JP5253232B2 - Elevation information interpolation device, elevation information interpolation program, and elevation information interpolation method - Google Patents

Description

  The present invention relates to a technique for interpolating missing elevation information, for example.

Many digital elevation data (DEM, Digital Elevation Model) are created by remote sensing such as synthetic aperture radar and optical sensors mounted on airplanes, satellites, space shuttles and the like. However, in remote sensing, observation may be incomplete due to the influence of clouds or the like. Digital elevation data is not created for areas where observations are incomplete. Therefore, the user who uses the digital elevation data needs to interpolate the digital elevation data for an area where the digital elevation data has not been created. Note that these digital elevation data are usually provided as raster data (grid data).
As a method of interpolating numerical elevation data, there is a method of interpolating using other numerical elevation data. In addition, there is a method of performing interpolation using numerical elevation data around a region where numerical elevation data is not created. Further, Patent Documents 1 and 2 describe a technique for interpolating a contour map.

JP 2006-293105 A Japanese Patent Laid-Open No. 2003-216023

In the method of interpolating using other numerical elevation data, other numerical elevation data must be prepared, which is not convenient. In addition, it requires a lot of knowledge of numerical elevation data and scientific and technical calculations, and the processing is complicated. In the method of interpolating using surrounding numerical elevation data, when the interpolated raster data is converted into contour line data, the interpolated portion may become unnatural data that is not consistent. Furthermore, Patent Documents 1 and 2 do not describe a method for interpolating numerical elevation data given as raster data.
For example, when a part of numerical elevation data given as raster data is missing, an object of the present invention is to generate missing numerical elevation data by interpolating the missing data.

The elevation information interpolation device according to the present invention is, for example,
Raster data input unit for inputting raster data indicating elevation information of a predetermined area by an input device, the raster data having a missing area in which elevation information of a part of the predetermined area is missing;
A contour data generator for converting the raster data input by the raster data input unit to generate contour line data indicating contour lines by a processing device;
A contour interpolation unit that interpolates the contour lines of the missing region by a predetermined method among the contour lines indicated by the contour line data generated by the contour line data generation unit by the processing device;
A raster data generation unit that converts the contour line data interpolated by the contour line interpolation unit and generates raster data indicating elevation information by a processing device;
Among the raster data generated by the raster data generation unit by the processing device, the altitude information indicated by the raster data of the missing region, the elevation information of the missing region interpolated by the contour interpolation unit, and the vicinity of the missing region And a raster data interpolating unit that interpolates using the altitude information of the region.

The raster data interpolation unit gives a predetermined weight to the elevation information of the missing region interpolated by the contour interpolation unit, and gives a weight heavier than the predetermined weight to the elevation information of the region near the missing region. Based on the weighted data, the interpolation data of the elevation information of the missing area is generated.

The raster data interpolation unit divides the missing area into a plurality of areas in a first direction, generates first interpolation data for each divided area, and interpolates the missing area from the generated first interpolation data. Is generated.

The raster data interpolation unit divides the missing area into a plurality of areas in a second direction different from the first direction, and uses the first interpolation data as the elevation information of the missing area. 2nd interpolation data is produced | generated for every area | region divided | segmented into this direction, The interpolation data of the said missing area are produced | generated from the produced | generated 2nd interpolation data.

The raster data interpolation unit calculates a coefficient of an expression representing a three-dimensional curved surface by a predetermined method based on the weighted data, and generates the three-dimensional curved surface represented by the calculated coefficient as interpolation data of the missing region It is characterized by doing.

The raster data interpolation unit generates the interpolation data by a different method according to at least one of the size of the missing area, the shape of the missing area, and the position of the missing area in the raster data. To do.

The elevation information program according to the present invention is, for example,
Raster data indicating elevation information of a predetermined area, raster data input processing for inputting raster data having missing areas in which elevation information of a part of the predetermined area is missing; and
Contour line data generation processing for converting the raster data input in the raster data input processing to generate contour line data indicating contour lines;
Of the contour lines indicated by the contour line data generated by the contour line data generation process, the contour line interpolation process for interpolating the contour lines of the missing region by a predetermined method;
Raster data generation processing for generating raster data indicating elevation information by converting the contour data interpolated in the contour interpolation processing;
Among the raster data generated by the raster data generation process, the elevation information indicated by the raster data of the missing area, the elevation information of the missing area interpolated by the contour interpolation process, and the elevation of the area near the missing area Raster data interpolation processing for performing interpolation using information is executed by a computer.

In the raster data interpolation processing, a predetermined weight is given to the elevation information of the missing region interpolated by the contour interpolation processing, and a weight heavier than the predetermined weight is given to the elevation information of the region near the missing region. Based on the weighted data, the interpolation data of the elevation information of the missing area is generated.

In the raster data interpolation process, the missing area is divided into a plurality of areas in a first direction, first interpolation data is generated for each divided area, and the interpolation data of the missing area is generated from the generated first interpolation data. Is generated.

In the raster data interpolation process, the missing area is divided into a plurality of areas in a second direction different from the first direction, and the second interpolation is performed using the first interpolation data as the elevation information of the missing area. 2nd interpolation data is produced | generated for every area | region divided | segmented into this direction, The interpolation data of the said missing area are produced | generated from the produced | generated 2nd interpolation data.

In the raster data interpolation process, a coefficient of an expression representing a three-dimensional curved surface is calculated by a predetermined method based on the weighted data, and the three-dimensional curved surface represented by the calculated coefficient is generated as interpolation data for the missing region. It is characterized by doing.

In the raster data interpolation process, the interpolation data is generated by a different method according to at least one of the size of the missing area, the shape of the missing area, and the position of the missing area in the raster data. To do.

