as for three-dimensional structures by expanding the radius of a circular range centered on each point.

[0023] FIG. 2 is a diagram for explaining the use of persistent homology in this embodiment. Figures 2(a) and 2(b) show examples of two point cloud data spread out on a plane in three-dimensional space. In the first point cloud data A shown in Figure 2(a), each point spreads out on the xy plane. In the second point cloud data B shown in Figure 2(b), the points near the center are located at a position that is elevated in the z direction compared to the other surrounding points. When the union C=A∪B of these two point cloud data is taken, as shown in Figure 2(c), this union C has a gap with no points between the elevated part of the second point cloud data and the flat part of the first point cloud data.

[0024] When persistent homology is applied (obtained) to the data of this union C, the above gap is detected as a gap region (hole shape). In particular, the lower half of this gap is bounded by the points of the first point cloud data, and the upper half is bounded by the points of the second point cloud data. In other words, the gap bounded by both the points of the first point cloud data A and the points of the second point cloud data B is generated by a deviation between the two point cloud data.

[0025] In persistent homology, when an isotropic space (here, a sphere) centered on each point is expanded as described above, the ranges of nearby spheres overlap and connect to enclose a gap region (hole) corresponding to the above void at a certain size (such as radius, generation parameter b). The point group, which is a set of center points of the spheres enclosing this gap region, is the partial point group Ek described below. When each sphere is further expanded, it is specified that the gap region (hole) is filled at a certain size (disappearance parameter d) and the gap region disappears. In a large void, the difference value db (persistent interval, generation / disappearance period) between the generation parameter b and the disappearance parameter d is large. In general, a small generation / disappearance period is likely to be noise. In addition, in principle, the disappearance parameter d cannot be determined in a space where one side of all points is an open surface.

[0026] Figure 3 shows an example of the appearance / disappearance periods obtained from point cloud data sorted in descending order. As described above, the upper limit Lt can be determined in order to exclude those with a significantly long occurrence / disappearance period. On the other hand, the lower limit Lb can be determined in order to exclude those with a short occurrence / disappearance period. A occurrence / disappearance period within a reference range of not less than the lower limit Lb and not more than the upper limit Lt can be determined as a gap region (hole) corresponding to the difference in the detection target between the two point cloud data. The lower limit Lb may be determined in accordance with the data density of the first point cloud data 2011 and the second point cloud data 2012. That is, the lower limit Lb may be defined as a constant multiple (e.g., 1 to 3 times) or a constant power (e.g., squared or cubed) of the minimum distance between two points belonging to the union C. Similarly, the upper limit Lt may be defined as a constant multiple or a constant power of the maximum distance between two points belonging to the union C. The lower limit Lb and the upper limit Lt may be determined in consideration of not only noise but also the content and type of the abnormality to be detected. For example, the lower limit Lb and the upper limit Lt may be determined by multiplying or raising to a predetermined constant the characteristic size of the deformation (range of difference) to be detected, for example, the maximum or minimum value (minimum and maximum sizes) of the width, length, etc. assumed to be the deformation to be detected. Examples of the constant multiplication include 0.2 to 0.9 times the minimum size, and 1.1 to 2.0 times the maximum size. Examples of the constant multiplication include the squared or cubed powers.

[0027] A set of connection points corresponding to the set of hole appearance parameters and disappearance parameters thus obtained, i.e., a group of points located surrounding a void, is extracted as a partial point group Ek (k=1 to N; N is the number of obtained voids) by inverse analysis. If the appearance / disappearance period of the partial point group Ek is within the above-mentioned reference range and the points constituting the partial point group Ek include both points of the first point cloud data 2011 and points of the second point cloud data 2012, the partial point group Ek is identified as a difference point group Dk indicating the range of difference between the first point cloud and the second point cloud to be detected.

[0028] In order to specify the difference point group Dk, it is determined again whether each point included in the partial point group Ek matches a point in the first point cloud data 2011 (or the second point cloud data 2012). As described above, the points in the first point cloud data 2011 and the points in the second point cloud data 2012 are different. Therefore, when the distance between the target point of the partial point group Ek and any point in the first point cloud data 2011 is zero, this means that the two compared points are the same point. In this case, the target point is a point in the first point cloud data 2011. When the distance between the target point and any point in the first point cloud data 2011 is not zero, the target point is a point in the second point cloud data 2012.

