JP7366227B1 - Ground point extraction device, ground point extraction method and program - Google Patents

Abstract

An object of the present invention is to provide a ground point extraction device and the like that can extract ground surface points with high precision from a three-dimensional point group. [Solution] A ground point extraction device acquires a plurality of constituent points included in a three-dimensional point cloud obtained by measuring a target area from an aircraft, and sets the acquired plurality of constituent points as candidate points. At each stage, the target area is divided into multiple unit areas smaller than the unit area at the previous stage, and an index is calculated for each candidate point according to the low altitude of the candidate point. , calculation means for setting a representative point of each unit area from candidate points included in each divided unit area based on the index, and calculating an approximate curved surface from the representative point of each unit area at each stage; In stages other than the final stage, among the plurality of obtained constituent points, constituent points whose relative altitude with respect to the approximate surface is less than a threshold are extracted as candidate points, and in the final stage, among the plurality of obtained constituent points, Constituent points whose relative altitudes are within a predetermined range are extracted as ground points. [Selection diagram] Figure 3

Description

The present invention relates to a ground point extraction device, a ground point extraction method, and a program.

2. Description of the Related Art A technique called filtering is known, which extracts ground points from a three-dimensional point group obtained by aerial laser surveying or the like for the purpose of generating a DEM (Digital Elevation Model) or the like.

Non-Patent Document 1 describes a filtering technique called MCC (Multiscale Curvature Classification). In MCC, an approximate curved surface of a three-dimensional point group within a window set in a geographical area to be processed is calculated, and points whose altitude is higher than the approximate curved surface by a certain level or more are excluded as non-ground points. The calculation of the approximate surface and the exclusion of non-ground points are repeated while increasing the window step by step, and the remaining points that are not excluded until the end are extracted as ground points.

A Multiscale Curvature Algorithm for Classifying Discrete Return LiDAR in Forested Environments, S. Evans and T. Hudak, IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 4, 2007

In MCC, when there are many non-ground points in a window, an approximate surface is calculated based on the non-ground points, so non-ground points may be incorrectly extracted (over-extracted) as ground points. .

The present invention has been made to solve the above-mentioned problems, and provides a surface point extraction device, a surface point extraction method, and a program that enable highly accurate extraction of ground points from a three-dimensional point group. The purpose is to

A ground point extraction device according to an embodiment of the present invention acquires a plurality of constituent points included in a three-dimensional point group obtained by measuring a target area from an aircraft, and selects the plurality of acquired constituent points as candidates. an acquisition means for setting a point as a point; a segmentation means for dividing a target area into a plurality of unit areas smaller than the unit area of the immediately preceding step in each of the plurality of stages; a setting means for calculating an index according to a low altitude and setting a representative point of each unit area from candidate points included in each divided unit area based on the index in each of the plurality of stages; , in each of the plurality of stages, a calculation means for calculating an approximated surface from the representative points of each unit area; candidate point extraction means for extracting constituent points whose relative altitudes are within a predetermined range as candidate points; It is characterized by having a surface point extraction means for extracting a certain component point as a surface point indicating the surface of the earth.

Moreover, it is preferable that the setting means sets the representative point only in a unit area that includes at least one candidate point among the plurality of unit areas.

Further, the setting means sets the candidate point as the representative point of the unit area when each unit area includes a candidate point that was set as the representative point in the immediately previous step, and also sets the candidate point as the representative point of the unit area. It is preferable to set a new representative point from among the candidate points that do not exist.

In addition, the calculation means is configured such that, among the representative points, the weight of the representative point that was set as a representative point in the immediately preceding step is greater than the weight of the representative point that was not set as a representative point in the immediately preceding step. It is preferable to calculate a temporary approximated curved surface by using the following method, and calculate the approximated curved surface such that the representative point having a higher relative altitude with respect to the tentative approximated curved surface is given a smaller weight.

Further, it is preferable that the setting means calculates an index based on the distance between each candidate point and the center position of a unit area including the candidate point.

Further, it is preferable that the calculating means calculates the approximated curved surface for each group consisting of the same number of the unit regions at each stage.

The ground point extraction method according to the embodiment of the present invention acquires a plurality of constituent points included in a three-dimensional point cloud obtained by measuring a target area from an aircraft, and uses the obtained plurality of constituent points as candidates. In each of the multiple stages, the target area is divided into multiple unit areas smaller than the unit area in the previous stage, and for each of the multiple candidate points, the In each of the plurality of stages, the representative point of each unit area is set from among the candidate points included in each divided unit area based on the index, and in each of the plurality of stages, each An approximate curved surface is calculated from the representative points of the unit area, and in a stage other than the final stage among the multiple stages, among the multiple constituent points obtained, constituent points whose relative altitudes with respect to the approximate curved surface are within a predetermined range are selected as candidate points. and, in the final step of the plurality of steps, extracting, among the plurality of obtained constituent points, constituent points whose relative altitudes with respect to the approximate curved surface are within a predetermined range as ground points indicating the ground surface. It is characterized by

A program according to an embodiment of the present invention acquires a plurality of constituent points included in a three-dimensional point group obtained by measuring a target area from an aircraft, and sets the acquired plurality of constituent points as candidate points. In each of the multiple stages, the target area is divided into multiple unit areas smaller than the unit area in the immediately preceding stage, and for each of the multiple candidate points, an index is determined according to the low altitude of the candidate point. In each of the plurality of stages, the representative point of each unit area is set from among the candidate points included in each divided unit area based on the index, and in each of the plurality of stages, the representative point of each unit area is set. An approximate curved surface is calculated from the representative points, and in a step other than the final stage among the multiple stages, constituent points whose relative altitudes with respect to the approximate curved surface are within a predetermined range are extracted as candidate points from among the plurality of constituent points obtained. , in the final stage of the plurality of stages, causing the computer to extract, from among the plurality of acquired constituent points, constituent points whose relative altitudes with respect to the approximate curved surface fall within a predetermined range as ground points indicating the ground surface; It is characterized by

A ground point extraction device, a ground point extraction method, and a program according to the present invention make it possible to extract ground points from a three-dimensional point group with high precision.