The elevation information method according to the present invention is, for example,
Raster data input step in which the input device is raster data indicating altitude information of a predetermined area, and the raster data has a missing area where the altitude information of a part of the predetermined area is missing;
A contour data generation step in which the processing device converts the raster data input in the raster data input step to generate contour line data indicating contour lines;
A contour interpolation step of interpolating the contour lines of the missing region by a predetermined method among the contour lines indicated by the contour line data generated by the contour line data generation step by the processing device;
A raster data generating step in which the processing device converts the contour data interpolated in the contour interpolation step to generate raster data indicating elevation information;
Among the raster data generated in the raster data generation step by the processing device, the elevation information indicated by the raster data of the missing region, the elevation information of the missing region interpolated in the contour interpolation step, and the vicinity of the missing region And a raster data interpolation step for performing interpolation using the altitude information of the area.

  The altitude information interpolating apparatus according to the present invention converts the given raster data into contour line data to interpolate the altitude information, converts the interpolated contour line data into raster data again, and further interpolates the altitude information. Accordingly, it is possible to appropriately interpolate the missing portion of the elevation information in the numerical elevation data given as the raster data, and to generate raster data having natural elevation information without missing.

FIG. 3 is a functional block diagram showing functions of the altitude information interpolation apparatus 10. The figure which shows an example of the raster data which the raster data input part 11 inputs. The figure which shows an example of the contour line data which the contour line data production | generation part 12 produces | generates. The figure which shows an example of the contour line data which the contour line interpolation part 13 interpolated. The figure which shows an example of the raster data which the raster data generation part 14 produces | generates. The figure which shows an example of the raster data which the raster data interpolation part 15 interpolated. The flowchart which shows the flow of a process of the altitude information interpolation apparatus. The figure which shows the invalid value flag data which the raster data input part 11 produced | generated. The figure which shows the invalid value flag data which the raster data interpolation part 15 updated. The flowchart which shows operation | movement of the update process of invalid value flag data. Explanatory drawing (1) of the process which determines the area | region updated to an interpolation value. Explanatory drawing (2) of the process which determines the area | region updated to an interpolation value. Explanatory drawing (3) of the process which determines the area | region updated to an interpolation value. Explanatory drawing (4) of the process which determines the area | region updated to an interpolation value. Explanatory drawing (5) of the process which determines the area | region updated to an interpolation value. Explanatory drawing of the update process of invalid value flag data. Explanatory drawing of the process by which the flag value of the invalid area | region 20a shown in FIG. 4 is updated to an interpolation value. The flowchart which shows the flow of an interpolation process (1). Explanatory drawing of the calculation method of the center coordinate of the invalid area | region 20. FIG. Explanatory drawing of the process which adjusts the altitude information of the invalid area | region 20 and its peripheral area | region. The flowchart (1) which shows the flow of an interpolation process (2). The flowchart (2) which shows the flow of an interpolation process (2). An explanatory view of a rectangle containing an invalid area 20. Explanatory drawing of the interpolation process of a horizontal direction. Explanatory drawing of the interpolation process of a vertical direction. The figure which shows an example of the hardware constitutions of the altitude information interpolation apparatus.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
In the following description, the processing device is a CPU 911 or the like which will be described later. The storage devices include a ROM 913, a RAM 914, a magnetic disk device 920, and the like which will be described later. The input devices are a keyboard 912, a communication board 915, and the like which will be described later.

Embodiment 1 FIG.
FIG. 1 is a functional block diagram illustrating functions of the altitude information interpolation apparatus 10.
The elevation information interpolation apparatus 10 includes a raster data input unit 11, a contour line data generation unit 12, a contour line interpolation unit 13, a raster data generation unit 14, and a raster data interpolation unit 15.

The raster data input unit 11 inputs raster data having elevation information (elevation value) of a predetermined area stored in the storage device using the input device. The raster data input by the raster data input unit 11 lacks elevation information of the invalid area 20 (missing area), which is a partial area of the predetermined area. When collecting altitude information by remote sensing etc., observation may be incomplete due to the influence of clouds and the like. The area that cannot be observed due to the influence of the cloud or the like and the altitude information cannot be acquired is the invalid area 20. A predetermined invalid value is assigned to the invalid area 20 as altitude information, and it is easy to determine whether the invalid area 20 has no altitude information or is an area having altitude information (effective area 21). .
FIG. 2 is a diagram illustrating an example of raster data input by the raster data input unit 11. The raster data shown in FIG. 2 expresses the altitude by shading. The darker the color, the lower the altitude, and the lighter the color, the higher the altitude. The raster data includes an invalid area 20 in which elevation information is missing. In FIG. 2, the shaded area is the invalid area 20. The area other than the invalid area 20 is the valid area 21.

The contour line data generation unit 12 converts the raster data input by the raster data input unit 11 by the processing device to generate contour line data indicating the contour lines. The contour line data generation unit 12 can generate contour line data indicating contour lines by converting raster data into vector data.
FIG. 3 is a diagram illustrating an example of contour line data generated by the contour line data generation unit 12. In particular, FIG. 3 shows contour data generated from the raster data shown in FIG. As shown in FIG. 3, for the invalid area 20 in the raster data, the contour lines in the contour data are also missing. This is because there is no elevation information in the invalid area 20, and therefore contour lines cannot be drawn. In FIG. 3, it is assumed that contour lines are drawn every 100 m above sea level. That is, the outermost contour line represents an altitude of 100 m, and the inner contour line represents an altitude of 200 m.

The contour line interpolating unit 13 interpolates the contour lines of the invalid area 20 portion among the contour lines indicated by the contour line data generated by the contour line data generating unit 12 by the processing device. Contour lines are essentially closed curves. However, for the invalid region 20, the contour line is not a closed curve because a part of the contour line is missing. For this reason, the contour interpolation unit 13 interpolates the missing part of the contour line so that the contour line forms a closed curve. The contour line interpolating unit 13 joins portions where the contour lines are missing with a smooth curve by, for example, spline interpolation.
FIG. 4 is a diagram showing an example of contour line data interpolated by the contour line interpolation unit 13. In particular, FIG. 4 shows contour line data obtained by interpolating a missing portion of the contour line indicated by the contour line data shown in FIG. As shown in FIG. 4, the portions where the contour lines indicated by the contour line data are missing are connected by a smooth curve, and the contour lines are closed curves.

