JP5252855B2 - Map coordinate correction method, coordinate correction apparatus, and coordinate correction program - Google Patents

Description

  The present invention relates to a coordinate correction technique for improving the position accuracy of a digitized map.

  Conventionally, in a geographic information system, various maps drawn with different scales and accuracy are handled. In particular, when a map drawn on paper is read and used by a scanner, reduction in accuracy due to paper expansion or contraction or distortion during scanner input is inevitable. In this way, the features on the map are shifted to various degrees from the position determined from the latitude and longitude of the actual installation position. For this reason, when different maps are overlapped, even the same feature does not overlap, but is drawn at different positions or double.

  In addition, when a high-precision GPS positioning result such as a survey result or Realtime Kinetic-Global Positioning System (hereinafter referred to as RTK-GPS) is superimposed on the map, if the map is insufficiently accurate, The relative positional relationship with the object was not correctly displayed on the map. For this reason, for example, even if the positioning is actually performed on the road, the inconvenience that the latitude and longitude are in the building on the map occurs. In this way, confusion occurs at which point on the map the positioning is made, and the positioning result cannot be used as it is.

  Furthermore, the geodetic system has been changed from the Japanese geodetic system to the world geodetic system, and it is necessary to convert the coordinate values represented by the Japanese geodetic system into the coordinate values of the world geodetic system. At the time of conversion, the coordinate values in the Japanese geodetic system have errors due to surveying accuracy during surveying, crustal movement after surveying, and due to reasons such as the expansion and contraction of paper as described above. Is required.

  As described above, in using the geographic information system, it is necessary to correct each point of the map so as to have accurate position information.

  As a correction technique for this, for example, a plurality of reference points where both coordinate values on a map and accurate coordinate values measured by RTK-GPS or the like are obtained are set, and Delaunay is set with the reference points as vertices. The whole area is divided into a plurality of triangles that do not overlap each other by a method called triangulation, and the three reference points that are the vertices are converted from the coordinate values on the map to the correct coordinate values for each triangle area. A technique for correcting an coordinate value by obtaining an affine transformation and applying the affine transformation to a point in each triangular area is shown (for example, see Patent Literature 1 and Non-Patent Literature 1).

JP-A-2005-70373 Japan Society of Civil Engineers, 625, IV-44, 89-98 (July 1999)

  In such a coordinate correction technique, a plurality of triangular regions having vertices as reference points are formed, and for each triangular region, the reference points that are vertices are corrected to correct coordinate values, etc. The coordinate value is corrected by determining the conversion of the above and applying the conversion to each point in the triangular area.

  At this time, Delaunay triangulation is used to divide the triangular area having the reference point as a vertex. Delaunay triangulation is a method of segmenting regions by triangles that are as close to regular triangles as possible by the principle of maximizing the minimum angle. Each triangular region is divided so that no other reference point enters the circumscribed circle. The details of Delaunay triangulation are described in, for example, Akiyoshi Sugihara, “Data Structure and Algorithm”, Chapter 11, Kyoritsu Shuppan, published in 2001.

  However, in Delaunay triangulation, the division pattern into triangle regions is determined only by the arrangement of reference points. For this reason, there is a specific pattern with a certain amount of correction to the correct coordinate value of each reference point, and in addition to Delaunay triangulation, there is a division pattern into triangular areas that increases the accuracy after correction. However, there was a problem that this could not be realized.

  As described above, the conventional coordinate correction technique has a problem in that an appropriate correction conversion cannot always be obtained and the correction is not performed to a correct coordinate value.

  On the other hand, as an example of triangulation calculation that does not depend only on the arrangement of the reference points, for example, in the shape representation such as CAD, the Hessian matrix at each point is calculated for the xy bivariate function, and the eigenvector direction is anisotropic A technique for performing anisotropic triangulation using the reciprocal of the square root of the eigenvalue corresponding to each eigenvector as the axis of the sex and maintaining the accuracy by executing the Frank J. et al. Bossen, Paul S .; Heckbert, “A Pliant Method for Anisotropic Mesh Generation”, 5th International Meshing Roundtable, pp. 63-76, issued in 1996. This technique uses a circumscribed ellipse with an anisotropy axis as the axis and an ellipticity as the size ratio for the triangular area, and satisfies the condition that no other vertex enters the circumscribed ellipse. Such triangulation is called “anisotropic Delaunay triangulation”.

  However, on the map, the reference points that give the correction amount are not always evenly and sufficiently arranged, and furthermore, since the coordinate values of the reference points include noise, each point accurately You cannot find the Hessian matrix. As described above, there is a problem that an appropriate anisotropic axis and section width cannot be obtained and a desired section pattern cannot be obtained.

  The present invention has been made to solve the above-described problems, and by dividing a region with a division pattern that matches the correction amount of each reference point, the coordinate value after correction conversion is obtained. Its purpose is to provide a coordinate correction technology for maps that maintains high accuracy.

A map coordinate correction method according to the subject of the present invention is a map coordinate correction method using a computer , wherein a reference point which is a vertex of each segmented triangular area for segmenting a digitized map is displayed on the map. From the coordinate value digital data before correction and the coordinate value digital data after correction of the reference point which is an accurate coordinate value, the axis setting means realized by the computer has anisotropy inherent to the map. Axis setting step for defining digital data for giving an axial direction, coordinate value digital data before correction on the map of each reference point, coordinate value digital data after correction of each reference point, and anisotropy based on the digital data to provide an axial ratio setting means which is realized by the computer to obtain digital data to provide a ratio of at anisotropy in the axial direction of the anisotropic ratio A setting step, the map on the basis of the digital data to provide a ratio of the digital data to provide the axial direction of the anisotropic said anisotropic, the triangulation means which is implemented by the computer, each segment triangular region The three triangular regions that constitute the sectioned triangular region within a circumscribed ellipse that passes through the three vertices constituting the axis, the axis direction of the anisotropy is the axis, and the ellipticity is the ratio of the anisotropy An anisotropic triangulation step for dividing into a plurality of segmented triangular regions that do not contain vertices other than the vertices, and the map of each reference point forming each vertex for each of the plurality of segmented triangular regions based on the uncorrected coordinate value digital data and the coordinate value digital data after the correction of the above conversion means which is implemented by the computer, correction conversion to be applied to the divided triangular area A conversion step of calculating digital data and correcting the coordinate value digital data on the map of each coordinate point by performing the correction conversion on each coordinate point inside the sectioned triangular region. Features.

  Hereinafter, various embodiments of the subject of the present invention will be described in detail along with the effects and advantages thereof with reference to the accompanying drawings.

  According to the subject matter of the present invention, it is possible to obtain a section of the map into divided triangular areas so as to reduce the error after correction conversion, and to correct the map with high accuracy.