1 is a functional block diagram of a ground point extraction device 1. FIG. It is a figure which shows the example of the data structure of composition point table T1. FIG. 3 is a flow diagram showing an example of the flow of a ground point extraction process. FIG. 3 is a schematic diagram for explaining the setting of unit areas and groups. FIG. 3 is a flow diagram showing an example of the flow of representative point setting processing. FIG. 3 is a schematic diagram for explaining calculation of an index and setting of a representative point. FIG. 3 is a flow diagram showing an example of the flow of detection processing. FIG. 3 is a schematic diagram for explaining conditions regarding the inclination angle of an approximate plane. FIG. 3 is a flow diagram showing an example of the flow of approximate curved surface calculation processing. (A) and (B) are schematic diagrams for explaining calculation of an approximate curved surface.

Hereinafter, various embodiments of the present invention will be described with reference to the drawings. It should be noted that the technical scope of the present invention is not limited to these embodiments, but extends to the claimed invention and its equivalents.

FIG. 1 is a functional block diagram of a ground point extraction device 1 according to an embodiment of the present invention. The ground point extraction device 1 extracts ground points indicating the ground surface from among the points constituting a three-dimensional point group obtained by measuring a target area from an aircraft. The three-dimensional point group is obtained by calculating the position of the reflection point when a laser is irradiated from the aircraft toward the ground surface of the target area. Since the laser is also reflected by features such as trees and buildings in the target area, the three-dimensional point group includes ground points indicating the ground surface and non-ground points indicating features other than the ground surface. That is, the ground point extraction device 1 extracts only ground points from a three-dimensional point group including ground points and non-ground points. The ground point extraction device 1 includes a storage section 11 , a communication section 12 , a display section 13 , an operation section 14 , and a processing section 15 .

The storage unit 11 is configured to store programs and data, and includes, for example, a semiconductor memory. The storage unit 11 stores, as programs, an operating system program, a driver program, an application program, etc. used in processing by the processing unit 15. The program is installed in the storage unit 11 from a computer-readable, non-temporary, portable storage medium such as a CD-ROM (Compact Disc Read Only Memory) or a DVD-ROM (Digital Versatile Disc Read Only Memory).

The communication unit 12 is configured to enable the ground point extraction device 1 to communicate with other devices, and includes a communication interface circuit. The communication interface circuit included in the communication unit 12 is a communication interface circuit such as a wired LAN (Local Area Network) or a wireless LAN. The communication unit 12 receives data from another device and supplies it to the processing unit 15, and also transmits the data supplied from the processing unit 15 to the other device.

The display unit 13 is configured to display images, and includes, for example, a liquid crystal display or an organic EL (Electro-Luminescence) display. The display unit 13 displays images based on display data supplied from the processing unit 15.

The operation unit 14 is configured to receive operations on the ground point extraction device 1, and includes, for example, a keyboard, a keypad, a mouse, and the like. The operation unit 14 may be a touch panel integrated with the display unit 13. The operation unit 14 generates an operation signal according to the received operation and supplies it to the processing unit 15.

The processing unit 15 is configured to collectively control the operation of the ground point extraction device 1, and includes one or more processors and their peripheral circuits. The processing unit 15 includes, for example, a CPU (Central Processing Unit). The processing unit 15 may include a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), an LSI (Large Scale Integration), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), and the like. The processing unit 15 controls the operation of each component and executes various processes so that various processes of the ground point extraction device 1 are executed in appropriate procedures based on the programs stored in the storage unit 11. do.

The processing unit 15 includes an acquisition unit 151, a classification unit 152, a selection unit 153, a setting unit 154, a detection unit 155, a calculation unit 156, a candidate point extraction unit 157, a ground point extraction unit 158, and an output unit 159 as functional blocks. Each of these units is a functional module realized by a program executed by the processing unit 15. Each of these parts may be implemented in the ground point extraction device 1 as firmware. The acquisition section 151, the classification section 152, the selection section 153, the setting section 154, the detection section 155, the calculation section 156, the candidate point extraction section 157, the ground point extraction section 158, and the output section 159 are an acquisition means, a classification means, and a selection means, respectively. , a setting means, a detection means, a calculation means, a candidate point extraction means, a ground point extraction means, and an output means.

FIG. 2 is a diagram showing an example of the data structure of the constituent point table T1 stored in the storage unit 11. Constituent points are points that make up a three-dimensional point group. The constituent point table T1 stores constituent point IDs, coordinates, and pulse types in association with each other.

The constituent point ID is information that identifies each constituent point that constitutes the three-dimensional point group. The coordinates are three-dimensional coordinates indicating the positions of the constituent points, and are defined, for example, in a plane orthogonal coordinate system. Note that, hereinafter, of the three-dimensional coordinates, the position defined by the x-coordinate or the y-coordinate may be referred to as a horizontal position, and the position defined by the z-coordinate may be referred to as an altitude. Any one of a first pulse, an intermediate pulse, and a last pulse is stored as the pulse type.

Each piece of data in the constituent point table T1 is generated in advance based on measurement data obtained by measuring the target area from the flying object. The aircraft is equipped with a GNSS (Global Navigation Satellite System), an IMU (Inertial Measurement Unit), and a laser measuring instrument. A laser measuring device measures the distance to a reflection point by emitting a laser toward a target area and detecting the reflected light. The positions of constituent points, which are reflection points, are calculated based on the position and attitude of the flying object based on the measurement results by GNSS and IMU, and the distance to the reflection point measured by the laser measuring instrument.

A laser emitted from a laser measuring device may be reflected at multiple reflection points, and multiple reflected lights may be detected. In this case, the reflected light detected first is the first pulse, the reflected light detected last is the last pulse, and the reflected light detected between the first pulse and the last pulse is the intermediate pulse. In general, the reflection points of the first and intermediate pulses are higher than the reflection points of the last pulse, so among the first, intermediate, and last pulses, the last pulse is most likely to have reflected at a surface point. . Note that if only one reflected light is detected for one laser irradiation, that reflected light is assumed to be the last pulse.

Instead of the pulse type, a reflection order indicating the number of reflected light among a plurality of reflected lights detected for one laser irradiation may be stored. In this case, the reflected light whose reflection order value is 1 is the first pulse, the reflected light whose reflection order value is the maximum is the last pulse, and the other reflected lights are intermediate pulses.

FIG. 3 is a flowchart illustrating an example of the flow of the ground point extraction process executed by the ground point extraction device 1. The ground point extraction process is realized by the processing unit 15 cooperating with other components of the ground point extraction device 1 based on a program stored in the storage unit 11.

Below, the outline of the flow of the ground point extraction process will be explained.