The raster data generation unit 14 generates raster data having elevation information by converting the contour line data interpolated by the contour line interpolation unit 13 by the processing device. The raster data generation unit 14 can generate raster data having elevation information by converting vector data into raster data.
FIG. 5 is a diagram illustrating an example of raster data generated by the raster data generation unit 14. In particular, FIG. 5 shows raster data generated from the contour data shown in FIG. As shown in FIG. 5, the invalid area 20 in which the altitude information is partially lost remains in the raster data generated by the raster data generation unit 14. This is because when the invalid area 20 covers the peak or valley bottom (the deepest part of the valley), or when the invalid area 20 is in contact with the end of the area indicated by the raster data input by the raster data input unit 11, This is because the contour line interpolation unit 13 does not perform contour line interpolation. That is, when the invalid area 20 covers the vicinity of the summit (or valley bottom), the entire contour line is missing. That is, a part of the closed curve is not lost, but the entire closed curve is lost. When the entire closed curve is missing, the contour interpolation unit 13 cannot appropriately interpolate. Further, when the invalid area 20 is in contact with the end of the area indicated by the raster data input by the raster data input unit 11, the contour lines may not form a closed curve in the area indicated by the raster data. For this reason, when the invalid region 20 is in contact with the end of the region indicated by the raster data input by the raster data input unit 11, the contour line interpolation unit 13 cannot perform appropriate interpolation. Therefore, the invalid area 20 remains in a part of the raster data generated by the raster data generation unit 14.

The raster data interpolation unit 15 interpolates the elevation information of the invalid area 20 remaining in the raster data generated by the raster data generation unit 14 by the processing device. In particular, the raster data interpolation unit 15 remains in the raster data generated by the raster data generation unit 14 using the elevation information of the invalid area 20 interpolated by the contour interpolation unit 13 and the elevation information of the area near the invalid area 20. The elevation information of the invalid area 20 is interpolated. For example, the raster data interpolation unit 15 does not interpolate the contour line interpolation unit 13 in the invalid region 20 from the elevation information of the region near the invalid region 20 and the elevation information interpolated by the contour interpolation unit 13 in the invalid region 20. By generating a three-dimensional approximate curved surface that encompasses the area, the elevation information of the invalid area 20 is interpolated.
FIG. 6 is a diagram illustrating an example of raster data interpolated by the raster data interpolation unit 15. In particular, FIG. 6 is a diagram showing raster data obtained by interpolating the raster data shown in FIG. As shown in FIG. 6, the interpolated raster data does not have the invalid area 20 and shows the altitude information of the entire area.

The operation of the altitude information interpolation apparatus 10 will be described in detail.
FIG. 7 is a flowchart showing a processing flow of the altitude information interpolation apparatus 10.
(S11)
The raster data input unit 11 inputs raster data as shown in FIG. The raster data input unit 11 generates invalid value flag data in which the invalid area 20 included in the input raster data is distinguished from the valid area 21.
FIG. 8 is a diagram showing invalid value flag data generated by the raster data input unit 11. Here, the raster data input unit 11 generates invalid value flag data by adding “1” indicating the invalid value to the flag value of the invalid area 20 and adding “0” indicating the valid value to the flag value other than the invalid area 20. To do.

(S12)
The contour line data generation unit 12 converts the raster data input by the raster data input unit 11 to generate contour line data as shown in FIG.

(S13)
The contour line interpolation unit 13 interpolates the missing portion of the contour lines indicated by the contour line data generated by the contour line data generation unit 12, and generates contour line data as shown in FIG.
For example, the contour line interpolation unit 13 counts the number of contour line end points at the boundary between the invalid area 20 and the effective area 21 for each contour line label (elevation). That is, for each contour line indicating an altitude of 100 m, contour line indicating an altitude of 200 m,..., The number of end points of the contour line is counted. Then, according to the count value, interpolation processing is performed as follows. The interpolation process is a process for smoothly connecting the end points to each other by spline interpolation or the like. It should be noted that no interpolation processing is necessary for contour lines whose end points are 0 (that is, contour lines forming a closed curve).
(1) First, the contour line interpolation unit 13 preferentially performs an interpolation process for a contour line having 2 endpoints.
(2) Next, the contour interpolation unit 13 performs an interpolation process on even contour lines having 4 or more endpoints. The contour line interpolation unit 13 selects two end points that are closest to each other, and performs an interpolation process so as to connect the two selected end points. Subsequently, the contour line interpolation unit 13 selects two end points that are closest to the remaining end points, and performs an interpolation process so as to connect the two selected end points. The contour interpolation unit 13 repeats this process to connect all end points. However, the contour line interpolation unit 13 connects the end points so as not to intersect with the contour line drawn in the interpolation process of (1). Do not interpolate if you must cross.
(3) The contour line interpolation unit 13 performs an interpolation process on odd-numbered contour lines having three or more endpoints. As in (2), the contour line interpolation unit 13 selects two end points that are closest to each other, and repeats an interpolation process that connects the two selected end points. However, the end points are connected so as not to intersect the contour lines drawn by the interpolation processing of (1) and (2). Do not interpolate if you must cross. Also, there is at least one end point, but this is not interpolated.
(4) Contour lines with 1 endpoint are considered to have an invalid area 20 at the end (corner or edge) of the input raster data. Therefore, in this case, no interpolation is performed.