(Embodiment 1)
The feature point of the present embodiment is based on the coordinate value before correction on the map of each vertex in the segmented triangular area that divides the digitized map and the coordinate value after correct positioning that has been measured. Calculate the two orthogonal axes of anisotropy and the ratio of the segment widths in the two axes, and give the anisotropy by that ratio in the two axis directions, so that the digitized map can be divided into multiple segments The point is to be divided (divided) into triangular regions. In this way, the ratio between the two orthogonal axes and the division width in the two axes is determined so as to minimize the error after the correction conversion, and in order to reflect this, the ratio is anisotropy by the ratio in the two axis directions. By dividing the map into segmented patterns having a symbol, the coordinate value of each coordinate point within each segmented triangular area on the map can be accurately corrected. Hereinafter, the feature points of the present embodiment will be described in detail with reference to the drawings.

  FIG. 1 is a block diagram showing a configuration of a digitized map coordinate correction apparatus according to the present embodiment.

  In FIG. 1, a storage device 1 as “storage means” stores map data 2, reference point data 3, and segmented triangle data 4. Here, the map data 2 includes the coordinate values of all the features on the map (including coordinate values on the map before correction of each reference point described later), the figure representing the feature, its attribute information, and the like. It is digital data comprised by. The reference point data 3 is digital data including coordinate values on a map before correction and accurate coordinate values (corrected coordinate values) of each reference point described later. The section triangle data 4 is digital data indicating each section triangle area constituting a section pattern obtained by sectioning a map into a plurality of triangles with a reference point as a vertex.

  The axis setting device 5 that is an “axis setting means” is a part that uses the reference point data 3 to perform electrical processing for setting two anisotropic axes orthogonal to each other on the map.

  The ratio setting device 6, which is a “ratio setting means”, uses the anisotropic biaxial data set by the reference point data 3 and the axis setting device 5 to determine the ratio of the segment width along the two anisotropic axes (different This is the part that performs electrical processing to calculate the ratio of the directivity.

  The dividing device 7 as the “dividing means” uses the reference point data 3, the biaxial data, and the ratio width ratio data calculated by the ratio setting device 6 to form a triangular segment having a reference point as a vertex on the map. This is a part for performing electrical processing for determining the pattern and creating the segmented triangle data 4.

  The conversion device 8, which is a “conversion unit”, applies a segmented triangular area formed by the reference point from the coordinate value of the reference point on the map and the accurate coordinate value (corrected coordinate value) of the reference point. This is a part for determining the correction conversion to be performed and performing an electrical process for obtaining the corrected coordinate value by executing the correction conversion on the points in the sectioned triangular area. The corrected coordinate value of each coordinate point inside each divided triangle area is stored in the map data 2 of the storage device 1, and as a result, the coordinate value of the feature on the map in the map data 2 is updated.

  2 to 14 are explanatory diagrams showing the operation of the coordinate correction apparatus of FIG. Each figure is as follows. That is, FIG. 2 is a diagram illustrating the division of the map 9 by the divided triangular area 12 related to the reference point 10. FIG. 3 is a diagram showing correction conversion of the segmented triangular area 12. FIG. 4 is a diagram showing the anisotropic axis 17 and the segment width. FIG. 5 is a diagram showing the correction vector 18. FIG. 6 is a diagram showing a first-order approximation of the correction vector 18. FIG. 7 is a diagram showing approximate error measurement of the correction vector 18 by the reference point 10. FIG. 8 is a diagram illustrating the function Gu (H). FIG. 9 is a diagram showing Gsum and its minimum value. FIG. 10 is a diagram showing the reference point data 3. FIG. 11 is a diagram illustrating Delaunay triangulation in the uw coordinate system. FIG. 12 is a diagram illustrating anisotropic Delaunay triangulation in the uv coordinate system. FIG. 13 is a diagram showing reference point data 29 for performing anisotropic triangulation. FIG. 14 is a diagram showing the segmented triangle data 4.

  FIG. 15 is a flowchart showing the operation of the coordinate correction apparatus of FIG.

  As shown in FIG. 2, the map coordinate correction apparatus (FIG. 1) according to the present embodiment forms a partitioned triangular region 12 by using partitioned edges 11 that connect adjacent reference points 10 with each reference point 10 as a vertex. Then, the map 9 is divided into divided triangular regions 12. Then, the coordinate correction apparatus of FIG. 1 is configured such that the coordinate value on the map 9 of the reference point 10 that is the vertex is converted into an accurate new coordinate value 13 for each divided triangular region 12 as shown in FIG. Thus, the point 15 inside the segmented triangle region 12 is corrected to the new coordinate value 16 in the segmented triangle region 14 by converting the segmented triangle region 12 into the segmented triangle region 14.

  The “reference point 10” referred to here is a point serving as a reference for conversion of coordinate values. The coordinate value on the map 9 and a coordinate system or geodetic position determined by, for example, GPS or used as a reference. It is the point where the correct coordinate value 13 is obtained together in the system.

  In the following, the coordinate values before correction of all the points on the map 9 are described as “old coordinate values”, and the above accurate coordinate values (corrected coordinate values) 13 at the reference point 10 and each A coordinate value obtained by performing correction conversion on each point (each coordinate point) inside the sectioned triangular region 12 is described as “new coordinate value”.

  The map coordinate correction apparatus (FIG. 1) according to the present embodiment determines a segmentation pattern for segmenting the digitized map 9 by anisotropic Delaunay triangulation. In other words, the normal Delaunay triangulation process divides into triangle division patterns that satisfy the condition that no other reference point 10 enters the circumscribed circle formed by the reference point 10 that is the apex of the division triangle region 12. On the other hand, the anisotropic Delaunay triangulation process is performed under the condition that the other reference point 10 does not enter the circumscribed ellipse formed by the reference point 10 that is the vertex of the sectioned triangular region 12. Are divided by a divided triangle area. In order to execute the anisotropic Delaunay triangulation, an anisotropic axis that is an axis of the ellipse for determining the circumscribed ellipse and a ratio (anisotropy ratio) that is an ellipticity are determined. The map coordinate correction apparatus (FIG. 1) according to the present embodiment sets the anisotropic axis and the anisotropic ratio so that the correction accuracy is improved as compared with the case where the normal Delaunay triangulation process is performed. To do.

  Hereinafter, with respect to the N reference points 10, the old coordinate value is Pi (xi, yi), the new coordinate value is Qi (Xi, Yi), and the correction vector 18 from the old coordinate value to the new coordinate value is fi (i = 1, 2, ..., N). The anisotropic axis 17 is defined as u axis and v axis.

  First, a model for setting (determining) the anisotropic axis 17 will be described.

  The axis setting device 5 in FIG. 1 determines the anisotropic axis 17 as follows. That is, an affine transformation that approximates the correction of the entire reference point 10 is obtained, and among these, an enlargement / reduction and shear component excluding the rotation transformation component and the translation component are considered. This approximates the region with a uniform two-dimensional strain field. The direction of the eigenvector of the strain tensor obtained from the affine transformation matrix becomes the “main strain direction” of the strain field. Enlargement / reduction and shear are expressed by biaxial enlargement / reduction with this principal strain direction. Since the main strain direction is considered to be the main correction direction for correcting the entire region, the axis setting device 5 sets the “main strain direction” to the anisotropic biaxial 17.