First, the target area is divided into a plurality of unit areas. Furthermore, at least some of the constituent points included in the target area are set as candidate points. For example, a component point corresponding to the last pulse among the component points stored in the component point table T1 is set as a candidate point. Next, a candidate point that is likely to be a ground point is set as a representative point of each unit area based on the altitude of the candidate point. Next, a unit area including a slope change point where the slope of the ground surface suddenly changes is detected based on the altitude of the representative point. Next, an approximate curved surface of the representative point is calculated such that the weight of the representative point of the unit area including the slope change point is greater than the weight of other representative points. Next, constituent points whose relative altitudes with respect to the approximate curved surface are within a predetermined range are extracted as candidate points. The predetermined range is, for example, a range less than a predetermined threshold. Candidate points with high relative altitudes correspond to reflection points reflected by trees and buildings above the ground surface, and are likely to be non-ground points, so component points with low relative altitudes are extracted as candidate points. be done. The above process is repeated while reducing the area to be processed step by step and decreasing the threshold value of the predetermined range of relative altitude. Among the constituent points stored in the constituent point table T1, constituent points whose relative altitudes with respect to the approximate curved surface are within a predetermined range are extracted as ground points in the final stage.

If many of the candidate points for a unit area are non-ground points, there is a high possibility that non-ground points will be set as representative points, making it difficult to calculate an approximate curved surface that appropriately reflects the shape of the ground surface. It may not be possible. However, by initially setting a wide unit area, there is a high possibility that each unit area in the first stage includes a ground point. By excluding non-ground points from candidate points in the first step, the proportion of candidate points that are ground points increases in the later stages, and an approximate curved surface that appropriately reflects the shape of the ground surface is calculated. Therefore, by reducing the unit area in stages, it becomes possible to extract ground points with high precision from a three-dimensional point group including an area where non-ground points are concentrated.

Furthermore, since the approximate curved surface is generally calculated as a surface whose slope changes continuously, it may not be possible to appropriately reflect the shape of the earth's surface in areas where the slope of the earth's surface changes suddenly. However, by assigning a large weight to the representative point of the unit area including the slope change point, the shape of the ground surface can be appropriately reflected in the approximated curved surface even in a region where the slope of the ground surface changes suddenly. Therefore, by setting a large weight to the representative point of the unit area including the slope change point, it becomes possible to extract the ground surface point with high precision from the three-dimensional point group including the area where the slope changes suddenly.

Below, details of the flow of the ground point extraction process will be explained.

First, the acquisition unit 151 acquires a target area from which surface points are to be extracted and a plurality of constituent points, and sets the plurality of constituent points as candidate points (step S101). For example, the acquisition unit 151 acquires a geographical area specified by a user's operation on the operation unit 14 as a target area. Although the target area may have any shape, it is assumed below that it is a rectangular area. Furthermore, the acquisition unit 151 acquires constituent points included in the target region from among the constituent points stored in the constituent point table T1. The constituent points included in the target area are constituent points whose horizontal positions of candidate points defined by the x and y coordinates are included in the target area.

The acquisition unit 151 may acquire, as the target area, a geographical area that includes the horizontal positions of all constituent points based on the measurement data specified by the user's operation on the operation unit 14. In that case, the target area is preferably a rectangular area having sides whose length is a multiple of the length of a side of a unit area, which will be described later. Further, the acquisition unit 151 may acquire the target area and constituent points from another device via the communication unit 12.

The acquisition unit 151 sets at least some of the plurality of constituent points as candidate points. For example, the acquisition unit 151 sets the constituent points corresponding to the last pulse among the constituent points included in the target region as candidate points.

Next, the dividing unit 152 divides the target area into a plurality of unit areas (step S102). The unit area may be an area of any shape, but in the following, it is assumed to be a rectangular area. Further, the dividing unit 152 sets a plurality of groups each consisting of a predetermined number of mutually adjacent unit areas.

FIGS. 4A and 4B are schematic diagrams for explaining the settings of unit areas and groups. FIG. 4(A) shows unit areas and groups at the first stage. In the example shown in FIG. 4(A), the square target area T is divided into 16 (4×4) unit areas U1, and the boundaries of each unit area are illustrated by broken lines. Further, a group G1 consisting of four (2×2) unit areas U1 adjacent to each other is set, and the boundaries of each group are illustrated by solid lines.

The processes in steps S102 to S109 are repeatedly executed while reducing the size of the unit area step by step. FIG. 4(B) shows unit areas and groups at the next stage of FIG. 4(A). In the example shown in FIG. 4B, the unit area U2 of the second stage (the unit area set in step S102 executed the second time) is the unit area U1 of the first stage (the unit area set in step S102 executed the first time). The unit area is set to be half the size (one-fourth the area) of the unit area set in . As a result, the target area T is divided into 64 (8×8) unit areas U2. That is, the target area T is divided into a plurality of unit areas U2 smaller than the unit area U1 at the immediately previous stage in the second and subsequent stages. Further, a group G2 consisting of four (2×2) unit areas U2 adjacent to each other is set. In this way, the unit areas are set such that the unit area in the subsequent stage is smaller than the unit area in the previous stage, and the group is set such that it consists of the same number of unit areas in each stage. Therefore, the group is reduced in stages.

The number of stages, the size of the unit area in each stage, and the number of unit areas forming a group may be set arbitrarily. The number of stages is set to six stages, for example. In this case, the unit areas at each stage are set as rectangular areas with four sides of 32 m, 16 m, 8 m, 4 m, 2 m, and 1 m, respectively. Further, the number of unit areas constituting a group is set to, for example, 100 (10×10). The number of stages is not limited to such an example, and may be appropriately set through prior experiments so as to reduce the possibility that a non-ground point will be erroneously extracted (excessively extracted) as a ground point. The size of the unit area, particularly the size of the unit area at the initial stage, may be appropriately set in consideration of the size of a building where non-ground points may be concentrated and the size of a densely populated area of trees. The number of unit regions constituting a group may be appropriately set in consideration of the trade-off between the accuracy of the approximate curved surface and the load of calculation processing of the approximate curved surface.

In the example shown in FIGS. 4(A) and 4(B), the unit area U2 at the second stage has half the size of the unit area U1 at the first stage, and the unit area U1 at the first stage is It is divided into two parts. That is, the unit area of the subsequent stage is set by dividing the unit area of the previous stage. The unit area is not limited to this example, and the unit area of the subsequent stage may be set regardless of the unit area of the previous stage. For example, if the unit area is set to be 0.9 times the size of the immediately preceding unit area, the unit area at the subsequent stage is no longer a division of the unit area at the previous stage.