[0029] Since it is time-consuming to find the distance between the target point and all points in the union C, the targets for which the distance is to be found may be limited to only some of the points in the union C surrounding the partial point group Ek. FIG. 4 shows an example of setting the distance calculation range. For example, the maximum and minimum values ​​may be specified for each component of the three-dimensional coordinates of the points included in the partial point group Ek, and only points whose three components are all within the range between the maximum and minimum values ​​may be extracted from the union C. Such a range M is a rectangular parallelepiped that contains, and in particular circumscribes, the partial point group Ek.

[0030] Moreover, since it is only necessary to know whether the distance is zero or not, the L1 distance (the sum of the absolute values ​​of the differences between the components) or the like may be calculated. Calculating the L1 distance requires less computational effort than calculating the L2 distance (Euclidean distance). Moreover, since it is only necessary to detect one point each of the first point cloud data 2011 and the second point cloud data 2012, calculation of the distance may be completed when each point cloud data is detected one by one.

[0031] The data of the difference point group Dk is output information. The points belonging to the difference point group Dk may be displayed on a display screen in a color different from other points of the union C, for example. Furthermore, each point belonging to the difference point group Dk is connected to surrounding points and polygonized to obtain a surface shape, etc. Furthermore, the size of the void can be quantitatively obtained by expressing the void as a combination of voxels using a polygon. The polygon includes a three-dimensional polygon and a two-dimensional polygon obtained by orthogonally projecting the difference point group onto a surface.

[0032] 5 is a flowchart showing a control procedure of the differential region detection process executed by the control unit 11 in the information processing device 1 of this embodiment. This differential region detection process including the difference detection method of this embodiment is executed by the program 121 together with the designation of two point cloud data to be compared or a further partial range thereof.

[0033] The control unit 11 acquires first point cloud data 2011 (S1). The control unit 11 acquires second point cloud data 2012 (S2). The control unit 11, as a data generating unit, generates a union C of the first point cloud data 2011 and the second point cloud data 2012 (S3; data generating step, data generating means).

[0034] The control unit 11, as an analysis unit, obtains persistent homology for the union C and extracts pairs (bk, dk) of hole appearance / disappearance (S4). The analysis unit excludes pairs whose hole appearance / disappearance periods (difference value dk-bk) are not within a reference range (S5). The process S4 and the process S5 constitute an analysis step in the difference discrimination method of this embodiment, and constitute an analysis means in the program 121 of this embodiment.

[0035] The control unit 11 performs an inverse analysis to obtain partial point groups Ek corresponding to the remaining pairs (bk, dk) of hole appearance / disappearance (S6). The control unit 11, as a determination unit, determines whether each partial point group Ek includes both points belonging to the first point cloud data 2011 and points belonging to the second point cloud data 2012, and determines whether each partial point group Ek is a difference point group Dk (S7; determination step, determination means).

[0036] The control unit 11, functioning as a polygon generating unit, converts each point of the identified difference point group Dk into a 3D polygon, and also converts it into a 2D polygon by orthogonally projecting it (S8). The control unit 11 calculates the difference amount (size of the gap) by using voxels or the like using the obtained polygon (S9). The control unit 11 causes the display screen of the display unit 14 to display the distribution of the union C (S10). At this time, the control unit 11 causes each point belonging to the difference point group Dk to be displayed in a display mode (color, size, shape, etc.) different from the other points of the union C. Then, the control unit 11 ends the difference region detection process.

[0037] The difference area (area represented by the difference point cloud) calculated and displayed as above shows the deviation between the designed structure and the actual structure, changes in the actual structure, etc. Therefore, if the structure is a river structure, it is possible to detect its bulge, slope, cracks, and subsidence.

[0038] The present invention is not limited to the above-described embodiment, but may be modified in various ways. For example, in the above embodiment, the case of identifying the deformation or the difference from the design of the river structure measured by laser surveying from the sky by an aircraft has been described, but the present invention is not limited to this. Any point cloud data representing coordinates may be compared. Specifically, the point cloud data may be data from a laser profiler using an aircraft, a drone, an artificial satellite, or the like, instead of the UAV. Alternatively, the point cloud data may be survey data using a laser mounted on a traveling vehicle. Furthermore, the point cloud data may be data obtained by processing a plurality of images taken from a UAV or a traveling vehicle using Structure from Motion (SfM). Furthermore, the measurement target may be used to identify changes in natural data such as changes in natural topography including the inflow and outflow of soil and sand, water levels, tides, and snowfall. Alternatively, the measurement target may be applied to structures other than river structures. For example, the measurement target may be used to detect deformations such as ruts on road surfaces and runways, cracks, the wall shapes of tunnels, cracks and peeling in concrete structures such as bridge piers, distortion of railroad tracks, and deflections of utility poles and overhead lines.