  When the transformation from the old coordinate value Pi (xi, yi) to the new coordinate value Qi (Xi, Yi) for the N reference points 10 is expressed by affine transformation,

i = 1, 2,. . , N. Parameters a, b, c, d, s, and t in this equation are obtained by the method of least squares. With these parameters, the strain tensor Φ, its two eigenvalues λ1, λ2, and the two eigenvectors e1, e2 are

It becomes. The anisotropic axis 17 to be obtained is taken in the eigenvector direction of this strain matrix, that is, the main strain direction. These two axes are defined as u-axis and v-axis. Of course, the u-axis and the v-axis are orthogonal.

  In the following description, it is assumed that there is no rotation conversion component. In actual correction, there is a rotation component, but again, the rotation tensor is derived from the affine transformation obtained above.

The effect of rotation can be canceled by calculating the triangulation by performing coordinate transformation that cancels the component on the new coordinate value.

  In the uv coordinate system, a true correction vector 18 (fi) from the old coordinate value Pi (xi, yi) of each point on the map 9 to the new coordinate value Qi (Xi, Yi) is represented by f (u, v ). At this time, it is considered that the correction vector fi is linearly approximated with the segment width H (Hu, Hv) for each of the u axis and the v axis. Even in the affine transformation divided into triangles, since the correction amount is linearly interpolated between the vertices, the division width H indicates the size of anisotropy when the triangle is divided. For example, as shown in FIG. 4, when a right triangle is considered, the widths Hu and Hv in the u-axis direction and the v-axis direction of the right triangle correspond to the section width H in each axis.

  Based on this model, a first-order approximation error due to the segment width H is estimated. This represents a correction error due to the affine transformation when the map 9 is divided into the divided triangular regions 12. The ratio setting device 6 shown in FIG. 1 determines (calculates) the ratio of the segment width H (Hu, Hv) that minimizes the error estimation value in both axes u and v, and uses the ratio as the circumscribed ellipse. Set to rate.

  The error estimation of the first-order approximation based on the segment width H will be described. Hereinafter, the case of the u axis will be described. The same applies to the v-axis. In order to perform first-order approximation error estimation, as shown in FIG. 5, a correction vector 18 (fi) is divided into a vector 19 (fu) determined only by u, a vector 20 (fv) determined only by v, and a random displacement. 21 (ε) and the sum of the translation component 22 (μ).

  However, Eu [] and Ev [] represent expected values over the u coordinate value and the v coordinate value, respectively. As will be described later, the accuracy of this model is improved as the absolute value of ε (u, v) in the actual correction vector is smaller and can be regarded as random noise. The principal strain direction when approximated by a uniform strain field satisfies this. Where

It is.

  Now, it is considered that the region is divided by u = U and u = U + H. At this time, as shown in FIG. 6, the approximate correction vector 23 (f * (U + h, v)) at the point (U + h, v) where the u coordinate value is U + h (0 <h <H) is 2 on the dividing point. It is assumed that linear interpolation using point displacements f (U, v ′) and f (U + H, v ″) is given as follows.

Transform this,

Therefore, the error 24 (δ (U + h, v)) from the true correction vector 18 (f (U + h, v)) is

It is. For the error 24 squared, the average of h, v, and U is expressed as a function of the segment width H, and the evaluation is performed.

  First, with respect to the square of the error δ (U + h, v), if the expected value when taking any v, v ′, v ″ is Fu (U + h),

  Here, v, v ′, v ″ are arbitrary,

Furthermore, the two are uncorrelated, that is,

It is said.

  In addition, regarding the variance Vv [] with respect to v,

given that,

It is.

  Furthermore, the average of the expected value Fu (U + h) when 0 <h <H is

It is.

  The expected value in U, that is, the mean square of the error squared when the segment width in the u-axis is H, is expressed as a function of H,

It becomes.

  Thus, the increase or decrease of Gu (H) is given by the first to third terms, which is the square of the error when the u-dependent term fu (u) is linearly approximated with the interval width H. It is an increase or decrease in value. On the other hand, the section width of the u axis is irrelevant to the approximation accuracy of fv (v). The same applies to the v-axis. If the average of the squares of errors obtained for the v-axis is Gv (H), Gv (H) represents the superiority or inferiority of the approximation accuracy of fv (v), and the segment width of the v-axis is an approximation of fu (u). It is independent of accuracy.

  That is, the approximation accuracy of the correction vector f (u, v) based on the u-axis and v-axis segment widths Hu and Hv is expressed by Gu (H) and Gv (H), respectively. ) And Gv (Hv), the approximate accuracy of the correction vector f (u, v) when the u-axis and v-axis segment widths are Hu and Hv, respectively, can be evaluated. This evaluation value Gsum is

And This value gives the average of the squares of errors in the piecewise approximation, and the smaller the value, the better the correction accuracy.

  The translation component μ can be corrected by piecewise approximation and does not appear in the error. Since ε (u, v) is modeled as ε (u, v) as random noise, the mean square of the error does not depend on the division width of the u axis and the v axis. Even if the noise deviates from random noise, if the absolute value is small, the influence of the segment width on the error is small. Here, the u-axis and the v-axis are set in the principal strain direction obtained by the least square method. For this reason, φ and ψ are used as magnifications so as to represent enlargement / reduction in the (u, v) axis direction.

, The sum of squares of ε (u, v) is the smallest with respect to the reference point 10. Actually, since it is not limited to enlargement / reduction, the absolute value of the ε (u, v) term can be further reduced, and it can be regarded as random noise.

  Gu (H) and Gv (v) are defined as error functions. The value is estimated by actually calculating from the coordinate value of the reference point 10, for example.

  As shown in FIG. 7, for two reference points Pn (un, vn), Pm (um, vm), un <um, a reference point Pk (uk, vk) where the u coordinate value uk is un <uk <um. ) Mean square of error of linear approximation in u-axis

, And this is taken as a measurement value 25 (FIG. 8) at H = um-un for an error function Gu (H) indicating an error due to the segment width H with respect to the u-axis. Note that fn, fm, and fk are correction vectors from the old coordinate values of the reference points Pn, Pm, and Pk to the new coordinate values, respectively.