Returning to FIG. 3, next, the selection unit 153 selects a group to be processed (step S103). The selection unit 153 selects a group that has not yet been selected as a processing target from among the plurality of groups set in step S102 as a processing target group.

Next, the setting unit 154 executes representative point setting processing to set a representative point from among the candidate points included in each unit area of the group to be processed (step S104). Details of the representative point setting process will be described later.

Next, the detection unit 155 executes a detection process of detecting a unit area including the slope change point (step S105). Details of the detection process will be described later.

Next, the calculation unit 156 executes an approximate curved surface calculation process that calculates an approximate curved surface from the representative points of each unit area (step S106). Details of the approximate curved surface calculation process will be described later.

Next, the selection unit 153 determines whether all the groups set in step S102 have been selected as groups to be processed (step S107).

If all the groups have not been selected as the processing target groups (step S107 - No), the ground point extraction process returns to step S103, and the selection unit 153 selects the groups that have not yet been selected as the processing target groups. Select as.

If all the groups have been selected as groups to be processed (step S107-Yes), the candidate point extraction unit 157 determines whether the final stage of processing has been executed (step S108). The candidate point extraction unit 157 determines that the final stage of processing has been performed when the processing of steps S102 to S107 has been performed a preset number of stages.

If the final stage of processing has not yet been executed (step S108-No), the candidate point extraction unit 157 determines that among the constituent points acquired in step S101, the relative altitude with respect to the approximate surface calculated at the current stage is within a predetermined range. The component points that are are extracted as candidate points (step S109). The relative altitude is the value obtained by subtracting the altitude of the approximate curved surface at the same horizontal position as the constituent points from the altitude of the constituent points. The predetermined range is, for example, a range less than a predetermined threshold. In this case, the threshold value is set to decrease in steps. That is, the threshold value is set to be smaller than the threshold value of the immediately previous stage in the second and subsequent stages. For example, the threshold value is set to be half of the threshold value of the previous stage.

After step S108, the ground point extraction process returns to step S102, and the dividing unit 152 divides the target area into unit areas of the next level of size. Further, the dividing unit 152 sets a plurality of groups each consisting of a predetermined number of mutually adjacent unit areas.

When the final stage process is executed (step S108-Yes), the ground point extraction unit 158 extracts the relative altitude of the approximate curved surface calculated for each group in the final stage among the plurality of constituent points acquired in step S101. Constituent points having a predetermined range are extracted as ground points (step S110). The predetermined range is, for example, a range less than a predetermined threshold. The threshold value may be set to be smaller than the threshold value in step S109 at the immediately previous stage, or may be set in advance regardless of the threshold value in step S109.

Next, the output unit 159 outputs the extracted ground point (step S111). For example, the output unit 159 transmits the data of the extracted ground point to another device via the communication unit 12. The output unit 159 may display the extracted ground points on the display unit 13. With this, the ground point extraction process is completed.

FIG. 5 is a flow diagram showing an example of the flow of representative point setting processing. The representative point setting process is a process of setting a representative point from among the candidate points included in each unit area of the group to be processed. The representative point setting process is executed in step S104 of the ground point extraction process.

First, the setting unit 154 selects a unit area to be processed for which a representative point is to be set (step S201). The setting unit 154 selects a unit area that has not yet been selected as a processing target from among the unit areas of the processing target group as a processing target unit area.

Next, the setting unit 154 determines whether a candidate point is included in the unit area to be processed (step S202). The setting unit 154 determines whether a candidate point is included in the unit area to be processed, depending on whether the horizontal position of any candidate point stored in the component point table T1 is included in the unit area to be processed. Determine.

If the candidate point of the unit area to be processed is not included (step S202-No), the setting unit 154 does not set a representative point in the unit area to be processed (step S203).

If the candidate point is included in the unit area to be processed (step S202 - Yes), the setting unit 154 determines whether the candidate point set as the representative point in the previous step is included in the candidate points in the unit area to be processed. It is determined whether or not (step S204). If the current stage is the first stage, the setting unit 154 determines that the candidate points of the unit area to be processed do not include the candidate points set as representative points in the immediately previous stage.

If the candidate points of the unit area to be processed include a candidate point that was set as a representative point in the immediately preceding step (step S204-Yes), the setting unit 154 sets the candidate point that was the representative point in the immediately preceding step as the representative point. settings (step S205). That is, the candidate point that was set as the representative point in the previous stage continues to be set as the representative point in the current stage.

If the candidate points of the unit area to be processed do not include the candidate points set as representative points in the previous step (step S204-No), the representative point setting process proceeds to step S206.

ここで、Ｈは候補点の高度であり、Ｄは候補点の位置と単位領域の中心位置との間の水平距離である。また、ａは重みであり、事前の実験を通じて０より大きい任意の値に設定される。 Next, the setting unit 154 calculates an index corresponding to the low altitude of the candidate point for each of the candidate points in the unit area to be processed (step S206). For example, the setting unit 154 calculates an index based on the distance between the candidate point and the center position of the unit area including the candidate point. The lower the altitude of the candidate point, the smaller the index becomes, and the shorter the distance between the candidate point and the center position of the unit area, the smaller the index becomes. For example, the index I is a weighted sum of the altitude of the candidate point and the horizontal distance between the candidate point and the center position of the unit area, and follows the following formula.

Here, H is the altitude of the candidate point, and D is the horizontal distance between the position of the candidate point and the center position of the unit area. Further, a is a weight, and is set to an arbitrary value greater than 0 through prior experiments.

Next, based on the index, the setting unit 154 sets one of the candidate points included in the unit area to be processed and not set as a representative point as a new representative point of the unit area to be processed. (Step S207). For example, the setting unit 154 sets the candidate point having the smallest index among the candidate points that are not set as representative points as the representative point. In other words, if a candidate point that was set as a representative point in the immediately previous step is included in the unit area to be processed, the candidate point that was set as a representative point in the immediately previous step and the candidate point that was set as a representative point in the immediately previous step are The candidate point having the smallest index among the candidate points that do not have the index is set as the representative point.