[0039] In the above embodiment, the data of each point in the union C includes only coordinates, but this is not limited to the above. The data of each point may be provided with flag data or the like for identifying whether it was originally the first point cloud data 2011 or the second point cloud data. In this case, it is possible to directly identify which point cloud data each point of the partial point group Ek belongs to without comparing it again with each point of the union C. Furthermore, data of the same coordinates may be included between a data point of the first point cloud data 2011 and a data point of the second point cloud data 2012.

[0040] Furthermore, when the data of each point of the union C includes coordinates, the range M may be set using other methods or criteria.

[0041] In the above, the points of the point cloud are connected to form polygons when outputting the data, but the data does not necessarily have to be formed into polygons. The output does not have to be a display screen. The data may be output as data in which the coordinates of the vertices of a polygon are grouped.

[0042] In the above embodiment, all the processes are performed by a single information processing device 1, but this is not limiting. Distributed processing may be performed by a plurality of devices.

[0043] In the above description, the storage unit 12 is exemplified by a non-volatile memory such as a HDD or a flash memory as a computer-readable medium for storing the program 121 related to the difference detection control of the present invention, but is not limited thereto. As other computer-readable media, other non-volatile memories such as MRAM and portable storage media such as CD-ROM and DVD disks can be applied. In addition, a carrier wave is also applied to the present invention as a medium for providing the data of the program according to the present invention via a communication line. In addition, the specific configurations, contents and procedures of the processing operations, etc. shown in the above embodiments can be modified as appropriate without departing from the spirit of the present invention. The scope of the present invention includes the scope of the invention described in the claims and its equivalents.

[0044] As described above, the information processing device 1, which is the difference detection device of this embodiment, includes the control unit 11. The control unit 11, as a data generating unit, obtains a union C of a first point group, which is a set of points representing three-dimensional positions on the surface of the object, and a second point group, which is a set of points different from the first point group. The control unit 11, as an analyzing unit, obtains persistent homology for the union C and extracts a partial point group Ek representing the hole shape. The control unit 11, as a determining unit, determines whether the points constituting the partial point group Ek include both points of the first point group and the second point group, and specifies the partial point group Ek including both points as a difference point group Dk indicating the range of differences occurring between the first point group and the second point group. According to this information processing device 1, the two point cloud data to be compared are mixed to obtain persistent homology, so the differences between these point cloud data appear as holes. Therefore, the positions, shapes, and sizes of the differences are efficiently detected. Therefore, the information processing device 1 does not need to align the point cloud data by interpolating it or convert it into mesh data, and can obtain an overall image of the distortion or deformation of the shape more efficiently.

[0045] The analysis unit may also extract a partial point group Ek in which the difference values ​​of the appearance parameters and disappearance parameters of the hole shape are within a reference range. In persistent homology, noise is likely to appear in areas where the difference values ​​are small. In addition, when detecting surface differences, semi-open spaces above the surface are also detected as holes. Therefore, by setting an appropriate reference range, it is possible to appropriately extract actual differences. Furthermore, by appropriately narrowing the reference range, it is possible to selectively extract differences according to factors to be detected.

[0046] Furthermore, the upper limit Lt of the reference range may be defined as a constant multiple or a constant power of the maximum distance between two points belonging to the union C or the maximum size of the range of the difference (hole) to be detected. The lower limit Lb of the reference range may be defined as a constant multiple or a constant power of the minimum distance between two points belonging to the union C or the minimum size of the range of the difference to be detected. In this way, by defining the reference range according to the spatial density of the point cloud data or the difference in the surface of the detection target, it is possible to appropriately exclude noise and unnecessary differences and extract the desired differences.

[0047] The determination unit may also set a part of the union C that includes the partial point group Ek, and determine whether or not the part includes both the first point group and the second point group. If the data of each point of the partial point group Ek does not include information on the original point group, it is necessary to compare and refer to the original first point group data or the second point group data again. At this time, it is a waste of time and effort to compare with data that clearly does not belong to the partial point group Ek. Therefore, by setting a part of the union C that includes the partial point group Ek as the comparison target, it is possible to reduce time and effort.