  If the measurement values are obtained for all the reference point pairs, an error function is applied to the result as shown in FIG. That is, the error function to be fitted is expressed by a linear expression, for example,

Or using a quadratic equation:

And a0, a1, and a2 are parameters obtained by fitting. Alternatively, function fitting may be performed following a model function of a semivariogram used in geophysics. The semivariogram and its model function are described in Shigeru Mase and Jun Takeda, “Spatial Data Modeling-Application of Spatial Statistics”, Chapter 6, Kyoritsu Shuppan, published in 2001.

  now,

The error function Gu (H) is defined as

It becomes. If γ (h) is expanded using a semivariogram spherical model function and a power model function, the error function Gu (H) is

It becomes the form. In this form, the error function Gu (H) may be applied as the error function 26 in FIG. s0, s1, s2, p0, p1, and p2 are parameters obtained by fitting. For these fittings, for example, the least square method is used. The same applies to the v axis.

  In determining the anisotropy ratio from the Gsum curve 27 of FIG. 9, the average area S (see FIG. 4) of the sectioned triangular region 12 is used. The average area S is, for example, a value obtained by dividing the area of the map 9 by {(number of reference points including four corners) × 2-6} which is the number of triangles. Alternatively, normal Delaunay triangulation is executed, and an average is obtained from the areas of the respective triangles to obtain an average area S. Alternatively, the average area S is the square root of the mean square of the area of each triangle. This is a weighted average with the area itself as a weight, and considers that the larger the area, the more general map figures in it and the greater the influence.

  When the section width of both axes is Hu, Hv,

And α is a parameter, for example, 2. This represents the situation in a right triangle as shown in FIG. Under this condition, as shown in FIG. 9, a point 28 giving the minimum value Gmin with respect to the Gsum ratio r shown by the curve 27 is obtained, and the ratio r = Hv / Hu at that time is set as the anisotropy ratio R. To do.

  In particular, when both error functions Gu (Hu) and Gv (Hv) are applied to a linear expression,

Therefore, when Gsum becomes the minimum value,

The anisotropy ratio R giving the minimum value is a constant value regardless of the area S.

  Based on the above, the operation and coordinate correction method of the coordinate correction apparatus of FIG. 1 according to the present embodiment will be described based on the flowchart of FIG.

  Old new coordinate values Pi, Qi (i = 1,..., N) for N reference points 10 are stored as reference point data 3 in the storage device 1. These coordinate value data are stored in a format as shown in FIG. 10, for example.

  In step ST1, the axis setting device 5 reads out the data of the old coordinate value Pi and the new coordinate value Qi from the storage device 1 for each of the N reference points 10 and approximates the correction according to the above equation 1. And a principal strain direction is obtained according to an equation that gives an eigenvector of a strain matrix determined based on Equation 2, and the calculated principal strain axis (principal strain direction) is set to the anisotropic axis 17 (u, v).

  In step ST2, the axis setting device 5 converts the old and new coordinates of the reference point 10 into the uv coordinate system. Regarding this conversion, for example, if the u-axis is in the direction of θ from the x-axis, the coordinate value (ui, vi) of the old coordinate value Pi in the uv coordinate system is

It is. The axis setting device 5 determines the coordinate value (Ui, Vi) in the uv coordinate system of the new coordinate value Qi in the same manner. At this time, the correction vector 18 (fi) is fi = (Ui−ui, Vi−vi).

  In step ST3, the ratio setting device 6 calculates measurement values of the error functions Gu (H) and Gv (H) based on the equation (18). If the two reference points are Pn (un, vn) and Pm (um, vm), the value of the error function Gu (H) at H = | un-um |, and H = | vn−vm | The value of the error function Gv (H) at is obtained. The ratio setting device 6 obtains this calculation process for all the sets of two reference points.

  In step ST4, the ratio setting device 6 applies each of the error functions Gu (H) and Gv (H) to the function of the segment width H.

  In step ST5, the ratio setting device 6 determines the area S and the coefficient α in Equation 25. That is, the ratio setting device 6 sets the area S as the average area of the segmented triangular area as described above, and sets the coefficient α to 2.

  In step ST6, the ratio setting device 6 obtains the segment widths Hu and Hv that minimize Gsum using the area S and the coefficient α, and determines the obtained ratio R = Hv / Hu as the anisotropy ratio. .

  In step ST7, the dividing device 7 executes anisotropic Delaunay triangulation in which the degree of anisotropy (ratio) is the ratio R with respect to the u axis and the v axis, and the map 9 is converted to the reference point 10 of the map 9. Is divided into divided triangular regions 12 having vertices as vertices. Regarding the processing of this point, for example, as shown in FIG. 11, the dividing device 7 sets a coordinate system uw multiplied by 1 / R in the v-axis direction, and converts the coordinate value of the reference point 10 to the coordinate point P′i ( After the temporary conversion to ui, wi) = (ui, vi / R), normal Delaunay triangulation is executed using the coordinate point P′i (ui, wi). Then, as shown in FIG. 12, the dividing device 7 forms a triangle as it is with respect to the original coordinate value Pi (ui, vi) using the divided side 31 and the divided triangular region 32 obtained by this dividing process. By doing so, a sectioned triangular region 12 in anisotropic Delaunay triangulation is obtained. For example, when there are no other reference points 30 in the circumscribed circle 33 of the coordinate point P′i1, the coordinate point P′i2, and the coordinate point P′i3 for the three reference points 10 of i1, i2, and i3. The three reference points P′i 1, P ′ i 2, and P ′ i 3 constitute a partitioned triangular region 32. At this time, the circumscribed circle 33 is a circumscribed ellipse 34 with an ellipticity R about the three reference points Pi1, Pi2, and Pi3 in the uv coordinate system, and the other reference point 10 exists inside the circle. do not do. That is, the segmented triangle 12 region satisfies the condition of the anisotropic Delaunay triangulation that the other reference point 10 does not enter the circumscribed ellipse 34. In this way, the dividing device 7 electrically executes anisotropic Delaunay triangulation processing. For execution of normal Delaunay triangulation with respect to the coordinate point P′i, the dividing device 7 uses, for example, a sequential addition method or a lifting method. At this time, for example, the dividing device 7 creates reference point data 29 as shown in FIG. 13 and stores the reference point data 29 in the storage device 1, and uses the reference point data 29 to partition the triangle as shown in FIG. 14. Data 4 is created and stored in the storage device 1.

  In step ST8, the conversion apparatus 8 calculates | requires the affine transformation which converts the old coordinate value into a new coordinate value about each of the division | segmentation triangular area | region 12 (FIG. 12) obtained by the division | segmentation apparatus 7. FIG. The old coordinate values of the reference point 10, which is the three vertices of the jth segmented triangular area 12, are (xn, yn), (xm, ym), (xk, yk), and the new coordinate values are (Xn, Yn), ( Xm, Ym), (Xk, Yk), the affine transformation can be performed using parameters aj, bj, cj, dj, sj, tj by referring to Equation 1.

And these equations are

Can be expressed. this,

More specifically, the conversion device 8 determines affine transformation parameters aj, bj, cj, dj, sj, and tj.