FIG. 6 is a schematic diagram for explaining calculation of indicators and setting of representative points. As described above, the representative point is the candidate point where the index corresponding to the low altitude H of the candidate point is the minimum. The candidate point, which is a non-ground point, is a reflection point of a laser reflected by a terrestrial object, and therefore has a higher altitude than the ground surface. By setting the representative point to the candidate point that minimizes the index according to the low altitude H of the candidate point, a candidate point that is likely to be a ground point is set as the representative point.

Further, the representative point is a candidate point with a minimum index based on the distance between each candidate point and the center position of a unit area including the candidate point. That is, the closer the candidate point is to the center of the unit area to be processed, the higher the possibility that the candidate point will be set as the representative point. When representative points are set without being based on the horizontal position of candidate points, when there is an area where the ground surface is depressed near the boundary of the unit area, as in area A in Figure 6, many representative points Candidate points included in the area may be set. In this case, the shape of the ground surface will not be appropriately reflected in the approximate curved surface for the representative point. By making candidate points near the center of the unit area to be processed more likely to be set as representative points, candidate points near the boundaries of the unit area are less likely to be set as representative points. Therefore, the representative points are dispersed, and it is more likely that an approximate curved surface that appropriately reflects the shape of the ground surface will be calculated.

Returning to FIG. 5, after step S203 or S207, the setting unit 154 determines whether all unit areas of the group to be processed have been selected as unit areas to be processed (step S208).

If all unit areas have not been selected as unit areas to be processed (step S207 - No), the representative point setting process returns to step S201, and the setting unit 154 processes unit areas that have not yet been selected as processing targets. Select as the target unit area.

If all the unit areas are selected as unit areas to be processed (step S207-Yes), the representative point setting process ends.

FIG. 7 is a flow diagram showing the flow of detection processing. The detection process is a process of detecting a unit area including a slope change point by determining whether each unit area includes a slope change point. The detection process is executed in step S105 of the ground point extraction process.

First, the detection unit 155 selects a unit area to be processed, which is to be determined as to whether or not it includes a slope change point (step S301). The detection unit 155 selects a unit area that has not yet been selected as a processing target from among the unit areas of the processing target group as a processing target unit area.

Next, the detection unit 155 calculates two approximate planes for the representative point of the unit area to be processed and the representative points of the unit areas surrounding the unit area to be processed (step S302). For example, the detection unit 155 uses the RANSAC (Random Sample Consensus) method to calculate two approximate planes whose boundaries are included in the unit area to be processed.

For example, the detection unit 155 obtains representative points of eight unit areas surrounding the unit area to be processed. The detection unit 155 randomly extracts two representative points from among the eight obtained representative points, and selects a first representative point that includes the representative point of the unit area to be processed and the two extracted representative points. Calculate the plane of Furthermore, the detection unit 155 similarly calculates a second plane different from the first plane. The detection unit 155 calculates the residual difference between each representative point and the first plane and the second plane. The residual is, for example, the root mean square of the smaller of the distance from each representative point to the first plane and the distance from each representative point to the second plane. The detection unit 155 selects the combination of the first plane and the second plane, which are calculated by repeating the above-described process, and which has the smallest residual difference as two approximate planes.

Next, the detection unit 155 determines whether the first condition regarding the inclination angle of the two approximate planes is satisfied (step S303). The first condition is a condition regarding the angle between two approximate planes.

If the first condition is satisfied (step S303-Yes), the detection unit 155 determines that the unit area to be processed includes a slope change point (step S304).

If the first condition is not satisfied (step S303-No), it is determined whether the second condition regarding the inclination angle of the two approximate planes is satisfied (step S305). The second condition is a condition regarding the inclination angle of each of the two approximate planes. The inclination angle of the approximate plane is the angle between the approximate plane and the horizontal plane.

If the second condition is satisfied (step S305-Yes), the detection unit 155 determines that the unit area to be processed includes a slope change point (step S304).

If the second condition is not satisfied (step S305-No), the detection unit 155 determines that the unit area to be processed does not include a slope change point (step S306).

FIG. 8 is a schematic diagram for explaining the first condition and second condition regarding the inclination angle of the approximate plane. In the example shown in FIG. 8, the representative point of the unit area to be processed and the representative points of the unit areas surrounding the unit area to be processed are approximated by two approximation planes P1 and P2. Further, in FIG. 8, the direction of the horizontal plane H is illustrated.

The first condition is, for example, that the smaller of the two angles formed by the two approximate planes P1 and P2 (in the example shown in FIG. 8, the angle α) is equal to or larger than a predetermined angle. The second condition is, for example, that the inclination angle (angle β in the example shown in FIG. 8) of one of the two approximate planes P1 is within a predetermined angle range including 0 degrees, and the other approximate plane P2 is The inclination angle (in the example shown in FIG. 8, angle γ) is equal to or larger than the predetermined inclination angle. The predetermined angle range is, for example, −10 degrees or more and +10 degrees or less, and the predetermined inclination angle is, for example, 40 degrees. The detection unit 155 determines that the unit area to be processed includes a slope change point when at least one of the first condition and the second condition is satisfied.

Note that the detection unit 155 may determine that the unit area to be processed includes a slope change point when both the first condition and the second condition are satisfied. Further, the detection unit 155 may determine whether the unit area to be processed includes a slope change point based only on one of the first condition and the second condition.

Returning to FIG. 7, after step S304 or S306, the detection unit 155 determines whether all unit areas of the group to be processed have been selected as unit areas to be processed (step S306).

If all unit regions have not been selected as processing targets (step S306 - No), the estimation process returns to step S301, and the detection unit 155 selects unit regions that have not yet been selected as processing targets as unit regions to be processed. select.

If all unit areas are selected as processing targets (step S306-Yes), the estimation process ends.

FIG. 9 is a flow diagram showing an example of the flow of approximate curved surface calculation processing. The approximate curved surface calculation process is a process of calculating an approximate curved surface for a representative point. The approximate curved surface calculation process is executed in step S106 of the ground point extraction process.

First, the calculation unit 156 sets a weight to the representative point of each unit area (step S401). The calculation unit 156 sets a larger weight to the representative point of the unit area estimated to include the slope change point than to the representative points of other unit areas. In addition, the calculation unit 156 calculates, among the representative points of the unit area estimated not to include slope change points, the representative points that were set as representative points in the immediately previous step, and the representative points that were not set as representative points in the immediately previous step. Set a weight greater than the representative point. For example, the calculation unit 156 sets a weight of 8.0 to the representative point of the unit area estimated to include the slope change point, and sets a weight of 2.0 to the representative point set as the representative point in the previous step. , set a weight of 1.0 to the other representative points.