(S14)
The contour interpolation unit 13 updates the invalid value flag data to invalid value flag data as shown in FIG. That is, the value of the invalid flag data in the area where the altitude information can be given is updated from the invalid value “1” to the interpolated value “2” by the interpolation process in (S13). An area to which the interpolation value “2” is assigned is referred to as an interpolation area 22.
FIG. 10 is a flowchart showing the operation of the invalid value flag data update process.
(S141)
In the interpolation processing at (S13), the contour line interpolation unit 13 updates the interpolated contour line flag value in the invalid value flag data to the interpolation value “2”. That is, the interpolated contour line flag value shown in FIG. 4 is updated to the interpolation value “2”.
(S142)
The contour line interpolation unit 13 determines, for each pixel, whether or not the flag value in the invalid value flag data corresponding to the pixel is an invalid value “1”. That is, the contour line interpolation unit 13 searches the interpolated contour line data for a pixel (= pixel (x, y)) in which the flag value in the corresponding invalid value flag data has an invalid value “1”.
(S143)
The contour interpolation unit 13 searches for the contour line La having the closest distance to the pixel (x, y) searched in (S142).
For example, the contour line interpolation unit 13 measures the distance between all points on the contour line and the pixel (x, y) for each contour line. Then, the contour line interpolation unit 13 records the point closest to the pixel (x, y) and the distance in each contour line. That is, for each contour line, “a point closest to the pixel (x, y)” and “a distance between the point and the pixel (x, y)” are calculated. The contour line interpolation unit 13 selects “the contour line having the point closest to the pixel (x, y)” as the contour line La.
(S144)
Similarly to (S143), the contour interpolation unit 13 searches for the contour line Lb that is second closest to the pixel (x, y).
(S145)
The contour interpolation unit 13 determines whether or not to update the invalid value flag data in the vicinity of the pixel (x, y) and its vicinity to the interpolation value. At the same time, the contour interpolation unit 13 determines a region to be updated to the interpolation value. FIG. 11 to FIG. 15 are explanatory diagrams of processing for determining a region to be updated to an interpolation value.
As shown in FIG. 11A, the contour interpolation unit 13 selects a point closest to the pixel (x, y) as the pixel a on the contour line La. The contour interpolation unit 13 sets Va as a vector from the pixel (x, y) to the pixel a. Similarly, the contour line interpolation unit 13 sets the point closest to the pixel (x, y) on the contour line Lb as the pixel b. Then, the contour line interpolation unit 13 sets a vector from the pixel (x, y) to the pixel b as Vb.
The contour interpolation unit 13 determines whether or not the following conditions (1) to (3) are satisfied.
(1) The difference between the elevation of the contour line La and the elevation of the contour line Lb is equal to the interval between the contour lines (here, since the contour line is drawn every 100 m, it is 100 m). That is, the contour line La and the contour line Lb are adjacent contour lines.
(2) The angle formed by Va and Vb is greater than 90 degrees.
(3) The vector Vb does not intersect the contour line La.
When all the conditions (1) to (3) are satisfied, the contour line interpolation unit 13 includes “contour line La”, “contour line Lb”, and “invalid region 20” so as to enclose and surround the pixel (x, y). Is used to generate as small a closed curve as possible. Note that the smallest possible closed curve is a closed curve in which the area of the region surrounded by the closed curve is minimized.
For example, in the case of FIG. 11, all the conditions (1) to (3) are satisfied. Then, as shown by a broken line in FIG. 11B, a closed curve is generated only by the “boundary line of the invalid region 20”.
For example, in the case of FIG. 12, as shown in FIG. 12A, the pixels a and b and the contour lines La and Lb are selected, and all the conditions (1) to (3) are satisfied. Then, as indicated by a broken line in FIG. 12B, a closed curve is generated at “contour line La”, “contour line Lb”, and “boundary line of invalid area 20”.
For example, in the case of FIG. 13, as shown in FIG. 13A, the pixels a and b and the contour lines La and Lb are selected, and all the conditions (1) to (3) are satisfied. Then, as shown by a broken line in FIG. 13B, a closed curve is generated by “contour line La” and “boundary line of invalid area 20”.
For example, in the case of FIG. 14, as shown in the figure, the pixels a and b and the contour lines La and Lb are selected. In this case, the angle θ is 90 degrees or less and does not satisfy the condition (2). Therefore, the contour interpolation unit 13 determines not to update the invalid value in the vicinity of the pixel (x, y) and its vicinity to the interpolation value.
For example, in the case of FIG. 15, the pixels a and b and the contour lines La and Lb are selected as shown in the figure. In this case, since the vector Vb intersects the contour line La, the condition (3) is not satisfied. Therefore, the contour interpolation unit 13 determines not to update the invalid value in the vicinity of the pixel (x, y) and its vicinity to the interpolation value.
(S146)
The flag value of the invalid value flag data corresponding to the region surrounded by the closed curve generated in (S145) is updated to the interpolation value “2”.
FIG. 16 is an explanatory diagram of invalid value flag data update processing. First, as shown in FIG. 16A, the contour interpolation unit 13 updates the flag value of the invalid value flag data corresponding to the pixel (x, y) to the interpolation value. Next, as shown in FIG. 16B, it is determined whether the upper, lower, left and right pixels of the pixel (x, y) are within a closed curve. Then, the flag value of the invalid value flag data corresponding to the pixel determined to be within the closed curve is updated to the interpolation value. Here, it is assumed that the upper, lower, left, and right pixels of the pixel (x, y) are within the closed curve. Next, as shown in FIG. 16C, for the updated pixel (here, 5 pixels), it is similarly determined whether the upper, lower, left, and right pixels are within a closed curve. Then, the flag value of the invalid value flag data corresponding to the pixel determined to be within the closed curve is updated to the interpolation value. Here, as shown in FIG. 16D, it is assumed that only the pixels 1, 2, and 3 are within the closed curve. This process is performed until all the pixels in the closed curve are updated.
FIG. 17 is an explanatory diagram of processing for updating the flag value of the invalid area 20a shown in FIG. 4 to an interpolation value. FIG. 17A shows a state before update. For example, it is assumed that a pixel in the invalid area 20a between the contour line at an altitude of 300 m and the contour line at an altitude of 400 m is selected in (S142). Then, in (S145), a closed curve is generated by the invalid area 20 and the contour line at an altitude of 400 m, and in (S146), the flag value of the area shown in FIG. 17B is updated to the interpolation value. Subsequently, it is assumed that a pixel in the invalid area 20a between the contour line at an altitude of 400 m and the contour line at an altitude of 500 m is selected in (S142). Then, in (S145), a closed curve is generated by the invalid area 20, the contour line at an altitude of 400 m, and the contour line at an altitude of 500 m, and in (S146), the flag value of the area shown in FIG. By repeating the same processing, the flag value of the area shown in FIG. 17D is updated to the interpolation value, the flag value of the area shown in FIG. 17E is updated to the interpolation value, and finally FIG. ), All the flag values in the invalid area 20a are updated to the interpolation values. Therefore, as shown in FIG. 9, the entire invalid area 20 a is an interpolation area 22.