  In step ST9, the conversion device 8 converts the coordinate values (x, y) of the points 15 (FIG. 3) of each feature in each segmented triangular area 12 into new coordinate values according to affine transformation. When the feature point 15 (x, y) is inside the j-th segmented triangular area 12, the converted coordinate value 16 is expressed as (X, Y) and the conversion device 8 Using the affine transformation parameters aj, bj, cj, dj, sj, tj obtained in ST8, the internal point 15 (x, y) is

Convert to Then, the conversion device 8 converts the coordinate values of all the points shown on the map 9 into new coordinate values, whereby the map coordinate correction processing in the coordinate correction device of FIG. 1 is completed.

  As described above, the coordinate correction apparatus of FIG. 1 operates so that the coordinate correction apparatus can set the anisotropic axis R and the ratio of the anisotropy ratio R by the ratio of the segment width so that the error is minimized. Based on the determination, anisotropic Delaunay triangulation can be performed, and coordinate correction that maintains high accuracy of coordinate values after correction conversion can be executed.

  Further, in the present embodiment, the anisotropic axis set by the axis setting device 5 approximates the displacement from the coordinate value before correction on the map 9 of each vertex to the coordinate value after correction. Since the two axes orthogonal to each other, which are the main strain directions of the dimensional strain field, are set, the anisotropic axis direction is determined from the coordinate value on the apex map 9 and the corrected coordinate value. It can be easily obtained, and the accuracy after correction can be improved by using this anisotropic axial direction.

  Further, in the present embodiment, the ratio set by the ratio setting device 6 is both when the sum in two axes of the error in the piecewise linear approximation of the anisotropic axial displacement is minimized. With this configuration, it is possible to obtain an anisotropy ratio that reduces the error using a function of the error, and to improve the accuracy after correction by using this ratio. I can do it.

Needless to say, the above-described coordinate correction processing or coordinate correction method of the coordinate correction apparatus of FIG. 1 can be realized by computer control by a computer program.
This point is also valid in the second and third embodiments described later.

(Embodiment 2)
In the first embodiment, the error function is estimated and the anisotropy ratio R is determined by using the area S of the segmented triangular region. However, by trying to correct the position reference point by coarser triangulation, Alternatively, the anisotropy ratio R may be obtained.

  FIG. 16 is a block diagram illustrating a configuration of a map coordinate correction apparatus according to the second embodiment.

  First, in the step of testing the anisotropy ratio, the ratio setting device 6 sets a certain number of reference points 10 among all the reference points 10 as sample reference points 36, and sets the remaining reference points 10 as evaluation points. 37, and the anisotropy ratio is assumed to be a predetermined value.

  The dividing device 7 performs anisotropic Delaunay triangulation using the sample reference point 36 based on the anisotropic ratio assumed for the anisotropic axis.

  The conversion device 8 converts the old coordinate value of the evaluation point 37 into a new coordinate value by affine transformation determined by the section triangle.

  The evaluation device 35 functioning as “evaluation means” uses the new coordinate value (accurate coordinate value) that holds the result (new coordinate value of the converted evaluation point 37) in the reference point data 3 of the storage device 1 in advance. ) And the accuracy is calculated as an evaluation value.

  The ratio setting device 6 changes the ratio of anisotropy and the evaluation device 35 obtains an evaluation value each time. The ratio setting device 6 determines the best value (minimum value) among the evaluation values obtained by the evaluation device 35. Value) is determined as the anisotropy ratio based on the ratio at which the evaluation value is obtained. If the error functions Gu (H) and Gv (H) can be approximated by a linear expression, the appropriate anisotropy ratio does not depend on the area of the section triangle. Therefore, this coordinate correction apparatus evaluates the anisotropy ratio using the sample reference point 36 sampled from the reference point 10, and the anisotropy ratio when obtaining the best evaluation value at this time is the reference point. A good division pattern is generated even in the triangulation by all ten.

  17 and 18 are explanatory diagrams showing the operation of the coordinate correction apparatus according to the present embodiment. Of these figures, FIG. 17 is a diagram showing the division of the map 9 into the segmented triangular regions 12 by the sample reference points 36. FIG. 18 is a diagram showing a comparative evaluation of correction by affine transformation of the segmented triangular region 12 divided by the sample reference point 36. FIG.

  FIG. 19 is a flowchart showing the operation of the coordinate correction apparatus according to this embodiment. The description of the same operation steps as those in the flowchart showing the operation of the coordinate correction apparatus according to Embodiment 1 shown in FIG. 15 is omitted.

  In step ST201, the ratio setting device 6 sets the number Nr of temporary ratios to be tested and Nr temporary ratios r [i] (i = 1, 2,..., Nr). Regarding the number setting of the temporary ratio r [i], for example, the number is set to 16 from 0.5 to 2.0 in increments of 0.1. The ratio setting device 6 initializes a variable i indicating the number of the temporary ratio r [i] to 0, and sets the number M of trials for selecting the sample reference point.

  In step ST202, the ratio setting device 6 increments the variable i indicating the temporary ratio number by 1 and initializes the variable m indicating the number of trials to 0.

  In step ST203, the ratio setting device 6 increases the number m of trials by 1 and selects a certain percentage of the reference points 10 among all the reference points 10 as sample reference points 36 as shown in FIG. For this selection, for example, the number of reference points 10 is half of the number, and selection is performed using a random number. Alternatively, the mth reference point 10 may be left and all the remaining reference points 10 may be selected as the sample reference points 36.

  In step ST204, the dividing device 7 performs anisotropic Delaunay triangulation by the sample reference point 36 using the i-th temporary ratio r [i].

  In step ST205, the conversion apparatus 8 determines an affine transformation for each partitioned triangular region.

  In step ST206, the conversion apparatus 8 performs affine transformation determined by the segmented triangular region including the evaluation point 37 on the evaluation point 37 that is a reference point that is not selected as the sample reference point 36, and executes the correction. Then, the coordinate value of the evaluation point 37 is converted into a new coordinate value.

  In step ST207, the evaluation device 35 evaluates the correction performed on the evaluation point 37. That is, as shown in FIG. 18, the evaluation device 35 has the old coordinate value (xj, yj), the new coordinate value 38 (Xj, Yj), and the interpolation correction coordinate value by affine transformation for the L evaluation points 37. 39 is (Xj ′, Yj ′) (j = 1, 2,..., L), and the affine transformation parameters are a, b, c, d, s, t, and the evaluation value g [ m] is the sum of squares of the difference between the new coordinate value 38 and the interpolation correction coordinate value 39, ie,

Asking.

  In step ST208, the evaluation apparatus 35 determines whether or not predetermined M trials have been completed. If so, the coordinate correction apparatus proceeds to step ST209, and if not, the coordinate correction apparatus proceeds to step ST203. Then, the set of sample reference points 36 is changed.

  In step ST209, the evaluation device 35 obtains the evaluation value G [i] of the i-th temporary ratio r [i]

Ask for. Then, the evaluation device 35 outputs the evaluation value G [i] data of the calculated i-th temporary ratio r [i] to the ratio setting device 6 each time.