Next, the calculation unit 156 calculates a temporary approximate curved surface from the representative points based on the set weights (step S402). In other words, the calculation unit 156 determines that the weight of the representative point that was set as a representative point in the immediately preceding step is greater than the weight of the representative point that was not set as a representative point in the immediately preceding step, and that the slope change point is A temporary approximate curved surface is calculated such that the weight of the representative point of the unit area that includes the slope change point is greater than the weight of the representative point of the unit area that does not include the slope change point. For example, the calculation unit 156 calculates a temporary approximate curved surface using the TPS (Thin Plate Spline) method.

ここで、ｗｉはｉ番目の代表点の重みであり、ｒｉはｉ番目の代表点と仮の近似曲面との間の相対高度である。相対高度は、代表点の高度から、代表点と同一の水平位置における仮の近似曲面の高度を減じた値である。 Next, the calculation unit 156 calculates the standard deviation of the relative altitude between each representative point and the temporary approximate curved surface (step S403). The calculation unit 156 calculates the standard deviation σ using the following formula.

Here, wi is the weight of the i-th representative point, and ri is the relative altitude between the i-th representative point and the temporary approximated surface. The relative altitude is the value obtained by subtracting the altitude of a temporary approximate curved surface at the same horizontal position as the representative point from the altitude of the representative point.

Next, the calculation unit 156 updates the weight of the representative point based on the relative altitude (step S404). For example, the calculation unit 156 updates the weight of a representative point that has not been set as a representative point in the previous step among the representative points of a unit area that does not include a slope change point so that the weight increases as the relative altitude decreases. For example, the calculation unit 156 updates the weight wi of the representative point based on the relative altitude ri according to the following formula.

Next, the calculation unit 156 calculates an approximate curved surface from the representative points based on the updated weights (step S405). That is, the calculation unit 156 calculates the approximate curved surface such that the weight of the representative point having a higher relative altitude with respect to the tentative approximate curved surface becomes smaller. For example, the calculation unit 156 uses the updated weights to calculate an approximate curved surface using the TPS method similar to step S402. This completes the approximate curved surface calculation process.

FIGS. 10A and 10B are schematic diagrams for explaining calculation of an approximate curved surface. FIG. 10A schematically shows the temporary approximate curved surface calculated in step S402. FIG. 10A shows an example in which there are more representative points that are non-ground points indicated by white circles than representative points that are ground points indicated by black circles. In this case, the temporary approximate curved surface is calculated to be closer to the representative point, which is a non-ground point, than to the representative point, which is a ground point. In other words, the temporary approximate curved surface reflects the shape of the surface of the feature rather than the ground surface.

FIG. 10(B) schematically shows the approximate curved surface calculated in step S405. In step S404, the weight of the representative point is updated so that the lower the relative altitude of the representative point with respect to the temporary approximated surface, the greater the weight, so in the example shown in FIG. The weight of the representative point is increasing. Therefore, the approximate curved surface is calculated so that it is closer to the representative point, which is a ground point, than to the representative point, which is a non-ground point. In other words, the approximate curved surface reflects the shape of the ground surface.

In this manner, the approximate curved surface calculation process calculates an approximate curved surface from the representative points of the group to be processed. That is, the approximate curved surface is not calculated from all the constituent points of the group to be processed, but only from representative points that are part of the constituent points. This reduces the processing load for calculating the approximate curved surface. Further, the approximate curved surface calculation process is executed for each group to be processed. That is, the approximate curved surface is not calculated from all the representative points included in the target area, but only from the representative points included in the group to be processed. This further reduces the processing load for calculating the approximate curved surface.

The following modifications may be applied to the ground point extraction device 1.

In the above description, in step S101 of the ground point extraction process, the acquisition unit 151 sets constituent points corresponding to the last pulse as candidate points, but the present invention is not limited to such an example. The acquisition unit 151 may set all of the acquired constituent points as candidate points. That is, the acquisition unit 151 may set constituent points corresponding to the first pulse and intermediate pulse as candidate points in addition to the constituent points corresponding to the last pulse. Even in this manner, the ground point extraction device 1 can extract ground points from the three-dimensional point group with high precision. In this case, in step S109, the candidate point extraction unit 157 excludes the candidate points corresponding to the first pulse, the candidate points corresponding to the intermediate pulses, and the candidate points corresponding to the last pulse whose relative altitude with respect to the approximate curved surface is equal to or higher than the threshold value. It's okay. Furthermore, the acquisition unit 151 may acquire only the constituent points corresponding to the last pulse among the constituent points stored in the constituent point table T1, and may not acquire the constituent points corresponding to the first pulse or the intermediate pulse.

In the above description, in step S102 of the ground point extraction process, the classification unit 152 sets a group consisting of the same number of unit areas for each stage, but the present invention is not limited to this example. The segmentation unit 152 may set groups consisting of a different number of unit areas for each stage. Even in this manner, the ground point extraction device 1 can extract ground points with high precision from a three-dimensional point group that includes a region where the slope of the ground surface changes suddenly. Even if you do this, if the group is set to shrink in stages, the ground point extraction device 1 can extract ground points with high accuracy from a three-dimensional point cloud that includes areas where non-ground points are concentrated. can be extracted into

In the above description, in step S107 of the ground point extraction process, the candidate point extraction unit 157 extracts constituent points whose relative altitude is less than a threshold as constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range. However, this is not the only example. The predetermined range may be less than the first threshold and greater than the second threshold. That is, the candidate point extraction unit 157 may extract constituent points whose relative altitude is less than the first threshold and greater than the second threshold as the constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range. . For example, the first threshold is a positive value and the second threshold is a negative value. In this case, the predetermined range is a range including ±0 m, for example, a range of -0.5 m or more and +0.3 m or less. By doing this, candidate points whose relative altitude with respect to the approximate curved surface is extremely low and are suspected to be noise are excluded, so that the ground point extraction device 1 extracts ground points from the three-dimensional point group with higher precision. be able to.

In the above description, in step S107 of the ground point extraction process, the candidate point extraction unit 157 extracts candidate points from among the constituent points acquired in step S101, but the present invention is not limited to such an example. . For example, among the candidate points at the current stage, candidate points whose relative altitude with respect to the approximate curved surface is less than a threshold value or candidate points whose relative altitude with respect to the approximate curved surface is within a predetermined range may be extracted as candidate points in the next stage. That is, the candidate point extracting unit 157 may exclude candidate points whose relative altitude is equal to or greater than the threshold value from the candidate points of the next stage in stages other than the final stage among the plurality of stages.