(S15)
The raster data generation unit 14 converts the contour line data interpolated by the contour line interpolation unit 13 to generate raster data as shown in FIG. However, the region where the flag value of the invalid value flag data is the invalid value “1” is not converted into grid data, and the flag value of the invalid value flag data is the valid region 21 where the flag value is the valid value “0” or the interpolation value “2”. Only the interpolation area 22 is converted into raster data.
The above processing from (S11) to (S15) is the first stage of interpolation. However, in the state where the first stage processing of interpolation is completed, the invalid area 20 remains as described above. Therefore, the interpolation is performed without the invalid area 20 in (S16).

(S16)
The raster data interpolation unit 15 interpolates the elevation information of the raster data generated by the raster data generation unit 14 by interpolation processing (1) or interpolation processing (2) described later.

The interpolation process (1) will be described. FIG. 18 is a flowchart showing the flow of the interpolation process (1).
In the interpolation process (1), the raster data interpolation unit 15 performs two-dimensional interpolation by a least square method using a three-variable polynomial, generates a three-dimensional approximated surface, and interpolates elevation information.

(S21)
The raster data interpolation unit 15 assigns an identification number to each invalid area 20. For example, in the case of raster data shown in FIG. 5, since there are two invalid areas 20, identification numbers (for example, “1” and “2”) are assigned to each invalid area 20.

(S22)
The raster data interpolation unit 15 calculates the center coordinates (Xc, Yc) for each invalid area 20.
FIG. 19 is an explanatory diagram of a method for calculating the center coordinates of the invalid area 20. As illustrated in FIG. 19, the raster data interpolation unit 15 acquires the maximum value (Xmax) and the minimum value (Xmin) of the invalid region 20 in the x-axis direction, and the maximum value (in the y-axis direction of the invalid region 20 ( Ymax) and the minimum value (Ymin) are acquired. Here, the x-axis direction and the y-axis direction are, for example, the horizontal direction and vertical direction of the raster data input by the raster data input unit 11. The raster data interpolation unit 15 calculates the center coordinates (Xc, Yc) from the acquired values by Xc = (Xmax−Xmin) / 2 and Yc = (Ymax−Ymin) / 2, respectively. If the shape of the invalid area 20 for calculating the center coordinates is a circle or a regular polygon, the center coordinates are the center of the invalid area 20.

(S23)
The raster data interpolation unit 15 acquires, as a predetermined number of samples, elevation information of the effective value “0” or the interpolation value “2” in the vicinity of the invalid value “1” for each invalid area 20. And the raster data interpolation part 15 calculates the altitude information of the invalid area | region 20 by Formula 1 based on the acquired sample, for example. Note that the number of samples to be acquired must be larger than the coefficient of the polynomial shown in Equation 1.
In Equation 1, H is elevation information, x is a pixel number in the horizontal direction of raster data, and y is a line number in the vertical direction of raster data. Further, x ′ = x−xc and y ′ = y−yc. That is, x ′ and y ′ are a pixel number and a line number obtained by shifting x and y so that the center coordinates of each invalid area 20 are the origin. a _ij (i = 0 to 4, j = 0 to 4) is an undetermined coefficient, and is determined by, for example, the least square method. In Equation 1, since i = 0 to 4 and j = 0 to 4, since there are 25 undetermined coefficients, the number of samples to be acquired must be 25 or more.
The raster data interpolation unit 15 calculates undetermined coefficients a _ij (i = 0-4, j = 0-4) by the least square method based on the acquired samples. Note that the raster data interpolation unit 15 weights the samples in the calculation by the least square method. For example, the raster data interpolation unit 15 gives the elevation information acquired from the effective value “0” a heavy weight (for example, a weight “10”). On the other hand, the raster data interpolating unit 15 gives the altitude information acquired from the interpolation value “2” a lighter weight (for example, the weight “1”) than the altitude information acquired from the effective value “0”. By doing so, the elevation information (H in Equation 1) of the invalid area 20 is calculated.
Instead of weighting the samples, more samples of effective value “0” may be obtained (for example, 10 times) than samples of interpolation value “2”.

(S24)
The raster data interpolation unit 15 interpolates by updating the elevation information of the invalid area 20 with the elevation information calculated in (S23).
However, if the elevation information is simply updated with the calculated elevation information, the elevation information may be discontinuous at the boundary between the invalid area 20 and the surrounding area. Therefore, the altitude information between the invalid area 20 and the surrounding area is adapted by weighted averaging as follows. FIG. 20 is an explanatory diagram of processing for blending elevation information between the invalid area 20 and the surrounding area.
As shown in FIG. 20A, the distance from the center coordinate of the invalid area 20 to a certain pixel is “R”. R for the pixel at the boundary between the invalid area 20 and the peripheral area is “Redge”. Here, the raster data interpolating unit 15 sets an overlap area for the length α to blend the altitude information calculated by Equation 1 with the altitude information indicated by the raster data generated by the raster data generating unit 14. For example, α is about 10 pixels. FIG. 20B is an enlarged view of the periphery of the overlapping area in FIG.
The raster data interpolating unit 15 converts the elevation information H ′ to “H ′ = f” for the pixels in the overlapping region, that is, the pixels whose distance R from the center coordinates (Xc, Yc) of the invalid region 20 is “Redge ≦ R ≦ Redge + α” (R ′) × H + [1-f (R ′)] × Horg ”
Calculate according to Here, H is elevation information calculated by the polynomial shown in Equation 1, and Horg is the original elevation information (elevation information indicated by the raster data generated by the raster data generation unit 14). Further, R ′ = R-Redge (0 ≦ R ′ ≦ α). That is, R ′ is the distance from the boundary between the invalid area 20 and the peripheral area. Further, f (R ′) is a function having a value of 0 to 1, and f (0) = 1 and f (α) = 0. For example, the function f (R ′) is “Example 1: f (R ′) = 1− (R ′ / α)” or “Example 2: f (R ′) = (1/2) × [1 + cos (πR '/ Α)]'. By calculating in this way, as shown in FIG. 20C, the altitude information between the invalid area 20 and the surrounding area can be familiarized.
That is, the raster data interpolation unit 15
(1) Elevation information is given to the pixels in the invalid area 20 (that is, pixels of R ≦ Redge) by H calculated by Equation 1.
(2) For the pixels in the overlapping area, the altitude information is given by H ′ calculated from H calculated by Equation 1 and Horg which is the original altitude information.
(3) For other areas, altitude information is given by Horg, which is the original altitude information.
In Example 2 of the function f (R ′), by using the cos function, the altitude information H calculated in (S23) is used with a heavy weight for the area close to the invalid area 20, and the invalid area is used. Employing a heavy weight for Horg as it moves away from 20.