  In step ST210, the evaluation device 35 determines whether or not the evaluation value G for all of the Nr temporary ratios has been calculated, and if so, the coordinate correction device proceeds to step ST211, otherwise. Proceeding to step ST202, the next evaluation is entered.

  In step ST211, the ratio setting device 6 provides the best evaluation value G [i] that gives the minimum value among the evaluation values G [i] of the Nr temporary ratios r [i] transmitted from the evaluation device 35. Select. The temporary ratio r [i] corresponding to the evaluation value G [i] selected here is the temporary ratio r [i] that gives the minimum value of the evaluation value G [i]. The temporary ratio r [i] is set to the ratio R.

  Alternatively, Gsum is estimated based on the evaluation value G [i]. For example, if both Gu (H) and Gv (H) are expressed by a quadratic polynomial,

Therefore, if r = Hv / Hu,

It becomes. Here, the area S is an average area Ss of the sectioned triangular region 12 constituted by the sample reference points 36, and Gsum is regarded as a function Gsum (r) of the ratio r. Since the temporary ratio r [i] and the evaluation value G [i] are obtained, Gsum (r [i]) = G [i] (i = 1, 1) is used when r = r [i]. 2,..., Nr), that is,

Then, parameters au2, au1, aV2, av1, (aU0 + au0) are obtained. This is based on, for example, the least square method. As described above, Gsum (r) is determined. Therefore, Ss is replaced with the average area S of the segmented triangular region 12 by all the reference points 10,

The ratio r that minimizes this Gsum (r) is obtained, and this is set as the anisotropy ratio R.

  In the following steps, the coordinate correction apparatus executes anisotropic Delaunay triangulation and map correction by affine transformation based on the ratio R obtained as described above.

By operating the function of the coordinate correction apparatus of FIG. 16 as described above, anisotropic Delaunay triangulation can be performed using the anisotropic ratio obtained by evaluation by actual triangulation, and correction conversion is performed. It is possible to execute coordinate correction that keeps the accuracy of subsequent coordinate values high. That is,
From the coordinate values on the map of the sampled vertices and the corrected coordinate values of the vertices, it is possible to obtain an anisotropy ratio that reduces the error. Accuracy can be improved.

(Embodiment 3)
In Embodiment 1 and Embodiment 2, anisotropic Delaunay triangulation was performed using the same ratio over the entire digitized map, but the ratio of anisotropy was changed according to the position on the map. It may be configured. The form of the present embodiment relates to this point.

  FIG. 20 is a block diagram showing a configuration of a map coordinate correction apparatus according to the present embodiment.

  The ratio setting device 6 evaluates the evaluation value based on the area Sj of the jth segmented triangular region 12 for the jth segmented triangular region 12 obtained by the segmentation of the map 9 using anisotropic Delaunay triangulation by the segmenting device 7. Evaluation by Gsum is performed to obtain a ratio Rj when the evaluation value Gsum is minimized, and the dividing device 7 uses the u-axis and v-axis of the j-th segmented triangular region 12 as an anisotropic axis and uses the evaluation value Gsum. It is determined whether or not another reference point 10 exists inside the circumscribed ellipse having the above-described ratio Rj obtained by the evaluation as the ellipticity Rj, and if it exists, the division into the jth partitioned triangular region 12 is performed. change. On the other hand, when the other reference point 10 does not exist inside the circumscribed ellipse, the dividing device 7 maintains the division into the j-th partitioned triangular region 12.

  Here, FIG. 21 is an explanatory diagram showing the operation of the coordinate correction apparatus according to the present embodiment. FIG. 22 is a flowchart showing the operation of the coordinate correction apparatus according to this embodiment. The description of the same operation steps as those in the flowchart showing the operation of the coordinate correction apparatus according to Embodiment 1 shown in FIG. 15 is omitted.

  In step ST301, the dividing device 7 selects one segmented triangular area 12. It is assumed that the selected section triangle area 12 is the jth section triangle area.

  In step ST <b> 302, the ratio setting device 6 obtains the area Sj of the jth segmented triangular region 12 selected by the dividing device 7.

  In step ST303, the ratio setting device 6 evaluates the evaluation value Gsum under the area Sj, and calculates the ratio Rj when the evaluation value Gsum is minimized.

  In step ST304, the dividing device 7 determines whether or not another reference point 10 exists inside the circumscribed ellipse having the ellipticity Ri in the selected j-th segmented triangular region. If it does not exist, the coordinate transformation apparatus proceeds to step ST306, and if it does exist, the coordinate transformation apparatus proceeds to step ST305.

  In step ST305, the dividing device 7 changes (updates division) the selected j-th segmented triangular area 12.

  For example, as shown in FIG. 21, it is assumed that the vertices of the selected j-th segmented triangular area 12 are A, B, and C. In step ST304, the dividing device 7 passes the vertices A, B, and C, which are circumscribed ellipses of the selected j-th segmented triangular area 12, the axes are u and v axes, and the evaluation value Gsum is obtained. It is checked whether or not another vertex is inside the circumscribed ellipse 42 having the ellipticity as the ratio Rj when minimizing. When the vertex D43 enters the circumscribed ellipse 42, the dividing device 7 changes the sectioned triangular area 12 in step ST305. With respect to this change, for example, in the case shown in FIG. 21, the dividing device 7 changes the divided side 11 to the side 41, and in accordance with this change, the divided triangle region 12 made of ΔABC and the divided side made of ΔABD. The triangular area is changed into a divided triangular area made of ΔCDA and a divided triangular area made of ΔCDB, respectively.

  In step ST306, the dividing device 7 determines whether or not the above processing has been completed for all the sectioned triangular regions 12, and the coordinate correcting device proceeds to step ST8 if completed, otherwise step ST301. The process proceeds to and the processing of the next selected section triangle area 12 is started.

  In the following steps, the coordinate correction apparatus determines the affine transformation parameters corresponding to each of the segmented triangular regions obtained in this way, and then performs affine transformation on the points of each feature belonging to each of the partitioned triangular regions. Then, the digital map 9 is corrected.

As described above, by operating the function of the coordinate correction apparatus, the optimum ratio R corresponds to the change in the area of the segmented triangle region, and the optimum anisotropy that matches the size of each segmented triangle region. An anisotropic triangulation based on the ratio R can be executed, and coordinate correction that maintains high accuracy of the coordinate values after correction conversion can be executed. That is, the ratio used for dividing the map 9 into the divided triangle areas can be set to a value suitable for each divided triangle area, and the accuracy after correction can be improved.
(Modification)
In Embodiments 1 and 2, anisotropic triangulation is performed using the same anisotropic ratio and the same anisotropic ratio over the entire map, and in Embodiment 3, Anisotropic triangulation is performed using the same anisotropic axis direction throughout the map. However, the map is divided into several parts, such as urban areas, agricultural land, and mountainous areas, for each latitude and longitude, and the anisotropic axial direction and anisotropic characteristics for each partial area. An anisotropic triangulation may be performed by obtaining the ratio.