In the above explanation, in step S205 of the representative point setting process, the setting unit 154 sets the candidate point that was set as the representative point at the immediately previous step as the representative point. It is not necessary to set the representative point as a candidate point. In this case, steps S203 and S204 of the representative point setting process are omitted. Furthermore, if the candidate point that was set as the representative point in the previous stage is set as the representative point, the setting unit 154 does not need to newly set the representative point based on the index.

In the above description, in step S206 of the representative point setting process, the setting unit 154 sets Although the index that decreases is calculated, the present invention is not limited to this example. The setting unit 154 may calculate an index that is not based on the horizontal position of the candidate point. For example, the setting unit 154 may use the altitude of the candidate point as an index. Even in this manner, the ground point extraction device 1 can extract ground points from the three-dimensional point group with high precision. Further, the index may become larger as the altitude of the candidate point becomes higher, or may become larger as the distance between the candidate point and the center position of the unit area becomes longer. In this case, in step S207, the setting unit 154 sets the candidate point having the largest index as the representative point.

In the above description, in step S207 of the representative point setting process, the setting unit 154 sets the candidate point having the smallest index among the candidate points that are not set as representative points as the representative point of the unit area to be processed. However, this is not the only example. The setting unit 154 may set a plurality of candidate points with small indexes as representative points among the candidate points that are not set as representative points.

In the above description, in step S302 of the estimation process, the detection unit 155 calculates two approximate planes whose boundaries are included in the unit area to be processed, but the present invention is not limited to such an example. The detection unit 155 may calculate two approximate planes without considering whether the boundary is included in the unit area to be processed. For example, the detection unit 155 calculates a first approximate plane from the representative points using the least squares method, excludes representative points whose distance from the first approximate plane is equal to or less than a threshold value, and calculates the first approximate plane using the least squares method. The second approximate plane may be calculated from representative points that are not excluded using . In this case, in step S303, the detection unit 155 determines whether the boundary between the two approximate planes is included in the unit area to be processed and the first condition is satisfied. Further, in step S305, the detection unit 155 determines whether the boundary between the two approximate planes is included in the unit area to be processed and the second condition is satisfied.

In the above description, in step S401 of the approximate curved surface calculation process, the calculation unit 156 assigns a larger weight to the representative point that was set as a representative point in the previous step than to the representative point that was not set as a representative point in the previous step. However, it is not limited to this example. The calculation unit 156 may set the same weight as the other representative points to the representative point set as the representative point in the immediately previous step, or may set a smaller weight than the other representative points.

Similarly, the calculation unit 156 may set the same weight as other representative points to the representative point of the unit area estimated to include the slope change point. In this case, the estimation process in step S105 of the ground point extraction process may be omitted. Even in this manner, the ground point extraction device 1 can extract ground points with high precision from a three-dimensional point group including a region where non-ground points are concentrated. Further, the calculation unit 156 may set a smaller weight than other representative points to the representative point of the unit area estimated to include the slope change point.

In the above description, in step S404 of the approximate curved surface calculation process, the calculation unit 156 calculates the weight of only the representative points that have not been set as representative points in the previous stage, among the representative points of the unit area that do not include slope change points. Although this example will be updated, it is not limited to this example. The calculation unit 156 may update the weight of the representative point of the unit area including the slope change point or the representative point that was set as the representative point in the immediately previous step. In step S401, a larger weight than other representative points is set to the representative point of the unit area including the slope change point or the representative point that was set as the representative point in the immediately previous step. Therefore, the relative heights of these representative points with respect to the temporary approximated surface calculated in step S402 are smaller than the relative heights of other representative points, and in step S404, the weights of these representative points are It is updated to be larger than the weight. As a result, in step S405, a ground surface that more appropriately reflects the shape of the ground surface is calculated.

Steps S403 to S405 of the approximate curved surface calculation process described above may be omitted. That is, the calculation unit 156 may calculate the approximated surface based on the weights set in step S401 without calculating the temporary approximated surface and updating the weights of the representative points.

In the above description, in the ground point extraction process, the processes of steps S102 to S108 are executed in multiple stages, but they may be executed only once. Even in this manner, the ground point extraction device 1 can extract ground points with high precision from a three-dimensional point group that includes a region where the slope of the ground surface changes suddenly.

In the above description, the three-dimensional point cloud is obtained by measuring the target area from the aircraft, but it may also be obtained by stereo analysis or multi-view image analysis of images such as aerial photographs. In this case, the constituent point table T1 does not need to store pulse types.

As explained above, the ground point extraction device 1 divides the target area into a plurality of unit areas set such that the unit area of the subsequent stage is smaller than the unit area of the previous stage, and In this step, a representative point is set based on an index corresponding to the low altitude indicated by each candidate point, and an approximate curved surface for the representative point is calculated. In addition, the ground point extraction device 1 extracts constituent points whose relative altitudes with respect to the approximate curved surface are within a predetermined range as candidate points in a stage other than the final stage among the plurality of stages, and in the final stage among the plurality of stages. , component points whose relative altitudes with respect to the approximate curved surface are within a predetermined range are extracted as ground points. By doing so, the ground point extraction device 1 makes it possible to extract ground points with high precision from a three-dimensional point group including a region where non-ground points are densely packed.

Furthermore, the ground point extraction device 1 sets representative points only in unit areas that include at least one candidate point. By doing so, a representative point will not be set in a unit area where candidate points have not been set or extracted due to the density of non-ground points, so that the ground point extraction device 1 can appropriately determine the shape of the ground surface. By calculating an approximate curved surface that reflects the

In addition, the ground point extraction device 1 sets the candidate point as the representative point if there is a candidate point set as the representative point in the immediately preceding step, and also sets the candidate point as the representative point in the immediately preceding step. The candidate point having the smallest index among them is set as the representative point. The candidate point set as the representative point in the immediately previous stage is particularly likely to be a ground point because it was set as the representative point in the stage when the unit area to be processed was wide. At each stage, the ground point extraction device 1 calculates an approximate curved surface that more appropriately reflects the shape of the ground surface by setting a candidate point that is particularly likely to be a ground point as a representative point. Enables extraction with higher precision.