The interpolation process (2) will be described. 21 and 22 are flowcharts showing the flow of the interpolation process (2) of the raster data interpolation unit 15.
The raster data interpolation unit 15 performs one-dimensional interpolation from one direction of the horizontal direction and the vertical direction, and performs one-dimensional interpolation from the other direction based on the interpolated data. That is, the raster data interpolation unit 15 interpolates the elevation information of the invalid area 20 in two stages.

(S31)
The raster data interpolation unit 15 assigns an identification number to each invalid area 20 in the same manner as (S21).

(S32)
The raster data interpolation unit 15 sets, for each invalid area 20, a rectangle that encloses the invalid area 20 (= a rectangle that circumscribes the invalid area 20). FIG. 23 is an explanatory diagram of a rectangle including the invalid area 20. Let the horizontal size of this rectangle be Sx and the vertical size be Sy.
This rectangle is a rectangle formed by sides parallel to the horizontal and vertical directions of the raster data input by the raster data input unit 11.

(S33)
The raster data interpolation unit 15 determines whether to perform interpolation from the horizontal direction or the vertical direction of the rectangle set in (S32) based on the following rules. When interpolation is performed from the horizontal direction, the process proceeds to (S34). On the other hand, when interpolation is performed from the vertical direction, the process proceeds to (S40). Note that performing interpolation from the horizontal direction means performing interpolation processing for each horizontal row (for each horizontal line), and performing interpolation from the vertical direction means for each vertical column (for each vertical line). ) To perform interpolation. The horizontal line is data for one pixel in the vertical direction, and the vertical line is data for one pixel in the horizontal direction.
(1) When the invalid area 20 is in contact with at least one of the left edge and the right edge of the raster data and is not in contact with either the upper edge or the lower edge, the vertical interpolation is performed first. Run. In this case, there are regions of the effective value “0” or the interpolation value “2” above and below the invalid region 20. For this reason, vertical interpolation is executed first using valid values or interpolation values existing at the upper and lower portions of the invalid area 20.
(2) If the invalid area 20 is in contact with at least one of the upper and lower edges of the raster data and is not in contact with either the left edge or the right edge, the horizontal interpolation is executed first. To do. In this case, there are regions of the effective value “0” or the interpolation value “2” in the left and right portions of the invalid region 20. Therefore, the horizontal interpolation is executed first using the effective values or the interpolation values existing in the left and right portions of the invalid area 20.
(3) If the invalid area 20 is not in contact with any of the left edge, right edge, upper edge, and lower edge of the raster data, interpolation in the direction of shorter distance is executed first. The reason why the interpolation in the short distance direction is performed first is that the shorter the distance, the better the interpolation accuracy. The determination of the distance uses rectangular sizes Sx and Sy. If Sx ≦ Sy (= square or vertically long rectangle), interpolation is performed from the horizontal direction (x direction), and Sx> Sy (horizontal rectangle). For example, interpolation is performed from the vertical direction (y direction).
(4) The invalid area 20 touches at least one of the four corners of the raster data (“left edge and upper edge”, “right edge and upper edge”, “left edge and lower edge”, “right edge and upper edge”). If it is, interpolation in the direction with a shorter distance is executed first as in (3).

When the horizontal direction (x direction) interpolation is performed first, the raster data interpolation unit 15 performs (S34) to (S36) for each horizontal line of the invalid area 20, and performs interpolation for all the lines. FIG. 24 is an explanatory diagram of the interpolation process in the horizontal direction.
(S34)
The raster data interpolation unit 15 obtains the maximum value (Xmax) and the minimum value (Xmin) in the x-axis direction of the invalid area 20 for the selected line, and calculates the center coordinate (Xc). That is, the raster data interpolation unit 15 calculates Xc = (Xmax−Xmin) / 2.

(S35)
The raster data interpolation unit 15 acquires the effective value “0” or the interpolation value “2” in the vicinity of the invalid value “1” as several samples for the selected line. Then, the raster data interpolation unit 15 calculates the elevation information of the invalid area 20 on each line based on the acquired sample. Note that the number of samples to be acquired must be larger than the coefficient of the polynomial shown in Equation 2.
In Equation 2, H is the altitude information, and x is the pixel number in the horizontal direction of the raster data. Further, x ′ = x−xc. a _ij (i = 0 to 4, j = 0) is an undetermined coefficient, and is determined by the least square method. In Equation 2, since i = 0 to 4 and j = 0, there are five unknown coefficients, so the number of samples to be acquired is five or more.
As in the case of the interpolation process (1), the raster data interpolation unit 15 weights samples and calculates undetermined coefficients a _ij (i = 0 to 4, j = 0) by the least square method to obtain elevation information. .

(S36)
The raster data interpolation unit 15 interpolates by updating the elevation information of the invalid area 20 of the selected line with the elevation information calculated in (S35). The raster data interpolation unit 15 adjusts the elevation information between the invalid area 20 and the surrounding area by the same process as in the interpolation process (1).