[0048] Furthermore, the control unit 11 of the information processing device 1 may function as a polygon generating unit to generate a three-dimensional polygon or a two-dimensional polygon by connecting the points that make up the identified difference point group Dk. By connecting the point group data to generate a polygon, the surface can be more appropriately recognized, and the surface area of ​​the entire surface or the difference part can be easily obtained quantitatively. Furthermore, by generating voxels using the three-dimensional polygon, the volume of the difference part can also be easily obtained.

[0049] The difference detection method of this embodiment also includes the following steps: a data generation step (process S3) of obtaining a union C of a first point group, which is a set of points representing three-dimensional positions on the surface of the object, and a second point group, which is a set of points different from the first point group; an analysis step (processes S4 and S5) of obtaining persistent homology for the union C and extracting a partial point group Ek representing the hole shape; and a determination step (process S7) of determining whether the points constituting the partial point group Ek include points from both the first point group and the second point group, and identifying the partial point group Ek including both points as a difference point group Dk indicating the range of differences occurring between the first point group and the second point group. According to this difference detection method, the two point cloud data to be compared are mixed to obtain persistent homology, so that the difference between these point cloud data can be appropriately extracted as holes. Therefore, this difference detection method can efficiently detect the position, shape, and size of the difference without aligning the positions of the points of the point cloud data or converting them into a mesh or the like. Therefore, the user can more efficiently grasp the overall picture of the distortion and deformation of the shape.

[0050] Furthermore, by installing and executing the program 121 relating to the above-mentioned difference detection method on a computer, it is possible to easily and effectively detect distortion or deformation of a shape and display the entire image without having special hardware. [Explanation of symbols]

[0051] 1. Information processing device 11 Control section 12 Storage section 121 Programs 13 Input / Output Interface 131 Connection terminal 132 Communications Department 14 Display section 15 Operation reception section 21 Database device 22 Optical reading device 201 Point Cloud Data C union Dk difference point cloud Ek subpoint cloud Lb lower limit Lt upper limit M range

Claims

1. a data generation unit that obtains a union of a first point cloud, which is a set of points that represent three-dimensional positions on a surface of an object, and a second point cloud, which is a set of points different from the first point cloud; an analysis unit that calculates persistent homology for the union and extracts a partial point group that represents a hole shape; a determination unit that determines whether or not the points constituting the partial point cloud include both the first point cloud and the second point cloud, and identifies the partial point cloud including both points as a difference point cloud that indicates a range of difference occurring between the first point cloud and the second point cloud; A differential detection device comprising:

2. The difference detection device according to claim 1 , wherein the analysis section extracts the partial point group in which difference values ​​of the appearance parameters and disappearance parameters of the hole shape are within a reference range.

3. the upper limit of the reference range is defined by a constant multiple or a constant power of the maximum distance between two points belonging to the union or the maximum size of the range of difference to be detected; The lower limit of the reference range is defined by the minimum distance between two points belonging to the union or the constant multiple or the constant power of the minimum size of the range of difference to be detected.

3. The differential detection device according to claim 2.

4. 2. The difference detection device according to claim 1, wherein the determination section sets a part of the union that includes the partial point group, and determines whether or not both of the points are included within a range of the part.

5. 2. The difference detection device according to claim 1, further comprising a polygon generation unit that generates a three-dimensional polygon or a two-dimensional polygon by connecting points that constitute the identified difference point group.

6. a data generation step of obtaining a union of a first point cloud, which is a set of points representing three-dimensional positions on a surface of the object, and a second point cloud, which is a set of points different from the first point cloud; An analysis step of calculating persistent homology for the union and extracting a partial point group representing a hole shape; a determination step of determining whether or not the points constituting the partial point cloud include both points of the first point cloud and the second point cloud, and identifying the partial point cloud including both points as a difference point cloud indicating the range of difference occurring between the first point cloud and the second point cloud; A differential detection method comprising:

7. Computer, a data generating means for obtaining a union of a first point cloud, which is a set of points representing three-dimensional positions on a surface of an object, and a second point cloud, which is a set of points different from the first point cloud; an analysis means for calculating persistent homology for the union and extracting a partial point group representing a hole shape; a determination means for determining whether or not the points constituting the partial point cloud include both points of the first point cloud and the second point cloud, and for identifying the partial point cloud including both points as a difference point cloud indicating the range of difference occurring between the first point cloud and the second point cloud; A program that functions as a

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