Furthermore, the ground point extraction device 1 sets a larger weight to a representative point that was set as a representative point in the immediately previous step than to a representative point that was not set as a representative point in the immediately previous step. The ground point extraction device 1 calculates an approximate curved surface that more appropriately reflects the shape of the ground surface by setting a larger weight than other representative points to representative points that are particularly likely to be ground points. This makes it possible to extract points with higher precision.

Furthermore, the ground point extraction device 1 updates the weight of the representative point so that the weight of the representative point having a higher relative altitude with respect to the approximate curved surface becomes smaller, and updates the approximate curved surface based on the updated weight. Thereby, the ground point extraction device 1 calculates an approximate curved surface that more appropriately reflects the shape of the ground surface, making it possible to extract ground points with higher precision.

Furthermore, the ground point extraction device 1 calculates an index that becomes smaller as the altitude of each candidate point is lower, and becomes smaller as the horizontal position of each candidate point is closer to the center of the unit area including the candidate point. This makes it difficult for candidate points near the boundaries of the unit area to be set as representative points, so the ground point extraction device 1 calculates an approximate curved surface that more appropriately reflects the shape of the ground surface, and selects the ground points with higher precision. It is possible to extract

In addition, the ground point extraction device 1 divides the target area into a plurality of unit areas, and approximates by making the weight of the representative point of the unit area including the slope change point larger than the weight of the representative point of other unit areas. A curved surface is calculated, and constituent points whose relative altitudes with respect to the approximate curved surface are within a predetermined range are extracted. By doing so, the ground point extraction device 1 makes it possible to extract ground points with high precision from a three-dimensional point group that includes a region where the slope of the ground surface changes suddenly.

In addition, the ground point extraction device 1 calculates a temporary approximate curved surface such that the weight of the representative point of the unit area including the slope change point is larger than the weight of the representative point of other unit areas, and calculates the temporary approximate curved surface. The weights are updated so that the higher the relative altitude is, the smaller the weights are, and an approximate curved surface is calculated based on the updated weights. By doing so, the ground point extraction device 1 calculates an approximate curved surface that appropriately reflects the shape of the ground surface, making it possible to extract ground points with higher precision.

It will be appreciated by those skilled in the art that various changes, substitutions and modifications can be made thereto without departing from the scope of the invention. For example, the embodiments and modifications described above may be implemented in appropriate combinations within the scope of the present invention.

1 Ground Point Extraction Device 151 Acquisition Unit 152 Classification Unit 153 Selection Unit 154 Setting Unit 155 Detection Unit 156 Calculation Unit 157 Candidate Point Extraction Unit 158 Ground Point Extraction Unit 159 Output Unit

Claims (8)

acquisition means for acquiring a plurality of constituent points included in a three-dimensional point group obtained by measuring a target area from an aircraft, and setting the acquired plurality of constituent points as candidate points;
In each of the plurality of stages, dividing means divides the target area into a plurality of unit areas smaller than the unit area of the immediately preceding stage;
For each of the plurality of candidate points, an index is calculated according to the low altitude of the candidate point, and in each of the plurality of stages, based on the index, candidates included in each of the divided unit areas are calculated. a setting means for setting a representative point of each unit area from among the points;
Calculating means for calculating an approximate curved surface from representative points of each unit area in each of the plurality of steps;
Candidate point extracting means for extracting, as candidate points, constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range from among the plurality of acquired constituent points in a stage other than the final stage of the plurality of stages;
A ground point extraction means for extracting, in the final stage of the plurality of stages, constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range from among the plurality of acquired constituent points as ground points indicating the ground surface;
A ground point extraction device characterized by having: The setting means sets the representative point only in a unit area that includes at least one candidate point among the plurality of unit areas.
The ground point extraction device according to claim 1. The setting means sets the candidate point as the representative point of the unit area when each unit area includes a candidate point that was set as the representative point in the immediately previous step, and also sets the candidate point as the representative point of the unit area. Set a new representative point from among the candidate points that have not been
The ground point extraction device according to claim 1 or 2. The calculation means is
Among the representative points, the weight of the representative point that was set as a representative point in the immediately preceding step is greater than the weight of the representative point that was not set as a representative point in the immediately preceding step, so that a temporary approximated surface is created. Calculate,
Calculating the approximated curved surface in such a manner that the weight of a representative point having a higher relative altitude with respect to the tentative approximated curved surface becomes smaller;
The ground point extraction device according to claim 3. The setting means calculates an index based on a distance between each candidate point and a center position of a unit area including the candidate point.
The ground point extraction device according to claim 1. The calculating means calculates the approximate curved surface for each group consisting of the same number of the unit regions at each stage.
The ground point extraction device according to claim 1. acquiring a plurality of constituent points included in a three-dimensional point group obtained by measuring a target area from an aircraft, and setting the acquired plurality of constituent points as candidate points;
In each of the plurality of steps, the target area is divided into a plurality of unit areas smaller than the unit area in the immediately previous step,
For each of the plurality of candidate points, an index is calculated according to the low altitude of the candidate point, and in each of the plurality of stages, based on the index, candidates included in each of the divided unit areas are calculated. Set the representative point of each unit area from among the points,
In each of the plurality of steps, an approximate curved surface is calculated from the representative points of each unit area,
In a stage other than the final stage of the plurality of stages, extracting constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range from among the plurality of acquired constituent points as candidate points;
In the final stage of the plurality of steps, among the plurality of acquired constituent points, constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range are extracted as ground points indicating the ground surface.
A ground point extraction method characterized by including the following. acquiring a plurality of constituent points included in a three-dimensional point group obtained by measuring a target area from an aircraft, and setting the acquired plurality of constituent points as candidate points;
In each of the plurality of steps, the target area is divided into a plurality of unit areas smaller than the unit area in the immediately previous step,
For each of the plurality of candidate points, an index is calculated according to the low altitude of the candidate point, and in each of the plurality of stages, based on the index, candidates included in each of the divided unit areas are calculated. Set the representative point of each unit area from among the points,
In each of the plurality of steps, an approximate curved surface is calculated from the representative points of each unit area,
In a stage other than the final stage of the plurality of stages, extracting constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range from among the plurality of acquired constituent points as candidate points;
In the final stage of the plurality of steps, among the plurality of acquired constituent points, constituent points whose relative altitude with respect to the approximate curved surface is within a predetermined range are extracted as ground points indicating the ground surface.
A program that causes a computer to perform certain tasks.

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