Next, interpolation in the vertical direction (y direction) is performed. The raster data interpolation unit 15 performs (S37) to (S39) for each line in the vertical direction of the invalid area 20, and performs interpolation for all the lines. FIG. 25 is an explanatory diagram of the interpolation process in the vertical direction. In principle, the vertical interpolation process is the same as the horizontal interpolation process. That is, the raster data interpolation unit 15 calculates the center coordinates (Yc) of the invalid area 20 for each line (S37). The raster data interpolating unit 15 acquires the effective value “0” or the interpolated value “2” in the vicinity of the invalid value “1” for each line as several samples, and obtains the elevation information of the invalid area 20 on each line. Calculate (S38). Then, the raster data interpolation unit 15 blends the elevation information between the invalid area 20 and the surrounding area, and interpolates the invalid area 20 of each line (S39).
In the vertical interpolation process, the elevation information of the invalid area 20 has already been calculated in the horizontal interpolation process. Therefore, in (S35), the elevation information inside the invalid area 20 may be acquired as a sample. When the altitude information inside the invalid area 20 is acquired as a sample, the influence on the calculation may be differentiated by weighting the sample acquired from the valid value “0” and the interpolation value “2”. For example, the weight of altitude information acquired from the effective value “0” is “10”, the weight of altitude information acquired from the interpolation value “2” is “3”, and the weight of the altitude information inside the invalid area 20 is “1”. Also good.

On the other hand, when the vertical direction (y direction) interpolation is performed first, the raster data interpolation unit 15 performs (S40) to (S42) for each line in the vertical direction of the invalid area 20, and performs interpolation for all the lines. The processes from (S40) to (S42) are basically the same as the processes from (S37) to (S39). However, since the elevation information of the invalid area 20 is not calculated, the elevation information of the invalid area 20 is not acquired as a sample.
Next, interpolation in the horizontal direction (x direction) is performed. The raster data interpolation unit 15 performs (S43) to (S45) for each horizontal line of the invalid area 20, and performs interpolation for all the lines. The processes from (S43) to (S45) are basically the same as the processes from (S34) to (S36). However, since the elevation information of the invalid area 20 has already been calculated, the elevation information inside the invalid area 20 may be acquired as a sample.

  Note that the process may return to (S32) again, and two-step interpolation in the horizontal direction and the vertical direction may be repeated a predetermined number of times.

  In the above description, the horizontal interpolation is performed for each horizontal line. However, the present invention is not limited to this, and the horizontal interpolation may be performed every several lines in the horizontal direction. For example, it may be performed every three lines in the horizontal direction (data for three pixels in the vertical direction). In this case, altitude information may be calculated based on data of one line (for example, the center line) of the three lines. By doing in this way, the amount of calculation can be reduced to 1/3. That is, in the horizontal direction interpolation, the invalid area 20 may be divided into a plurality of areas in the horizontal direction, and the interpolation may be performed for each divided area. The same applies to the vertical interpolation. That is, the vertical interpolation may be performed every several vertical lines.

  The altitude information interpolation apparatus 10 can generate appropriate raster data without omission by interpolating the altitude information for the invalid area 20 portion of the raster data input as described above. In particular, the elevation information interpolating device 10 converts raster data into contour data once, interpolates the missing portion, and then returns to the raster data for interpolation, thus generating raster data that is not unnatural as contour data. can do.

Next, the hardware configuration of the altitude information interpolation apparatus 10 will be described.
FIG. 26 is a diagram illustrating an example of a hardware configuration of the elevation information interpolation apparatus 10.
As shown in FIG. 26, the altitude information interpolation apparatus 10 includes a CPU 911 (also referred to as a central processing unit, a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, and a processor) that executes a program. . The CPU 911 is connected to the ROM 913, the RAM 914, the LCD 901 (Liquid Crystal Display), the keyboard 902 (K / B), the communication board 915, and the magnetic disk device 920 via the bus 912, and controls these hardware devices. Instead of the magnetic disk device 920 (fixed disk device), a storage device such as an optical disk device or a memory card read / write device may be used. The magnetic disk device 920 is connected via a predetermined fixed disk interface.

  The ROM 913 and the magnetic disk device 920 are examples of a nonvolatile memory. The RAM 914 is an example of a volatile memory. The ROM 913, the RAM 914, and the magnetic disk device 920 are examples of a storage device (memory). The keyboard 902 and the communication board 915 are examples of input devices. The communication board 915 is an example of a communication device (network interface). Furthermore, the LCD 901 is an example of a display device.

  An operating system 921 (OS), a window system 922, a program group 923, and a file group 924 are stored in the magnetic disk device 920 or the ROM 913. The programs in the program group 923 are executed by the CPU 911, the operating system 921, and the window system 922.

The program group 923 includes “raster data input unit 11”, “contour line data generation unit 12”, “contour line interpolation unit 13”, “raster data generation unit 14”, “raster data interpolation unit 15” and the like in the above description. It stores software, programs and other programs that execute the functions described. The program is read and executed by the CPU 911.
In the file group 924, information, data, signal values, variable values, and parameters such as “raster data”, “contour data”, “first interpolation data”, “second interpolation data”, etc. And “database”. The “file” and “database” are stored in a recording medium such as a disk or a memory. Information, data, signal values, variable values, and parameters stored in a storage medium such as a disk or memory are read out to the main memory or cache memory by the CPU 911 via a read / write circuit, and extracted, searched, referenced, compared, and calculated. Used for the operation of the CPU 911 such as calculation / processing / output / printing / display. Information, data, signal values, variable values, and parameters are temporarily stored in the main memory, cache memory, and buffer memory during the operation of the CPU 911 for extraction, search, reference, comparison, calculation, calculation, processing, output, printing, and display. Is remembered.

In the above description, the arrows in the flowchart mainly indicate input / output of data and signals, and the data and signal values are recorded in a memory of the RAM 914, other recording media such as an optical disk, and an IC chip. Data and signals are transmitted online by a bus 912, signal lines, cables, other transmission media, and radio waves.
In addition, what is described as “to part” in the above description may be “to circuit”, “to device”, “to device”, “to means”, and “to function”. It may be “step”, “˜procedure”, “˜processing”. In addition, what is described as “˜device” may be “˜circuit”, “˜device”, “˜device”, “˜means”, “˜function”, and “˜step”, “ ~ Procedure "," ~ process ". Furthermore, what is described as “to process” may be “to step”. That is, what is described as “˜unit” may be realized by firmware stored in the ROM 913. Alternatively, it may be implemented only by software, or only by hardware such as elements, devices, substrates, and wirings, by a combination of software and hardware, or by a combination of firmware. Firmware and software are stored in a recording medium such as ROM 913 as a program. The program is read by the CPU 911 and executed by the CPU 911. That is, the program causes a computer or the like to function as the “˜unit” described above. Alternatively, the computer or the like is caused to execute the procedures and methods of “to part” described above.