  In the first to third embodiments, a single principal strain direction is set as an anisotropic axis over the entire map. However, anisotropic u-axis and v-axis may be set on a curve connecting the principal strain directions obtained locally at each point of the map. Since the principal strain directions are orthogonal at each point, the uv directions are orthogonal to each other even if the anisotropic axis is set in this way. Also in this case, anisotropic triangulation is performed in the uv coordinate system, and each divided triangular region obtained by the anisotropic triangulation is used as it is.

  In the first embodiment and the third embodiment, the ratio R obtained by using the sample reference point 36 by the operation of the ratio setting device 6 shown in the second embodiment and the section triangle region 12 by the sample reference point 36 are displayed. The parameter α may be set using the average area S. Under the condition of the average area S, a ratio Hv / Hu when the evaluation value Gsum becomes the minimum value Gmin is obtained, and the parameter α is adjusted so that this ratio matches the anisotropy ratio R. In the first embodiment and the third embodiment, the adjusted parameter α is set in step ST5.

  In the first to third embodiments, the anisotropic axial direction is set to the principal strain axial direction, but the present invention is not limited to this. For example, the error function is obtained by rotating the axial direction at every fixed angle such as every 5 degrees, the direction in which the sum Gsum is smallest is set as the anisotropic axial direction, and at that time, by the ratio R that gives the smallest error You may comprise so that anisotropic Delaunay triangulation may be performed.

  As an alternative to the storage device 1, a storage medium external to the coordinate correction device may be used.

(Appendix)
In the above, the “new coordinate value” that is the coordinate value digital data after correction of the reference point that is an accurate coordinate value is assumed to be a value measured by GPS, but is limited to this example. Instead, a coordinate value on a main map such as a basic map or a coordinate value authorized by a triangular point or the like may be executed as a “new coordinate value”.

  In addition, although the example which implements this invention in correction | amendment of the coordinate value of a map was demonstrated, in addition to this, this invention can be applied, for example in the bonding of maps, aerial photographs, and satellite photographs. I can do it. In this case, the coordinate value of the reference point on the main map or photo is set as “new coordinate value”, and the coordinate value on the map or photo to be pasted is set as “old coordinate value”. As a result, each point on the map or photo to be pasted can be accurately superimposed on the main map or photo.

  While the embodiments of the present invention have been disclosed and described in detail above, the above description exemplifies aspects to which the present invention can be applied, and the present invention is not limited thereto. In other words, various modifications and variations to the described aspects can be considered without departing from the scope of the present invention.

  The present invention is suitable for application to a geographic information system, for example.

It is a block diagram which shows the structure of the coordinate correction apparatus which concerns on Embodiment 1 of this invention. FIG. 3 is an explanatory diagram showing a triangulation of a map in the first embodiment. 6 is an explanatory diagram illustrating a correction operation of the coordinate correction apparatus according to Embodiment 1. FIG. FIG. 6 is an explanatory diagram illustrating an operation of the coordinate correction apparatus according to the first embodiment. 3 is an explanatory diagram showing a correction model of the coordinate correction apparatus according to Embodiment 1. FIG. 3 is an explanatory diagram illustrating an approximate model of the coordinate correction apparatus according to Embodiment 1. FIG. 3 is an explanatory diagram illustrating an approximate model of the coordinate correction apparatus according to Embodiment 1. FIG. It is explanatory drawing which shows the error function which the coordinate correction apparatus which concerns on Embodiment 1 uses. 6 is an explanatory diagram illustrating an evaluation function used by the coordinate correction apparatus according to Embodiment 1. FIG. 6 is an explanatory diagram showing reference point data of the coordinate correction apparatus according to Embodiment 1. FIG. 6 is an explanatory diagram illustrating a triangulation operation of the coordinate correction apparatus according to Embodiment 1. FIG. 6 is an explanatory diagram illustrating a triangulation operation of the coordinate correction apparatus according to Embodiment 1. FIG. 6 is an explanatory diagram showing reference point data of the coordinate correction apparatus according to Embodiment 1. FIG. It is explanatory drawing which shows the division | segmentation triangle data of the coordinate correction apparatus which concerns on Embodiment 1. FIG. 3 is a flowchart illustrating an operation of the coordinate correction apparatus according to the first embodiment. It is a block diagram which shows the structure of the coordinate correction apparatus which concerns on Embodiment 2 of this invention. FIG. 10 is an explanatory diagram illustrating an operation of the coordinate correction apparatus according to the second embodiment. FIG. 10 is an explanatory diagram illustrating an operation of the coordinate correction apparatus according to the second embodiment. 10 is a flowchart showing the operation of the coordinate correction apparatus according to the second embodiment. It is a block diagram which shows the structure of the coordinate correction apparatus which concerns on Embodiment 3 of this invention. FIG. 10 is an explanatory diagram illustrating an operation of the coordinate correction apparatus according to the third embodiment. 10 is a flowchart showing the operation of the coordinate correction apparatus according to the third embodiment.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 Memory | storage device, 2 map data, 3 reference point data, 4 division | segmentation triangle data, 5 axis setting apparatus, 6 ratio setting apparatus, 7 division | segmentation apparatus, 8 conversion apparatus, 35 evaluation apparatus.

Claims (11)