  DESCRIPTION OF SYMBOLS 10 Elevation information interpolation apparatus, 11 Raster data input part, 12 Contour line data generation part, 13 Contour line interpolation part, 14 Raster data generation part, 15 Raster data interpolation part, 20 Invalid area | region, 21 Effective area | region, 22 Interpolation area | region.

Claims (13)

Raster data input unit for inputting raster data indicating elevation information of a predetermined area by an input device, the raster data having a missing area in which elevation information of a part of the predetermined area is missing;
A contour data generator for converting the raster data input by the raster data input unit to generate contour line data indicating contour lines by a processing device;
A contour interpolation unit that interpolates the contour lines of the missing region by a predetermined method among the contour lines indicated by the contour line data generated by the contour line data generation unit by the processing device;
A raster data generation unit that converts the contour line data interpolated by the contour line interpolation unit and generates raster data indicating elevation information by a processing device;
Among the raster data generated by the raster data generation unit by the processing device, the altitude information indicated by the raster data of the missing region, the elevation information of the missing region interpolated by the contour interpolation unit, and the vicinity of the missing region An elevation information interpolation apparatus comprising: a raster data interpolation unit that interpolates using elevation information of a region. The raster data interpolation unit gives a predetermined weight to the elevation information of the missing region interpolated by the contour interpolation unit, and gives a weight heavier than the predetermined weight to the elevation information of the region near the missing region. The altitude information interpolation apparatus according to claim 1, wherein interpolation data of altitude information of the missing area is generated based on the weighted data. The raster data interpolation unit divides the missing area into a plurality of areas in a first direction, generates first interpolation data for each divided area, and interpolates the missing area from the generated first interpolation data. The altitude information interpolating apparatus according to claim 2, wherein the altitude information interpolating apparatus is generated. The raster data interpolation unit divides the missing area into a plurality of areas in a second direction different from the first direction, and uses the first interpolation data as the elevation information of the missing area. The altitude information interpolating apparatus according to claim 3, wherein second interpolation data is generated for each area divided in the direction, and interpolation data of the missing area is generated from the generated second interpolation data. The raster data interpolation unit calculates a coefficient of an expression representing a three-dimensional curved surface by a predetermined method based on the weighted data, and generates the three-dimensional curved surface represented by the calculated coefficient as interpolation data of the missing region The altitude information interpolating apparatus according to claim 2, wherein The raster data interpolation unit generates the interpolation data by a different method according to at least one of the size of the missing area, the shape of the missing area, and the position of the missing area in the raster data. The altitude information interpolation apparatus according to any one of claims 1 to 5. Raster data indicating elevation information of a predetermined area, raster data input processing for inputting raster data having missing areas in which elevation information of a part of the predetermined area is missing; and
Contour line data generation processing for converting the raster data input in the raster data input processing to generate contour line data indicating contour lines;
Of the contour lines indicated by the contour line data generated by the contour line data generation process, the contour line interpolation process for interpolating the contour lines of the missing region by a predetermined method;
Raster data generation processing for generating raster data indicating elevation information by converting the contour data interpolated in the contour interpolation processing;
Among the raster data generated by the raster data generation process, the elevation information indicated by the raster data of the missing area, the elevation information of the missing area interpolated by the contour interpolation process, and the elevation of the area near the missing area An elevation information interpolation program that causes a computer to execute raster data interpolation processing for interpolation using information. In the raster data interpolation processing, a predetermined weight is given to the elevation information of the missing region interpolated by the contour interpolation processing, and a weight heavier than the predetermined weight is given to the elevation information of the region near the missing region. The elevation information interpolation program according to claim 7, wherein interpolation data of elevation information of the missing area is generated based on the weighted data. In the raster data interpolation process, the missing area is divided into a plurality of areas in a first direction, first interpolation data is generated for each divided area, and the interpolation data of the missing area is generated from the generated first interpolation data. altitude information interpolating program according to claim 8, characterized in that to produce a. In the raster data interpolation process, the missing area is divided into a plurality of areas in a second direction different from the first direction, and the second interpolation is performed using the first interpolation data as the elevation information of the missing area. 10. The altitude information interpolation program according to claim 9, wherein second interpolation data is generated for each area divided in the direction, and the interpolation data of the missing area is generated from the generated second interpolation data. In the raster data interpolation process, a coefficient of an expression representing a three-dimensional curved surface is calculated by a predetermined method based on the weighted data, and the three-dimensional curved surface represented by the calculated coefficient is generated as interpolation data for the missing region. The altitude information interpolation program according to claim 8, wherein: In the raster data interpolation process, the interpolation data is generated by a different method according to at least one of the size of the missing area, the shape of the missing area, and the position of the missing area in the raster data. The elevation information interpolation program according to any one of claims 7 to 11 . Raster data input step in which the input device is raster data indicating altitude information of a predetermined area, and the raster data has a missing area where the altitude information of a part of the predetermined area is missing;
A contour data generation step in which the processing device converts the raster data input in the raster data input step to generate contour line data indicating contour lines;
A contour interpolation step of interpolating the contour lines of the missing region by a predetermined method among the contour lines indicated by the contour line data generated by the contour line data generation step by the processing device;
A raster data generating step in which the processing device converts the contour data interpolated in the contour interpolation step to generate raster data indicating elevation information;
Among the raster data generated in the raster data generation step by the processing device, the elevation information indicated by the raster data of the missing region, the elevation information of the missing region interpolated in the contour interpolation step, and the vicinity of the missing region And a raster data interpolation step for interpolating using the elevation information of the area of the elevation information.