A method for correcting coordinates of a map using a computer,
Coordinate value digital data before correction on the map of the reference point which is each vertex of each divided triangular area for dividing the digitized map, and coordinate value digital after correction of the reference point which is an accurate coordinate value An axis setting step in which the axis setting means realized by the computer determines digital data that gives an anisotropic axis direction inherent to the map from the data;
By the computer based on the coordinate value digital data before correction on the map of each reference point, the coordinate value digital data after correction of each reference point, and the digital data that gives the axial direction of the anisotropy A ratio setting step in which the realized ratio setting means obtains digital data giving the ratio of anisotropy in the anisotropic axial direction;
Based on the digital data giving the anisotropic axial direction and the digital data giving the anisotropy ratio to the map, the computer-implemented triangulation means constitutes each divided triangular area 3 Other than the three vertices constituting the segmented triangular region inside a circumscribed ellipse passing through the vertices and having the anisotropy axis direction as the axis and the anisotropy ratio as the ellipticity An anisotropic triangulation process that divides into a plurality of segmented triangular regions that do not contain vertices,
For each of the plurality of segmented triangular regions , the computer is realized based on the coordinate value digital data before correction and the coordinate value digital data after correction on the map of each reference point forming each vertex. The converted conversion means calculates digital data of correction conversion to be applied to the segmented triangle area, and performs the correction conversion on each coordinate point in the segmented triangle area, thereby converting the coordinate points on the map. And a conversion step of correcting the coordinate value digital data at
Map coordinate correction method. A map coordinate correction method according to claim 1,
The axis of anisotropy defined by the axis setting step is
Each of the reference points is a principal strain direction of a two-dimensional strain field that approximates the displacement of the reference point from the uncorrected coordinate value digital data on the map to the corrected coordinate value digital data of the reference point. It is characterized by two axes orthogonal to each other,
Map coordinate correction method. The coordinate correction method for a map according to claim 1 or 2,
The anisotropic ratio determined by the ratio setting step is:
Both of the two anisotropic axes when the digital data of the sum of the two anisotropic axes is the minimum of the error in the piecewise linear approximation of the anisotropic axial displacement It is a ratio of division width,
Map coordinate correction method. The coordinate correction method for a map according to claim 1,
The ratio setting step includes
After sampling only a certain number of reference points among all reference points on the map as vertices of the segmented triangular region, the map is subjected to anisotropic triangulation using the assumed ratio. Each divided triangular area is divided into a plurality of divided triangular areas, and each correction triangle calculated based on the digital data of the coordinate values before correction and the corrected coordinate values on the map at the sampled reference points is used. The digital data of the coordinate value before correction on the map of the reference point that was not sampled entered is corrected and converted, and the digital data of the corrected coordinate value and the digital value of the coordinate value after correction of the reference point that was not sampled Comparing the difference with the data, changing the assumed ratio and setting the assumed ratio when the difference is the smallest as the ratio of the anisotropy, That,
Map coordinate correction method. The coordinate correction method for a map according to claim 1,
The ratio setting step includes
It is a step of determining digital data giving an anisotropic ratio for each of the sectioned triangular regions,
Map coordinate correction method. Coordinate value digital data before correction on the map of the reference point which is each vertex of each divided triangular area for dividing the digitized map, and coordinate value digital after correction of the reference point which is an accurate coordinate value An axis setting means for determining digital data that gives an anisotropic axial direction specific to the map from the data;
Based on the coordinate value digital data before the correction on the map of each reference point, the coordinate value digital data after the correction of each reference point, and the digital data that gives the anisotropic axial direction , the anisotropic Ratio setting means for obtaining digital data giving the ratio of anisotropy in the axial direction of the sex;
Based on the digital data giving the anisotropic axial direction and the digital data giving the ratio of the anisotropy, the map passes through the three vertices constituting each segmented triangular region, and the anisotropic A plurality of segmented triangular regions in which no vertex other than the three vertices constituting the segmented triangular region is placed inside a circumscribed ellipse having the axial direction as its axis and the anisotropy ratio as its ellipticity And an anisotropic triangulation means for dividing,
For each of the plurality of segmented triangular regions, the reference triangular points are formed in the segmented triangular region based on the coordinate value digital data before correction and the coordinate value digital data after correction on the map. Conversion means for calculating digital data of correction conversion to be applied and correcting the coordinate value digital data on the map of each coordinate point by performing the correction conversion on each coordinate point inside the sectioned triangular region Characterized by comprising
Map coordinate correction device. The map coordinate correction apparatus according to claim 6,
The anisotropic axis defined by the axis setting means is:
Each of the reference points is a principal strain direction of a two-dimensional strain field that approximates the displacement of the reference point from the uncorrected coordinate value digital data on the map to the corrected coordinate value digital data of the reference point. It is characterized by two axes orthogonal to each other,
Map coordinate correction device. The coordinate correction apparatus for a map according to claim 6 or 7,
The anisotropic ratio determined by the ratio setting means is:
Both of the two anisotropic axes when the digital data of the sum of the two anisotropic axes is the minimum of the error in the piecewise linear approximation of the anisotropic axial displacement It is a ratio of division width,
Map coordinate correction device. The coordinate correction apparatus for a map according to claim 6,
Further comprising an evaluation means,
The ratio setting means sets a plurality of temporary ratio digital data, and selects a fixed ratio of reference points as sample reference points among all reference points,
Each time the ratio setting means sequentially outputs the digital data of the plurality of temporary ratios, the anisotropic triangulation means outputs the digital data giving the anisotropic axial direction and the ratio setting means And dividing the map into a plurality of sample division triangle regions having three sample reference points as vertices based on the temporary ratio data to be
Each time the ratio setting means sequentially outputs the digital data of the plurality of temporary ratios, the conversion means calculates correction conversion data for each sample section triangle area and is included in each sample section triangle area. For the evaluation points that are the remaining reference points that are not selected as sample reference points by the ratio setting means, the corresponding correction conversion data is applied to perform interpolation correction of the evaluation points,
Each time the ratio setting unit sequentially outputs the digital data of the plurality of temporary ratios, the evaluation unit includes accurate corrected coordinate value digital data obtained by positioning each evaluation point, and the conversion unit. The evaluation value digital data is calculated based on the difference from the interpolation correction coordinate value digital data of the evaluation point subjected to the interpolation correction by the step, and the evaluation value digital data is output to the ratio setting unit.
After the ratio setting means outputs all of the plurality of temporary ratio digital data, the ratio setting means includes a plurality of evaluation value digital data corresponding to the number of the plurality of temporary ratio digital data. Selecting the evaluation value digital data of the minimum value, and setting the temporary ratio digital data that gives the selected evaluation value digital data to the digital data that gives the ratio of anisotropy in the axial direction of the anisotropy Features
Map coordinate correction device. The coordinate correction apparatus for a map according to claim 6,
The ratio setting means includes
The digital data giving the ratio of anisotropy is determined for each of the sectioned triangular regions,
Map coordinate correction device. On the computer,
Coordinate value digital data before correction on the map of the reference point which is each vertex of each divided triangular area for dividing the digitized map, and coordinate value digital after correction of the reference point which is an accurate coordinate value An axis setting process for determining digital data that gives an anisotropic axial direction specific to the map from the data;
Based on the coordinate value digital data before the correction on the map of each reference point, the coordinate value digital data after the correction of each reference point, and the digital data that gives the anisotropic axial direction , the anisotropic A ratio setting process for obtaining digital data giving the ratio of anisotropy in the axial direction of the sex;
Based on the digital data giving the anisotropic axial direction and the digital data giving the ratio of the anisotropy, the map passes through the three vertices constituting each segmented triangular region, and the anisotropic A plurality of segmented triangular regions in which no vertex other than the three vertices constituting the segmented triangular region is placed inside a circumscribed ellipse having the axial direction as its axis and the anisotropy ratio as its ellipticity And an anisotropic triangulation process to divide,
For each of the plurality of segmented triangular regions, the reference triangular points are formed in the segmented triangular region based on the coordinate value digital data before correction and the coordinate value digital data after correction on the map. Conversion processing for calculating digital data of correction conversion to be applied and correcting the coordinate value digital data on the map of each coordinate point by performing the correction conversion on each coordinate point inside the sectioned triangular region It is characterized by letting
Map coordinate correction program.

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